System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses

System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses Alisson Lopes Rodrigues, Ricardo Santos Silva Amorim, Pedro Manuel Villa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7767474/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Dec, 2025 Read the published version in Water Resources Management → Version 1 posted 5 You are reading this latest preprint version Abstract Large reservoirs play a crucial role in regulating global water availability, with a storage capacity equivalent to 2% of the world’s surface freshwater, while covering only 0.33% of the Earth’s land surface. These hydraulic infrastructures supply 42% of global irrigation and are vital for domestic, industrial, and energy production purposes. In Brazil, the water demand of large reservoirs in the São Francisco River Basin is expected to increase substantially by 2050. This study aimed to evaluate the water dynamics of a large reservoir and its capacity to meet multiple uses over time. The study was conducted at the Três Marias Hydropower Plant (HPP) reservoir, located in the São Francisco River Basin, Brazil. For this purpose, a System Dynamics model was developed to quantify all inflows and outflows of the reservoir and simulate different operational scenarios, including the application of hedging strategies and the reduction of evaporation rates. Daily inflow and withdrawal data from January 2004 to June 2024 were used. The developed model was calibrated and validated using historical data on water level variations. Overall, the results highlight that the proposed System Dynamics model is a valuable tool to support strategic planning and decision-making in the management of large reservoirs. In the case of the Três Marias HPP, the application of the model revealed the need for adaptive operational strategies capable of reconciling hydropower generation with increasing consumptive uses and the maintenance of environmental flows. This study contributes to strengthening the scientific and practical foundation for integrated water resources management through the implementation of more sustainable operational rules. Finally, it is emphasized that the combination of trigger and cut-off rules, associated with minor evaporation control, can improve the balance between energy generation and meeting multiple water uses. Large reservoirs System Dynamics Water resources Hedging operation Multiple water uses Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction More than half of the world’s river basins contain large artificial reservoirs built to regulate river flows (Grill et al. 2019 ). The total storage capacity of large reservoirs corresponds to approximately 2% of global surface freshwater, covering an area of nearly 500.000 km², or about 0.33% of the Earth’s land surface (Zhou et al. 2016 ; ICOLD 2019). Large reservoirs are considered lentic environments and are usually constructed in sections of drainage networks with significant elevation differences, mainly in plateau basins (Rahmati et al. 2019 ; Wang et al. 2021 ). These reservoirs supply around 42% of the water used for irrigation and also support industrial and domestic sectors (Hanasaki et al. 2018 ). In addition, large reservoirs are used for other activities such as recreation, navigation, hydropower generation, aquaculture, flow regulation, and flood-wave attenuation. Therefore, they provide countless benefits for millions of people worldwide (Zeng et al. 2017 ; Hogeboom et al. 2018 ). Globally, large reservoirs meet essential energy, agricultural, domestic, and industrial demands (Mulligan et al. 2020; Eriyagama et al. 2020 ; Turgut et al. 2019 ). Worldwide water requirements for agriculture, domestic, and industrial uses are projected to increase by approximately 4%, 65%, and 127%, respectively, by 2050 compared with 2010 estimates (Burek et al. 2016 ; Eriyagama et al. 2020 ). In Brazil, the average water demand of large reservoirs located in the São Francisco River Basin is projected to rise by about 31% between 2025 (2.315 million m 3 yr − 1 ) and 2050 (3.038 million m 3 yr − 1 ) (Ferrarini et al. 2020; Bettencourt et al. 2022 ; ANA 2023). The water resources plan for the São Francisco River Basin included an expansion of irrigated agriculture by 559.249 ha between 2016 and 2025, averaging 50.840 ha per year (ANA 2017a; CBHSF 2016). Although the expansion of irrigated areas is important for income generation and food production, such growth is expected to cause conflicts with other competing water uses, such as hydropower generation and industrial supply, among others (ANA 2022). An increase in water scarcity is evident in the São Francisco River Basin, which can be attributed to rapid economic development and inefficiencies in water resources management (Bettencourt et al. 2022 ; CBHSF 2017). Reduced water availability combined with the expansion of agricultural and industrial sectors may intensify conflicts over water access in the large reservoirs of the basin (Bettencourt et al. 2022 ; ANA 2023). Despite Brazil’s considerable water potential, since April 2013 the basin has experienced unfavorable hydro-meteorological conditions, with streamflow and precipitation levels below the historical average from 1931 to 2010 (ONS 2021). This has affected water storage in large reservoirs, generating risks of not meeting multiple water-use demands during periods of reduced availability (ANA 2023; CBHSF 2016). Surface water abstraction from large reservoirs will likely continue to be a common practice to meet future water demand (Zarfl et al. 2015 ; Castello and Macedo, 2015). However, global climate change coupled with increasing water demand requires improved water management strategies to establish sustainable operational limits (Eriyagama et al. 2021 ; Muzammil et al. 2023 ). This necessitates determining the capacity of large reservoirs to meet diverse water demands during scarcity, with the aim of mitigating conflicts and overcoming limitations in access to this vital resource. Such knowledge can maximize efficiency in water storage and use, as well as guide the construction of new reservoirs (Eriyagama et al. 2020 ). The scientific community has advocated the use of systemic approaches to establish reservoir operating rules as an effective way to address the complexity and variability of hydrological processes (Elsawah et al. 2017; Mirchi et al. 2012 ; Simonovic and Arunkumar 2016 ; Jiang et al. 2020 ). In this context, System Dynamics models, developed to simulate hydrological dynamics in large reservoirs within watersheds, become fundamental for planning and supporting water resources management (Kim et al. 2021 ; Simonovic and Arunkumar 2016 ). Therefore, System Dynamics models are extremely relevant tools for regulatory agencies and water managers, as they can aid in the development of new management strategies to ensure the sustainable use of water resources (Al-Jawad et al. 2019 ; Jing et al. 2022 ). Despite their importance, the availability and application of System Dynamics models to evaluate water supply and demand in large reservoirs remain limited (Phan et al. 2021 ; Al-Jawad et al. 2019 ). While models have been developed specifically for small reservoirs (Rodrigues et al. 2023 ), their hydrological, operational, and management characteristics are less complex, limiting direct applicability to larger-scale contexts (Habets et al. 2018 ; Sankarbalaji et al. 2025 ). Conversely, large reservoirs involve greater spatial and temporal variability, multiple users, and specific operating rules, and are more susceptible to extreme events and climate change (Jiang et al. 2020 ; Okkan et al. 2023 ; Bekri et al. 2021 ). In this context, the development of System Dynamics models is a valuable tool for strategic planning and sustainable water resources management, as they allow simulating different operational scenarios and predicting situations in which storage volumes may be insufficient to meet multiple water uses (Kim et al. 2021 ; Jing et al. 2022 ). Considering this relevance, the objective of the present study was to develop a System Dynamics model capable of assessing water dynamics in a large reservoir of the São Francisco River Basin (Brazil), as well as estimating its capacity to meet multiple water-use demands over time. 2 Material and Methods 2.1 Study area description The System Dynamics (SD) model proposed in this study was developed for the Três Marias Hydropower Plant (HPP) reservoir (Fig. 1D), located in the São Francisco River Basin between latitude 18°55′06″ S and longitude 45°40′01″ W, Brazil. The Três Marias reservoir was selected due to its hydrological and socioeconomic relevance for Brazil, particularly because it is situated in a basin facing increasing water scarcity and conflicts among different water-use sectors (Bettencourt et al. 2022 ; CBHSF 2017). This context makes the reservoir a particularly relevant case study for evaluating water dynamics and the capacity to meet multiple uses under scenarios of pressure on water resources. Hydrologically, the Três Marias HPP plays a fundamental role in flood control and flow regulation, directly influencing water availability throughout the São Francisco River Basin (ANA 2022). From a socioeconomic perspective, the reservoir supplies water for multiple purposes, including hydropower generation, irrigation, industrial uses, and navigation (ANA 2022). Figure 1 Três Marias Hydropower Plant reservoir, located in the Upper São Francisco region, with emphasis on streamflow and rainfall stations. The Três Marias HHP reservoir was built between 1957 and 1961 and began operating in 1962. It is one of the largest reservoirs in Brazil, with an approximate surface area of 1,092.52 km², a total storage capacity of about 18,855.26 hm³, and a maximum crest height of 75 m (CEMIG 2023). The drainage area contributing to the reservoir covers approximately 51.000 km² (ANA 2023). The main physical characteristics of the reservoir and morphometry of the drainage area are presented in Table 1 . According to Köppen’s classification, the climate of the region where the reservoir is located is Aw, characterized as tropicais savanna with a dry winter, and an average temperature above 18°C in the coldest month. The highest rainfall occurs between December and March, with an annual average of 1.270 mm (INMET 2023). The population living near the reservoir has a density of 7.85 inhabitants per km², totaling 116.014 residents (IBGE 2022). Table 1 Physical characteristics of the Três Marias Hydropower Plant reservoir and morphometry of its drainage area. Characteristics Values Usable volume 14,974.128 hm 3 Total volume 18,855.26 hm 3 Dead volume 3,881.132 hm 3 Water surface 1,092.52 km 2 length 2.700 m Reservoir wall length 75 m Minimum operating level 549.20 m Maximum operating level 572.56 m Drainage area 51.000 km 2 Perimeter 2,130.60 km Main channel length 4.23 km Equivalent slope 0.0805 m m − 1 Average elevation 815 m Concentration time 97.48 min Compactness coefcient 1.56 Shape fator 0.51 2.2 Hydrological Monitoring Estimates of inflow and precipitation to the reservoir were obtained from time series (01/2004 to 06/2024) of 14 streamflow stations and nine rainfall stations (Fig. 1D), belonging to the National Hydrometeorological Network (RHN) and the National Institute of Meteorology (INMET), respectively (ANA 2024; INMET 2024). Withdrawals from the reservoir were obtained from water-use rights declared to the National Water and Basic Sanitation Agency (ANA), through the National Water Resources Information System (SNIRH). These data include 306 points of abstraction for agriculture and livestock watering, 18 points for aquaculture in cages and ponds, four abstraction points for public supply operated by COPASA, two points for hydraulic works, and nine points for industrial use (ANA 2023). The Minas Gerais Energy Company (CEMIG), responsible for electricity generation, transmission, distribution, and commercialization, operates six power generation units that, together with water withdrawals, represent the multiple uses of water in the reservoir. Water level variation is monitored using pressure sensors installed at the reservoir bottom, programmed to record hourly changes (ANA 2024b). These data were used for calibration and validation of the System Dynamics model. 2.3 Operating Rules of the Três Marias HPP The outflow from the HPP Três Marias reservoir is regulated by three operating rules (ONS 2018; ANA 2017b): 1) A minimum discharge of 100 m 3 s − 1 must be ensured for maintaining environmental flows when storage is below 30% of the usable volume. 2) When storage exceeds 30% of the usable volume, the minimum daily outflow must be 150 m 3 s − 1 . 3) Spillway discharges must be ≤ 3,500 m 3 s − 1 to avoid severe damage to inhabited islands downstream, in the municipality of Pirapora, MG. These three operating rules were incorporated into the development of the System Dynamics model. 2.4 Development of the system dynamics model The mathematical model to simulate reservoir water dynamics was developed using Vensim® PLE Plus v10.2.1 (Ventana Systems 2024 ), which allows building dynamic simulation models with equations representing temporal changes. The SD model was developed under the following assumptions: (i) water infiltration into the soil is uniform across the reservoir bed, considered over 65% of the water surface area; (ii) evaporation occurs uniformly over the entire water surface; (iii) precipitation is uniformly distributed across the water surface; (iv) capillary rise is negligible; (v) inflows and withdrawals are computed on a daily basis. These assumptions were based on Rodrigues et al. ( 2023 ), who studied water dynamics in small reservoirs in the Brazilian Cerrado, and adapted here for application to large reservoirs. Additional assumptions, such as uniform precipitation over the water surface, were necessary given the large extent of the reservoir. The SD model structure for assessing water dynamics and multiple water uses in the Três Marias reservoir is shown in Fig. 2 . 2.5 System Dynamics Model The description of the SD model developed to evaluate water dynamics and assist in meeting multiple water uses at the Três Marias HPP reservoir was based on previous studies (e.g., Wu et al. 2013 ; Sun et al. 2017 ; Luo et al. 2009; Rodrigues et al. 2021 , 2023 ; Stojkovic and Simonovic 2019 ). Unlike these earlier works, the present model stands out by incorporating hedging operation rules, specifically aimed at managing situations of water scarcity, with the goal of ensuring a balanced allocation for multiple water uses in the reservoir. The SD model consists of three types of variables: State variable – represented by the stored water volume in the reservoir. Flow variables – expressed as derivatives of the state variable, such as inflow and evaporation. Auxiliary variables – directly influence flow variables, such as water column height and water surface area (Fig. 3). This categorization of variables is essential for capturing the complexity of system behavior over time. By modeling the interactions among state, flow, and auxiliary variables, the SD approach allows simulating dynamic responses of the reservoir under different operational scenarios, supporting more robust and adaptive water management strategies. Figure 3 Causal loop diagram of the System Dynamics model developed to evaluate the dynamics and the capacity to meet multiple water uses in the Três Marias Hydropower Plant reservoir. (Q A = inflow; R A = water withdrawal; Hu = usable height; Hm = minimum operating level; H V = water head above the spillway crest; Q DE = total outflow; Q UM = multiple water uses; Hi = water level elevation, m; Q TO = turbine outflow; Q EV = evaporation; G O = gate opening height; P = precipitation; E V = evaporated water depth; P D = daily precipitation; Q SV = spillway outflow; V O = volume variation; A ES = water surface area; k = soil hydraulic conductivity at the reservoir bed; R1, R2, and R3 = operating rules 1, 2, and 3; a, b, c, d, e, f, g, h, i, j, l, and m = dimensionless coefficients; UNG1, UNG2, UNG3, UNG4, UNG5, and UNG6 = power generation units. Trigger: firing rule (set to 0 to disable hedging operation/water dynamics simulation). Operating rules: R1, R2, and R3 (enabled from 2018 onwards, and disabled when hedging operation is activated).” 2.6 Model Equations 2.6.1 Water Balance of Reservoir The water balance in a reservoir follows the principle of mass conservation, where the difference between the total inflows and outflows is equal to the variation in water storage over time (Dessie et al. 2015 ). $$\:{\text{V}}_{\text{O}\left(\text{t}\right)}={\text{V}}_{\text{O}\left(\text{t}\text{o}\right)}+{\int\:}_{\text{t}\text{o}}^{\text{t}}[{\text{Q}}_{\text{A}\left(\text{t}\right)}+{\text{Q}}_{\text{P}\left(\text{t}\right)}-{\text{Q}}_{\text{E}\text{V}\left(\text{t}\right)}-{\text{Q}}_{\text{I}\left(\text{t}\right)}-\:{\text{Q}}_{\text{T}\text{o}\left(\text{t}\right)}-{\text{Q}}_{\text{S}\text{V}\left(\text{t}\right)}-{\text{R}}_{\text{A}\left(\text{t}\right)}\left]\:\:\:\:\:\:\:\:\:\right(1)$$ Where: V O (t) = water volume at time t; V O (to) = water volume at initial time to; Q A (t) = inflow at time t; Q P (t) = precipitation at time t; Q EV (t) = evaporation at time t; Q I (t) = infiltration at time t; Q TO (t) = turbine outflow at time t; Q SV (t) = spillway outflow at time t; R A (t) = water withdrawal at time t. 2.6.2 Water level elevation To determine the water level (Hi) at time i, the initial stored volume was set as that of January 1, 2004, corresponding to 19.26% of the usable volume. Daily values of Hi were calculated using a sixth-degree polynomial (Eq. 2 ), developed by CEMIG (2016) from stage–storage data of the Três Marias HPP reservoir: obtained from the bathymetric survey at a 1:10.000 scale. $$\:{\text{H}}_{\text{i}}={\text{a}+\text{b}\left({\text{V}}_{\text{O}}\right)+\text{c}{\left({\text{V}}_{\text{O}}\right)}^{2}+\:\text{d}{\left({\text{V}}_{\text{O}}\right)}^{3\:\:}+\text{e}{\left({\text{V}}_{\text{O}}\right)}^{4\:\:}+\:\text{f}{\left({\text{V}}_{\text{O}}\right)}^{5\:\:\:\:}+\text{g}{\left({\text{V}}_{\text{O}}\right)}^{6\:\:\:}\:\:}_{\:\:\:\:}\:$$ 2 Where: \(\:{\text{H}}_{\text{i}}\) = reservoir water level at time i, m; Vo = actual volume, hm 3 . The coefficients ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, ‘f’ e ‘g’ are, respectively, 519.813; 0.0177101; -4.3982 ×10 − 06 ; 6.291 ×10 − 10 ; -4.79667×10 − 14 ; 1.83241×10 − 18 ; e -2.75665×10 − 23 (CEMIG 2016). 2.6.3 Water surface To estimate the surface area of the reservoir as a function of stored volume, the following equation was applied (CEMIG 2016): obtained from the bathymetric survey at a 1:10.000 scale. $$\:{\text{A}}_{\text{E}\text{S}}={\text{h}+\text{i}\left({\text{H}}_{\text{i}}\right)+\:\text{j}{\left({\text{H}}_{\text{i}}\right)}^{2\:\:}+\text{k}{\left({\text{H}}_{\text{i}}\right)}^{3\:\:}+\:\text{l}{\left({\text{H}}_{\text{i}}\right)}^{4\:\:\:\:}}_{\:\:\:\:}$$ 3 Where: A ES = water surface area, m². The coefficients ‘h’, ‘i’, ‘j’, ‘k’, and ‘l’, adjusted based on the area–elevation relationships of the Três Marias HPP reservoir, are respectively 4.56634 × 10 12 ; -3.43895 × 10 10 ; 9.72922 × 10 7 ; and − 122.578 (CEMIG 2016). 2.6.4 Evaporation The average flows equivalent to the net evaporated depth were estimated based on the amount of water evaporated from the reservoir’s water surface area, as expressed in Eq. 4. $$\:{\text{Q}}_{\text{E}\text{V}}=\frac{\text{E}\text{v}\:{\text{A}}_{\text{E}\text{S}}}{1000000}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$ Where: Q EV = average flow equivalent to the evaporated water depth in the reservoir, hm³day − 1 ; Ev = daily evaporation rate in the reservoir, m day − 1 . The daily evaporation rates throughout the year for the Três Marias HPP reservoir, as proposed by Vieira et al. ( 2016 ), were adopted, which were estimated using the Penman–Monteith model (Table 2 ). Table 2 Average daily evaporation rate in the reservoir (m day − 1 ) of the Três Marias Hydropower Plant during the period 2000–2002. January February March April May June 0.00532 0.00489 0.00455 0.00437 0.00363 0.00313 July August September October November December 0.00342 0.00452 0.00471 0.00583 0.00456 0.00480 Font: Vieira et al. ( 2016 ). 2.6.5 Infiltration The water surface area is always larger than the bottom area of the reservoir, where most of the infiltration occurs. Therefore, it was assumed that large reservoirs have a trapezoidal shape, with the base width representing approximately 65% of the water surface area (Sjöberg et al. 2018). The assumption of uniform infiltration is a reasonable simplification, given the relative homogeneity of the soil composition observed in geotechnical surveys conducted during the construction of the reservoir (Casagrande 1957; Wu et al. 2022 ). In the present study, the daily volume of water infiltrated into the reservoir bed was calculated using a modified version of Darcy’s Law, as shown in Eq. 5. $$\:{\text{Q}}_{\text{I}}=\frac{\left(\text{k}\:{\text{A}}_{\text{E}\text{S}}\frac{\left({\text{H}}_{\text{i}}-{\text{H}}_{0}\right)}{\text{C}\text{r}}\right)\:\text{T}}{1000000}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$ Where: Q I = infiltration, hm 3 day − 1 ; k = hydraulic conductivity of the medium, m s − 1 ; Cr = reservoir length, m; H₀ = minimum water level, 510.44 m; T = 86.400 seconds. Therefore, when H i = H₀, infiltration is zero, indicating that there is no water flow infiltrating into the soil when the reservoir water level reaches the minimum elevation. The average conductivity was 1.3 × 10 − 06 m s − 1 , obtained from k values reported in studies and technical reports conducted in the Três Marias HPP reservoir area, which indicate the predominance of sandy and sandy–clayey soils, considering the heterogeneity of the soil at the reservoir bed (Casagrande 1957; CPRM 2025). 2.6.6 Precipitation The determination of the flow corresponding to the direct contribution of precipitation to the Três Marias HPP reservoir was carried out using Eq. 6. $$\:{\text{Q}}_{\text{P}}=\frac{{\text{P}}_{\text{D}}\:{\text{A}}_{\text{E}\text{S}}}{1000000}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$ Where: Q P = precipitation, hm 3 day − 1 ; P D = daily precipitation, m day − 1 ; A ES = water surface area, m². 2.6.7 Turbine outflow The turbine outflow of the Três Marias HPP was estimated in a simplified manner from the water level by applying Torricelli’s principle (Adeeyo et al. 2023 ), as represented in Eq. (7). $$\:{\text{Q}}_{\text{T}\text{o}}=\frac{\left({\text{C}\text{d}\:\text{A}\left(2\text{g}\:{\text{H}}_{\text{i}}-{\text{H}}_{\text{m}}\right)}^{0.5}\right)\:\text{T}\:}{1000000}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(7\right)$$ Where: Q TO = turbine outflow, hm 3 day − 1 ; Cd = discharge coefficient (dimensionless; 0.73); A = turbine opening area, m²; g = gravitational acceleration, 9.81 m s − 2 ; Hm = minimum operating level (m); T = 86.400 seconds. Thus, when H i = Hm, the turbine outflow will be zero. This means that there will be no water flow through the turbines when the reservoir water level is equal to the minimum operating elevation. The maximum and minimum operating levels, equal to 572.50 m and 549.20 m, respectively, relative to mean sea level, were adopted based on the new bathymetric survey conducted in the reservoir in 2016 (CEMIG 2016). 2.6.8 Spillway outflow During the rainy season, it is common for the Três Marias HPP reservoir to reach its maximum capacity and begin to overflow through a rectangular spillway with seven gates. Whenever H i exceeds the maximum operating level (maximum elevation of 572.5 m), the gates are opened, and the corresponding spillway discharge is computed (Fig. 2 ). The spillway discharge was estimated using Eq. (8), as proposed by Porto ( 2006 ). The physical characteristics of the reservoir spillway were obtained from the Companhia Energética de Minas Gerais (CEMIG 2023). $$\:{\text{Q}}_{\text{S}\text{V}}=\frac{\left(\:\left({\text{C}}_{\text{O}}\:{\text{L}}_{\text{C}}\:{\text{G}}_{\text{O}}\:\sqrt{2\text{g}}\:\text{H}\text{v}\:\right)\:{\text{C}}_{\text{P}}\right)\:\text{T}\:}{1000000}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(8\right)$$ Where: Q SV = spillway discharge, hm 3 day − 1 ; C O = spillway discharge coefficient (dimensionless; 0.75); L C = gate width, m; T = 86.400 seconds; G O = gate opening height, m, with a maximum value of 1.56 m to ensure outflows equal to or lower than 3.500 m³ s⁻¹; H V = water head over the spillway, m; C P = number of gates. 2.6.9 Multiple water uses and Total outflow The total flow demanded to meet multiple water uses, which represents the sum of the flows for hydropower generation (turbine outflow) and the flows required to satisfy other demands, was obtained using Eq. (9). $$\:{\text{Q}}_{\text{U}\text{M}}=\:{\text{Q}}_{\text{T}}+{\text{R}}_{\text{A}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(9\right)$$ Where: Q UM = multiple water uses; R A = water withdrawal from the reservoir obtained from water rights, hm 3 day − 1 . The total outflow, which refers to the amount of water released from the reservoir, was obtained using Eq. (10). $$\:{\text{Q}}_{\text{D}\text{E}}=\:{\text{Q}}_{\text{T}}+{\text{Q}}_{\text{S}\text{V}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(10\right)$$ Where: Q DE = total reservoir outflow, hm 3 day − 1 . 2.7 Evaluation of the Capacity to Meet Multiple Water Uses in the Três Marias HPP Reservoir To assess the capacity of the Três Marias HPP reservoir to meet multiple water uses during periods of reduced water availability between January 2004 and June 30, 2024, a hedging operation was implemented in the System Dynamics (SD) model (Bayazit and Ünal 1990 ; Chong et al. 2021 ). The hedging operation introduces small but more frequent reductions in withdrawals, aiming to conserve water in the reservoir and decrease the likelihood of a large future reduction caused by complete reservoir depletion (Chong et al. 2021 ). To implement the hedging operation in the SD model, two main rules were adopted: 1) Trigger rule: defines the minimum storage volume in the reservoir required to ensure the supply for multiple water uses (You and Cai 2008 ). 2) Cutback rule: establishes the magnitude of the reduction in water demand supply, with the cutback being triggered by changes in storage volume (Bayesteh and Azari 2021 ). The hedging operation to evaluate the ability of the reservoir to supply multiple water uses was performed based on water dynamics and the sensitivity of the SD model. Two scenarios were proposed to activate the hedging operation, considering an annual growth trend of 6.26% in water withdrawals: 1) triggers of 52% and 62% of the total volume with cutbacks applied to turbine outflow. 2) triggers of 52% and 62% of the total volume with cutbacks applied to turbine outflow and evaporation. 2.8 Evaluation and Calibration of the System Dynamics Model The records of water level variations observed between January 2004 and June 2024 in the Três Marias HPP reservoir were used to evaluate the performance of the proposed SD model. For this purpose, the dataset was divided into three time intervals, following the methodology proposed by Althoff and Rodrigues ( 2021 ). The first interval, comprising the initial 731 days (9.99% of the data), was used to warm up the SD model, sufficient to stabilize and dissipate the effects of initial conditions. The subsequent 4.758 days (64.95% of the data) were used for calibration; a longer period was required to adjust the SD model variables, allowing the capture of hydrological variability over time. Finally, the last 1.998 days (25.06% of the data) were used for validation, testing the ability of the SD model to predict hydrological behavior using data not included in calibration. This helps to identify potential overfitting, in which the SD model adapts excessively to calibration data and loses its ability to generalize to new data. To evaluate the performance of the proposed SD model, the following statistical metrics were applied: Mean Absolute Relative Error – MARE (Eq. 11); Mean Absolute Error – MAE (Eq. 12) (Abro et al. 2020 ); Root Mean Square Error – RMSE (Eq. 13); Coefficient of Determination – R² (Eq. 14); Nash–Sutcliffe Efficiency Index – NSE (Eq. 15) (Nash and Sutcliffe 1970 ); and Kling–Gupta Efficiency Index – KGE (Eq. 16) (Gupta et al. 2009 ). Finally, a Pearson correlation was performed, as expressed in Eq. (17), to evaluate the linear relationship between observed and simulated data from the proposed model (Acevedo et al. 2017 ). All these statistical metrics were calculated using the R software (R Development Core Team 2018). $$\:\text{M}\text{A}\text{R}\text{E}=\frac{1}{\text{n}}{\sum\:}_{\text{i}=1}^{\text{n}}\frac{\left|{(\text{S}\text{i}\text{m}}_{\text{i}}-{\text{O}\text{b}\text{s}}_{\text{i}})\right|}{{\text{O}\text{b}\text{s}}_{\text{i}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(11\right)$$ $$\:\text{M}\text{A}\text{E}=\frac{1}{\:\text{n}}\sum\:_{\text{i}=1}^{\text{n}}|{\text{S}\text{i}\text{m}}_{\text{i}}-{\text{O}\text{b}\text{s}}_{\text{i}}\left|\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right(12)$$ $$\:\text{R}\text{M}\text{S}\text{E}=\sqrt{\frac{1}{\text{n}}{\sum\:}_{\text{i}=1}^{\text{n}}{{(\text{S}\text{i}\text{m}}_{\text{i}}-{\text{O}\text{b}\text{s}}_{\text{i}})}^{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(13\right)$$ $$\:{\text{R}}^{2}=\frac{\sum\:_{\text{i}=1}^{\text{n}}\left({\text{O}\text{b}\text{s}}_{\text{i}\:}-\:{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}}\right).\:\left({\text{S}\text{i}\text{m}}_{\text{i}\:}-\:{\stackrel{-}{\text{S}}\text{i}\text{m}}_{i}\right)}{\sqrt{\sum\:_{\text{i}=1}^{\text{n}}({\text{O}\text{b}\text{s}}_{\text{i}\:}-\:{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}})²}\:.\sqrt{\sum\:_{\text{i}=1}^{\text{n}}({\text{S}\text{i}\text{m}}_{\text{i}\:}-\:{\stackrel{-}{\text{S}}\text{i}\text{m}}_{\text{i}})²}\:\:\:}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(14\right)$$ $$\:\text{N}\text{S}\text{E}=1-\frac{\sum\:_{\text{i}=1}^{\text{n}}({\text{O}\text{b}\text{s}}_{\text{i}\:}-\:{\text{S}\text{i}\text{m}}_{\text{i}\:})²}{\:\sum\:_{\text{i}=1}^{\text{n}}({\text{O}\text{b}\text{s}}_{\text{i}\:}-\:{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}})²\:\:}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(15\right)$$ $$\:\text{K}\text{G}\text{E}=1-\:\sqrt{{\left(\text{r}-1\:\right)}^{2\:}+{\left({\beta\:}-1\right)}^{2}+\:{\left({\gamma\:}-1\right)}^{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(16\right)$$ Where: $$\:\:\:\:\:\:\:\:\:\:\:\:\text{r}=\frac{\sum\:_{\text{i}=1}^{\text{n}}\left({\text{O}\text{b}\text{s}}_{\text{i}\:}-{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}}\right)}{\sqrt{\sum\:_{\text{i}=1}^{\text{n}}{(\text{O}\text{b}\text{s}}_{\text{i}\:}-{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}})\:.}\:\sqrt{\sum\:_{\text{i}=1}^{\text{n}}\left({\text{S}\text{i}\text{m}}_{\text{i}}-{\stackrel{-}{\text{S}}\text{i}\text{m}}_{\text{i}}\right)}}$$ $$\:\:\:\:\:\:\:\:\:\:\:\:{\beta\:}=\frac{{{\mu\:}}_{\text{s}}}{{{\mu\:}}_{\text{o}}}$$ $$\:\:\:\:\:\:\:\:\:\:\:{\gamma\:}=\frac{{\text{C}\text{V}}_{\text{s}}}{{\text{C}\text{V}}_{\text{o}}}=\:\frac{\frac{{{\sigma\:}}_{\text{s}}}{{{\mu\:}}_{\text{s}}}}{\frac{{{\sigma\:}}_{\text{o}}}{{{\mu\:}}_{\text{o}}}}$$ $$\:\text{r}=\:\:\frac{1}{\text{n}-1}\sum\:\left(\frac{{{\text{S}\text{i}\text{m}}_{\text{i}}}_{\:}-\:{\stackrel{-}{\text{S}}\text{i}\text{m}}_{\text{i}}\:}{{\sigma\:}\text{s}\:}\right)\left(\frac{{\text{O}\text{b}\text{s}}_{\text{i}}-\:{\stackrel{-}{\text{O}}\text{b}\text{s}}_{\text{i}}\:}{{\sigma\:}\text{s}\:}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(17\right)$$ Where: n = number of observations; µs and µo = means of simulated and observed data; r = Pearson correlation; σs and σo = standard deviations of simulated and observed data; Cvs and Cvo = coefficients of variation of simulated and observed data; Oi and Si = observed and simulated values (SPPs) on day i; Ō and S̄ = arithmetic means of observed and simulated data (SPPs), respectively. 2.8 Sensitivity Analysis of the Variation in Stored Volume in the Três Marias HPP Reservoir to the Main Key Variables A sensitivity analysis was carried out with the objective of identifying which variables exert the greatest influence on the variation of stored volume in the Três Marias HPP reservoir. The stored water volume was defined as the variable of interest, as it directly reflects the system’s capacity to meet multiple water uses over time. The considered inflow and outflow variables (inflow, infiltration, evaporation, precipitation, turbine outflow, and water withdrawal) represent the main components of the reservoir’s water balance and, consequently, the most relevant elements for the system’s operation and management. To evaluate the response of the SD model to uncertainties and natural or anthropogenic fluctuations, the values of each of these variables were individually adjusted by ± 10% relative to their reference values for the period from January 2004 to June 2024. This percentage variation was defined in the literature as an adequate range to test the robustness of hydrological models and to capture possible nonlinearities in the system’s responses (Alifujiang et al. 2017 ; Rodrigues et al. 2023 ). 3 Results 3.1 Calibration and Evaluation of the System Dynamics Model The results show the variation of the observed and simulated water level over time in the reservoir, highlighting a considerable decrease after September 18, 2014, which stabilized at safe levels to meet multiple water uses from January 19, 2019 onward (Fig. 4). Figure 4 Observed and simulated water level for the training, calibration, and validation periods of the System Dynamics model. Consistency is observed between the simulated and observed water level values over time, according to the different performance indices applied. During the warm-up period, the following performance indices were obtained: R 2 = 0.899, NSE = 0.901, KGE = 0.944, MAE = 0.885, RMSE = 1.038, MARE = 0.0015 e R = 0.954. During the calibration phase of the SD model, the following values were obtained: R² = 0.958, NSE = 0.967, KGE = 0.974, MAE = 0.869, RMSE = 1.252, MARE = 0.00153; and a positive Pearson correlation of 0.980. The performance of the SD model showed a slight loss of accuracy in the validation phase, with R² = 0.956, NSE = 0.961, KGE = 0.952, MAE = 0.873, RMSE = 1.263, MARE = 0.00161 and a decrease in the positive Pearson correlation to 0.975. These results indicate that the SD model is classified in the ‘very good’ category according to the classification proposed by Mararakanye et al. ( 2020 ). 3.2 Sensitivity Analysis of the System Dynamics Model The results of the sensitivity analysis of water dynamics in the Três Marias HPP reservoir to changes in the main key variables (Fig. 5 and Table 3 ). Figure 5 Variation in reservoir volume (%) over time as a function of ± 10% changes in inflow, turbine outflow, evaporation, precipitation, infiltration, and water withdrawal for the period from January 2004 to June 2024. Table 3 Results of the sensitivity analysis of the System Dynamics model applied to the Três Marias Hydropower Plant reservoir. (∆Vo = volume variation (%); Q A = inflow; R A = water withdrawal; Q TO = turbine outflow; Q EV = evaporation; Q P = precipitation; Q I = infiltration). (%) ∆ Vo Q A Q P Q EV +10 -10 +10 -10 +10 -10 66.24 41.70 58.36 54.68 53.78 59.31 Q TO R A Q I +10 -10 +10 -10 +10 -10 49.67 63.17 55.70 57.45 55.61 57.58 The variation in stored water volume in the Três Marias HPP reservoir showed low sensitivity to changes in the flow variables infiltration, precipitation, and water withdrawal, indicating that variations in these variables had less influence on the stored volume. However, the stored water volume in the reservoir was highly sensitive to the flow variables inflow, turbine outflow, and evaporation. A + 10% variation in inflow resulted in an average increase of 66.24% in storage volume, while a -10% variation led to an average reduction of 41.70% (Fig. 5, Table 3 ). A + 10% variation in precipitation, evaporation, infiltration, turbine outflow, and water withdrawal values (Fig. 5, Table 3 ) resulted in average variations in reservoir storage volume of 58.36%, 53.78%, 55.61%, 49.67%, and 55.70%, respectively. A -10% variation in precipitation, evaporation, infiltration, turbine outflow, and water withdrawal values (Fig. 5, Table 3 ) implied average variations of 54.68%, 59.31%, 57.58%, 63.17%, and 57.45%, respectively, in the stored volume. The flow variables inflow, turbine outflow, and evaporation are therefore the most sensitive factors affecting the stored volume in the Três Marias HPP reservoir. 3.3 Simulation and Evaluation of Water Dynamics in the Reservoir The results of the simulation of the behavior of the main flow, auxiliary, and state variables that determine the water dynamics in the Três Marias HPP reservoir are presented in Fig. 6 . The maximum, mean, and minimum values of the state, flow, and auxiliary variables for the Três Marias HPP reservoir are presented in Table 4 . When analyzing the simulation results, it is observed that inflow values (Fig. 6 A, Table 4 ) ranged from 663.125 hm³day⁻ 1 to 0.009 hm³day⁻ 1 , with an average value of 45.197 hm³day⁻ 1 . A reduction in inflow was identified in three periods. The first reduction extended from May 14 to November 10, 2014, with an average flow of 4.912 hm³day⁻ 1 . The second reduction lasted from July 19 to November 11, 2015, with an average of 5.941 hm³day⁻ 1 . The third reduction occurred from July 6 to November 25, 2017, with an average of 2.543 hm³day⁻ 1 . An overall average inflow decline of 4.462 hm 3 day − 1 was observed during these periods. High variability in inflow was recorded during the rainy season, with an average of 50.571 hm³day⁻ 1 . Inflow is the main input variable in the water balance of large reservoirs, directly or indirectly influencing the behavior of other flow, auxiliary, and state variables, which followed the same trend as inflow. Water surface area values ranged from 1102.8 km 2 to 366.767 km 2 , with an average of 786.67 km 2 (Table 4 ). A mean reduction of 0.926 km 2 per day was observed during the dry seasons (Fig. 6 B), and during the driest period (May 14 to November 10, 2014) the average daily reduction was approximately 0.521 km 2 , reaching the minimum value of 366.767 km 2 on October 31, 2014. The largest infiltration and evaporation losses occurred on the days when the largest water surface areas were recorded. Infiltration flow into the reservoir bed (Fig. 6 C, Table 4 ) ranged from 1.862 hm 3 day − 1 to 0.391 hm³day − 1 , with an average of 1.182 hm 3 day − 1 . Evaporation from the water surface (Fig. 6 D, Table 4 ) ranged from 5.672 hm³day − 1 to 1.315 hm³day − 1 , with an average of 3.443 hm³day − 1 . Precipitated water volume over the reservoir surface area (Fig. 6 E, Table 4 ) reached a maximum of 100.861 hm 3 day − 1 and a minimum of 0.065 hm 3 day − 1 , with an average of 2.613 hm 3 day − 1 . Water withdrawal for agriculture, livestock watering, public supply, and industrial use (Fig. 6 F, Table 4 ) had an average of 1.10 hm 3 day − 1 , with a minimum of 0.053 hm 3 day − 1 and a maximum of 4.032 hm 3 day − 1 in June 2024. This significant increase was mainly due to higher demand for irrigation of annual crops. Since 2004, continuous growth in water withdrawals has been observed, from a minimum of 0.053 hm 3 day − 1 to current maximum values. The average annual growth trend in withdrawals was approximately 5.84%, equivalent to 0.817 hm 3 year − 1 between 2004 and 2024. However, from 2017 onward, this growth intensified, with an average annual rate of 6.26%, reflecting a continuous upward trend of 0.876 hm 3 year − 1 in water withdrawals in the coming years. Turbine outflow (Fig. 6 G, Table 4 ), responsible for power generation, averaged 61.462 hm 3 day − 1 , reaching a maximum of 77.321 hm 3 day − 1 and a minimum of 12.852 hm 3 day − 1 on October 31, 2014, mainly due to the reduced inflow in the first period. Multiple water uses (Fig. 6 H, Table 4 ) reached a maximum demand of 79.983 hm 3 day − 1 and a minimum of 13.522 hm 3 day − 1 , with an average of 62.562 hm 3 day − 1 . Multiple water uses accounted for 90.23% of total demand, of which turbine outflow was the main outflow, representing 98.23%, followed by water withdrawals at 1.77%. Therefore, turbine outflow is approximately 50.97 times greater than withdrawals. The remaining 9.45% was due to losses from evaporation, infiltration, and spillway outflow, which together represented 4.84%, 1.96%, and 2.97%, respectively, of the reservoir water balance. The lowest volume variations were observed on days when the smallest water surface areas were recorded (Fig. 6 I). On October 31, 2014, the reservoir volume reached its lowest value of 3721.312 hm³, representing 0.34% of usable storage (Table 4 ). The maximum volume of 18,855.26 hm³ was reached during five periods (Fig. 6 I). Over the analyzed period, the average volume was 12,438.691 hm³ (Table 4 ). Between July 6 and November 25, 2017, a second significant downward trend in volume occurred, with a decrease of approximately 19.66 hm 3 day − 1 . This decline resulted in a minimum volume of 4693.37 hm³, recorded on November 22, 2017. The reservoir water level (Fig. 6 J, Table 4 ) ranged from 572.863 m to 549.551 m, with an average of 564.789 m. Maximum spillway discharge (Fig. 6 K, Table 4 ) was 181.883 hm³day⁻ 1 , recorded on February 21, 2022, while the minimum was 7.789 hm 3 day − 1 , with an average of 92.357 hm 3 day − 1 , operating approximately 1.81% of the time. The maximum outflow released from the reservoir (Fig. 6 L, Table 4 ) was 259.213 hm 3 day − 1 , with an average of 63.432 hm 3 day − 1 and a minimum of 12.852 hm 3 day − 1 . Table 4 Maximum, mean, and minimum values of the state, flow, and auxiliary variables in the Três Marias Hydropower Plant reservoir, São Francisco River Basin, Brazil. Variable Unity Maximum Medium Minimum Inflow hm³dia − 1 663.125 45.197 0.009 Precipitation 100.861 2.613 0.065 Infiltration 1.862 1.182 0.391 Evaporation 5.672 3.441 1.315 Turbine outflow 77.321 61.451 12.852 Spillaway outflow 181.883 92.357 7.789 Multiple water uses 79.983 62.562 13,522 Water abstration 4.032 1.102 0.053 Total outflow 259.213 63.432 12.852 Volume hm 3 19185.9 12438.691 3721.312 Water surface km 2 572.863 564.789 549.551 Water level m 1102.845 786.671 366.751 3.4 Evaluation of the capacity to supply multiple water uses in the Três Marias HPP reservoir The simulation results for the different scenarios with hedging operation, with variations in the triggers and cutbacks applied to turbine outflow, highlight the changes in flow for supplying multiple water uses, the number of cutback days, and the impacts on the reservoir’s stored volume (Fig. 7 , Fig. 8 , Table 5 ). In Scenario 1, with a trigger of 52% and a 39% cutback applied, turbine outflow was reduced by an average of 17.27 hm 3 day − 1 over 1.088 days (14.53% of the time) throughout the entire simulation period (Fig. 7 A). In the periods prior to October 31, 2014, when the greatest reduction in water availability occurred, turbine outflow was reduced by an average of 17.13 hm 3 day − 1 over 351 days. This reduction was necessary to maintain a minimum flow of 21.89 hm 3 day − 1 to ensure the supply of multiple water uses, as opposed to the 13.516 hm 3 day − 1 observed during the reservoir’s water dynamics (Fig. 7 A). During the same period, the reservoir volume increased from the lowest recorded value of 3,721.31 hm³ to 6,066.76 hm³, representing an increase of approximately 63.06% to meet multiple water uses (Fig. 7 B). Another trend in Scenario 1 was observed with a 62% trigger and a 21% cutback applied: turbine outflow was reduced by an average of 12.66 hm 3 day − 1 over 2.461 days (32.87% of the time) during the entire simulation period (Fig. 7 C). The main reason for the smaller cutback, which occurs more frequently with a 62% trigger, is that turbine outflow reductions began shortly after the start of the simulation. However, the initial cutback was followed by four additional reductions averaging 13.37 hm 3 day − 1 , lasting 915 days (12.22%), to mitigate the decline in volume that began on May 14, 2014, reaching its most critical value on October 31, 2014. This intervention raised the minimum observed flow from 13.51 hm 3 day − 1 to 21.61 hm 3 day − 1 (Fig. 7 C). Consequently, the reservoir’s critical volume (Fig. 7 D) increased from 3,721.31 hm³, observed during the water dynamics, to 5,873.47 hm³, representing a storage increase of approximately 57.84%. This increase ensured the supply of multiple water uses, the maintenance of environmental flows, and compliance with operational rules. In Scenario 2, by maintaining the 52% trigger and reducing the cutback to 29%, while applying a 0.11% reduction in evaporation-equivalent to a reduction of 0.55 km² in the water surface área-there was a decrease in the number of cutbacks in turbine outflow, which was reduced by an average of 10.54 hm 3 day − 1 over 543 days (7.05% of the time) during the entire simulation period (Fig. 8 A). In the periods prior to October 31, 2014, the day with the greatest reduction in water availability, turbine outflow was reduced by an average of 9.71 hm 3 day − 1 over 282 days (3.77% of the time). This reduction ensured a minimum flow of 22.87 hm 3 day − 1 to supply multiple water uses, as opposed to the 13.516 hm 3 day − 1 observed on October 31, 2014, during the reservoir’s water dynamics (Fig. 8 A). In the same period, the reservoir volume increased from the lowest recorded value of 3,721.21 hm³ to 6,311.32 hm³, representing an increase of approximately 69.59% to supply multiple water uses (Fig. 8 B). It is observed in Scenario 2 that, by maintaining the 62% trigger and reducing the cutback to 11%, while keeping the 0.11% reduction in evaporation, there was, as expected, a decrease in the number of cutbacks (Fig. 8 C). As a consequence, turbine outflow was reduced by an average of 8.14 hm 3 day − 1 over 1.940 days (25.91% of the time) throughout the simulation period (Fig. 8 C). The main reason for the decrease in the number of cutbacks is that with the reduction in evaporation, the reservoir volume tends to increase, thereby enhancing the water availability to supply multiple uses. However, prior to October 31, 2014, the average reduction in turbine outflow due to the smaller cutback was 6.36 hm³day⁻ 1 over 792 days (10.6% of the time), resulting in the minimum observed flow increasing from 13.51 hm 3 day − 1 to 22.46 hm 3 day − 1 (Fig. 8 C). Consequently, the critical reservoir volume (Fig. 8 D) increased from 3,721.31 hm³, observed during the water dynamics, to 6,160.4 hm 3 , representing an increase in stored volume of approximately 65.42%, ensuring the supply of multiple water uses during periods of greater reductions in water availability. Table 5 Results of the different hedging operation scenarios with variations in triggers and cutbacks applied to turbine outflow, showing the impacts on flows and on the stored volume in the Três Marias Hydropower Plant reservoir. (Ga = trigger; C O = cutback; RQ EV = evaporation reduction; RQ TO = average reduction in turbine outflow; D C = days with reduction; T R = reduction period; Q M = minimum observed flow to supply multiple water uses; Avo = volume increase; C = scenario; Un = unit; C1 = scenario 1; C2 = scenario 2). C Ga Co RQ EV RQ TO D C T R Q M Avo Un (%) (%) (%) (hm 3 dia − 1 ) (dias) (%) (hm 3 dia − 1 ) (%) C1 52 39 - 17.27 1088 14.53 21.89 63.06 C1 62 21 - 12.66 2461 32.87 21.61 57.84 C2 52 29 0.11 10.54 543 7.25 22.87 69.59 C2 62 11 0.11 8.14 1940 25.91 22.46 65.42 The results show that the hedging operation strategy in Scenario 2 (with a trigger of 52% of the total volume, a 29% cutback in turbine outflow, and a 0.11% reduction in evaporation) favored the increase of the minimum stored volume in the reservoir, thereby enhancing the capacity to supply multiple water uses during periods of greater reduction in water availability (Fig. 9). Figure 9 Relationship between the average reduction in turbine outflow and the increase in stored volume in the Três Marias HPP reservoir under different hedging operation scenarios. (Ga52 = 52% trigger; Ga62 = 62% trigger; Co = 39% cutback; Co = 21% cutback; Co = 29% cutback; Co = 11% cutback; RQ TO = average reduction in turbine outflow; Avo = volume increase; C1 = Scenario 1; C2 = Scenario 2). 4 Discussion The results indicate significant variability in inflow, with an average of 45.197 hm 3 day − 1 , directly reflecting the low precipitation rates in the São Francisco River Basin region (Paredes-Trejo et al. 2021 ; Capozzoli et al. 2016; Lucas et al. 2021 ). The reduction in the water surface area during dry periods, with an average decrease of 0.926 km² per day, is associated with significant evaporation losses, which reached a maximum value of 5.672 hm 3 day − 1 and an average of 3.443 hm 3 day − 1 . These results indicate that water resources management must consider not only the amount of available water but also evaporation rates, which can impact the sustainability of water sources (Nevermann et al. 2024 ; Zhang et al. 2017 ). Evaporation losses not only reduce the volume of available water but also affect the reservoir’s capacity to meet demand during critical periods (Wang et al. 2018 ; Zhao and Gao 2019 ; Scherer and Pfister 2016 ). Infiltration was limited to a maximum of 1.862 hm 3 day − 1 and a minimum of 0.391 hm 3 day − 1 , with an average variation of 1.182 hm 3 day − 1 . These values were close to the 0.13 hm 3 day − 1 to 2.4 hm 3 day − 1 with an average of 1.464 hm 3 day − 1 , estimated for the Boura reservoir, located in central-west Burkina Faso (Fower et al. 2015). The continuous increase in water withdrawals, with an annual growth rate of 6.26%, reinforces the need to reassess water management to ensure sustainability, especially in the irrigation sector (Bettencourt et al. 2022 ). The predominance of turbine outflow, which accounts for 88.63% of total demand, highlights the importance of optimizing reservoir operation to balance power generation with other competing water uses (Stojkovic and Simonovic 2019 ; Ivetić et al. 2022; Bettencourt et al. 2022 ). However, the simulations show the adoption of emergency operations that prioritize the electricity sector at the expense of other water uses. The analysis of the results demonstrates that turbine outflow, with an average of 77.321 hm 3 day − 1 , is fundamental for hydropower generation, although it shows significant variations, especially during periods of reduced inflow. Potential changes in turbine outflow, together with reduced inflows, may lead to sudden drops in the reservoir water level (Jiang et al. 2020 ). This dynamic highlights the importance of efficient water management, as emphasized by Ivetić et al. (2022), who suggest that seasonal and climatic variations must be considered in reservoir operation. In this context, researchers highlight the importance of hedging operations with adjustable triggers and cutbacks as an effective strategy to mitigate the impacts of droughts and optimize water supply. This approach can enhance reservoir operational efficiency, even in the face of uncertainties imposed by climate change (Mostaghimzadeh et al. 2022 ; Chang et al. 2019 ; Ashrafi 2021 ; Bayesteh and Azari 2021 ; Okkan et al. 2023 ). In this study, for example, using a 52% trigger and a 39% cutback resulted in a turbine outflow reduction of 17.27 hm 3 day − 1 over 1.088 days, contributing to a 63.06% increase in reservoir volume. Flexible operational rules may allow for the mitigation of climate change effects, enabling an adaptive response that accounts for climatic uncertainties (Beshavard et al. 2022 ). The reduction in evaporation improves storage efficiency, as demonstrated by the 69.59% increase in reservoir volume when applying a 52% trigger with a 29% cutback and a 0.11% reduction in evaporation, through the implementation of floating solar power plants (Niccolai et al. 2023 ; Sunny et al. 2024 ; Luo et al. 2024 ). These results emphasize the importance of implementing hedging operations to ensure more efficient water resource management, particularly to minimize the risks of failing to supply multiple water uses under climate change. This can also support CEMIG in its project to use part of the reservoir surface to add an alternative source of hydraulic generation. 4.1 Implications for Water Resources Management When analyzing the impacts of operational scenarios on water resources management, specifically on flow rate and water storage, it is observed that adjustments in triggers and cutbacks directly affect flow rate and the stored water volume in the reservoir. For example, the reduction in turbine outflow (RQ TO ) is more pronounced in Scenarios 1 and 2, with lower trigger percentages (52%), compared with higher trigger scenarios (62%). This suggests that a more aggressive operational approach may facilitate better water management, optimizing reservoir levels during periods of high demand and low inflows (Badr et al. 2023 ; Ilich 2024 ). Meanwhile, the introduction of evaporation reduction measures (RQ EV ) in Scenario 2 provides a notable advantage in terms of water conservation, with fewer turbine outflow cutbacks. Although the impact is minimal (0.11%), it highlights the importance of integrating evaporation control strategies into reservoir operations, particularly in arid regions, thereby maintaining reservoir levels during dry periods. The higher number of flow reductions in Scenario 1 (2.461 days) compared with Scenario 2 (1.940 days) indicates that scenarios with evaporation reduction and cutbacks may alleviate operational stress on the reservoir, enabling more sustainable long-term water resources management. The substantial difference in the number of days with reductions emphasizes the need to carefully consider operational thresholds to minimize negative impacts on water availability for multiple uses (Garrote et al. 2023 ; Garcia et al. 2020 ). Finally, it is noteworthy that despite variations in operational scenarios, the maintenance of adequate flows to supply multiple water uses (ranging from 21.46 to 22.87 hm 3 day − 1 ) in all scenarios demonstrates sustainable management. However, a slight increase in the available volume for supplying multiple water uses, with higher or lower cutbacks and other evaporation reduction measures, requires further investigation within the SD model to ensure that water demands are consistently met under different climate change scenarios. 5 Conclusions The System Dynamics model developed in this study proved efficient in simulating the water dynamics of the Três Marias HPP reservoir and assessing its capacity to supply multiple water uses. Calibration and validation confirmed the robustness of the model, with high agreement between simulated and observed water levels over two decades of monitoring. The sensitivity analysis highlighted inflow as the most influential variable on stored volume, followed by turbine outflow and evaporation, underscoring the relevance of these components for system management. In the Três Marias HPP reservoir, water demand for power generation, represented by turbine outflow, accounts for more than 90% of the reservoir’s total demand. There has been a significant increase in consumptive withdrawals since 2017, with a projected average annual growth trend of 6.26%. This scenario reinforces the imminence of conflicts between power generation and other user sectors, particularly during water scarcity periods. The hedging operation implemented with the aid of the proposed SD model proved effective for reservoir management, as it enabled preventive reductions in turbine outflow, increasing stored volume and ensuring water security during critical periods. In addition, small reductions in evaporation losses also contributed to enhancing system resilience in the face of growing demands. Overall, the results show that the proposed System Dynamics-based model is a valuable tool to support strategic planning and decision-making in the management of large reservoirs. In the case of the Três Marias HPP, the application of the proposed model highlighted the need for adaptive operational strategies capable of reconciling hydropower generation with increasing consumptive uses and the maintenance of environmental flows. Thus, this study contributes to strengthening the scientific and practical foundation of integrated water resources management through the implementation of more sustainable operational rules. Finally, it is emphasized that the combination of triggers and cutbacks, along with small evaporation control measures, can improve the balance between energy generation and the supply of multiple water uses. Declarations Acknowledgements The authors thank to the Federal University of Viçosa (UFV). This study was partly financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES-In English: Coordination of Improvement of Higher Education Personnel) - Finance code 001, and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ - In English: National Council for Scientific and Technological Development) – Grant number 155594/2023-0. Funding This work was supported by (CAPES - In English: Coordination of Improvement of Higher Education Personnel) – Finance code 001, and by the (CNPQ – In English: National Council for Scientific and Technological Development) – Grant number 155594/2023-0. The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Contributions All authors contributed to the study conception and design. Alisson Lopes Rodrigues: Conceptualization, Methodology, Software, Writing - original draft and all authors commented on previous versions of the manuscript. Ricardo Santos Silva Amorim: Conceptualization, Methodology, Writing-review & editing. Pedro Manuel Villa: Methodology, Software; Writing -review & editing. All authors read and approved the final manuscript. Availability of data and materials I, Alisson Lopes Rodrigues, first author of the manuscript entitled ‘System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses’ declare, for the due purposes of data access, availability, right, and use during the development of this research, through the link https://drive.google.com/drive/folders/1-jcu9y1nIXVG65ENpB281097-vYUWwsQ?usp=drive_link . Viçosa (MG), 02/10/2025. Ethical Approval I, Alisson Lopes Rodrigues, the first author of the manuscript entitled ‘System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses’, declare that the submitted manuscript is original and has not been submitted to more than one publication for simultaneous appreciation. The results were presented clearly, honestly and without falsification or inappropriate manipulation of data. And we certify that we use free software for the development of this work. Viçosa (MG), 02/10/2025. Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Abro MI, Zhu D, Khaskheli MA, Elahi E (2020) Statistical and qualitative evaluation of multi-sources for hydrological suitability inflood-prone areas of Pakistan. J Hydrol 588:125117. https:// doi. org/ 10.1016/j. jhydr ol. 2020. 125117. https://doi.org/10.1016/j.jhydrol.2020.125117. Acevedo Y P O, Rivera M E, Rodríguez J R D (2017) Sistema de Pearson y modelos matemáticos aplicados a la hidrología. Avances Investigación en Ingeniería, 14(1), 95-108. 10.18041/1794-4953/avances.1.1288. Adeeyo O A, Adefila S S, Ayeni, A O (2023) Dynamics of steady-state gravity-driven inviscid flow in an open system. International Journal of Innovative Research and Scientific Studies, 6(1), 80-88. https://doi.org/10.53894/ijirss.v6i1.1101. Alifujiang Y, Abuduwaili J, Ma L, Samat A, & Groll, M (2017) System dynamics modeling of water level variations of Lake Issyk-Kul, Kyrgyzstan. Water, 9(12), 989. https://doi.org/10.3390/w9120989. Al-Jawad J Y, Alsaffar H M, Bertram D, Kalin R M (2019) A comprehensive optimum integrated water resources management approach for multidisciplinary water resources management problems. J Environ Manag 239:211–224. https:// doi. org/ 10. 1016/j. jenvm an. 2019. 03. 045. Althoff D, Rodrigues L N (2021) Goodness-of-fit criteria for hydrological models: Model calibration and performance assessment. Journal of Hydrology 600:126674. https:// doi. org/ 10. 1016/j. jhydr ol. 2021. 126674. ANA - Agência Nacional de Águas e Saneamento Básico (2017a) Reservatórios do Semiárido Brasileiro: Hidrologia, Balanço e Operação-Relatório Síntese; Superintendência de Planejamento de Recursos Hídricos-SPR: Brasília, Brazil, p. 88. http://www.ana.gov.br. ANA - Agência Nacional de Águas e Saneamento Básico (2017b) Resolução nº 2.081, de 04 de dezembro de 2017. Dispõe sobre as condições para a operação do Sistema Hídrico do Rio São Francisco. Brasília: Ministério do Meio Ambiente, p.2,3. http://www.ana.gov.br. ANA - Agência Nacional de Águas e Saneamento Básico (2022) Usos da Água: Demandas Consultivas. Disponível em: https://dadosabertos.ana.gov.br. Acesso em: 10 de julho de 2022. http://www.ana.gov.br. ANA - Agência Nacional de Águas e Saneamento Básico (2023) Sistema Nacional de Informações Sobre Recursos Hídricos (SNIRH). Brasília: Ministério do Meio Ambiente. Disponível em:www.snirh.gov.br. Acesso em: 22 de agosto de 2023. http://www.ana.gov.br. ANA - Agência Nacional de Águas e Saneamento Básico (2024a) Sistema Nacional de Informações Sobre Recursos Hídricos (SNIRH). Brasília: Ministério do Meio Ambiente. http://www.snirh.gov.br. Acesso em 2 de fevereiro de 2024. http://www.ana.gov.br. ANA - Agência Nacional de Águas e Saneamento Básico (2024b) Sistema Nacional de Informações Sobre Recursos Hídricos (SNIRH). SAR - Sistema de Acompanhamento de Reservatórios. Brasília: Ministério do Meio Ambiente. http://www.snirh.gov.br. Acesso em 23 de abriu de 2024. http://www.ana.gov.br. Ashrafi S M (2021) Two - stage metaheuristic mixed integer nonlinear programming approach to extract optimum hedging rules for multireservoir systems. J. Water Res. Plan. Manag. 147 (10), 10.1061/(ASCE)WR.1943-5452.0001460. Badr A, Li Z, El - Dakhakhni W (2023) Dynamic resilience quantification of hydropower infrastructure in multihazard environments. Journal of Infrastructure Systems, 29(2), 04023012. https://doi.org/10.1061/JITSE4.ISENG-2188. Bayazit M, Ünal N E (1990) Effects of hedging on reservoir performance. Water resources research, 26(4), 713-719. https://doi.org/10.1029/WR026i004p00713. Bayesteh M, Azari A (2021) Stochastic optimization of reservoir operation by applying hedging rules. Journal of Water Resources Planning and Management, 147(2), 04020099. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001312. Bekri E S, Economou P, Yannopoulos P C, Demetracopoulos A C (2021). Reassessing existing reservoir supply capacity and management resilience under climate change and sediment deposition. Water, 13(13), 1819. https://doi.org/10.3390/w13131819. Beshavard M, Adib A, Ashrafi S M, Kisi O (2022) Establishing effective warning storage to derive optimal reservoir operation policy based on the drought condition. Agricultural Water Management, 274, 107948. https://doi.org/10.1016/j.agwat.2022.107948. Bettencourt P, de Oliveira R P, Fulgêncio C, Canas Â, Wasserman J C (2022) Prospective Water Balance Scenarios (2015–2035) for the Management of São Francisco River Basin, Eastern Brazil. Water, 14(15), 2283. https://doi.org/10.3390/w14152283. Burek P, Satoh Y, Fischer G, Kahil M T, Scherzer A, Tramberend S, Nava LF, Wada Y, Eisner S, Flörke M, Hanasaki N, Magnuszewski P, Cosgrove B, Wiberg D (2016). Water Futures and Solution: Fast Track Initiative (Final Report). IIASA Working Paper. International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. https://pure.iiasa.ac.at/13008. Casagande, A (1957) Report Earth Works and Foundation Engineering of the Três Marias project. Castello L, Macedo M N (2016) Large‐scale degradation of Amazonian freshwater ecosystems. Global change biology, 22(3), 990-1007. https://doi.org/10.1111/gcb.13173. CBHSF - Comitê da Bacia Hidrográfica do Rio São Francisco (2016) Plano de Recursos Hídricos da Bacia Hidrográfica do Rio São Francisco 2016–2025: Compatibilização do Balanço Hídrico com os Cenários Estudados da Bacia Hidrográfica do Rio São Francisco; Comitê da Bacia Hidrográfica do rio São Francisco: Belo Horizonte, Brazil, p. 102. https://cbhsaofrancisco.org.br. CEMIG - Companhia Energética de Minas Gerais (2016) Relatório Técnico: Atualização das Curvas Cota x Área x Volume da UHE Três Marias. Rural Tech Comércio e Serviços Eireli. Disponível em: https://portal1.snirh.gov.br/arquivos/ONS/UHE_Tres_Marias/Relatorio_Batimetria.pdf. CEMIG - Companhia Energética de Minas Gerais (2023) Usinas. Disponível em: www.cemig.com.br/usina/tres-marias. Acesso em 15 de janeiro de 2023. Chang J, Guo A, Wang Y, Ha Y, Zhang R, Xue L, Tu Z (2019) Reservoir operations to mitigate drought effects with a hedging policy triggered by the drought prevention limiting water level. Water Resources Research, 55(2), 904-922. https://doi.org/10.1029/2017WR022090. Chong K L, Lai S H, Ahmed A N, Jaafar W Z W, El-Shafie A (2021) Optimization of hydropower reservoir operation based on hedging policy using Jaya algorithm. Applied Soft Computing, 106, 107325. https://doi.org/10.1016/j.asoc.2021.107325. CPRM - Serviço Geológico do Brasil. Plano estratégico SGB/CPRM 2021-.2025. Brasília: CPRM, 2025. Estudos Hidrológicos e Hidrogeológicos. Acesso em: 4 mai. 2023. Dessie, M, Verhoest N E, Pauwels V R, Adgo E, Deckers J, Poesen J, Nyssen J (2015) Water balance of a lake with floodplain buffering: Lake Tana, Blue Nile Basin, Ethiopia. Journal of Hydrology, 522, 174-186. https://doi.org/10.1016/j.jhydrol.2014.12.049. Eriyagama N, Smakhtin V, Udamulla L (2020) How much artificial surface storage is acceptable in a river basin and where should it be located: a review. Earth-Science Reviews, 208, 103294. https://doi.org/10.1016/j.earscirev.2020.103294. Eriyagama N, Smakhtin V, Udamulla L (2021) Sustainable surface water storage development pathways and acceptable limits for river basins. Water, 13(5), 645. https://doi.org/10.3390/w13050645. Ferrarin A D S F, Ferreira Filho J B D S, Cuadra S V, Victoria D D C (2020) Water demand prospects for irrigation in the São Francisco River: Brazilian public policy. Water Policy, 22(3), 449-467. https://doi.org/10.2166/wp.2020.215. Fowe T, Karambiri H, Paturel J E, Poussin J C, Cecchi P (2015) Water balance of small reservoirs in the volta basin: a case study of Boura reservoir in Burkina Faso. Agric Water Manag 152:99 - 109. https:// doi. org/ 10. 1016/j. agwat. 2015. 01. 006. Garcia M, Ridolfi E, Di Baldassarre G (2020) The interplay between reservoir storage and operating rules under evolving conditions. Journal of Hydrology, 590, 125270. https://doi.org/10.1016/j.jhydrol.2020.125270. Garrote L, Granados A, Spiliotis M, & Martin-Carrasco F (2023) Effectiveness of adaptive operating rules for reservoirs. Water Resources Management, 37(open in a new window) (6–7(open in a new window)), 2527–2542. doi:10.1007/s11269 - 022 - 03386-9. Grill G, Lehner B, Thieme M, Geenen B, Tickner D, Antonelli F, Babu S, Borrelli P, Cheng L, Crochetiere H, Ehalt Macedo H, Filgueiras R, Goichot M, Higgins J, Hogan Z, Lip B, McClain M E, Meng J, Mulligan M, Nilsson C, Olden J D, Opperman J J, Petry P, Reidy Liermann C, Sáenz L, Salinas-Rodríguez S, Schelle P, Schmitt R J P, Snider J, Tan F, Tockner K, Valdujo P H A, Van Soesbergen, Zarfl C (2019) Mapping the world’s free-flowing rivers. Nature, 984 215–221. https://doi.org/10.1038/s41586-019-1111-9. Gupta H V, Kling H, Yilmaz K K, Martinez G F (2009) Decomposition of the mean squared error and NSE performance criteria: Implications for improving hy-drological modelling. Journal of hydrology 377(1 - 2):80-91. https://doi.org/10.1016/j.jhydrol.2009.08.003. Habets F, Molénat J, Carluer N, Douez O, Leenhardt D (2018) The cumulative impacts of small reservoirs on hydrology: A review. Science of the Total Environ-ment 643:850-867. Https://doi.org/10.1016/j.scitotenv.2018.06.188 Hanasaki N, Yoshikawa S, Pokhrel Y, Kanae S (2018) A global hydrological simulation to specify the sources of water used by humans. Hydrology and Earth System Sciences, 22(1), 789 - 817. https://doi.org/10.5194/hess-22-789 - 2018, 2018. Hogeboom R J, Knook L, Hoekstra A Y (2018) The blue water footprint of the world's artificial reservoirs for hydroelectricity, irrigation, residential and industrial water supply, flood protection, fishing and recreation. Advances in water resources, 113, 285 - 294. https://doi.org/10.1016/j.advwatres.2018.01.028. IBGE - Instituto Brasileiro de Geografia e Estatística. Censo (2022). Disponível em: www.ibge.gov.br/cidades-e-estados/mg/tres-marias. Acesso em: 10 de abril de 2023. ICOLD (International Commission on Large Dams) (2019) World Register of Dams. https://www.icold-cigb.org/GB/world_register/general_synthesis.asp. Ilich N (2024) Dynamic reservoir rule curves-Their creation and utilization. Journal of Hydrology X, 22, 100166. https://doi.org/10.1016/j.hydroa.2023.100166. INMET - Instituto Nacional de Meteorologia (2023) Dados meteorológicos. Disponível em: http://www.inmet.gov.br/portal. Acesso em 15 de abriu de 2023. INMET - Instituto Nacional de Meteorologia (2024) Dados meteorológicos. Disponível em: http://www.inmet.gov.br/portal. Acesso em 6 de março de 2024. Jiang H, Simonovic S P, Yu Z, Wang W (2020) A system dynamics simulation approach for environmentally friendly operation of a reservoir system. Journal of Hydrology, 587, 124971. https://doi.org/10.1016/j.jhydrol.2020.124971. Jing P, Sheng J, HU T, Mahmoud A, Guo L, Liu Y, Wu Y (2022) Spatiotemporal evolution of sustainable utilization of water resources in the Yangtze River Economic Belt based on an integrated water ecological footprint model. Journal of Cleaner Production, 358, 132035. https://doi.org/10.1016/j.jclepro.2022.132035. Kim T W, Kim M J, Kim J G, Yoo J (2023) Development of Dynamic Drought Vulnerability Assessment Considering Global Climate Change and Regional Water Demand-Supply Networks. In EGU General Assembly Conference Abstracts (pp. EGU-3708). 10.5194/egusphere-egu23-3708. Kim Y G, Jo M B, Kim P, Oh S N, Paek C H, So S R (2021) Effective Optimization-Simulation Model for Flood Control of Cascade Barrage Network. Water Resources Management 35(1):135-157. https://doi.org/10.1007/s11269-020-02715-0. Lucas M C, Kublik N, Rodrigues D B B, Meira Neto A A, Almagro A, Melo D D C D, Zipper S C, Oliveira P T S (2021) Significant baseflow reduction in the Sao Francisco river basin. Water, 13, 2. https://doi.org/10.3390/w13010002. Luo W, Zhang X, Tian X, Cheng Z, Wen B, Li X, Luo Y (2024) Conceptual design and model test of a pontoon-truss type offshore floating photovoltaic system with soft connection. Ocean Engineering, 309, 118518. https://doi.org/10.1016/j.oceaneng.2024.118518. Mararakanye N, Le Roux J J, Franke A C (2020) Using satellite-based weather data as input to SWAT in a data poor catchment. Phys Chem Earth Parts A/B/C 117:102871. https:// doi. org/ 10. 1016/j. pce. 2020.102871. Mirchi A, Madani K, Watkins D, Ahmad S (2012). Synthesis of system dynamics tools for holistic conceptualization of water resources problems. Water Resour. Manage.26, 2421–2442. https://doi.org/10.1007/s11269-012-0024-2. Mostaghimzadeh E, Adib A, Ashrafi S M, Kisi O (2022) Investigation of a composite two-phase hedging rule policy for a multi reservoir system using streamflow forecast. Agricultural Water Management, 265, 107542. https://doi.org/10.1016/j.agwat.2022.107542. Muzammil M, Zahid A, Farooq U, Saddique N, Breuer L (2023) Climate change adaptation strategies for sustainable water management in the Indus basin of Pakistan. Science of The Total Environment, v. 878, p. 163143. https://doi.org/10.1016/j.scitotenv.2023.163143. Nash J E, Sutcliffe J V (1970) River flow forecasting through conceptual models part I: A discussion of principles. J Hydrol 10(3):282–290. https:// doi. org/ 10. 1016/ 0022-1694(70) 90255-6. Nevermann H, Aminzadeh M, Madani K, Shokri N (2024) Quantifying water evaporation from large reservoirs: Implications for water management in water-stressed regions. Environmental research, 262, 119860. https://doi.org/10.1016/j.envres.2024.119860. Niccolai A, Grimaccia F, Di Lorenzo G, Araneo R, Ughi F, Polenghi M (2023) A review of floating PV systems with a techno-economic analysis. IEEE Journal of Photovoltaics.10.1109/JPHOTOV.2023.3319601. Okkan U, Fistikoglu O, Ersoy Z B, Noori A T (2023) Investigating adaptive hedging policies for reservoir operation under climate change impacts. Journal of Hydrology, v. 619, p. 129286. https://doi.org/10.1016/j.jhydrol.2023.129286. ONS - Operador Nacional do Sistema Elétrico (2018) Inventário das Restrições Operativas Hidráulicas dos Aproveitamentos Hidrelétricos. Operador Nacional do Sistema Elétrico, Rio de Janeiro: ONS, p.191. https://www.ons.org.br/. ONS - Operador Nacional do Sistema Elétrico (2021) Avaliação das condições de atendimento eletroenergético do Sistema Interligado Nacional – estudo prospectivo outubro de 2021 a abril de 2022 (Relatório NT-ONS DGL 0136/2021, 84 p.). Operador Nacional do Sistema Elétrico, Rio de Janeiro: ONS, p.84. https://www.ons.org.br/. Paredes-Trejo F, Barbosa H A, Giovannettone J, Kumar T V L, Thakur M K, Buriti, C D O, Uzcátegui-Briceño C (2021) Drought assessment in the São Francisco river basin using satellite-based and ground-based indices. Remote Sens. 2021, 13, 3921. https://doi.org/10.3390/rs13193921. Phan T D, Bertone E, Stewart R (2021) A Critical review of system dynamics modelling applications for water resources planning and management. Cleaner Environmental Systems, v. 2, p. 100031, https://doi.org/10.1016/j.cesys.2021.100031. Porto R D M (2006) Hidráulica básica. rev. EESC-USP, São Carlos-SP, p.44. R Development Core Team. R (2018) A language and environment for statistical compu-ting’. Vienna: R Foundation for Statistical Computing. Rahmati O, Kalantari Z, Samadi M, Uuemaa E, Moghaddam D D, Nalivan O A, Bui D T (2019) GIS-based site selection for check dams in watersheds: considering geomorphometric and topo-hydrological factors. Sustainability, 11(20), 5639. https://doi.org/10.3390/su11205639. Rodrigues A L, Villa P M, Rodrigues L N (2021) Water balance estimate of beans using a dynamic systems model based on crop coefficient (Kc) variation. Revista Engenharia Na Agricultura, 29: 81 - 89. https://doi.org/10.13083/reveng.v29i1.9767. Rodrigues A L, Rodrigues L N, Marques G F, Vill P M (2023) Simulation model to assess the water dynamics in small reservoirs. Water Resources Management, 37(5), 2019-2038. https://doi.org/10.1007/s11269-023-03468 - 2. Sankarbalaji A R, Duraisekaran E, Sangeetha K, Modi K, Narasimhan B (2025) Assessment of increasing hydrologic model complexity in the representation of small and medium reservoirs within a river basin scale model and its impact on process simulation and parameter uncertainty. Journal of Hydrology, 655, 132925. https://doi.org/10.1016/j.jhydrol.2025.132925. Scherer L, Pfister S (2016) Global water footprint assessment of hydropower. Renewable Energy, 99, 711-720. https://doi.org/10.1016/j.renene.2016.07.021. Simonovic S P, Arunkumar R (2016) Comparison of static and dynamic resilience for a multipurpose reservoir operation. Water Resour. Res. 52, 8630 - 8649. https://doi.org/10.1002/2016WR019551. Sjöberg Y, Dessirier B, Ghajarnia N, Jaramillo F, Jarsjö J, Panahi D M, Xu D, Zou L, Manzoni S (2022) Scaling relations reveal global and regional differences in morphometry of reservoirs and natural lakes. Science of The Total Environment, 822, 153510. https://doi.org/10.1016/j.scitotenv.2022.153510. Stojkovic M, Simonovic S P (2019) System dynamics approach for assessing the behaviour of the Lim Reservoir system (Serbia) under changing climate conditions. Water, 11(8), 1620. https://doi.org/10.3390/w11081620. Sun Y, Liu N, Shang J, Zhang J (2017) Sustainable utilization of water resources in China: A system dynamics model. Journal of cleaner production, 142, 613 - 625. https://doi.org/10.1016/j.jclepro.2016.07.110. Sunny M R, Kabir M A, Sarker M S Z, Aghaloo K, Ali T (2024) Feasibility study of floating solar photovoltaic systems using techno-economic assessment and multi-criteria decision-making method: A case study of Bangladesh. Energy, 133202. https://doi.org/10.1016/j.energy.2024.133202. Tran V N, Dinh D D, Pham B D H, Dang K D, Anh T N, Ngoc H N, Nguyen G T (2024) Data-Driven Dam Outflow Prediction Using Deep Learning with Simultaneous Selection of Input Predictors and Hyperparameters Using the Bayesian Optimization Algorithm. Water Resources Management, 38(2), 401 - 421. https://doi.org/10.1007/s11269-023-03677-9. Turgut MS, Turgut O E, Afan H A, El-Shafie A (2019) A novel Master-Slave optimization algorithm for generating an optimal release policy in case of reservoir operation. Journal of Hydrology. 577, 123959. https://doi.org/10.1016/j.jhydrol.2019.123959. Ventana Systems (2024) Vensim User’s Guide Version 6. Harvard, MA, USA: VENTANA Systems Inc. https://vensim.com/. Vieira N P, Pereira S B, Martinez M A, Silva D D D, Silva F B (2016) Estimativa da evaporação nos reservatórios de Sobradinho e Três Marias usando diferentes modelos. Engenharia Agrícola, 36(3), 433-448. https://doi.org/10.1590/1809-4430-Eng.Agric.v36n3p433-448/2016. Wang W, Lee X, Xiao W, Liu S, Schultz N, Wang Y, Zhang M, Zhao L (2018) Global lake evaporation accelerated by changes in surface energy allocation in a warmer climate. Nat. Geosci. 11 (6), 410–414. https://doi.org/10.1038/s41561-018-0114-8. Wang Y, Tian Y, Cao Y (2021) Dam siting: a review. Water, 13(15), 2080. https://doi.org/10.3390/w13152080. Wu G, Li L, Ahmad S, Chen X, Pan X (2013) A dynamic model for vulnerability assessment of regional water resources in arid areas: a case study of Bayingolin. China Water Resour Manag 27(8):3085–3101. https://doi.org/10.1007/s11269-013-0334-z. Wu H, Cheng S, Li Z, Ke G, Liu H (2022) Study on Soil water infiltration process and model applicability of check dams. Water, 14(11), 1814. https://doi.org/10.3390/w14111814. Xu Y, Fu Q, Zhou Y (2019) Inventory Theory-Based Stochastic Optimization for Reservoir Water Allocation. Water Resour Manage 33:3873-3898. https://doi.org/10.1007/s11269-019-02332-6. You J Y, Cai X (2008) Hedging rule for reservoir operations: 1. A theoretical analysis. Water resources research,44(1). https://doi.org/10.1029/2006WR005481. Zarfl C, Lumsdon A E, Berlekamp J, Tydecks L, Tockner K (2015) A global boom in hydropower dam construction. Aquatic Sciences, 77, 161-170. https://doi.org/10.1007/s00027-014-0377-0. Zeng X T, Zhang S J, Feng J, Huang G H, Li Y P, Zhang P, Li K L (2017) A multi - reservoir-based water-hydroenergy management model for identifying the risk horizon of regional resources-energy policy under uncertainties. Energy Conversion and Management, 143, 66-84. https://doi.org/10.1016/j.enconman.2017.02.020. Zhang H, Gorelick S M, Zimba P V, Zhang (2017) A remote sensing method for estimating regional reservoir area and evaporative loss. Journal of Hydrology, 555, 213-227. https://doi.org/10.1016/j.jhydrol.2017.10.007. Zhao G, Gao H (2019) Estimating reservoir evaporation losses for the United States: Fusing remote sensing and modeling approaches. Remote Sensing of Environment, 226, 109-124. https://doi.org/10.1016/j.rse.2019.03.015. Zhao T, Zhao J, Lund J R, Yang, D (2014) Optimal hedging rules for reservoir flood operation from forecast uncertainties. Journal of Water Resources Planning and Management, 140(12), 04014041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432. Zhou T, Nijssen B, Gao H, Lettenmaier D P (2016) The contribution of reservoirs to global land surface water storage variations. Journal of Hydrometeorology, 17(1), 309-325. https://doi.org/10.1175/JHM-D-15-0002.1. Supplementary Files Highlights.docx Cite Share Download PDF Status: Published Journal Publication published 23 Dec, 2025 Read the published version in Water Resources Management → Version 1 posted Editorial decision: Major revisions 22 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers invited by journal 07 Oct, 2025 Editor assigned by journal 04 Oct, 2025 First submitted to journal 03 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7767474","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":525955871,"identity":"50f6b228-dadd-454b-8e0b-10e8079c79b5","order_by":0,"name":"Alisson Lopes Rodrigues","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIiWNgGAWjYDACdsYGECUDxAYMCWCRBoYPDAwHcGthhmjhQWjhOcA4A78WCAXRAgYSCfi18DczN3/8UXGHx7y9eduHB78Oy8nPfGPYzMNwJx+XFonDjG3SPGee8cicOVY8I7HvsLHB7RyQlmeWDbj0ALUwM7Yd5pGQyDFmSOw5nLhBOsf84QyGwwa4dMgfZmz++BNJS/38mWcMG/FpMTjM2CDBC9OS8ONwAsMNHsOGD3i0GEL8AtTCc6yYIbEh3XDDmbTChg8Gz3BqkTve/hgYYoflJNibNzP++GMtL99+eGNDQsUdnFpQAWMb3MHEaQCCP0SrHAWjYBSMghEEAOsyW6GTZYEgAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-1219-7416","institution":"UFV: Universidade Federal de Vicosa","correspondingAuthor":true,"prefix":"","firstName":"Alisson","middleName":"Lopes","lastName":"Rodrigues","suffix":""},{"id":525955872,"identity":"a0da8649-2029-43eb-9139-7b48e50f1377","order_by":1,"name":"Ricardo Santos Silva Amorim","email":"","orcid":"","institution":"Universidade Federal de Viçosa: Universidade Federal de Vicosa","correspondingAuthor":false,"prefix":"","firstName":"Ricardo","middleName":"Santos Silva","lastName":"Amorim","suffix":""},{"id":525955873,"identity":"a2e3d33e-eed5-452a-ab75-780ec66f9ac5","order_by":2,"name":"Pedro Manuel Villa","email":"","orcid":"","institution":"Universidade Federal de Juiz de Fora","correspondingAuthor":false,"prefix":"","firstName":"Pedro","middleName":"Manuel","lastName":"Villa","suffix":""}],"badges":[],"createdAt":"2025-10-02 14:58:53","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7767474/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7767474/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11269-025-04347-8","type":"published","date":"2025-12-23T15:57:39+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93917017,"identity":"315638cd-5e5e-462c-a905-872435024100","added_by":"auto","created_at":"2025-10-20 08:55:21","extension":"xml","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8928,"visible":true,"origin":"","legend":"","description":"","filename":"warmWARMD2502959.xml","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/008de81100afe471f42ebdb0.xml"},{"id":93914577,"identity":"0d470c4e-c38a-4cc7-b6db-bc06277a6535","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":963,"visible":true,"origin":"","legend":"","description":"","filename":"WARMD250295944901.go.xml","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/188d2c525add3060ab149a1d.xml"},{"id":93914556,"identity":"1a615e9b-6236-4fc9-a629-98d4fbfd359a","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":886,"visible":true,"origin":"","legend":"","description":"","filename":"WARMD2502959Import.xml","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/77c40852218a24894a8a69ff.xml"},{"id":93914548,"identity":"a9ee3f3b-8423-4c10-af78-72260fcdf6fb","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"xml","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":225835,"visible":true,"origin":"","legend":"","description":"","filename":"WARMD25029590enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/9250c00d647130bebbf864bb.xml"},{"id":93915893,"identity":"d602650d-c6e2-4bd8-9b5c-0e1abd76a66f","added_by":"auto","created_at":"2025-10-20 08:47:22","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2622650,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/6d102cc672ee54033a5bb62f.png"},{"id":93915887,"identity":"59b26c0f-b0d7-4125-85c6-b6c9beb7b399","added_by":"auto","created_at":"2025-10-20 08:47:21","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":471150,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/f89e38c41425839bd017e9f6.png"},{"id":93915885,"identity":"f5e41464-d60a-429b-b5d1-974d677cff19","added_by":"auto","created_at":"2025-10-20 08:47:20","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":58848,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/1064824c3463dd9d1b125db6.png"},{"id":93914552,"identity":"f3a05593-ccd4-4b12-8b00-b62f1e9591de","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":21486,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/d5814b81a524fc8456784b4c.png"},{"id":93914551,"identity":"df57a1b8-9faf-479d-b80c-dd2fa8fe008a","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":39778,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/fa1265eca79d4a55a9418ba2.png"},{"id":93914561,"identity":"8985ac52-81dc-42dd-830d-50ecd4380b46","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"jpeg","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1990360,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/572c3350216c805a878b99be.jpeg"},{"id":93914555,"identity":"9b634bd5-c2c5-44a3-9e48-adf2311d97b1","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":60550,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/162688375a400f9ea5e0d526.png"},{"id":93914563,"identity":"5b5e8ced-7b18-4a8b-aa65-9623e14a4613","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63907,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/b8c84f6a94a07a43eb5ac969.png"},{"id":93914562,"identity":"2191b0e0-aa2b-497f-b2ba-ca5612b1683f","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11185,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/448598240723ac2d84f5ffab.png"},{"id":93914535,"identity":"37a37010-d00a-43a4-ad1f-d07aa793a2bd","added_by":"auto","created_at":"2025-10-20 08:39:19","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":467568,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/f08bd2acf29e4a0109d342ae.png"},{"id":93914544,"identity":"3d1a907f-c279-41bc-9728-853de580578d","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":42634,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/26316f952ee567658c035cfc.png"},{"id":93915891,"identity":"cab86a73-8917-4ab1-8eb4-8b4ba7c7fb76","added_by":"auto","created_at":"2025-10-20 08:47:21","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29941,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/d28c9031603f7c4e0bbe85a6.png"},{"id":93914543,"identity":"6f962329-4c82-40ec-82e3-b3d6defa542b","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":20789,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/320768a9955ab22f8c400d31.png"},{"id":93914540,"identity":"3e1c93b7-db27-40f1-96ca-f7c4613f7419","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":38023,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/abb59c5ee21ea94c5f2a72bb.png"},{"id":93914572,"identity":"83c17991-e34d-45d6-877f-80064c0c20ca","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":261539,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/79c944d070aeb98f8ac81e55.png"},{"id":93914575,"identity":"c577f061-eb58-49b1-a48f-7adacacd0fdb","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57839,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/060f14e51c507c2fd015c26b.png"},{"id":93914554,"identity":"c82a589b-fbc1-458a-ae8e-6ee67268001b","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":61308,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/bb9eddd68c5f466540b58542.png"},{"id":93914567,"identity":"df38b2d8-d43f-4697-8455-dd1b1220143f","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10963,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/2534e084ca193f718823db4b.png"},{"id":93914576,"identity":"c491316a-07e2-47a3-97c8-eae4e03433c0","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"xml","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":228693,"visible":true,"origin":"","legend":"","description":"","filename":"WARMD25029590structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/db96b1e2d531b119f7be4568.xml"},{"id":93914560,"identity":"17d22f0c-28c4-41f7-9ca2-8c43561c38bb","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"html","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":237010,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/ce43b7aa2f14ac35821a8746.html"},{"id":93915894,"identity":"3f0b7a54-619b-4683-9ce4-65b2dc4c09e4","added_by":"auto","created_at":"2025-10-20 08:47:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2517213,"visible":true,"origin":"","legend":"\u003cp\u003eTrês Marias Hydropower Plant reservoir, located in the Upper São Francisco region, with emphasis on streamflow and rainfall stations.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/0db4615e4922f6c16885c14f.png"},{"id":93915889,"identity":"20b5a2d4-139f-4c61-ac40-73d2bf3269b0","added_by":"auto","created_at":"2025-10-20 08:47:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":471150,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of the System Dynamics model (m); (Hi = reservoir water level at time i; H\u003csub\u003eV\u003c/sub\u003e = water head above spillway crest; H\u003csub\u003e0\u003c/sub\u003e = minimum level).\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/c831189192d931fad23b1ce7.png"},{"id":93915886,"identity":"b657a14b-c96b-401f-ab5b-20c4fddf9b05","added_by":"auto","created_at":"2025-10-20 08:47:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":58848,"visible":true,"origin":"","legend":"\u003cp\u003eCausal loop diagram of the System Dynamics model developed to evaluate the dynamics and the capacity to meet multiple water uses in the Três Marias Hydropower Plant reservoir. (Q\u003csub\u003eA\u003c/sub\u003e = inflow; R\u003csub\u003eA\u003c/sub\u003e = water withdrawal; Hu = usable height; Hm = minimum operating level; H\u003csub\u003eV\u003c/sub\u003e = water head above the spillway crest; Q\u003csub\u003eDE\u003c/sub\u003e = total outflow; Q\u003csub\u003eUM\u003c/sub\u003e = multiple water uses; Hi = water level elevation, m; Q\u003csub\u003eTO\u003c/sub\u003e = turbine outflow; Q\u003csub\u003eEV \u003c/sub\u003e= evaporation; G\u003csub\u003eO\u003c/sub\u003e = gate opening height; P = precipitation; E\u003csub\u003eV\u003c/sub\u003e = evaporated water depth; P\u003csub\u003eD\u003c/sub\u003e = daily precipitation; Q\u003csub\u003eSV\u003c/sub\u003e = spillway outflow; V\u003csub\u003eO\u003c/sub\u003e = volume variation; A\u003csub\u003eES\u003c/sub\u003e = water surface area; k = soil hydraulic conductivity at the reservoir bed; R1, R2, and R3 = operating rules 1, 2, and 3; a, b, c, d, e, f, g, h, i, j, l, and m = dimensionless coefficients; UNG1, UNG2, UNG3, UNG4, UNG5, and UNG6 = power generation units. \u003cem\u003eTrigger: firing rule (set to 0 to disable hedging operation/water dynamics simulation). Operating rules: R1, R2, and R3 (enabled from 2018 onwards, and disabled when hedging operation is activated).”\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/f723326666ff5f99e6d23e73.png"},{"id":93914573,"identity":"6f3ff29c-204f-4660-b3dd-8263072539a7","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":21486,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and simulated water level for the training, calibration, and validation periods of the System Dynamics model.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/8d3d0b1d05ea2025e123f2ea.png"},{"id":93917018,"identity":"f63d4d35-1588-45b3-94d0-c1a8bc5fd0b7","added_by":"auto","created_at":"2025-10-20 08:55:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":39778,"visible":true,"origin":"","legend":"\u003cp\u003eVariation in reservoir volume (%) over time as a function of ±10% changes in inflow, turbine outflow, evaporation, precipitation, infiltration, and water withdrawal for the period from January 2004 to June 2024.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/ca8f3441847b6248be6f0f57.png"},{"id":93914559,"identity":"616460dc-2ed9-4730-b8d5-59b4e4c6bba8","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":408574,"visible":true,"origin":"","legend":"\u003cp\u003eFlow, auxiliary, and state variables that determine the water dynamics in the Três Marias Hydropower Plant reservoir.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/3a2dfc4cfe6b5cab3e47fa09.png"},{"id":93914564,"identity":"95e89196-25d0-4565-a132-43544a619f5b","added_by":"auto","created_at":"2025-10-20 08:39:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":60550,"visible":true,"origin":"","legend":"\u003cp\u003eScenario 1: hedging\u003cem\u003e \u003c/em\u003eoperation with different cutbacks and triggers applied to turbine outflow, with an annual growth trend of 6.26% in water withdrawal to supply multiple water uses in the Três Marias Hydropower Plant reservoir, São Francisco River Basin, Brazil. (Vmax = Maximum volume).\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/e70b47a97625a1afe3140ef8.png"},{"id":93914550,"identity":"37882898-0858-431c-86c8-efae8974b2bc","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":63907,"visible":true,"origin":"","legend":"\u003cp\u003eScenario 2: hedging operation with different cutbacks and triggers applied to turbine outflow, with an annual growth trend of 6.26% in water withdrawal and a 0.11% reduction in evaporation to supply multiple water uses in the Três Marias Hydropower Plant reservoir, São Francisco River Basin, Brazil. (Vmax = Maximum volume).\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/d482c07aea2a312487542526.png"},{"id":93914570,"identity":"754b8346-74ef-4947-ae8b-eefd8356352e","added_by":"auto","created_at":"2025-10-20 08:39:22","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":11185,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between the average reduction in turbine outflow and the increase in stored volume in the Três Marias HPP reservoir under different hedging operation scenarios. (Ga52 = 52% trigger; Ga62 = 62% trigger; Co = 39% cutback; Co = 21% cutback; Co = 29% cutback; Co = 11% cutback; RQ\u003csub\u003eTO\u003c/sub\u003e = average reduction in turbine outflow; Avo = volume increase; C1 = Scenario 1; C2 = Scenario 2).\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/4d740804dd2cae75898e41da.png"},{"id":99172316,"identity":"f593e913-1c4e-4665-a59b-059647c192b5","added_by":"auto","created_at":"2025-12-29 16:07:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4865229,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/2d9d050d-7d18-4f2c-9c5e-4fe578e17264.pdf"},{"id":93914546,"identity":"0f3e1daf-16d2-4654-8b21-4f2994fce0af","added_by":"auto","created_at":"2025-10-20 08:39:20","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":18169,"visible":true,"origin":"","legend":"","description":"","filename":"Highlights.docx","url":"https://assets-eu.researchsquare.com/files/rs-7767474/v1/b2edc689ead9f893236afe9f.docx"}],"financialInterests":"","formattedTitle":"System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eMore than half of the world\u0026rsquo;s river basins contain large artificial reservoirs built to regulate river flows (Grill et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The total storage capacity of large reservoirs corresponds to approximately 2% of global surface freshwater, covering an area of nearly 500.000 km\u0026sup2;, or about 0.33% of the Earth\u0026rsquo;s land surface (Zhou et al. \u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; ICOLD 2019). Large reservoirs are considered lentic environments and are usually constructed in sections of drainage networks with significant elevation differences, mainly in plateau basins (Rahmati et al. \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These reservoirs supply around 42% of the water used for irrigation and also support industrial and domestic sectors (Hanasaki et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In addition, large reservoirs are used for other activities such as recreation, navigation, hydropower generation, aquaculture, flow regulation, and flood-wave attenuation. Therefore, they provide countless benefits for millions of people worldwide (Zeng et al. \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Hogeboom et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eGlobally, large reservoirs meet essential energy, agricultural, domestic, and industrial demands (Mulligan et al. 2020; Eriyagama et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Turgut et al. \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Worldwide water requirements for agriculture, domestic, and industrial uses are projected to increase by approximately 4%, 65%, and 127%, respectively, by 2050 compared with 2010 estimates (Burek et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Eriyagama et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In Brazil, the average water demand of large reservoirs located in the S\u0026atilde;o Francisco River Basin is projected to rise by about 31% between 2025 (2.315\u0026nbsp;million m\u003csup\u003e3\u003c/sup\u003eyr\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and 2050 (3.038\u0026nbsp;million m\u003csup\u003e3\u003c/sup\u003eyr\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) (Ferrarini et al. 2020; Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; ANA 2023). The water resources plan for the S\u0026atilde;o Francisco River Basin included an expansion of irrigated agriculture by 559.249 ha between 2016 and 2025, averaging 50.840 ha per year (ANA 2017a; CBHSF 2016). Although the expansion of irrigated areas is important for income generation and food production, such growth is expected to cause conflicts with other competing water uses, such as hydropower generation and industrial supply, among others (ANA 2022).\u003c/p\u003e\u003cp\u003eAn increase in water scarcity is evident in the S\u0026atilde;o Francisco River Basin, which can be attributed to rapid economic development and inefficiencies in water resources management (Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; CBHSF 2017). Reduced water availability combined with the expansion of agricultural and industrial sectors may intensify conflicts over water access in the large reservoirs of the basin (Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; ANA 2023). Despite Brazil\u0026rsquo;s considerable water potential, since April 2013 the basin has experienced unfavorable hydro-meteorological conditions, with streamflow and precipitation levels below the historical average from 1931 to 2010 (ONS 2021). This has affected water storage in large reservoirs, generating risks of not meeting multiple water-use demands during periods of reduced availability (ANA 2023; CBHSF 2016).\u003c/p\u003e\u003cp\u003eSurface water abstraction from large reservoirs will likely continue to be a common practice to meet future water demand (Zarfl et al. \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Castello and Macedo, 2015). However, global climate change coupled with increasing water demand requires improved water management strategies to establish sustainable operational limits (Eriyagama et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Muzammil et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This necessitates determining the capacity of large reservoirs to meet diverse water demands during scarcity, with the aim of mitigating conflicts and overcoming limitations in access to this vital resource. Such knowledge can maximize efficiency in water storage and use, as well as guide the construction of new reservoirs (Eriyagama et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe scientific community has advocated the use of systemic approaches to establish reservoir operating rules as an effective way to address the complexity and variability of hydrological processes (Elsawah et al. 2017; Mirchi et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Simonovic and Arunkumar \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Jiang et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In this context, System Dynamics models, developed to simulate hydrological dynamics in large reservoirs within watersheds, become fundamental for planning and supporting water resources management (Kim et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Simonovic and Arunkumar \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Therefore, System Dynamics models are extremely relevant tools for regulatory agencies and water managers, as they can aid in the development of new management strategies to ensure the sustainable use of water resources (Al-Jawad et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Jing et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite their importance, the availability and application of System Dynamics models to evaluate water supply and demand in large reservoirs remain limited (Phan et al. \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Al-Jawad et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). While models have been developed specifically for small reservoirs (Rodrigues et al. \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), their hydrological, operational, and management characteristics are less complex, limiting direct applicability to larger-scale contexts (Habets et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Sankarbalaji et al. \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Conversely, large reservoirs involve greater spatial and temporal variability, multiple users, and specific operating rules, and are more susceptible to extreme events and climate change (Jiang et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Okkan et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Bekri et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn this context, the development of System Dynamics models is a valuable tool for strategic planning and sustainable water resources management, as they allow simulating different operational scenarios and predicting situations in which storage volumes may be insufficient to meet multiple water uses (Kim et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Jing et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Considering this relevance, the objective of the present study was to develop a System Dynamics model capable of assessing water dynamics in a large reservoir of the S\u0026atilde;o Francisco River Basin (Brazil), as well as estimating its capacity to meet multiple water-use demands over time.\u003c/p\u003e"},{"header":"2 Material and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Study area description\u003c/h2\u003e\u003cp\u003eThe System Dynamics (SD) model proposed in this study was developed for the Tr\u0026ecirc;s Marias Hydropower Plant (HPP) reservoir (Fig.\u0026nbsp;1D), located in the S\u0026atilde;o Francisco River Basin between latitude 18\u0026deg;55\u0026prime;06\u0026Prime; S and longitude 45\u0026deg;40\u0026prime;01\u0026Prime; W, Brazil.\u003c/p\u003e\u003cp\u003eThe Tr\u0026ecirc;s Marias reservoir was selected due to its hydrological and socioeconomic relevance for Brazil, particularly because it is situated in a basin facing increasing water scarcity and conflicts among different water-use sectors (Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; CBHSF 2017). This context makes the reservoir a particularly relevant case study for evaluating water dynamics and the capacity to meet multiple uses under scenarios of pressure on water resources.\u003c/p\u003e\u003cp\u003eHydrologically, the Tr\u0026ecirc;s Marias HPP plays a fundamental role in flood control and flow regulation, directly influencing water availability throughout the S\u0026atilde;o Francisco River Basin (ANA 2022). From a socioeconomic perspective, the reservoir supplies water for multiple purposes, including hydropower generation, irrigation, industrial uses, \u003c/p\u003e\u003cp\u003eand navigation (ANA 2022).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;1\u003c/b\u003e Tr\u0026ecirc;s Marias Hydropower Plant reservoir, located in the Upper S\u0026atilde;o Francisco region, with emphasis on streamflow and rainfall stations.\u003c/p\u003e\u003cp\u003eThe Tr\u0026ecirc;s Marias HHP reservoir was built between 1957 and 1961 and began operating in 1962. It is one of the largest reservoirs in Brazil, with an approximate surface area of 1,092.52 km\u0026sup2;, a total storage capacity of about 18,855.26 hm\u0026sup3;, and a maximum crest height of 75 m (CEMIG 2023). The drainage area contributing to the reservoir covers approximately 51.000 km\u0026sup2; (ANA 2023). The main physical characteristics of the reservoir and morphometry of the drainage area are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAccording to K\u0026ouml;ppen\u0026rsquo;s classification, the climate of the region where the reservoir is located is Aw, characterized as tropicais savanna with a dry winter, and an average temperature above 18\u0026deg;C in the coldest month. The highest rainfall occurs between December and March, with an annual average of 1.270 mm (INMET 2023). The population living near the reservoir has a density of 7.85 inhabitants per km\u0026sup2;, totaling 116.014 residents (IBGE 2022).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePhysical characteristics of the Tr\u0026ecirc;s Marias Hydropower Plant reservoir and morphometry of its drainage area.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCharacteristics\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eValues\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUsable volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e14,974.128 hm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e18,855.26 hm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDead volume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3,881.132 hm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater surface\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1,092.52 km\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elength\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.700 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eReservoir wall length\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e75 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMinimum operating level\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e549.20 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaximum operating level\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e572.56 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDrainage area\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e51.000 km\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePerimeter\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2,130.60 km\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMain channel length\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4.23 km\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEquivalent slope\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0805 m m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAverage elevation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e815 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConcentration time\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e97.48 min\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCompactness coefcient\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.56\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eShape fator\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Hydrological Monitoring\u003c/h2\u003e\u003cp\u003eEstimates of inflow and precipitation to the reservoir were obtained from time series (01/2004 to 06/2024) of 14 streamflow stations and nine rainfall stations (Fig.\u0026nbsp;1D), belonging to the National Hydrometeorological Network (RHN) and the National Institute of Meteorology (INMET), respectively (ANA 2024; INMET 2024).\u003c/p\u003e\u003cp\u003eWithdrawals from the reservoir were obtained from water-use rights declared to the National Water and Basic Sanitation Agency (ANA), through the National Water Resources Information System (SNIRH). These data include 306 points of abstraction for agriculture and livestock watering, 18 points for aquaculture in cages and ponds, four abstraction points for public supply operated by COPASA, two points for hydraulic works, and nine points for industrial use (ANA 2023).\u003c/p\u003e\u003cp\u003eThe Minas Gerais Energy Company (CEMIG), responsible for electricity generation, transmission, distribution, and commercialization, operates six power generation units that, together with water withdrawals, represent the multiple uses of water in the reservoir.\u003c/p\u003e\u003cp\u003eWater level variation is monitored using pressure sensors installed at the reservoir bottom, programmed to record hourly changes (ANA 2024b). These data were used for calibration and validation of the System Dynamics model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Operating Rules of the Tr\u0026ecirc;s Marias HPP\u003c/h2\u003e\u003cp\u003eThe outflow from the HPP Tr\u0026ecirc;s Marias reservoir is regulated by three operating rules (ONS 2018; ANA 2017b): 1) A minimum discharge of 100 m\u003csup\u003e3\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e must be ensured for maintaining environmental flows when storage is below 30% of the usable volume. 2) When storage exceeds 30% of the usable volume, the minimum daily outflow must be 150 m\u003csup\u003e3\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. 3) Spillway discharges must be \u0026le;\u0026thinsp;3,500 m\u003csup\u003e3\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to avoid severe damage to inhabited islands downstream, in the municipality of Pirapora, MG. These three operating rules were incorporated into the development of the System Dynamics model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Development of the system dynamics model\u003c/h2\u003e\u003cp\u003eThe mathematical model to simulate reservoir water dynamics was developed using Vensim\u0026reg; PLE Plus v10.2.1 (Ventana Systems \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which allows building dynamic simulation models with equations representing temporal changes.\u003c/p\u003e\u003cp\u003eThe SD model was developed under the following assumptions: (i) water infiltration into the soil is uniform across the reservoir bed, considered over 65% of the water surface area; (ii) evaporation occurs uniformly over the entire water surface; (iii) precipitation is uniformly distributed across the water surface; (iv) capillary rise is negligible; (v) inflows and withdrawals are computed on a daily basis.\u003c/p\u003e\u003cp\u003eThese assumptions were based on Rodrigues et al. (\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), who studied water dynamics in small reservoirs in the Brazilian Cerrado, and adapted here for application to large reservoirs. Additional assumptions, such as uniform precipitation over the water surface, were necessary given the large extent of the reservoir. The SD model structure for assessing water dynamics and multiple water uses in the Tr\u0026ecirc;s Marias reservoir is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 System Dynamics Model\u003c/h2\u003e\u003cp\u003eThe description of the SD model developed to evaluate water dynamics and assist in meeting multiple water uses at the Tr\u0026ecirc;s Marias HPP reservoir was based on previous studies (e.g., Wu et al. \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Sun et al. \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Luo et al. 2009; Rodrigues et al. \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Stojkovic and Simonovic \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Unlike these earlier works, the present model stands out by incorporating hedging operation rules, specifically aimed at managing situations of water scarcity, with the goal of ensuring a balanced allocation for multiple water uses in the reservoir.\u003c/p\u003e\u003cp\u003eThe SD model consists of three types of variables: State variable \u0026ndash; represented by the stored water volume in the reservoir. Flow variables \u0026ndash; expressed as derivatives of the state variable, such as inflow and evaporation. Auxiliary variables \u0026ndash; directly influence flow variables, such as water column height and water surface area (Fig.\u0026nbsp;3).\u003c/p\u003e\u003cp\u003e This categorization of variables is essential for capturing the complexity of system behavior over time. By modeling the interactions among state, flow, and auxiliary variables, the SD approach allows simulating dynamic responses of the reservoir under different operational scenarios, supporting more robust and adaptive water management strategies.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;3\u003c/b\u003e Causal loop diagram of the System Dynamics model developed to evaluate the dynamics and the capacity to meet multiple water uses in the Tr\u0026ecirc;s Marias Hydropower Plant reservoir. (Q\u003csub\u003eA\u003c/sub\u003e = inflow; R\u003csub\u003eA\u003c/sub\u003e = water withdrawal; Hu\u0026thinsp;=\u0026thinsp;usable height; Hm\u0026thinsp;=\u0026thinsp;minimum operating level; H\u003csub\u003eV\u003c/sub\u003e = water head above the spillway crest; Q\u003csub\u003eDE\u003c/sub\u003e = total outflow; Q\u003csub\u003eUM\u003c/sub\u003e = multiple water uses; Hi\u0026thinsp;=\u0026thinsp;water level elevation, m; Q\u003csub\u003eTO\u003c/sub\u003e = turbine outflow; Q\u003csub\u003eEV\u003c/sub\u003e = evaporation; G\u003csub\u003eO\u003c/sub\u003e = gate opening height; P\u0026thinsp;=\u0026thinsp;precipitation; E\u003csub\u003eV\u003c/sub\u003e = evaporated water depth; P\u003csub\u003eD\u003c/sub\u003e = daily precipitation; Q\u003csub\u003eSV\u003c/sub\u003e = spillway outflow; V\u003csub\u003eO\u003c/sub\u003e = volume variation; A\u003csub\u003eES\u003c/sub\u003e = water surface area; k\u0026thinsp;=\u0026thinsp;soil hydraulic conductivity at the reservoir bed; R1, R2, and R3\u0026thinsp;=\u0026thinsp;operating rules 1, 2, and 3; a, b, c, d, e, f, g, h, i, j, l, and m\u0026thinsp;=\u0026thinsp;dimensionless coefficients; UNG1, UNG2, UNG3, UNG4, UNG5, and UNG6\u0026thinsp;=\u0026thinsp;power generation units. \u003cem\u003eTrigger: firing rule (set to 0 to disable hedging operation/water dynamics simulation). Operating rules: R1, R2, and R3 (enabled from 2018 onwards, and disabled when hedging operation is activated).\u0026rdquo;\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.6 Model Equations\u003c/h2\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e2.6.1 Water Balance of Reservoir\u003c/h2\u003e\u003cp\u003eThe water balance in a reservoir follows the principle of mass conservation, where the difference between the total inflows and outflows is equal to the variation in water storage over time (Dessie et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\text{V}}_{\\text{O}\\left(\\text{t}\\right)}={\\text{V}}_{\\text{O}\\left(\\text{t}\\text{o}\\right)}+{\\int\\:}_{\\text{t}\\text{o}}^{\\text{t}}[{\\text{Q}}_{\\text{A}\\left(\\text{t}\\right)}+{\\text{Q}}_{\\text{P}\\left(\\text{t}\\right)}-{\\text{Q}}_{\\text{E}\\text{V}\\left(\\text{t}\\right)}-{\\text{Q}}_{\\text{I}\\left(\\text{t}\\right)}-\\:{\\text{Q}}_{\\text{T}\\text{o}\\left(\\text{t}\\right)}-{\\text{Q}}_{\\text{S}\\text{V}\\left(\\text{t}\\right)}-{\\text{R}}_{\\text{A}\\left(\\text{t}\\right)}\\left]\\:\\:\\:\\:\\:\\:\\:\\:\\:\\right(1)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: V\u003csub\u003eO\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;water volume at time t; V\u003csub\u003eO\u003c/sub\u003e(to)\u0026thinsp;=\u0026thinsp;water volume at initial time to; Q\u003csub\u003eA\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;inflow at time t; Q\u003csub\u003eP\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;precipitation at time t; Q\u003csub\u003eEV\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;evaporation at time t; Q\u003csub\u003eI\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;infiltration at time t; Q\u003csub\u003eTO\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;turbine outflow at time t; Q\u003csub\u003eSV\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;spillway outflow at time t; R\u003csub\u003eA\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;water withdrawal at time t.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e2.6.2 Water level elevation\u003c/h2\u003e\u003cp\u003eTo determine the water level (Hi) at time i, the initial stored volume was set as that of January 1, 2004, corresponding to 19.26% of the usable volume. Daily values of Hi were calculated using a sixth-degree polynomial (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e2\u003c/span\u003e), developed by CEMIG (2016) from stage\u0026ndash;storage data of the Tr\u0026ecirc;s Marias HPP reservoir: obtained from the bathymetric survey at a 1:10.000 scale.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\text{H}}_{\\text{i}}={\\text{a}+\\text{b}\\left({\\text{V}}_{\\text{O}}\\right)+\\text{c}{\\left({\\text{V}}_{\\text{O}}\\right)}^{2}+\\:\\text{d}{\\left({\\text{V}}_{\\text{O}}\\right)}^{3\\:\\:}+\\text{e}{\\left({\\text{V}}_{\\text{O}}\\right)}^{4\\:\\:}+\\:\\text{f}{\\left({\\text{V}}_{\\text{O}}\\right)}^{5\\:\\:\\:\\:}+\\text{g}{\\left({\\text{V}}_{\\text{O}}\\right)}^{6\\:\\:\\:}\\:\\:}_{\\:\\:\\:\\:}\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{H}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e = reservoir water level at time i, m; Vo = actual volume, hm\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe coefficients \u0026lsquo;a\u0026rsquo;, \u0026lsquo;b\u0026rsquo;, \u0026lsquo;c\u0026rsquo;, \u0026lsquo;d\u0026rsquo;, \u0026lsquo;e\u0026rsquo;, \u0026lsquo;f\u0026rsquo; e \u0026lsquo;g\u0026rsquo; are, respectively, 519.813; 0.0177101; -4.3982 \u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;06\u003c/sup\u003e; 6.291 \u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e; -4.79667\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;14\u003c/sup\u003e; 1.83241\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;18\u003c/sup\u003e; e -2.75665\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;23\u003c/sup\u003e (CEMIG 2016).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\u003ch2\u003e2.6.3 Water surface\u003c/h2\u003e\u003cp\u003eTo estimate the surface area of the reservoir as a function of stored volume, the following equation was applied (CEMIG 2016): obtained from the bathymetric survey at a 1:10.000 scale.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\text{A}}_{\\text{E}\\text{S}}={\\text{h}+\\text{i}\\left({\\text{H}}_{\\text{i}}\\right)+\\:\\text{j}{\\left({\\text{H}}_{\\text{i}}\\right)}^{2\\:\\:}+\\text{k}{\\left({\\text{H}}_{\\text{i}}\\right)}^{3\\:\\:}+\\:\\text{l}{\\left({\\text{H}}_{\\text{i}}\\right)}^{4\\:\\:\\:\\:}}_{\\:\\:\\:\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: A\u003csub\u003eES\u003c/sub\u003e = water surface area, m\u0026sup2;.\u003c/p\u003e\u003cp\u003eThe coefficients \u0026lsquo;h\u0026rsquo;, \u0026lsquo;i\u0026rsquo;, \u0026lsquo;j\u0026rsquo;, \u0026lsquo;k\u0026rsquo;, and \u0026lsquo;l\u0026rsquo;, adjusted based on the area\u0026ndash;elevation relationships of the Tr\u0026ecirc;s Marias HPP reservoir, are respectively 4.56634 \u0026times; 10\u003csup\u003e12\u003c/sup\u003e; -3.43895 \u0026times; 10\u003csup\u003e10\u003c/sup\u003e; 9.72922 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e; and \u0026minus;\u0026thinsp;122.578 (CEMIG 2016).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e2.6.4 Evaporation\u003c/h2\u003e\u003cp\u003eThe average flows equivalent to the net evaporated depth were estimated based on the amount of water evaporated from the reservoir\u0026rsquo;s water surface area, as expressed in Eq.\u0026nbsp;4.\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{E}\\text{V}}=\\frac{\\text{E}\\text{v}\\:{\\text{A}}_{\\text{E}\\text{S}}}{1000000}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eEV\u003c/sub\u003e = average flow equivalent to the evaporated water depth in the reservoir, hm\u0026sup3;day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; Ev\u0026thinsp;=\u0026thinsp;daily evaporation rate in the reservoir, m day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe daily evaporation rates throughout the year for the Tr\u0026ecirc;s Marias HPP reservoir, as proposed by Vieira et al. (\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), were adopted, which were estimated using the Penman\u0026ndash;Monteith model (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAverage daily evaporation rate in the reservoir (m day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) of the Tr\u0026ecirc;s Marias Hydropower Plant during the period 2000\u0026ndash;2002.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJanuary\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFebruary\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMarch\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eApril\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMay\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eJune\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00532\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.00489\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00455\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00437\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00363\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.00313\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eJuly\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eAugust\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003eSeptember\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003eOctober\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003eNovember\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003eDecember\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00342\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.00452\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00471\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00583\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00456\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.00480\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eFont: Vieira et al. (\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003e2.6.5 Infiltration\u003c/h2\u003e\u003cp\u003eThe water surface area is always larger than the bottom area of the reservoir, where most of the infiltration occurs. Therefore, it was assumed that large reservoirs have a trapezoidal shape, with the base width representing approximately 65% of the water surface area (Sj\u0026ouml;berg et al. 2018). The assumption of uniform infiltration is a reasonable simplification, given the relative homogeneity of the soil composition observed in geotechnical surveys conducted during the construction of the reservoir (Casagrande 1957; Wu et al. \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn the present study, the daily volume of water infiltrated into the reservoir bed was calculated using a modified version of Darcy\u0026rsquo;s Law, as shown in Eq.\u0026nbsp;5.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{I}}=\\frac{\\left(\\text{k}\\:{\\text{A}}_{\\text{E}\\text{S}}\\frac{\\left({\\text{H}}_{\\text{i}}-{\\text{H}}_{0}\\right)}{\\text{C}\\text{r}}\\right)\\:\\text{T}}{1000000}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eI\u003c/sub\u003e = infiltration, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; k\u0026thinsp;=\u0026thinsp;hydraulic conductivity of the medium, m s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; Cr\u0026thinsp;=\u0026thinsp;reservoir length, m; H₀ = minimum water level, 510.44 m; T\u0026thinsp;=\u0026thinsp;86.400 seconds. Therefore, when H\u003csub\u003ei\u003c/sub\u003e = H₀, infiltration is zero, indicating that there is no water flow infiltrating into the soil when the reservoir water level reaches the minimum elevation.\u003c/p\u003e\u003cp\u003eThe average conductivity was 1.3 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;06\u003c/sup\u003e m s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, obtained from k values reported in studies and technical reports conducted in the Tr\u0026ecirc;s Marias HPP reservoir area, which indicate the predominance of sandy and sandy\u0026ndash;clayey soils, considering the heterogeneity of the soil at the reservoir bed (Casagrande 1957; CPRM 2025).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003ch2\u003e2.6.6 Precipitation\u003c/h2\u003e\u003cp\u003eThe determination of the flow corresponding to the direct contribution of precipitation to the Tr\u0026ecirc;s Marias HPP reservoir was carried out using Eq.\u0026nbsp;6.\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{P}}=\\frac{{\\text{P}}_{\\text{D}}\\:{\\text{A}}_{\\text{E}\\text{S}}}{1000000}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eP\u003c/sub\u003e = precipitation, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; P\u003csub\u003eD\u003c/sub\u003e = daily precipitation, m day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; A\u003csub\u003eES\u003c/sub\u003e = water surface area, m\u0026sup2;.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\u003ch2\u003e2.6.7 Turbine outflow\u003c/h2\u003e\u003cp\u003eThe turbine outflow of the Tr\u0026ecirc;s Marias HPP was estimated in a simplified manner from the water level by applying Torricelli\u0026rsquo;s principle (Adeeyo et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), as represented in Eq.\u0026nbsp;(7).\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{T}\\text{o}}=\\frac{\\left({\\text{C}\\text{d}\\:\\text{A}\\left(2\\text{g}\\:{\\text{H}}_{\\text{i}}-{\\text{H}}_{\\text{m}}\\right)}^{0.5}\\right)\\:\\text{T}\\:}{1000000}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eTO\u003c/sub\u003e = turbine outflow, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; Cd\u0026thinsp;=\u0026thinsp;discharge coefficient (dimensionless; 0.73); A\u0026thinsp;=\u0026thinsp;turbine opening area, m\u0026sup2;; g\u0026thinsp;=\u0026thinsp;gravitational acceleration, 9.81 m s\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e; Hm\u0026thinsp;=\u0026thinsp;minimum operating level (m); T\u0026thinsp;=\u0026thinsp;86.400 seconds.\u003c/p\u003e\u003cp\u003eThus, when H\u003csub\u003ei\u003c/sub\u003e = Hm, the turbine outflow will be zero. This means that there will be no water flow through the turbines when the reservoir water level is equal to the minimum operating elevation.\u003c/p\u003e\u003cp\u003eThe maximum and minimum operating levels, equal to 572.50 m and 549.20 m, respectively, relative to mean sea level, were adopted based on the new bathymetric survey conducted in the reservoir in 2016 (CEMIG 2016).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\u003ch2\u003e2.6.8 Spillway outflow\u003c/h2\u003e\u003cp\u003eDuring the rainy season, it is common for the Tr\u0026ecirc;s Marias HPP reservoir to reach its maximum capacity and begin to overflow through a rectangular spillway with seven gates. Whenever H\u003csub\u003ei\u003c/sub\u003e exceeds the maximum operating level (maximum elevation of 572.5 m), the gates are opened, and the corresponding spillway discharge is computed (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe spillway discharge was estimated using Eq.\u0026nbsp;(8), as proposed by Porto (\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). The physical characteristics of the reservoir spillway were obtained from the Companhia Energ\u0026eacute;tica de Minas Gerais (CEMIG 2023).\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{S}\\text{V}}=\\frac{\\left(\\:\\left({\\text{C}}_{\\text{O}}\\:{\\text{L}}_{\\text{C}}\\:{\\text{G}}_{\\text{O}}\\:\\sqrt{2\\text{g}}\\:\\text{H}\\text{v}\\:\\right)\\:{\\text{C}}_{\\text{P}}\\right)\\:\\text{T}\\:}{1000000}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(8\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eSV\u003c/sub\u003e = spillway discharge, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; C\u003csub\u003eO\u003c/sub\u003e = spillway discharge coefficient (dimensionless; 0.75); L\u003csub\u003eC\u003c/sub\u003e = gate width, m; T\u0026thinsp;=\u0026thinsp;86.400 seconds; G\u003csub\u003eO\u003c/sub\u003e = gate opening height, m, with a maximum value of 1.56 m to ensure outflows equal to or lower than 3.500 m\u0026sup3; s⁻\u0026sup1;; H\u003csub\u003eV\u003c/sub\u003e = water head over the spillway, m; C\u003csub\u003eP\u003c/sub\u003e = number of gates.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e2.6.9 Multiple water uses and Total outflow\u003c/h2\u003e\u003cp\u003eThe total flow demanded to meet multiple water uses, which represents the sum of the flows for hydropower generation (turbine outflow) and the flows required to satisfy other demands, was obtained using Eq.\u0026nbsp;(9).\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{U}\\text{M}}=\\:{\\text{Q}}_{\\text{T}}+{\\text{R}}_{\\text{A}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(9\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eUM\u003c/sub\u003e = multiple water uses; R\u003csub\u003eA\u003c/sub\u003e = water withdrawal from the reservoir obtained from water rights, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe total outflow, which refers to the amount of water released from the reservoir, was obtained using Eq.\u0026nbsp;(10).\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\:{\\text{Q}}_{\\text{D}\\text{E}}=\\:{\\text{Q}}_{\\text{T}}+{\\text{Q}}_{\\text{S}\\text{V}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(10\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: Q\u003csub\u003eDE\u003c/sub\u003e = total reservoir outflow, hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003e2.7 Evaluation of the Capacity to Meet Multiple Water Uses in the Tr\u0026ecirc;s Marias HPP Reservoir\u003c/h2\u003e\u003cp\u003eTo assess the capacity of the Tr\u0026ecirc;s Marias HPP reservoir to meet multiple water uses during periods of reduced water availability between January 2004 and June 30, 2024, a hedging operation was implemented in the System Dynamics (SD) model (Bayazit and \u0026Uuml;nal \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Chong et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe hedging operation introduces small but more frequent reductions in withdrawals, aiming to conserve water in the reservoir and decrease the likelihood of a large future reduction caused by complete reservoir depletion (Chong et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo implement the hedging operation in the SD model, two main rules were adopted:\u003c/p\u003e\u003cp\u003e1) Trigger rule: defines the minimum storage volume in the reservoir required to ensure the supply for multiple water uses (You and Cai \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e2) Cutback rule: establishes the magnitude of the reduction in water demand supply, with the cutback being triggered by changes in storage volume (Bayesteh and Azari \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe hedging operation to evaluate the ability of the reservoir to supply multiple water uses was performed based on water dynamics and the sensitivity of the SD model. Two scenarios were proposed to activate the hedging operation, considering an annual growth trend of 6.26% in water withdrawals:\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003e1) triggers of 52% and 62% of the total volume with cutbacks applied to turbine outflow.\u003c/h3\u003e\n\u003cp\u003e2) triggers of 52% and 62% of the total volume with cutbacks applied to turbine outflow and evaporation.\u003c/p\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e2.8 Evaluation and Calibration of the System Dynamics Model\u003c/h2\u003e\u003cp\u003eThe records of water level variations observed between January 2004 and June 2024 in the Tr\u0026ecirc;s Marias HPP reservoir were used to evaluate the performance of the proposed SD model.\u003c/p\u003e\u003cp\u003eFor this purpose, the dataset was divided into three time intervals, following the methodology proposed by Althoff and Rodrigues (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The first interval, comprising the initial 731 days (9.99% of the data), was used to warm up the SD model, sufficient to stabilize and dissipate the effects of initial conditions. The subsequent 4.758 days (64.95% of the data) were used for calibration; a longer period was required to adjust the SD model variables, allowing the capture of hydrological variability over time. Finally, the last 1.998 days (25.06% of the data) were used for validation, testing the ability of the SD model to predict hydrological behavior using data not included in calibration. This helps to identify potential overfitting, in which the SD model adapts excessively to calibration data and loses its ability to generalize to new data.\u003c/p\u003e\u003cp\u003eTo evaluate the performance of the proposed SD model, the following statistical metrics were applied: Mean Absolute Relative Error \u0026ndash; MARE (Eq.\u0026nbsp;11); Mean Absolute Error \u0026ndash; MAE (Eq.\u0026nbsp;12) (Abro et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); Root Mean Square Error \u0026ndash; RMSE (Eq.\u0026nbsp;13); Coefficient of Determination \u0026ndash; R\u0026sup2; (Eq.\u0026nbsp;14); Nash\u0026ndash;Sutcliffe Efficiency Index \u0026ndash; NSE (Eq.\u0026nbsp;15) (Nash and Sutcliffe \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e1970\u003c/span\u003e); and Kling\u0026ndash;Gupta Efficiency Index \u0026ndash; KGE (Eq.\u0026nbsp;16) (Gupta et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Finally, a Pearson correlation was performed, as expressed in Eq.\u0026nbsp;(17), to evaluate the linear relationship between observed and simulated data from the proposed model (Acevedo et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). All these statistical metrics were calculated using the R software (R Development Core Team 2018).\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\:\\text{M}\\text{A}\\text{R}\\text{E}=\\frac{1}{\\text{n}}{\\sum\\:}_{\\text{i}=1}^{\\text{n}}\\frac{\\left|{(\\text{S}\\text{i}\\text{m}}_{\\text{i}}-{\\text{O}\\text{b}\\text{s}}_{\\text{i}})\\right|}{{\\text{O}\\text{b}\\text{s}}_{\\text{i}}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(11\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\:\\text{M}\\text{A}\\text{E}=\\frac{1}{\\:\\text{n}}\\sum\\:_{\\text{i}=1}^{\\text{n}}|{\\text{S}\\text{i}\\text{m}}_{\\text{i}}-{\\text{O}\\text{b}\\text{s}}_{\\text{i}}\\left|\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\right(12)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$$\\:\\text{R}\\text{M}\\text{S}\\text{E}=\\sqrt{\\frac{1}{\\text{n}}{\\sum\\:}_{\\text{i}=1}^{\\text{n}}{{(\\text{S}\\text{i}\\text{m}}_{\\text{i}}-{\\text{O}\\text{b}\\text{s}}_{\\text{i}})}^{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(13\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equl\" name=\"EquationSource\"\u003e\n$$\\:{\\text{R}}^{2}=\\frac{\\sum\\:_{\\text{i}=1}^{\\text{n}}\\left({\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-\\:{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}}\\right).\\:\\left({\\text{S}\\text{i}\\text{m}}_{\\text{i}\\:}-\\:{\\stackrel{-}{\\text{S}}\\text{i}\\text{m}}_{i}\\right)}{\\sqrt{\\sum\\:_{\\text{i}=1}^{\\text{n}}({\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-\\:{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}})\u0026sup2;}\\:.\\sqrt{\\sum\\:_{\\text{i}=1}^{\\text{n}}({\\text{S}\\text{i}\\text{m}}_{\\text{i}\\:}-\\:{\\stackrel{-}{\\text{S}}\\text{i}\\text{m}}_{\\text{i}})\u0026sup2;}\\:\\:\\:}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(14\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equm\" name=\"EquationSource\"\u003e\n$$\\:\\text{N}\\text{S}\\text{E}=1-\\frac{\\sum\\:_{\\text{i}=1}^{\\text{n}}({\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-\\:{\\text{S}\\text{i}\\text{m}}_{\\text{i}\\:})\u0026sup2;}{\\:\\sum\\:_{\\text{i}=1}^{\\text{n}}({\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-\\:{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}})\u0026sup2;\\:\\:}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(15\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equn\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equn\" name=\"EquationSource\"\u003e\n$$\\:\\text{K}\\text{G}\\text{E}=1-\\:\\sqrt{{\\left(\\text{r}-1\\:\\right)}^{2\\:}+{\\left({\\beta\\:}-1\\right)}^{2}+\\:{\\left({\\gamma\\:}-1\\right)}^{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(16\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003cdiv id=\"Equo\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equo\" name=\"EquationSource\"\u003e\n$$\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\text{r}=\\frac{\\sum\\:_{\\text{i}=1}^{\\text{n}}\\left({\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}}\\right)}{\\sqrt{\\sum\\:_{\\text{i}=1}^{\\text{n}}{(\\text{O}\\text{b}\\text{s}}_{\\text{i}\\:}-{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}})\\:.}\\:\\sqrt{\\sum\\:_{\\text{i}=1}^{\\text{n}}\\left({\\text{S}\\text{i}\\text{m}}_{\\text{i}}-{\\stackrel{-}{\\text{S}}\\text{i}\\text{m}}_{\\text{i}}\\right)}}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equp\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equp\" name=\"EquationSource\"\u003e\n$$\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{\\beta\\:}=\\frac{{{\\mu\\:}}_{\\text{s}}}{{{\\mu\\:}}_{\\text{o}}}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equq\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equq\" name=\"EquationSource\"\u003e\n$$\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{\\gamma\\:}=\\frac{{\\text{C}\\text{V}}_{\\text{s}}}{{\\text{C}\\text{V}}_{\\text{o}}}=\\:\\frac{\\frac{{{\\sigma\\:}}_{\\text{s}}}{{{\\mu\\:}}_{\\text{s}}}}{\\frac{{{\\sigma\\:}}_{\\text{o}}}{{{\\mu\\:}}_{\\text{o}}}}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equr\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equr\" name=\"EquationSource\"\u003e\n$$\\:\\text{r}=\\:\\:\\frac{1}{\\text{n}-1}\\sum\\:\\left(\\frac{{{\\text{S}\\text{i}\\text{m}}_{\\text{i}}}_{\\:}-\\:{\\stackrel{-}{\\text{S}}\\text{i}\\text{m}}_{\\text{i}}\\:}{{\\sigma\\:}\\text{s}\\:}\\right)\\left(\\frac{{\\text{O}\\text{b}\\text{s}}_{\\text{i}}-\\:{\\stackrel{-}{\\text{O}}\\text{b}\\text{s}}_{\\text{i}}\\:}{{\\sigma\\:}\\text{s}\\:}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(17\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere: n\u0026thinsp;=\u0026thinsp;number of observations; \u0026micro;s and \u0026micro;o\u0026thinsp;=\u0026thinsp;means of simulated and observed data; r\u0026thinsp;=\u0026thinsp;Pearson correlation; σs and σo\u0026thinsp;=\u0026thinsp;standard deviations of simulated and observed data; Cvs and Cvo\u0026thinsp;=\u0026thinsp;coefficients of variation of simulated and observed data; Oi and Si\u0026thinsp;=\u0026thinsp;observed and simulated values (SPPs) on day i; Ō and S̄ = arithmetic means of observed and simulated data (SPPs), respectively.\u003c/p\u003e\u003cp\u003e\u003cb\u003e2.8 Sensitivity Analysis of the Variation in Stored Volume in the Tr\u0026ecirc;s Marias HPP Reservoir to the Main Key Variables\u003c/b\u003e\u003c/p\u003e\u003cp\u003eA sensitivity analysis was carried out with the objective of identifying which variables exert the greatest influence on the variation of stored volume in the Tr\u0026ecirc;s Marias HPP reservoir. The stored water volume was defined as the variable of interest, as it directly reflects the system\u0026rsquo;s capacity to meet multiple water uses over time. The considered inflow and outflow variables (inflow, infiltration, evaporation, precipitation, turbine outflow, and water withdrawal) represent the main components of the reservoir\u0026rsquo;s water balance and, consequently, the most relevant elements for the system\u0026rsquo;s operation and management.\u003c/p\u003e\u003cp\u003eTo evaluate the response of the SD model to uncertainties and natural or anthropogenic fluctuations, the values of each of these variables were individually adjusted by \u0026plusmn;\u0026thinsp;10% relative to their reference values for the period from January 2004 to June 2024. This percentage variation was defined in the literature as an adequate range to test the robustness of hydrological models and to capture possible nonlinearities in the system\u0026rsquo;s responses (Alifujiang et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Rodrigues et al. \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Calibration and Evaluation of the System Dynamics Model\u003c/h2\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe results show the variation of the observed and simulated water level over time in the reservoir, highlighting a considerable decrease after September 18, 2014, which stabilized at safe levels to meet multiple water uses from January 19, 2019 onward (Fig.\u0026nbsp;4).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;4\u003c/b\u003e Observed and simulated water level for the training, calibration, and validation periods of the System Dynamics model.\u003c/p\u003e\u003cp\u003eConsistency is observed between the simulated and observed water level values over time, according to the different performance indices applied. During the warm-up period, the following performance indices were obtained:\u003c/p\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.899, NSE\u0026thinsp;=\u0026thinsp;0.901, KGE\u0026thinsp;=\u0026thinsp;0.944, MAE\u0026thinsp;=\u0026thinsp;0.885, RMSE\u0026thinsp;=\u0026thinsp;1.038, MARE\u0026thinsp;=\u0026thinsp;0.0015 e R\u0026thinsp;=\u0026thinsp;0.954.\u003c/p\u003e\u003cp\u003eDuring the calibration phase of the SD model, the following values were obtained: R\u0026sup2; = 0.958, NSE\u0026thinsp;=\u0026thinsp;0.967, KGE\u0026thinsp;=\u0026thinsp;0.974, MAE\u0026thinsp;=\u0026thinsp;0.869, RMSE\u0026thinsp;=\u0026thinsp;1.252, MARE\u0026thinsp;=\u0026thinsp;0.00153; and a positive Pearson correlation of 0.980. The performance of the SD model showed a slight loss of accuracy in the validation phase, with R\u0026sup2; = 0.956, NSE\u0026thinsp;=\u0026thinsp;0.961, KGE\u0026thinsp;=\u0026thinsp;0.952, MAE\u0026thinsp;=\u0026thinsp;0.873, RMSE\u0026thinsp;=\u0026thinsp;1.263, MARE\u0026thinsp;=\u0026thinsp;0.00161 and a decrease in the positive Pearson correlation to 0.975. These results indicate that the SD model is classified in the \u0026lsquo;very good\u0026rsquo; category according to the classification proposed by Mararakanye et al. (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cb\u003e3.2 Sensitivity Analysis of the System Dynamics Model\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe results of the sensitivity analysis of water dynamics in the Tr\u0026ecirc;s Marias HPP reservoir to changes in the main key variables (Fig.\u0026nbsp;5 and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;5\u003c/b\u003e Variation in reservoir volume (%) over time as a function of \u0026plusmn;\u0026thinsp;10% changes in inflow, turbine outflow, evaporation, precipitation, infiltration, and water withdrawal for the period from January 2004 to June 2024.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of the sensitivity analysis of the System Dynamics model applied to the Tr\u0026ecirc;s Marias Hydropower Plant reservoir. (∆Vo\u0026thinsp;=\u0026thinsp;volume variation (%); Q\u003csub\u003eA\u003c/sub\u003e = inflow; R\u003csub\u003eA\u003c/sub\u003e = water withdrawal; Q\u003csub\u003eTO\u003c/sub\u003e = turbine outflow; Q\u003csub\u003eEV\u003c/sub\u003e = evaporation; Q\u003csub\u003eP\u003c/sub\u003e = precipitation; Q\u003csub\u003eI\u003c/sub\u003e = infiltration).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003cp\u003e∆ Vo\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eQ\u003csub\u003eA\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eQ\u003csub\u003eP\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eQ\u003csub\u003eEV\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e66.24 41.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e58.36 54.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e53.78 59.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eQ\u003c/b\u003e\u003csub\u003e\u003cb\u003eTO\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csub\u003e\u003cb\u003eA\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003eQ\u003c/b\u003e\u003csub\u003e\u003cb\u003eI\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e+10 -10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e49.67 63.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e55.70 57.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e55.61 57.58\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe variation in stored water volume in the Tr\u0026ecirc;s Marias HPP reservoir showed low sensitivity to changes in the flow variables infiltration, precipitation, and water withdrawal, indicating that variations in these variables had less influence on the stored volume. However, the stored water volume in the reservoir was highly sensitive to the flow variables inflow, turbine outflow, and evaporation.\u003c/p\u003e\u003cp\u003eA\u0026thinsp;+\u0026thinsp;10% variation in inflow resulted in an average increase of 66.24% in storage volume, while a -10% variation led to an average reduction of 41.70% (Fig.\u0026nbsp;5, Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). A\u0026thinsp;+\u0026thinsp;10% variation in precipitation, evaporation, infiltration, turbine outflow, and water withdrawal values (Fig.\u0026nbsp;5, Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) resulted in average variations in reservoir storage volume of 58.36%, 53.78%, 55.61%, 49.67%, and 55.70%, respectively.\u003c/p\u003e\u003cp\u003eA -10% variation in precipitation, evaporation, infiltration, turbine outflow, and water withdrawal values (Fig.\u0026nbsp;5, Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) implied average variations of 54.68%, 59.31%, 57.58%, 63.17%, and 57.45%, respectively, in the stored volume. The flow variables inflow, turbine outflow, and evaporation are therefore the most sensitive factors affecting the stored volume in the Tr\u0026ecirc;s Marias HPP reservoir.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Simulation and Evaluation of Water Dynamics in the Reservoir\u003c/h2\u003e\u003cp\u003eThe results of the simulation of the behavior of the main flow, auxiliary, and state variables that determine the water dynamics in the Tr\u0026ecirc;s Marias HPP reservoir are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The maximum, mean, and minimum values of the state, flow, and auxiliary variables for the Tr\u0026ecirc;s Marias HPP reservoir are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWhen analyzing the simulation results, it is observed that inflow values (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eA, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) ranged from 663.125 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e to 0.009 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e, with an average value of 45.197 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e. A reduction in inflow was identified in three periods. The first reduction extended from May 14 to November 10, 2014, with an average flow of 4.912 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e. The second reduction lasted from July 19 to November 11, 2015, with an average of 5.941 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e. The third reduction occurred from July 6 to November 25, 2017, with an average of 2.543 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e. An overall average inflow decline of 4.462 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e was observed during these periods. High variability in inflow was recorded during the rainy season, with an average of 50.571 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eInflow is the main input variable in the water balance of large reservoirs, directly or indirectly influencing the behavior of other flow, auxiliary, and state variables, which followed the same trend as inflow. Water surface area values ranged from 1102.8 km\u003csup\u003e2\u003c/sup\u003e to 366.767 km\u003csup\u003e2\u003c/sup\u003e, with an average of 786.67 km\u003csup\u003e2\u003c/sup\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). A mean reduction of 0.926 km\u003csup\u003e2\u003c/sup\u003e per day was observed during the dry seasons (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eB), and during the driest period (May 14 to November 10, 2014) the average daily reduction was approximately 0.521 km\u003csup\u003e2\u003c/sup\u003e, reaching the minimum value of 366.767 km\u003csup\u003e2\u003c/sup\u003e on October 31, 2014. The largest infiltration and evaporation losses occurred on the days when the largest water surface areas were recorded. Infiltration flow into the reservoir bed (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eC, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) ranged from 1.862 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 0.391 hm\u0026sup3;day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 1.182 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Evaporation from the water surface (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eD, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) ranged from 5.672 hm\u0026sup3;day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 1.315 hm\u0026sup3;day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 3.443 hm\u0026sup3;day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Precipitated water volume over the reservoir surface area (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eE, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) reached a maximum of 100.861 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a minimum of 0.065 hm\u003csup\u003e3\u003c/sup\u003e day\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 2.613 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eWater withdrawal for agriculture, livestock watering, public supply, and industrial use (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eF, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) had an average of 1.10 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with a minimum of 0.053 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a maximum of 4.032 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in June 2024. This significant increase was mainly due to higher demand for irrigation of annual crops. Since 2004, continuous growth in water withdrawals has been observed, from a minimum of 0.053 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to current maximum values. The average annual growth trend in withdrawals was approximately 5.84%, equivalent to 0.817 hm\u003csup\u003e3\u003c/sup\u003eyear\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e between 2004 and 2024. However, from 2017 onward, this growth intensified, with an average annual rate of 6.26%, reflecting a continuous upward trend of 0.876 hm\u003csup\u003e3\u003c/sup\u003eyear\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in water withdrawals in the coming years.\u003c/p\u003e\u003cp\u003eTurbine outflow (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eG, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), responsible for power generation, averaged 61.462 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, reaching a maximum of 77.321 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a minimum of 12.852 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e on October 31, 2014, mainly due to the reduced inflow in the first period. Multiple water uses (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eH, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) reached a maximum demand of 79.983 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a minimum of 13.522 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 62.562 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Multiple water uses accounted for 90.23% of total demand, of which turbine outflow was the main outflow, representing 98.23%, followed by water withdrawals at 1.77%. Therefore, turbine outflow is approximately 50.97 times greater than withdrawals. The remaining 9.45% was due to losses from evaporation, infiltration, and spillway outflow, which together represented 4.84%, 1.96%, and 2.97%, respectively, of the reservoir water balance.\u003c/p\u003e\u003cp\u003eThe lowest volume variations were observed on days when the smallest water surface areas were recorded (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eI). On October 31, 2014, the reservoir volume reached its lowest value of 3721.312 hm\u0026sup3;, representing 0.34% of usable storage (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The maximum volume of 18,855.26 hm\u0026sup3; was reached during five periods (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eI). Over the analyzed period, the average volume was 12,438.691 hm\u0026sup3; (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Between July 6 and November 25, 2017, a second significant downward trend in volume occurred, with a decrease of approximately 19.66 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. This decline resulted in a minimum volume of 4693.37 hm\u0026sup3;, recorded on November 22, 2017. The reservoir water level (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eJ, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) ranged from 572.863 m to 549.551 m, with an average of 564.789 m. Maximum spillway discharge (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eK, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) was 181.883 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e, recorded on February 21, 2022, while the minimum was 7.789 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 92.357 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, operating approximately 1.81% of the time. The maximum outflow released from the reservoir (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e6\u003c/span\u003eL, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) was 259.213 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average of 63.432 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a minimum of 12.852 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMaximum, mean, and minimum values of the state, flow, and auxiliary variables in the Tr\u0026ecirc;s Marias Hydropower Plant reservoir, S\u0026atilde;o Francisco River Basin, Brazil.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMaximum\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMinimum\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInflow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"8\" rowspan=\"9\"\u003e\u003cp\u003ehm\u0026sup3;dia\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e663.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e45.197\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.009\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrecipitation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e100.861\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.613\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.065\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInfiltration\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.862\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.182\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.391\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEvaporation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.672\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.441\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.315\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTurbine outflow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e77.321\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e61.451\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e12.852\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpillaway outflow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e181.883\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e92.357\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e7.789\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMultiple water uses\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e79.983\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e62.562\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e13,522\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater abstration\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.032\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.102\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.053\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal outflow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e259.213\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e63.432\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e12.852\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVolume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ehm\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19185.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e12438.691\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3721.312\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater surface\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ekm\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e572.863\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e564.789\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e549.551\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater level\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003em\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1102.845\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e786.671\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e366.751\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Evaluation of the capacity to supply multiple water uses in the Tr\u0026ecirc;s Marias HPP reservoir\u003c/h2\u003e\u003cp\u003eThe simulation results for the different scenarios with hedging operation, with variations in the triggers and cutbacks applied to turbine outflow, highlight the changes in flow for supplying multiple water uses, the number of cutback days, and the impacts on the reservoir\u0026rsquo;s stored volume (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn Scenario 1, with a trigger of 52% and a 39% cutback applied, turbine outflow was reduced by an average of 17.27 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 1.088 days (14.53% of the time) throughout the entire simulation period (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eA). In the periods prior to October 31, 2014, when the greatest reduction in water availability occurred, turbine outflow was reduced by an average of 17.13 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 351 days. This reduction was necessary to maintain a minimum flow of 21.89 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to ensure the supply of multiple water uses, as opposed to the 13.516 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e observed during the reservoir\u0026rsquo;s water dynamics (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eA). During the same period, the reservoir volume increased from the lowest recorded value of 3,721.31 hm\u0026sup3; to 6,066.76 hm\u0026sup3;, representing an increase of approximately 63.06% to meet multiple water uses (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eB).\u003c/p\u003e\u003cp\u003eAnother trend in Scenario 1 was observed with a 62% trigger and a 21% cutback applied: turbine outflow was reduced by an average of 12.66 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 2.461 days (32.87% of the time) during the entire simulation period (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eC). The main reason for the smaller cutback, which occurs more frequently with a 62% trigger, is that turbine outflow reductions began shortly after the start of the simulation. However, the initial cutback was followed by four additional reductions averaging 13.37 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, lasting 915 days (12.22%), to mitigate the decline in volume that began on May 14, 2014, reaching its most critical value on October 31, 2014. This intervention raised the minimum observed flow from 13.51 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 21.61 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eC). Consequently, the reservoir\u0026rsquo;s critical volume (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e7\u003c/span\u003eD) increased from 3,721.31 hm\u0026sup3;, observed during the water dynamics, to 5,873.47 hm\u0026sup3;, representing a storage increase of approximately 57.84%. This increase ensured the supply of multiple water uses, the maintenance of environmental flows, and compliance with operational rules.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn Scenario 2, by maintaining the 52% trigger and reducing the cutback to 29%, while applying a 0.11% reduction in evaporation-equivalent to a reduction of 0.55 km\u0026sup2; in the water surface \u0026aacute;rea-there was a decrease in the number of cutbacks in turbine outflow, which was reduced by an average of 10.54 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 543 days (7.05% of the time) during the entire simulation period (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eA). In the periods prior to October 31, 2014, the day with the greatest reduction in water availability, turbine outflow was reduced by an average of 9.71 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 282 days (3.77% of the time). This reduction ensured a minimum flow of 22.87 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to supply multiple water uses, as opposed to the 13.516 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e observed on October 31, 2014, during the reservoir\u0026rsquo;s water dynamics (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eA). In the same period, the reservoir volume increased from the lowest recorded value of 3,721.21 hm\u0026sup3; to 6,311.32 hm\u0026sup3;, representing an increase of approximately 69.59% to supply multiple water uses (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eB).\u003c/p\u003e\u003cp\u003eIt is observed in Scenario 2 that, by maintaining the 62% trigger and reducing the cutback to 11%, while keeping the 0.11% reduction in evaporation, there was, as expected, a decrease in the number of cutbacks (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eC). As a consequence, turbine outflow was reduced by an average of 8.14 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 1.940 days (25.91% of the time) throughout the simulation period (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eC). The main reason for the decrease in the number of cutbacks is that with the reduction in evaporation, the reservoir volume tends to increase, thereby enhancing the water availability to supply multiple uses. However, prior to October 31, 2014, the average reduction in turbine outflow due to the smaller cutback was 6.36 hm\u0026sup3;day⁻\u003csup\u003e1\u003c/sup\u003e over 792 days (10.6% of the time), resulting in the minimum observed flow increasing from 13.51 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 22.46 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e(Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eC). Consequently, the critical reservoir volume (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e8\u003c/span\u003eD) increased from 3,721.31 hm\u0026sup3;, observed during the water dynamics, to 6,160.4 hm\u003csup\u003e3\u003c/sup\u003e, representing an increase in stored volume of approximately 65.42%, ensuring the supply of multiple water uses during periods of greater reductions in water availability.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of the different hedging operation scenarios with variations in triggers and cutbacks applied to turbine outflow, showing the impacts on flows and on the stored volume in the Tr\u0026ecirc;s Marias Hydropower Plant reservoir. (Ga\u0026thinsp;=\u0026thinsp;trigger; C\u003csub\u003eO\u003c/sub\u003e = cutback; RQ\u003csub\u003eEV\u003c/sub\u003e = evaporation reduction; RQ\u003csub\u003eTO\u003c/sub\u003e = average reduction in turbine outflow; D\u003csub\u003eC\u003c/sub\u003e = days with reduction; T\u003csub\u003eR\u003c/sub\u003e = reduction period; Q\u003csub\u003eM\u003c/sub\u003e = minimum observed flow to supply multiple water uses; Avo\u0026thinsp;=\u0026thinsp;volume increase; C\u0026thinsp;=\u0026thinsp;scenario; Un\u0026thinsp;=\u0026thinsp;unit; C1\u0026thinsp;=\u0026thinsp;scenario 1; C2\u0026thinsp;=\u0026thinsp;scenario 2).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGa\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRQ\u003csub\u003eEV\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRQ\u003csub\u003eTO\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eD\u003csub\u003eC\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eT\u003csub\u003eR\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eQ\u003csub\u003eM\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eAvo\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eUn\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(hm\u003csup\u003e3\u003c/sup\u003edia\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(dias)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(hm\u003csup\u003e3\u003c/sup\u003e dia\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eC1\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e17.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1088\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e14.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e21.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e63.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eC1\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e12.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2461\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e32.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e21.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e57.84\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eC2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e10.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e543\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e7.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e22.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e69.59\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eC2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1940\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e25.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e22.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e65.42\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe results show that the hedging operation strategy in Scenario 2 (with a trigger of 52% of the total volume, a 29% cutback in turbine outflow, and a 0.11% reduction in evaporation) favored the increase of the minimum stored volume in the reservoir, thereby enhancing the capacity to supply multiple water uses during periods of greater reduction in water availability (Fig.\u0026nbsp;9).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;9\u003c/b\u003e Relationship between the average reduction in turbine outflow and the increase in stored volume in the Tr\u0026ecirc;s Marias HPP reservoir under different hedging operation scenarios. (Ga52\u0026thinsp;=\u0026thinsp;52% trigger; Ga62\u0026thinsp;=\u0026thinsp;62% trigger; Co\u0026thinsp;=\u0026thinsp;39% cutback; Co\u0026thinsp;=\u0026thinsp;21% cutback; Co\u0026thinsp;=\u0026thinsp;29% cutback; Co\u0026thinsp;=\u0026thinsp;11% cutback; RQ\u003csub\u003eTO\u003c/sub\u003e = average reduction in turbine outflow; Avo\u0026thinsp;=\u0026thinsp;volume increase; C1\u0026thinsp;=\u0026thinsp;Scenario 1; C2\u0026thinsp;=\u0026thinsp;Scenario 2).\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe results indicate significant variability in inflow, with an average of 45.197 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, directly reflecting the low precipitation rates in the S\u0026atilde;o Francisco River Basin region (Paredes-Trejo et al. \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Capozzoli et al. 2016; Lucas et al. \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The reduction in the water surface area during dry periods, with an average decrease of 0.926 km\u0026sup2; per day, is associated with significant evaporation losses, which reached a maximum value of 5.672 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and an average of 3.443 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. These results indicate that water resources management must consider not only the amount of available water but also evaporation rates, which can impact the sustainability of water sources (Nevermann et al. \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Evaporation losses not only reduce the volume of available water but also affect the reservoir\u0026rsquo;s capacity to meet demand during critical periods (Wang et al. \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zhao and Gao \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Scherer and Pfister \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Infiltration was limited to a maximum of 1.862 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a minimum of 0.391 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with an average variation of 1.182 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. These values were close to the 0.13 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 2.4 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e with an average of 1.464 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, estimated for the Boura reservoir, located in central-west Burkina Faso (Fower et al. 2015).\u003c/p\u003e\u003cp\u003eThe continuous increase in water withdrawals, with an annual growth rate of 6.26%, reinforces the need to reassess water management to ensure sustainability, especially in the irrigation sector (Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The predominance of turbine outflow, which accounts for 88.63% of total demand, highlights the importance of optimizing reservoir operation to balance power generation with other competing water uses (Stojkovic and Simonovic \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Ivetić et al. 2022; Bettencourt et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the simulations show the adoption of emergency operations that prioritize the electricity sector at the expense of other water uses. The analysis of the results demonstrates that turbine outflow, with an average of 77.321 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, is fundamental for hydropower generation, although it shows significant variations, especially during periods of reduced inflow. Potential changes in turbine outflow, together with reduced inflows, may lead to sudden drops in the reservoir water level (Jiang et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This dynamic highlights the importance of efficient water management, as emphasized by Ivetić et al. (2022), who suggest that seasonal and climatic variations must be considered in reservoir operation.\u003c/p\u003e\u003cp\u003eIn this context, researchers highlight the importance of hedging operations with adjustable triggers and cutbacks as an effective strategy to mitigate the impacts of droughts and optimize water supply. This approach can enhance reservoir operational efficiency, even in the face of uncertainties imposed by climate change (Mostaghimzadeh et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chang et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Ashrafi \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Bayesteh and Azari \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Okkan et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this study, for example, using a 52% trigger and a 39% cutback resulted in a turbine outflow reduction of 17.27 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e over 1.088 days, contributing to a 63.06% increase in reservoir volume. Flexible operational rules may allow for the mitigation of climate change effects, enabling an adaptive response that accounts for climatic uncertainties (Beshavard et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The reduction in evaporation improves storage efficiency, as demonstrated by the 69.59% increase in reservoir volume when applying a 52% trigger with a 29% cutback and a 0.11% reduction in evaporation, through the implementation of floating solar power plants (Niccolai et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sunny et al. \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Luo et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). These results emphasize the importance of implementing hedging operations to ensure more efficient water resource management, particularly to minimize the risks of failing to supply multiple water uses under climate change. This can also support CEMIG in its project to use part of the reservoir surface to add an alternative source of hydraulic generation.\u003c/p\u003e\u003cdiv id=\"Sec26\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Implications for Water Resources Management\u003c/h2\u003e\u003cp\u003eWhen analyzing the impacts of operational scenarios on water resources management, specifically on flow rate and water storage, it is observed that adjustments in triggers and cutbacks directly affect flow rate and the stored water volume in the reservoir. For example, the reduction in turbine outflow (RQ\u003csub\u003eTO\u003c/sub\u003e) is more pronounced in Scenarios 1 and 2, with lower trigger percentages (52%), compared with higher trigger scenarios (62%). This suggests that a more aggressive operational approach may facilitate better water management, optimizing reservoir levels during periods of high demand and low inflows (Badr et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Ilich \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Meanwhile, the introduction of evaporation reduction measures (RQ\u003csub\u003eEV\u003c/sub\u003e) in Scenario 2 provides a notable advantage in terms of water conservation, with fewer turbine outflow cutbacks. Although the impact is minimal (0.11%), it highlights the importance of integrating evaporation control strategies into reservoir operations, particularly in arid regions, thereby maintaining reservoir levels during dry periods.\u003c/p\u003e\u003cp\u003eThe higher number of flow reductions in Scenario 1 (2.461 days) compared with Scenario 2 (1.940 days) indicates that scenarios with evaporation reduction and cutbacks may alleviate operational stress on the reservoir, enabling more sustainable long-term water resources management. The substantial difference in the number of days with reductions emphasizes the need to carefully consider operational thresholds to minimize negative impacts on water availability for multiple uses (Garrote et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Garcia et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Finally, it is noteworthy that despite variations in operational scenarios, the maintenance of adequate flows to supply multiple water uses (ranging from 21.46 to 22.87 hm\u003csup\u003e3\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) in all scenarios demonstrates sustainable management. However, a slight increase in the available volume for supplying multiple water uses, with higher or lower cutbacks and other evaporation reduction measures, requires further investigation within the SD model to ensure that water demands are consistently met under different climate change scenarios.\u003c/p\u003e\u003c/div\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003eThe System Dynamics model developed in this study proved efficient in simulating the water dynamics of the Tr\u0026ecirc;s Marias HPP reservoir and assessing its capacity to supply multiple water uses. Calibration and validation confirmed the robustness of the model, with high agreement between simulated and observed water levels over two decades of monitoring. The sensitivity analysis highlighted inflow as the most influential variable on stored volume, followed by turbine outflow and evaporation, underscoring the relevance of these components for system management. In the Tr\u0026ecirc;s Marias HPP reservoir, water demand for power generation, represented by turbine outflow, accounts for more than 90% of the reservoir\u0026rsquo;s total demand. There has been a significant increase in consumptive withdrawals since 2017, with a projected average annual growth trend of 6.26%. This scenario reinforces the imminence of conflicts between power generation and other user sectors, particularly during water scarcity periods. The hedging operation implemented with the aid of the proposed SD model proved effective for reservoir management, as it enabled preventive reductions in turbine outflow, increasing stored volume and ensuring water security during critical periods. In addition, small reductions in evaporation losses also contributed to enhancing system resilience in the face of growing demands. Overall, the results show that the proposed System Dynamics-based model is a valuable tool to support strategic planning and decision-making in the management of large reservoirs. In the case of the Tr\u0026ecirc;s Marias HPP, the application of the proposed model highlighted the need for adaptive operational strategies capable of reconciling hydropower generation with increasing consumptive uses and the maintenance of environmental flows. Thus, this study contributes to strengthening the scientific and practical foundation of integrated water resources management through the implementation of more sustainable operational rules. Finally, it is emphasized that the combination of triggers and cutbacks, along with small evaporation control measures, can improve the balance between energy generation and the supply of multiple water uses.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors thank to the Federal University of Vi\u0026ccedil;osa (UFV). This study was partly financed by the Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior (CAPES-In English: Coordination of Improvement of Higher Education Personnel) - Finance code 001, and by the Conselho Nacional de Desenvolvimento Cient\u0026iacute;fico e Tecnol\u0026oacute;gico (CNPQ - In English: National Council for Scientific and Technological Development) \u0026ndash; Grant number 155594/2023-0.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by (CAPES - In English: Coordination of Improvement of Higher Education Personnel) \u0026ndash; Finance code 001, and by the (CNPQ \u0026ndash; In English: National Council for Scientific and Technological Development) \u0026ndash; Grant number 155594/2023-0. The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study conception and design. Alisson Lopes Rodrigues: Conceptualization, Methodology, Software, Writing - original draft and all authors commented on previous versions of the manuscript. Ricardo Santos Silva Amorim: Conceptualization, Methodology, Writing-review \u0026amp; editing. Pedro Manuel Villa: Methodology, Software; Writing -review \u0026amp; editing. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI, Alisson Lopes Rodrigues, first author of the manuscript entitled \u0026lsquo;System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses\u0026rsquo; declare, for the due purposes of data access, availability, right, and use during the development of this research, through the link https://drive.google.com/drive/folders/1-jcu9y1nIXVG65ENpB281097-vYUWwsQ?usp=drive_link . Vi\u0026ccedil;osa (MG), 02/10/2025.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI, Alisson Lopes Rodrigues, the first author of the manuscript entitled \u0026lsquo;System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses\u0026rsquo;, declare that the submitted manuscript is original and has not been submitted to more than one publication for simultaneous appreciation. The results were presented clearly, honestly and without falsification or inappropriate manipulation of data. And we certify that we use free software for the development of this work. Vi\u0026ccedil;osa (MG), 02/10/2025.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbro MI, Zhu D, Khaskheli MA, Elahi E (2020) Statistical and qualitative evaluation of multi-sources for hydrological suitability inflood-prone areas of Pakistan. J Hydrol 588:125117. https:// doi. org/ 10.1016/j. jhydr ol. 2020. 125117. https://doi.org/10.1016/j.jhydrol.2020.125117.\u003c/li\u003e\n\u003cli\u003eAcevedo Y P O, Rivera M E, Rodr\u0026iacute;guez J R D (2017) Sistema de Pearson y modelos matem\u0026aacute;ticos aplicados a la hidrolog\u0026iacute;a. Avances Investigaci\u0026oacute;n en Ingenier\u0026iacute;a, 14(1), 95-108. 10.18041/1794-4953/avances.1.1288.\u003c/li\u003e\n\u003cli\u003eAdeeyo O A, Adefila S S, Ayeni, A O (2023) Dynamics of steady-state gravity-driven inviscid flow in an open system. International Journal of Innovative Research and Scientific Studies, 6(1), 80-88. https://doi.org/10.53894/ijirss.v6i1.1101.\u003c/li\u003e\n\u003cli\u003eAlifujiang Y, Abuduwaili J, Ma L, Samat A, \u0026amp; Groll, M (2017) System dynamics modeling of water level variations of Lake Issyk-Kul, Kyrgyzstan. Water, 9(12), 989. https://doi.org/10.3390/w9120989.\u003c/li\u003e\n\u003cli\u003eAl-Jawad J Y, Alsaffar H M, Bertram D, Kalin R M (2019) A comprehensive optimum integrated water resources management approach for multidisciplinary water resources management problems. J Environ Manag 239:211\u0026ndash;224. https:// doi. org/ 10. 1016/j. jenvm an. 2019. 03. 045.\u003c/li\u003e\n\u003cli\u003eAlthoff D, Rodrigues L N (2021) Goodness-of-fit criteria for hydrological models: Model calibration and performance assessment. Journal of Hydrology 600:126674. https:// doi. org/ 10. 1016/j. jhydr ol. 2021. 126674.\u003c/li\u003e\n\u003cli\u003eANA\u003cstrong\u003e -\u003c/strong\u003e Ag\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2017a) Reservat\u0026oacute;rios do Semi\u0026aacute;rido Brasileiro: Hidrologia, Balan\u0026ccedil;o e Opera\u0026ccedil;\u0026atilde;o-Relat\u0026oacute;rio S\u0026iacute;ntese; Superintend\u0026ecirc;ncia de Planejamento de Recursos H\u0026iacute;dricos-SPR: Bras\u0026iacute;lia, Brazil, p. 88. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eANA\u003cstrong\u003e -\u003c/strong\u003e Ag\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2017b) Resolu\u0026ccedil;\u0026atilde;o n\u0026ordm; 2.081, de 04 de dezembro de 2017. Disp\u0026otilde;e sobre as condi\u0026ccedil;\u0026otilde;es para a opera\u0026ccedil;\u0026atilde;o do Sistema H\u0026iacute;drico do Rio S\u0026atilde;o Francisco. Bras\u0026iacute;lia: Minist\u0026eacute;rio do Meio Ambiente, p.2,3. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eANA \u003cstrong\u003e-\u003c/strong\u003e Ag\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2022) Usos da \u0026Aacute;gua: Demandas Consultivas. Dispon\u0026iacute;vel em: https://dadosabertos.ana.gov.br. Acesso em: 10 de julho de 2022. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eANA \u003cstrong\u003e- \u003c/strong\u003eAg\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2023) Sistema Nacional de Informa\u0026ccedil;\u0026otilde;es Sobre Recursos H\u0026iacute;dricos (SNIRH). Bras\u0026iacute;lia: Minist\u0026eacute;rio do Meio Ambiente. Dispon\u0026iacute;vel em:www.snirh.gov.br. Acesso em: 22 de agosto de 2023. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eANA \u003cstrong\u003e- \u003c/strong\u003eAg\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2024a) Sistema Nacional de Informa\u0026ccedil;\u0026otilde;es Sobre Recursos H\u0026iacute;dricos (SNIRH). Bras\u0026iacute;lia: Minist\u0026eacute;rio do Meio Ambiente. http://www.snirh.gov.br. Acesso em 2 de fevereiro de 2024. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eANA\u003cstrong\u003e -\u003c/strong\u003e Ag\u0026ecirc;ncia Nacional de \u0026Aacute;guas e Saneamento B\u0026aacute;sico (2024b) Sistema Nacional de Informa\u0026ccedil;\u0026otilde;es Sobre Recursos H\u0026iacute;dricos (SNIRH). SAR - Sistema de Acompanhamento de Reservat\u0026oacute;rios. Bras\u0026iacute;lia: Minist\u0026eacute;rio do Meio Ambiente. http://www.snirh.gov.br. Acesso em 23 de abriu de 2024. http://www.ana.gov.br.\u003c/li\u003e\n\u003cli\u003eAshrafi S M (2021) Two\u003cstrong\u003e-\u003c/strong\u003estage metaheuristic mixed integer nonlinear programming approach to extract optimum hedging rules for multireservoir systems. J. Water Res. Plan. Manag. 147 (10), 10.1061/(ASCE)WR.1943-5452.0001460.\u003c/li\u003e\n\u003cli\u003eBadr A, Li Z, El\u003cstrong\u003e-\u003c/strong\u003eDakhakhni W (2023) Dynamic resilience quantification of hydropower infrastructure in multihazard environments. Journal of Infrastructure Systems, 29(2), 04023012. https://doi.org/10.1061/JITSE4.ISENG-2188.\u003c/li\u003e\n\u003cli\u003eBayazit M, \u0026Uuml;nal N E (1990) Effects of hedging on reservoir performance. Water resources research, 26(4), 713-719. https://doi.org/10.1029/WR026i004p00713.\u003c/li\u003e\n\u003cli\u003eBayesteh M, Azari A (2021) Stochastic optimization of reservoir operation by applying hedging rules. Journal of Water Resources Planning and Management, 147(2), 04020099. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001312.\u003c/li\u003e\n\u003cli\u003eBekri E S, Economou P, Yannopoulos P C, Demetracopoulos A C (2021). Reassessing existing reservoir supply capacity and management resilience under climate change and sediment deposition. Water, 13(13), 1819. https://doi.org/10.3390/w13131819.\u003c/li\u003e\n\u003cli\u003eBeshavard M, Adib A, Ashrafi S M, Kisi O (2022) Establishing effective warning storage to derive optimal reservoir operation policy based on the drought condition. Agricultural Water Management, 274, 107948. https://doi.org/10.1016/j.agwat.2022.107948.\u003c/li\u003e\n\u003cli\u003eBettencourt P, de Oliveira R P, Fulg\u0026ecirc;ncio C, Canas \u0026Acirc;, Wasserman J C (2022) Prospective Water Balance Scenarios (2015\u0026ndash;2035) for the Management of S\u0026atilde;o Francisco River Basin, Eastern Brazil. Water, 14(15), 2283. https://doi.org/10.3390/w14152283.\u003c/li\u003e\n\u003cli\u003eBurek P, Satoh Y, Fischer G, Kahil M T, Scherzer A, Tramberend S, Nava LF, Wada Y, Eisner S, Fl\u0026ouml;rke M, Hanasaki N, Magnuszewski P, Cosgrove B, Wiberg D (2016). Water Futures and Solution: Fast Track Initiative (Final Report). IIASA Working Paper. International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. https://pure.iiasa.ac.at/13008.\u003c/li\u003e\n\u003cli\u003eCasagande, A (1957) Report Earth Works and Foundation Engineering of the Tr\u0026ecirc;s Marias project. \u003c/li\u003e\n\u003cli\u003eCastello L, Macedo M N (2016) Large‐scale degradation of Amazonian freshwater ecosystems. Global change biology, 22(3), 990-1007. https://doi.org/10.1111/gcb.13173. \u003c/li\u003e\n\u003cli\u003eCBHSF - Comit\u0026ecirc; da Bacia Hidrogr\u0026aacute;fica do Rio S\u0026atilde;o Francisco (2016) Plano de Recursos H\u0026iacute;dricos da Bacia Hidrogr\u0026aacute;fica do Rio S\u0026atilde;o Francisco 2016\u0026ndash;2025: Compatibiliza\u0026ccedil;\u0026atilde;o do Balan\u0026ccedil;o H\u0026iacute;drico com os Cen\u0026aacute;rios Estudados da Bacia Hidrogr\u0026aacute;fica do Rio S\u0026atilde;o Francisco; Comit\u0026ecirc; da Bacia Hidrogr\u0026aacute;fica do rio S\u0026atilde;o Francisco: Belo Horizonte, Brazil, p. 102. https://cbhsaofrancisco.org.br.\u003c/li\u003e\n\u003cli\u003eCEMIG - Companhia Energ\u0026eacute;tica de Minas Gerais (2016) Relat\u0026oacute;rio T\u0026eacute;cnico: Atualiza\u0026ccedil;\u0026atilde;o das Curvas Cota x \u0026Aacute;rea x Volume da UHE Tr\u0026ecirc;s Marias. Rural Tech Com\u0026eacute;rcio e Servi\u0026ccedil;os Eireli. Dispon\u0026iacute;vel em: https://portal1.snirh.gov.br/arquivos/ONS/UHE_Tres_Marias/Relatorio_Batimetria.pdf. \u003c/li\u003e\n\u003cli\u003eCEMIG - Companhia Energ\u0026eacute;tica de Minas Gerais (2023) Usinas. Dispon\u0026iacute;vel em: www.cemig.com.br/usina/tres-marias. Acesso em 15 de janeiro de 2023.\u003c/li\u003e\n\u003cli\u003eChang J, Guo A, Wang Y, Ha Y, Zhang R, Xue L, Tu Z (2019) Reservoir operations to mitigate drought effects with a hedging policy triggered by the drought prevention limiting water level. Water Resources Research, 55(2), 904-922. https://doi.org/10.1029/2017WR022090.\u003c/li\u003e\n\u003cli\u003eChong K L, Lai S H, Ahmed A N, Jaafar W Z W, El-Shafie A (2021) Optimization of hydropower reservoir operation based on hedging policy using Jaya algorithm. Applied Soft Computing, 106, 107325. https://doi.org/10.1016/j.asoc.2021.107325.\u003c/li\u003e\n\u003cli\u003eCPRM - Servi\u0026ccedil;o Geol\u0026oacute;gico do Brasil. Plano estrat\u0026eacute;gico SGB/CPRM 2021-.2025. Bras\u0026iacute;lia: CPRM, 2025. Estudos Hidrol\u0026oacute;gicos e Hidrogeol\u0026oacute;gicos. Acesso em: 4 mai. 2023.\u003c/li\u003e\n\u003cli\u003eDessie, M, Verhoest N E, Pauwels V R, Adgo E, Deckers J, Poesen J, Nyssen J (2015) Water balance of a lake with floodplain buffering: Lake Tana, Blue Nile Basin, Ethiopia. Journal of Hydrology, 522, 174-186. https://doi.org/10.1016/j.jhydrol.2014.12.049.\u003c/li\u003e\n\u003cli\u003eEriyagama N, Smakhtin V, Udamulla L (2020) How much artificial surface storage is acceptable in a river basin and where should it be located: a review. Earth-Science Reviews, 208, 103294. https://doi.org/10.1016/j.earscirev.2020.103294.\u003c/li\u003e\n\u003cli\u003eEriyagama N, Smakhtin V, Udamulla L (2021) Sustainable surface water storage development pathways and acceptable limits for river basins. Water, 13(5), 645. https://doi.org/10.3390/w13050645.\u003c/li\u003e\n\u003cli\u003eFerrarin A D S F, Ferreira Filho J B D S, Cuadra S V, Victoria D D C (2020) Water demand prospects for irrigation in the S\u0026atilde;o Francisco River: Brazilian public policy. Water Policy, 22(3), 449-467. https://doi.org/10.2166/wp.2020.215.\u003c/li\u003e\n\u003cli\u003eFowe T, Karambiri H, Paturel J E, Poussin J C, Cecchi P (2015) Water balance of small reservoirs in the volta basin: a case study of Boura reservoir in Burkina Faso. Agric Water Manag 152:99\u003cstrong\u003e-\u003c/strong\u003e109. https:// doi. org/ 10. 1016/j. agwat. 2015. 01. 006.\u003c/li\u003e\n\u003cli\u003eGarcia M, Ridolfi E, Di Baldassarre G (2020) The interplay between reservoir storage and operating rules under evolving conditions. Journal of Hydrology, 590, 125270. https://doi.org/10.1016/j.jhydrol.2020.125270.\u003c/li\u003e\n\u003cli\u003eGarrote L, Granados A, Spiliotis M, \u0026amp; Martin-Carrasco F (2023) Effectiveness of adaptive operating rules for reservoirs. Water Resources Management, 37(open in a new window) (6\u0026ndash;7(open in a new window)), 2527\u0026ndash;2542. doi:10.1007/s11269\u003cstrong\u003e-\u003c/strong\u003e022\u003cstrong\u003e-\u003c/strong\u003e03386-9.\u003c/li\u003e\n\u003cli\u003eGrill G, Lehner B, Thieme M, Geenen B, Tickner D, Antonelli F, Babu S, Borrelli P, Cheng L, Crochetiere H, Ehalt Macedo H, Filgueiras R, Goichot M, Higgins J, Hogan Z, Lip B, McClain M E, Meng J, Mulligan M, Nilsson C, Olden J D, Opperman J J, Petry P, Reidy Liermann C, S\u0026aacute;enz L, Salinas-Rodr\u0026iacute;guez S, Schelle P, Schmitt R J P, Snider J, Tan F, Tockner K, Valdujo P H A, Van Soesbergen, Zarfl C (2019) Mapping the world\u0026rsquo;s free-flowing rivers. Nature, 984 215\u0026ndash;221. https://doi.org/10.1038/s41586-019-1111-9.\u003c/li\u003e\n\u003cli\u003eGupta H V, Kling H, Yilmaz K K, Martinez G F (2009) Decomposition of the mean squared error and NSE performance criteria: Implications for improving hy-drological modelling. Journal of hydrology 377(1\u003cstrong\u003e-\u003c/strong\u003e2):80-91. https://doi.org/10.1016/j.jhydrol.2009.08.003.\u003c/li\u003e\n\u003cli\u003eHabets F, Mol\u0026eacute;nat J, Carluer N, Douez O, Leenhardt D (2018) The cumulative impacts of small reservoirs on hydrology: A review. Science of the Total Environ-ment 643:850-867. Https://doi.org/10.1016/j.scitotenv.2018.06.188\u003c/li\u003e\n\u003cli\u003eHanasaki N, Yoshikawa S, Pokhrel Y, Kanae S (2018) A global hydrological simulation to specify the sources of water used by humans. Hydrology and Earth System Sciences, 22(1), 789\u003cstrong\u003e-\u003c/strong\u003e817. https://doi.org/10.5194/hess-22-789\u003cstrong\u003e-\u003c/strong\u003e2018, 2018.\u003c/li\u003e\n\u003cli\u003eHogeboom R J, Knook L, Hoekstra A Y (2018) The blue water footprint of the world\u0026apos;s artificial reservoirs for hydroelectricity, irrigation, residential and industrial water supply, flood protection, fishing and recreation. Advances in water resources, 113, 285\u003cstrong\u003e-\u003c/strong\u003e294. https://doi.org/10.1016/j.advwatres.2018.01.028. \u003c/li\u003e\n\u003cli\u003eIBGE - Instituto Brasileiro de Geografia e Estat\u0026iacute;stica. Censo (2022). Dispon\u0026iacute;vel em: www.ibge.gov.br/cidades-e-estados/mg/tres-marias. Acesso em: 10 de abril de 2023.\u003c/li\u003e\n\u003cli\u003eICOLD (International Commission on Large Dams) (2019) World Register of Dams. https://www.icold-cigb.org/GB/world_register/general_synthesis.asp.\u003c/li\u003e\n\u003cli\u003eIlich N (2024) Dynamic reservoir rule curves-Their creation and utilization. Journal of Hydrology X, 22, 100166. https://doi.org/10.1016/j.hydroa.2023.100166.\u003c/li\u003e\n\u003cli\u003eINMET - Instituto Nacional de Meteorologia (2023) Dados meteorol\u0026oacute;gicos. Dispon\u0026iacute;vel em: http://www.inmet.gov.br/portal. Acesso em 15 de abriu de 2023.\u003c/li\u003e\n\u003cli\u003eINMET - Instituto Nacional de Meteorologia (2024) Dados meteorol\u0026oacute;gicos. Dispon\u0026iacute;vel em: http://www.inmet.gov.br/portal. Acesso em 6 de mar\u0026ccedil;o de 2024.\u003c/li\u003e\n\u003cli\u003eJiang H, Simonovic S P, Yu Z, Wang W (2020) A system dynamics simulation approach for environmentally friendly operation of a reservoir system. Journal of Hydrology, 587, 124971. https://doi.org/10.1016/j.jhydrol.2020.124971. \u003c/li\u003e\n\u003cli\u003eJing P, Sheng J, HU T, Mahmoud A, Guo L, Liu Y, Wu Y (2022) Spatiotemporal evolution of sustainable utilization of water resources in the Yangtze River Economic Belt based on an integrated water ecological footprint model. Journal of Cleaner Production, 358, 132035. https://doi.org/10.1016/j.jclepro.2022.132035.\u003c/li\u003e\n\u003cli\u003eKim T W, Kim M J, Kim J G, Yoo J (2023) Development of Dynamic Drought Vulnerability Assessment Considering Global Climate Change and Regional Water Demand-Supply Networks. In EGU General Assembly Conference Abstracts (pp. EGU-3708). 10.5194/egusphere-egu23-3708.\u003c/li\u003e\n\u003cli\u003eKim Y G, Jo M B, Kim P, Oh S N, Paek C H, So S R (2021) Effective Optimization-Simulation Model for Flood Control of Cascade Barrage Network. Water Resources Management 35(1):135-157. https://doi.org/10.1007/s11269-020-02715-0.\u003c/li\u003e\n\u003cli\u003eLucas M C, Kublik N, Rodrigues D B B, Meira Neto A A, Almagro A, Melo D D C D, Zipper S C, Oliveira P T S (2021) Significant baseflow reduction in the Sao Francisco river basin. Water, 13, 2. https://doi.org/10.3390/w13010002.\u003c/li\u003e\n\u003cli\u003eLuo W, Zhang X, Tian X, Cheng Z, Wen B, Li X, Luo Y (2024) Conceptual design and model test of a pontoon-truss type offshore floating photovoltaic system with soft connection. Ocean Engineering, 309, 118518. https://doi.org/10.1016/j.oceaneng.2024.118518.\u003c/li\u003e\n\u003cli\u003eMararakanye N, Le Roux J J, Franke A C (2020) Using satellite-based weather data as input to SWAT in a data poor catchment. Phys Chem Earth Parts A/B/C 117:102871. https:// doi. org/ 10. 1016/j. pce. 2020.102871.\u003c/li\u003e\n\u003cli\u003eMirchi A, Madani K, Watkins D, Ahmad S (2012). Synthesis of system dynamics tools for holistic conceptualization of water resources problems. Water Resour. Manage.26, 2421\u0026ndash;2442. https://doi.org/10.1007/s11269-012-0024-2.\u003c/li\u003e\n\u003cli\u003eMostaghimzadeh E, Adib A, Ashrafi S M, Kisi O (2022) Investigation of a composite two-phase hedging rule policy for a multi reservoir system using streamflow forecast. Agricultural Water Management, 265, 107542. https://doi.org/10.1016/j.agwat.2022.107542.\u003c/li\u003e\n\u003cli\u003eMuzammil M, Zahid A, Farooq U, Saddique N, Breuer L (2023) Climate change adaptation strategies for sustainable water management in the Indus basin of Pakistan. Science of The Total Environment, v. 878, p. 163143. https://doi.org/10.1016/j.scitotenv.2023.163143.\u003c/li\u003e\n\u003cli\u003eNash J E, Sutcliffe J V (1970) River flow forecasting through conceptual models part I: A discussion of principles. J Hydrol 10(3):282\u0026ndash;290. https:// doi. org/ 10. 1016/ 0022-1694(70) 90255-6.\u003c/li\u003e\n\u003cli\u003eNevermann H, Aminzadeh M, Madani K, Shokri N (2024) Quantifying water evaporation from large reservoirs: Implications for water management in water-stressed regions. Environmental research, 262, 119860. https://doi.org/10.1016/j.envres.2024.119860.\u003c/li\u003e\n\u003cli\u003eNiccolai A, Grimaccia F, Di Lorenzo G, Araneo R, Ughi F, Polenghi M (2023) A review of floating PV systems with a techno-economic analysis. IEEE Journal of Photovoltaics.10.1109/JPHOTOV.2023.3319601.\u003c/li\u003e\n\u003cli\u003eOkkan U, Fistikoglu O, Ersoy Z B, Noori A T (2023) Investigating adaptive hedging policies for reservoir operation under climate change impacts. Journal of Hydrology, v. 619, p. 129286. https://doi.org/10.1016/j.jhydrol.2023.129286.\u003c/li\u003e\n\u003cli\u003eONS \u003cstrong\u003e-\u003c/strong\u003e Operador Nacional do Sistema El\u0026eacute;trico (2018) Invent\u0026aacute;rio das Restri\u0026ccedil;\u0026otilde;es Operativas Hidr\u0026aacute;ulicas dos Aproveitamentos Hidrel\u0026eacute;tricos. Operador Nacional do Sistema El\u0026eacute;trico, Rio de Janeiro: ONS, p.191. https://www.ons.org.br/.\u003c/li\u003e\n\u003cli\u003eONS - Operador Nacional do Sistema El\u0026eacute;trico (2021) Avalia\u0026ccedil;\u0026atilde;o das condi\u0026ccedil;\u0026otilde;es de atendimento eletroenerg\u0026eacute;tico do Sistema Interligado Nacional \u0026ndash; estudo prospectivo outubro de 2021 a abril de 2022 (Relat\u0026oacute;rio NT-ONS DGL 0136/2021, 84 p.). Operador Nacional do Sistema El\u0026eacute;trico, Rio de Janeiro: ONS, p.84. https://www.ons.org.br/.\u003c/li\u003e\n\u003cli\u003eParedes-Trejo F, Barbosa H A, Giovannettone J, Kumar T V L, Thakur M K, Buriti, C D O, Uzc\u0026aacute;tegui-Brice\u0026ntilde;o C (2021) Drought assessment in the S\u0026atilde;o Francisco river basin using satellite-based and ground-based indices. Remote Sens. 2021, 13, 3921. https://doi.org/10.3390/rs13193921.\u003c/li\u003e\n\u003cli\u003ePhan T D, Bertone E, Stewart R (2021) A Critical review of system dynamics modelling applications for water resources planning and management. Cleaner Environmental Systems, v. 2, p. 100031, https://doi.org/10.1016/j.cesys.2021.100031.\u003c/li\u003e\n\u003cli\u003ePorto R D M (2006) Hidr\u0026aacute;ulica b\u0026aacute;sica. rev. EESC-USP, S\u0026atilde;o Carlos-SP, p.44.\u003c/li\u003e\n\u003cli\u003eR Development Core Team. R (2018) A language and environment for statistical compu-ting\u0026rsquo;. Vienna: R Foundation for Statistical Computing.\u003c/li\u003e\n\u003cli\u003eRahmati O, Kalantari Z, Samadi M, Uuemaa E, Moghaddam D D, Nalivan O A, Bui D T (2019) GIS-based site selection for check dams in watersheds: considering geomorphometric and topo-hydrological factors. Sustainability, 11(20), 5639. https://doi.org/10.3390/su11205639.\u003c/li\u003e\n\u003cli\u003eRodrigues A L, Villa P M, Rodrigues L N (2021) Water balance estimate of beans using a dynamic systems model based on crop coefficient (Kc) variation. Revista Engenharia Na Agricultura, 29: 81\u003cstrong\u003e-\u003c/strong\u003e89. https://doi.org/10.13083/reveng.v29i1.9767.\u003c/li\u003e\n\u003cli\u003eRodrigues A L, Rodrigues L N, Marques G F, Vill P M (2023) Simulation model to assess the water dynamics in small reservoirs. Water Resources Management, 37(5), 2019-2038. https://doi.org/10.1007/s11269-023-03468\u003cstrong\u003e-\u003c/strong\u003e2.\u003c/li\u003e\n\u003cli\u003eSankarbalaji A R, Duraisekaran E, Sangeetha K, Modi K, Narasimhan B (2025) Assessment of increasing hydrologic model complexity in the representation of small and medium reservoirs within a river basin scale model and its impact on process simulation and parameter uncertainty. Journal of Hydrology, 655, 132925. https://doi.org/10.1016/j.jhydrol.2025.132925.\u003c/li\u003e\n\u003cli\u003eScherer L, Pfister S (2016) Global water footprint assessment of hydropower. Renewable Energy, 99, 711-720. https://doi.org/10.1016/j.renene.2016.07.021.\u003c/li\u003e\n\u003cli\u003eSimonovic S P, Arunkumar R (2016) Comparison of static and dynamic resilience for a multipurpose reservoir operation. Water Resour. Res. 52, 8630\u003cstrong\u003e-\u003c/strong\u003e8649. https://doi.org/10.1002/2016WR019551.\u003c/li\u003e\n\u003cli\u003eSj\u0026ouml;berg Y, Dessirier B, Ghajarnia N, Jaramillo F, Jarsj\u0026ouml; J, Panahi D M, Xu D, Zou L, Manzoni S (2022) Scaling relations reveal global and regional differences in morphometry of reservoirs and natural lakes. Science of The Total Environment, 822, 153510. https://doi.org/10.1016/j.scitotenv.2022.153510. \u003c/li\u003e\n\u003cli\u003eStojkovic M, Simonovic S P (2019) System dynamics approach for assessing the behaviour of the Lim Reservoir system (Serbia) under changing climate conditions. Water, 11(8), 1620. https://doi.org/10.3390/w11081620.\u003c/li\u003e\n\u003cli\u003eSun Y, Liu N, Shang J, Zhang J (2017) Sustainable utilization of water resources in China: A system dynamics model. Journal of cleaner production, 142, 613\u003cstrong\u003e-\u003c/strong\u003e625. https://doi.org/10.1016/j.jclepro.2016.07.110.\u003c/li\u003e\n\u003cli\u003eSunny M R, Kabir M A, Sarker M S Z, Aghaloo K, Ali T (2024) Feasibility study of floating solar photovoltaic systems using techno-economic assessment and multi-criteria decision-making method: A case study of Bangladesh. Energy, 133202. https://doi.org/10.1016/j.energy.2024.133202.\u003c/li\u003e\n\u003cli\u003eTran V N, Dinh D D, Pham B D H, Dang K D, Anh T N, Ngoc H N, Nguyen G T (2024) Data-Driven Dam Outflow Prediction Using Deep Learning with Simultaneous Selection of Input Predictors and Hyperparameters Using the Bayesian Optimization Algorithm. Water Resources Management, 38(2), 401\u003cstrong\u003e-\u003c/strong\u003e421. https://doi.org/10.1007/s11269-023-03677-9.\u003c/li\u003e\n\u003cli\u003eTurgut MS, Turgut O E, Afan H A, El-Shafie A (2019) A novel Master-Slave optimization algorithm for generating an optimal release policy in case of reservoir operation. Journal of Hydrology. 577, 123959. https://doi.org/10.1016/j.jhydrol.2019.123959.\u003c/li\u003e\n\u003cli\u003eVentana Systems (2024) Vensim User\u0026rsquo;s Guide Version 6. Harvard, MA, USA: VENTANA Systems Inc. https://vensim.com/.\u003c/li\u003e\n\u003cli\u003eVieira N P, Pereira S B, Martinez M A, Silva D D D, Silva F B (2016) Estimativa da evapora\u0026ccedil;\u0026atilde;o nos reservat\u0026oacute;rios de Sobradinho e Tr\u0026ecirc;s Marias usando diferentes modelos. Engenharia Agr\u0026iacute;cola, 36(3), 433-448. https://doi.org/10.1590/1809-4430-Eng.Agric.v36n3p433-448/2016.\u003c/li\u003e\n\u003cli\u003eWang W, Lee X, Xiao W, Liu S, Schultz N, Wang Y, Zhang M, Zhao L (2018) Global lake evaporation accelerated by changes in surface energy allocation in a warmer climate. Nat. Geosci. 11 (6), 410\u0026ndash;414. https://doi.org/10.1038/s41561-018-0114-8.\u003c/li\u003e\n\u003cli\u003eWang Y, Tian Y, Cao Y (2021) Dam siting: a review. Water, 13(15), 2080. https://doi.org/10.3390/w13152080.\u003c/li\u003e\n\u003cli\u003eWu G, Li L, Ahmad S, Chen X, Pan X (2013) A dynamic model for vulnerability assessment of regional water resources in arid areas: a case study of Bayingolin. China Water Resour Manag 27(8):3085\u0026ndash;3101. https://doi.org/10.1007/s11269-013-0334-z.\u003c/li\u003e\n\u003cli\u003eWu H, Cheng S, Li Z, Ke G, Liu H (2022) Study on Soil water infiltration process and model applicability of check dams. Water, 14(11), 1814. https://doi.org/10.3390/w14111814.\u003c/li\u003e\n\u003cli\u003eXu Y, Fu Q, Zhou Y (2019) Inventory Theory-Based Stochastic Optimization for Reservoir Water Allocation. Water Resour Manage 33:3873-3898. https://doi.org/10.1007/s11269-019-02332-6.\u003c/li\u003e\n\u003cli\u003eYou J Y, Cai X (2008) Hedging rule for reservoir operations: 1. A theoretical analysis. Water resources research,44(1). https://doi.org/10.1029/2006WR005481.\u003c/li\u003e\n\u003cli\u003eZarfl C, Lumsdon A E, Berlekamp J, Tydecks L, Tockner K (2015) A global boom in hydropower dam construction. Aquatic Sciences, 77, 161-170. https://doi.org/10.1007/s00027-014-0377-0.\u003c/li\u003e\n\u003cli\u003eZeng X T, Zhang S J, Feng J, Huang G H, Li Y P, Zhang P, Li K L (2017) A multi\u003cstrong\u003e-\u003c/strong\u003ereservoir-based water-hydroenergy management model for identifying the risk horizon of regional resources-energy policy under uncertainties. Energy Conversion and Management, 143, 66-84. https://doi.org/10.1016/j.enconman.2017.02.020.\u003c/li\u003e\n\u003cli\u003eZhang H, Gorelick S M, Zimba P V, Zhang (2017) A remote sensing method for estimating regional reservoir area and evaporative loss. Journal of Hydrology, 555, 213-227. https://doi.org/10.1016/j.jhydrol.2017.10.007.\u003c/li\u003e\n\u003cli\u003eZhao G, Gao H (2019) Estimating reservoir evaporation losses for the United States: Fusing remote sensing and modeling approaches. Remote Sensing of Environment, 226, 109-124. https://doi.org/10.1016/j.rse.2019.03.015.\u003c/li\u003e\n\u003cli\u003eZhao T, Zhao J, Lund J R, Yang, D (2014) Optimal hedging rules for reservoir flood operation from forecast uncertainties. Journal of Water Resources Planning and Management, 140(12), 04014041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432.\u003c/li\u003e\n\u003cli\u003eZhou T, Nijssen B, Gao H, Lettenmaier D P (2016) The contribution of reservoirs to global land surface water storage variations. Journal of Hydrometeorology, 17(1), 309-325. https://doi.org/10.1175/JHM-D-15-0002.1.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Large reservoirs, System Dynamics, Water resources, Hedging operation, Multiple water uses","lastPublishedDoi":"10.21203/rs.3.rs-7767474/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7767474/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLarge reservoirs play a crucial role in regulating global water availability, with a storage capacity equivalent to 2% of the world\u0026rsquo;s surface freshwater, while covering only 0.33% of the Earth\u0026rsquo;s land surface. These hydraulic infrastructures supply 42% of global irrigation and are vital for domestic, industrial, and energy production purposes. In Brazil, the water demand of large reservoirs in the S\u0026atilde;o Francisco River Basin is expected to increase substantially by 2050. This study aimed to evaluate the water dynamics of a large reservoir and its capacity to meet multiple uses over time. The study was conducted at the Tr\u0026ecirc;s Marias Hydropower Plant (HPP) reservoir, located in the S\u0026atilde;o Francisco River Basin, Brazil. For this purpose, a System Dynamics model was developed to quantify all inflows and outflows of the reservoir and simulate different operational scenarios, including the application of hedging strategies and the reduction of evaporation rates. Daily inflow and withdrawal data from January 2004 to June 2024 were used. The developed model was calibrated and validated using historical data on water level variations. Overall, the results highlight that the proposed System Dynamics model is a valuable tool to support strategic planning and decision-making in the management of large reservoirs. In the case of the Tr\u0026ecirc;s Marias HPP, the application of the model revealed the need for adaptive operational strategies capable of reconciling hydropower generation with increasing consumptive uses and the maintenance of environmental flows. This study contributes to strengthening the scientific and practical foundation for integrated water resources management through the implementation of more sustainable operational rules. Finally, it is emphasized that the combination of trigger and cut-off rules, associated with minor evaporation control, can improve the balance between energy generation and meeting multiple water uses.\u003c/p\u003e","manuscriptTitle":"System Dynamics Model for Assessing the Water Dynamics and the Capacity of Large Reservoirs to Supply Multiple Uses","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-20 08:38:43","doi":"10.21203/rs.3.rs-7767474/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revisions","date":"2025-10-22T10:59:51+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-10-07T15:27:30+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-07T12:29:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-04T04:17:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Water Resources Management","date":"2025-10-03T07:39:13+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"599a1c07-db41-490e-b1b4-df1395bbedf0","owner":[],"postedDate":"October 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-29T16:00:58+00:00","versionOfRecord":{"articleIdentity":"rs-7767474","link":"https://doi.org/10.1007/s11269-025-04347-8","journal":{"identity":"water-resources-management","isVorOnly":false,"title":"Water Resources Management"},"publishedOn":"2025-12-23 15:57:39","publishedOnDateReadable":"December 23rd, 2025"},"versionCreatedAt":"2025-10-20 08:38:43","video":"","vorDoi":"10.1007/s11269-025-04347-8","vorDoiUrl":"https://doi.org/10.1007/s11269-025-04347-8","workflowStages":[]},"version":"v1","identity":"rs-7767474","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7767474","identity":"rs-7767474","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}