Adaptive hedging rules for a data-scarce dryland reservoir: integrating simple drought index, water user participation, and short-term hydrological monitoring

Adaptive hedging rules for a data-scarce dryland reservoir: integrating simple drought index, water user participation, and short-term hydrological monitoring | 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 Adaptive hedging rules for a data-scarce dryland reservoir: integrating simple drought index, water user participation, and short-term hydrological monitoring Arthur Jordan de Azevedo Toné, Daniel Antônio Camelo Cid, Alexandre Cunha Costa, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8725090/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract A numerical hedging model for a dryland reservoir, featuring an early rationing system based on the identification of drought events, is presented. Key advantages include the optimization of decision variables (trigger volumes and rationing coefficients) using a genetic algorithm (NSGA-II), integration of water user participation, water allocation connected with drought assessments through a simple drought index, streamflow prediction based on river-aquifer dynamics, and the use of short-term field-measured hydrological data. The results show that the proposed hedging rule maintained system vulnerability below 10% using both simulated and measured inflow data, and the objective function (the modified shortage index) was successfully optimized even when early rationing occurred during the rainy season. The quantitative analysis suggests that for adaptive hedging in data-scarce drylands, the calculation method (the rule itself) is more critical than the availability of onsite inflow measurements. Therefore, operating rules for a dryland reservoir optimized using simulated data may be effective in satisfying water demands and stakeholder requirements, even when integrated with a simple drought index and in the presence of data uncertainties. Reservoir operation hedging rules early rationing system water allocation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Recent climate changes in dryland regions have shown higher warming rates and declining precipitation, extending the duration of dry periods (Daramola and Xu 2022 ). The rapid negative impacts of meteorological droughts on subsurface and surface water supplies in drylands shorten early warning times, highlighting the need for adaptive management to reduce the effects of climate variability on water scarcity in the region (Ahana et al. 2025 ). An effective drought management framework requires risk reduction strategies and tools. Two common strategies for long- and short-term water vulnerability mitigation are the construction of reservoirs and the implementation of demand restrictions through the regulation of river and groundwater exploitation (Cid et al. 2023 ; Akram 2025 ). Drought indices serve as decision support tools, and there is extensive literature on their use in drought monitoring and triggering mitigation measures based on onsite conditions. While the utility of any single index can be limited depending on the type of drought being analyzed, their primary advantages are the straightforward interpretation of their values and their role in drought contingency planning (Zargar et al. 2011 a, Zaniolo et al. 2018 , Gonçalves et al. 2023 ). As reservoirs are typically the only water source available in drylands (Lopes and Freitas 2007 ), effective reservoir operation during periods of drought can mitigate the imbalance between planned demand and water availability through reasonable allocation. Known as hedging, this policy is driven by the idea of accepting minor present shortages to prevent critical future shortages and is implemented through rationing factors and rule curves (Tu Ming-Yen et al. 2008; Luo et al. 2023 ). Numerical approaches have been used to define optimal hedging rules, as the decision to ration water must account for the complexity of water allocation in data-scarce regions. Optimization models proposed in the literature for drylands seek to identify optimal solutions by optimizing an objective function that either diminishes the maximum extent of a single-period deficit in the system or enhances the economic benefits. These solutions are normally hedging triggers or indicators of when and by how much to hedge. They are selected by comparing and ranking the system performance (i.e., reducing failures in satisfying demand) against the metrics of vulnerability, reliability, and resilience (Shih and ReVelle 1995 ; Neelakantan and Sasireka 2015 ; Ashrafi and Dariane 2017 ; Hong et al. 2022 ). In this context, Cid et al. ( 2023 ) proposed a collaborative model that optimizes hedging rules to meet the rationing frequencies defined by water allocation agents. The numerical approach is based on the discrete hedging rule for a monthly reservoir proposed by Shih and ReVelle ( 1995 ) and does not assess monthly drought conditions using a drought index. Tributary flow series were obtained using a soil moisture accounting procedure that was adjusted via regionalization. This approach relies on the implicit assumption that catchments with similar characteristics exhibit similar hydrological behaviors. However, this assumption can be problematic because these catchments, although similar, are not identical (Guo et al. 2021 ). Chang et al. ( 2019 ) developed a numerical framework to determine the minimal reservoir water level required to satisfy water users during different drought events. This hedging trigger is useful for drought mitigation because future operating policies can be made suitable for specific emergence conditions. The model requires long-term meteorological and hydrological information for its applicability, particularly for inflow and drought assessments, as it integrates three drought indices (the streamflow drought index (SDI), standardized precipitation index (SPI), and relative moisture index (RMI)). This extensive data requirement can limit its use in data-scarce drylands (Kumar et al. 2024 ). Similar to the framework of Cid et al. ( 2023 ), in which water users define temporal allocation values based on reservoir storage conditions, the model also depends on previous optimal operation decisions to define the hedging policy. Beshavard et al. ( 2022 ), on the other hand, proposed a numerical hedging model that calculates rationing ratios and rule curves linked to a warning storage based on a drought index (SDI). The model advances the state of the art by allowing earlier rationing responses to identified drought periods, and its application is simple in data-scarce areas. Notwithstanding, hedging policies are not only numerical issues, and they are more likely to be effective when the numerical model is united with a collaborative approach, where rationing ratios and acceptable risks are built together with water users (Sandoval-Solis et al. 2013 ). Numerous studies have employed multi-objective genetic algorithms, specifically the NSGA-II, to propose optimal operation rules. Ahmadianfar et al. ( 2017 ) utilized this method to define a hedging rule capable of gradually changing the rationing factors across operation zones in a dryland reservoir in southern Iran. In the Brazilian semi-arid region, Gomes et al. ( 2022 ) applied NSGA-II to design an operation rule that balances the stakeholder water supply with acceptable water quality standards. In another study, Karnatapu et al. ( 2020 ) derived optimal rules for a generic dryland reservoir in India, addressing both water supply and hydropower generation, and found better performance metrics with the proposed rules than with the standard operating policy. Based on these results, the authors suggested that NSGA-II is suitable for optimizing the operation rules in any reservoir with limited water availability. Nevertheless, few studies have proposed an adaptive operational policy for a multi-use dryland reservoir that can deal with the rapid impacts of climate change on streamflow (Mujere et al. 2022 ; Coulibaly et al. 2025 ). Furthermore, existing operation policies rarely integrate water user participation, short-term field-measured hydrological monitoring, and early rationing based on a simple drought index simultaneously. Moreover, few approaches have proposed a hedging rule based on a water balance that considers river-aquifer dynamics, an important feature of dryland hydrology, coupled with a multi-objective genetic algorithm (NSGA-II) to find optimal decision variables. Thus, the objectives of this study are as follows: (1) to develop a hedging rule for a data-scarce dryland reservoir that seeks to balance the complexity of water allocation, drought assessment, and dryland hydrological processes while maintaining operational simplicity; (2) to evaluate the performance of the proposed hedging rules using simulated and measured inflow data; and (3) to provide insight into the requirements for the development of hedging rules in dryland reservoirs. 2. Methods 2.1. Study site The study site is a multi-use reservoir in the Middle Jaguaribe sub-basin in the Brazilian semiarid region (Fig. 1 ). The Castanhão Reservoir has a surface area of 325 km 2 and a storage capacity of 6.7 billion m 3 , with depths exceeding 60 m in certain areas (Arantes et al. 2025 ; Lima Neto 2025 ). The catchment area is 45,309 km 2 , and the rainfall regime is concentrated from January to May and only for a few days, ranging from 500 to 900 mm/year. During the dry season, potential evaporation rates throughout the year may exceed rainfall values by up to four times. These meteorological conditions, combined with shallow soils over crystalline geological formations, have resulted in extensive dry periods with minimal baseflow and streamflow within a few months (De Araújo and Medeiros 2013 ; Raulino et al. 2021 ). The Castanhão Reservoir experiences high variability in storage and inflow. For instance, following occasional floods in 2008, it reached 96% of its total storage capacity. However, during the subsequent severe drought (2012–2018), its volume plummeted to just 2%, significantly increasing water treatment costs. In recent years, the reservoir has recovered to more than 30% of its capacity (Lima Neto 2025 ). No significant inflow, on the other hand, is observed during the dry season, such that reservoir management policies to satisfy human supply and other demands are defined during the rainy season (Molisani et al. 2010 ). 2.2. Dataset For the study site, monthly rainfall data were obtained from the National Hydrometeorological Network of the National Water and Sanitation Agency (ANA), and evaporation data were sourced from a regional study by ANA ( 2016 ) on dryland reservoirs in Brazil. This study also provides the total demand used in the operation model (D = 18.85 m 3 /s). The elevation-area-volume curve of the Castanhão Reservoir was obtained from the Ceará Hydrological Portal of the Ceará Foundation of Meteorology and Water Resources (FUNCEME). Recognizing that improved inflow data can enhance hedging rules (Neelakantan and Sasireka 2015 ), we conducted field measurements to obtain these data. In the first half of 2021, the inflow at the entrance of the Castanhão Reservoir was measured using a SonTek RiverSurveyor M9 ADCP. Because of technical difficulties at this site, we could not perform daily measurements. Therefore, in 2022, monitoring was relocated to a gauge approximately 21 km upstream of the Jaguaribe River. At this new location, the ANA provided daily inflow and river stage data, which were used to forecast the inflow at the Castanhão Reservoir entrance. The daily flow volume was defined as the total 24-hour discharge derived from the ANA records. We also used monthly inflow data generated for the study site using a soil moisture accounting procedure (SMAP) and later adjusted via regionalization by the Federal University of Ceará (UFC) and COGERH (2013) to propose the hedging policies. This inflow series data spans the period from January 1912 to December 2012. We estimated the streamflow into the study site during the first semester of 2022 using the river routing equation proposed by Toné et al. ( 2025 ) for dryland and data-scarce catchments. This numerical model requires few parameters and estimates river-aquifer dynamics, such as aquifer recharge and hyporheic flow. The outflow from a river reach is calculated as follows: $$\:{\text{O}}_{\text{t}+\varDelta\:\text{t}}=\frac{1}{1-\text{X}}(\frac{{\text{V}}_{\text{t}}}{\text{K}}{)}^{\frac{1}{{\gamma\:}\text{m}}}-\frac{\text{X}\bullet\:{\text{Q}}_{\text{t}}+{\pi\:}+{\mu\:}+{\Omega\:}+{\delta\:}}{1-\text{X}}$$ 1 Where O t+Δt is the outflow (m³/s), V t is the volume (m³), X is a weighting factor, K is the storage constant (s), and γ and m are calibrated exponents. According to Toné et al. ( 2025 ), for the 21 km river reach between the Jaguaribe gauge and the study site, exponent m is set to 1.6. Exponent γ is set to 0.9 when the river stage is equal to or below the mean river head at the measurement location, and 0.5 when it is higher. Additionally, the model accounts for direct in-river flux (π), sub-catchment runoff (µ), and river-aquifer interaction (Ω), with all terms expressed in m³/s. A detailed description of the steps required to calculate each term in Eq. 1 are provided in Toné et al. ( 2025 ). In addition to the previously described data, Eq. 1 requires the determination of geometric, sub-catchment, and hydrogeological parameters. The geometric parameters were derived as follows: the channel length, river slope, and sub-catchment area were obtained from the Copernicus GLO-30 digital elevation model (DEM) using the QGIS raster analysis tool. The other parameters (perimeter, area, hydraulic radius, and top width) were derived from river stage measurements, assuming a triangular cross-section of the river. We assumed a constant top width because no flow beyond the main channel was considered in this study. The sub-catchment curve number (assuming type 2 soil moisture) was provided by ANA ( 2018 ). The hydrogeological parameters were obtained separately. The aquifer width and hydraulic conductivity of the alluvium were obtained from surveys conducted by the Brazilian Geological Service (CPRM) (2014, 2015). The hydraulic conductivity of the riverbed was calculated using Hazen's method, which was applied to the riverbed grain size data from Wiegand ( 2009 ) for the Jaguaribe River. 2.3. Drought index This study used the SPI, which is commonly adopted in operational models in drylands. The SPI is calculated by dividing the difference between precipitation and its long-term mean by the standard deviation (Faye 2022 ). The criteria for identifying drought events are SPI values that are continuously negative and equal to or below − 1.0 for any time scale (McKee et al. 1993 ). A major advantage of the index is that it relies only on precipitation data and can be calculated for different timescales, allowing for adaptable drought analysis and hydrological monitoring (Zargar et al. 2011 ). To implement adaptive reservoir operations on short time scales, it is necessary to address the rapid and significant impact of climate change on streamflow in drylands (Swain et al. 2020 ; Saedi et al. 2022 ; Werede et al. 2024 ). Since intermittent streamflow patterns are best characterized by SPI values at the 2–6-month scale (Mishra and Desai 2005 ), this study calculated the SPI on a 3-month time scale (SPI3) using historical precipitation records from the study site, as described in the Dataset section. Although evaporation driven by higher temperatures plays an important role in trends toward drier conditions, suggesting the utility of drought indices that consider potential evapotranspiration, such as the Standardized Precipitation Evapotranspiration Index (SPEI), the SPI3 and SPEI3 showed significant agreement at the study site based on historical data from 1980 to 2019 (Tomasella et al. 2023 ). However, De Araújo Júnior et al. 2020 observed that the SPI failed to capture reservoir storage fluctuations in another reservoir in the Brazilian semiarid region because of the time lag between precipitation and water volume variations. Nevertheless, other studies have suggested its utility in this region. Recently, Gonçalves et al. ( 2023 ) evaluated several drought indices for the Castanhão Reservoir based on six criteria: treatability, robustness, transparency, sophistication, dimensionality, and extensibility. Their findings indicated that the SPI outperformed other indices by identifying more drought events. Given the rapid impact of meteorological droughts on surface water in drylands (Ahana et al. 2025 ), we selected the SPI to identify these events. The rationale is to start rationing earlier, owing to the application of a drought index, than conventional operation rules that rely solely on the actual reservoir storage. The SPI classification adapted to the study site is presented in Table 1 . Table 1 SPI classification for water management at the study site (Santos 2020 ; Gonçalves et al. 2023 ). SPI values Classification ≥ 2.00 Extreme rainfall 1.49 to 1.99 Severe rainfall 0.99 to 1.49 Moderate rainfall 0.49 to 0.99 Weak rainfall -0.49 to 0.49 Almost normal -0.99 to -0.49 Mild drought -1.49 to -1.00 Moderate drought -1.99 to -1.50 Severe drought ≤ -2.00 Extreme drought 2.4. Operation rules The operating rules are defined based on the reservoir storage and rationing ratios established by the water allocation agents. These ratios were established through a stakeholder consultation process conducted by Cid et al. ( 2023 ), wherein participants defined the values for the Castanhão Reservoir corresponding to various drought scenarios. The resulting consensus values are listed in Table 2 . In this study, each drought condition will be assessed using SPI values (Table 1 ). One of the conditions to be optimized is that the operation rules must meet the consensus rationing ratios for each drought state (Table 2 ); otherwise, there will be a failure in the system performance. Table 2 Stakeholder consensus on rationing ratios at the study site under different drought conditions. Drought state Castanhão Almost normal Mild drought Moderate drought Severe drought Extreme drought SPI3 > -0.49 -0.99 to -0.49 -1.49 to -1.00 -1.99 to -1.50 ≤ -2.00 Rationing ratios 0.00 0.05 0.15 0.50 0.95 Reservoir storage is divided into three zones defined by monthly upper (S1) and lower (S2) trigger volumes. Typically, these thresholds determine the water allocation ratio based on the storage and inflow at the beginning of each operational period. To address the impacts of climate change in drylands, we adopted a monthly dynamic warning storage (WS t ) proposed by Beshavard et al. ( 2022 ). In this study, this parameter integrates the 3-month SPI to enable earlier rationing measures. Specifically, this mechanism ensures that rationing is triggered if the SPI3 indicates a drought condition, even when the observed reservoir storage (S t ) remains high. WS t = S t • (1 + α 3 • SPI3) (2) In other words, when the SPI3 is positive, the warning storage remains equal to the current monthly storage. However, when SPI3 is negative, the warning storage is effectively reduced by a factor derived from the product of the SPI3 value and an optimized monthly coefficient α 3 ranging from 0 to 1 (see next section). Consequently, even if the actual reservoir storage is near or above the upper S1 trigger, the reduced warning storage forces early rationing to mitigate the impact of future droughts on the water supply. In this study, we compare two water allocation rules. For both, the total demand considered encompasses priority demands (human and livestock consumption) and non-priority demands (irrigation). This total demand is adjusted using stakeholder ratios depending on the drought conditions identified by SPI3 values (D’= Table 2 factors • D). Rule 1 is a standard three-zone policy. If the WS (Eq. 2) and inflow are above the upper trigger (S1), no rationing is applied to the demand. If it is between the S1 and S2 triggers, the demand is rationed using a fixed coefficient, α 1 . If it is below the lower trigger (S2), demand is rationed by a fixed coefficient α 2 (Eq. 3–5), as follows: If S 1 ≤ WS t + Q t then R t = D’ (3) If S 2 ≤ WS t + Q t < S 1 then R t = α 1 • D’ (4) If WS t + Q t < S 2 then R t = α 2 • D’ (5) Rule 2 is similar to Rule 1 and was adapted from Cid et al. ( 2023 ) to consider WS (Eq. 2). It also releases D’ when the warning storage (Eq. 1 ) and inflow exceed S1 (Eq. 6). However, in the other two zones, both rationing coefficients (α 1 and α 2 ) can be used to calculate water allocation, and coefficient β is considered to reduce R t when the SPI3 value is above − 0.49 (from “almost normal” to “extreme rainfall” conditions) (Eq. 7). If S 1 ≤ WS t + Q t then R t = D’ (6) If S 1 > WS t + Q t then R t = min(D’; D • (1 + β) • (1 – y 1,t • α 1 – y 2,t • (α 2 - α 1 ))) (7) Where Q t is the monthly inflow (m³), R t is the monthly water release (m³), and β is a monthly coefficient, respectively. The variable y 1,t is a binary indicator equal to 1 if the warning storage (WS t ) is below trigger S1 during month t, and 0 otherwise; similarly, y 2,t is equal to 1 if WS t is below trigger S2, and 0 otherwise. To propose an operating curve that divides the reservoir storage into three zones, we used a multiobjective genetic algorithm, NSGA-II, to calculate the decision variables (Deb et al. 2002 ) (see next section). This tool was selected based on its demonstrated effectiveness in estimating optimal monthly operational rules in previous studies (Chang et al. 2005 ; Aboutalebi Mahyar et al. 2015; Gomes et al. 2022 ). These variables were calculated using an inflow dataset that included the historical period from the start of the Castanhão Reservoir’s operation until 2012 (SMAP-estimated) and inflow data from the rainy seasons in the first halves of 2021 and 2022 (see Dataset section). The genetic algorithm estimated two sets of optimized decision values: the first, considering Equations 3–5 for monthly water release (R1), and the second, considering Equations 6–7 for monthly water release (R2). The necessary restrictions for the operation rules are as follows: for reservoir storage, the condition is Smin ≤ S2 < S1 ≤ Smax, where Smax is the maximum storage volume of the Castanhão reservoir (6700 hm³) and Smin is the minimum volume required to meet priority demand (58.1 hm³) (ANA 2016 ); for the rationing coefficients, the constraints are 0 < α 2 < α 1 < 1 and 0 < β < 1. An additional constraint is introduced to prevent the S1 and S2 trigger values from being too close, which is necessary for effective rule operation. This constraint is defined as S1 ≥ (1 + γ) ⋅ S2, with the coefficient γ restricted to the range [0.3, 1.0]. 2.5. Operation simulation To determine the reservoir storage (S t ) at the end of each monthly time step (t), we applied the following water balance equation: S t+1 = S t – E t + Q t – Spill t – Inf t – R t (8) The variables E t , Inf t , and Spill t represent the monthly evaporation, monthly infiltration, and spill volumes (m³), respectively. The spill volume is determined as follows: if the storage at the end of the month, S t+1 , is greater than the maximum capacity, Smax, then the spill is the excess volume (Spill t = S t+1 − Smax). Otherwise, Spill t = 0. Monthly infiltration was considered zero in the study site. With the rationing ratios already established in consultation with water agents ("how much to hedge"), the focus now shifts to optimizing the operating rules. This optimization must provide simple rules for operators to implement, but these rules must also be robust enough to handle the impacts of climate change on water supply deficits (Neelakantan and Sasireka 2015 ; Şen 2021 ; Raulino et al. 2022 ). The first goal, robustness against climate change, is achieved using storage triggers and warning storage linked to the SPI3 drought index, as described previously. This mechanism determines "when to hedge" to conserve water and reduce socioeconomic impacts. The second goal, simplicity, is intended to facilitate the development and execution of drought preparedness plans. Therefore, to optimize the operating rules, we aimed to minimize the total water supply deficit. This was achieved by minimizing the modified shortage index (MSI) (Eq. 9 ), proposed by Hsu and Cheng ( 2002 ) for a region experiencing extreme hydrological variability. For this optimization, we employed NSGA-II to determine the optimal values for 39 decision variables, encoded as a single chromosome string. These variables were the 24 monthly reservoir triggers (S1 and S2), 12 monthly α 3 coefficients for the warning storage calculation, and three rationing coefficients (α 1 , α 2 , and β). NSGA-II generates a random population of size N. Following the selection, crossover, and mutation processes, the algorithm categorizes different individuals according to their level of non-domination within the population. The operation is repeated until a defined stopping criterion is met. To minimize the computational time required for simulation, we set this criterion to 100 generations. Although this implies that the calculated decision variables may not guarantee the global optimum, they provide satisfactory solutions that meet the objectives and restrictions defined in this study. In each generation, the objective function for each individual was calculated, and the decision variables were evaluated against the restrictions and performance metrics (see the next section). This iterative process continued until the final generation, which determined the optimal values for the decision variables. $$\:\text{O}\text{B}\text{J}=\text{M}\text{S}\text{I}=\frac{100}{\text{n}}\bullet\:\sum\:_{\text{t}=1}^{\text{n}}{\left(\frac{{\text{T}\text{S}}_{\text{t}}}{{\text{T}\text{D}}_{\text{t}}}\right)}^{2}$$ 9 Where n is the total number of simulated months, TS t is the shortage during month t (the difference between D’ and monthly water release), and TD t is the D’ demand during month t. 2.6. Evaluation of operation rules We evaluated the effectiveness of the hedging rules using the following performance measures: time-based reliability, volumetric reliability, resilience, and vulnerability. These indicators are described in detail by McMahon et al. ( 2006 ) and are presented as follows. 1. Time-based reliability (REL t ): For a monthly simulation, it is the number of months in which the total demand is fully satisfied (N s ) divided by the total amount of months (n). The REL t value is restricted to the range |0.0,1.0]. $$\:{\text{R}\text{E}\text{L}}_{\text{t}}=\frac{{\text{N}}_{\text{s}}}{\text{n}}$$ 10 2. Volumetric reliability (REL v ): Similarly, this is the volume of water transferred to meet demand, divided by the amount of volume of water demanded over the simulation period. The REL v value is also restricted to the range |0.0,1.0]. $$\:{\text{R}\text{E}\text{L}}_{\text{v}}=1-\frac{{\sum\:}_{\text{i}=1}^{\text{n}}\left({\text{T}\text{S}}_{\text{i}}\right)}{\sum\:_{\text{i}=1}^{\text{n}}{\text{D}}_{\text{i}}}$$ 11 3. Resilience (RES): This indicates the speed at which a reservoir system recovers from a failure state. It is calculated as the number of consecutive failure events (f s ) divided by the total number of months in which the system was in a state of failure (f d ). The RES value is restricted to the range [0.0,1.0]. $$\:\text{R}\text{E}\text{S}=\frac{{\text{f}}_{\text{s}}}{{\text{f}}_{\text{d}}}$$ 12 4. Vulnerability (VUL): It is an indicator of the severity of failure in volumetric terms during its occurrence. The VUL value is also restricted to the range |0.0,1.0]. $$\:\text{V}\text{U}\text{L}=\frac{\sum\:_{\text{i}=1}^{{\text{f}}_{\text{d}}}\frac{{\text{T}\text{S}}_{\text{i}}}{{\text{D}}_{\text{i}}}}{{\text{f}}_{\text{d}}}$$ 13 The genetic algorithm was constrained to find solutions (decision variables) that satisfy the following performance criteria: REL t,v ≥ 0.95 and VUL ≤ 0.1, as the RES value requires careful interpretation. Figure 2 illustrates the methodological flowchart of this study, which is valid for each water allocation rule. 3. Results The SPI3 values required to calculate the warning storage were compiled for the 228-month period from the start of the Castanhão Reservoir’s operation (January 2004) to the measurements at the Jaguaribe River gauge (2022) (Fig. 3 ). In this timeframe, while annual rainfall varied widely (366.2 to 2438.1 mm), SPI3 values were predominantly negative (67% of the time), with 47% of values falling below − 0.5 (mild to extreme drought). This was most evident during the 2012–2016 drought, the region's most severe in the last century, when reservoir storage experienced declines of up to 80% (FUNCEME 2026), and 68% of SPI3 values were below − 0.5. Critically, the SPI3 values in our study period showed a significant decreasing trend (P-value < 0.009) compared to the two earlier periods (1985–2003 and 1966–1984), which is consistent with the global trend of increasing drought frequency in drylands (Hazbavi et al. 2018 ; Satoh et al. 2022 ). Regarding streamflow, the maximum observed value in 2021 was 31.81 m³/s at the entrance of the Castanhão reservoir and 483.19 m³/s at the Jaguaribe gauge in 2022. The inflow values estimated with SMAP (2004–2012) varied from 0 to 475 m³/s, whereas those from Eq. 1 (2022) varied from 0 to 561.77 m³/s. These four series are shown in Fig. 4 , and their values are similar to those observed in previous studies on the Jaguaribe River (Costa et al. 2012 ). Figure 4 b indicates greater peak flows at the end of the 21 km river reach compared with the observed streamflow at its beginning. This suggests that groundwater fluxes (such as hyporheic flow) and sub-catchment runoff contribute to the water balance of the Castanhão Reservoir. Table 3 shows the optimized α 3 values for decision variable sets 1 and 2, respectively. This coefficient is used to calculate the warning storage, which determines the monthly water release. Table 3 Optimized α 3 values for warning storage estimation in each set of decision variables. Months Sets Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 0.20 0.66 0.53 0.84 0.31 0.99 0.32 0.52 0.52 0.91 0.95 0.45 2 0.29 0.36 0.45 0.35 0.29 0.30 0.56 0.02 0.31 0.42 0.23 0.32 Throughout the simulation, the monthly warning storage was calculated using α 3 , SPI3, and S t (Eq. 8) and then compared against the optimized triggers S1 and S2. This SPI3-based mechanism enabled early rationing to mitigate the impacts of future droughts. This effect is visualized in Fig. 5 , which plots the mean monthly WS against the S1 and S2 triggers for the 2004–2012 SMAP inflow period. Figures 5 a-b illustrate WS values falling below the S1 trigger, even during the rainy season. The water rationing coefficients derived from the optimization were α 1 = 0.96 and α 2 = 0.61 for set 1, and α 1 = 0.13, α 2 = 0.12, and β = 0.14 for set 2, respectively. Four performance parameters (REL t , REL v , RES, and VUL) were used to evaluate the drought-informed operating rules (set 1 and set 2) for the reservoir. Using the SMAP inflow data, the simulation indicated satisfactory performance for both rules, which was attributed to the water transfer volumes (R1 and R2) based on the optimized S1/S2 triggers and monthly WS variation. Specifically, set 1 experienced four months of failure, yielding REL t = 0.96, REL v = 0.99, RES = 0, and VUL = 0.10; set 2 performed with only one failure, resulting in REL t = 0.98, REL v = 0.99, RES = 0, and VUL = 0.08. In the first set, the objective function (Eq. 9 ) was 0.096; for the second set, it was 0.008. Figure 6 compares the water releases from R1 and R2 with the total demand, alongside the resulting variation in the storage volume for each set. The monthly variations in water demand (also shown in the figure) result from the application of the stakeholder rationing ratios (Table 2 ), which are selected based on the SPI3 value for each month (D’). There was no significant variation between the storage volumes in either set, as these values were significantly greater than the water release. When applied to the measured inflow data, the operating rules produced performance metrics that differed significantly based on the water transfer equation (R1 and R2) and drought index. The SPI3 values between March and June of 2021 were consistently negative (-1.08, -0.58, -0.54, and − 0.36, respectively), corresponding to moderate to mild drought (Table 1 ), whereas they were positive in almost all the first half of 2022 and negative only in April (-0.20). In 2021 (Fig. 7 a-b), the continuous drought pushed the warning storage below the S2 trigger, which significantly reduced the R1 value, whereas the R2 transfer was able to maintain itself above the required demand in March and June (Fig. 8 a). Consequently, R1 experienced system failures in all months except April, even when the rationing ratios were applied to the total demand, whereas R2 experienced two failures. This exception was possible because the warning storage was slightly higher than the S2 trigger. The performance metrics for set 1 were REL t = 0.25, REL v = 0.74, RES = 0.67, and VUL = 0.35. Set 2 yielded REL t = 0.50, REL v = 0.96, RES = 0.5, and VUL = 0.08. The objective function was 9.109 for set 1 and 0.310 for set 2. In 2022, the consistently positive SPI3 values maintained a constant monthly demand throughout the first half of the year (Fig. 8 b). These precipitation conditions kept the warning storage above the S2 trigger during the simulation, except in January for R1 and February for R2 (Fig. 7 c-d). The system operation with set 1 decision variables (R1) failed during the entire simulation period, even though R1 values were close to the demand required, whereas there was no failure with set 2 parameters (R2). This condition improved the performance metrics for set 2 compared to those in 2021. For set 2, REL t = 1.0 and REL v = 1.0, and it was not possible to calculate RES and VUL. For set 1, failure in all months dropped REL t to zero; the other metrics were REL v = 0.90, RES = 0.83, and VUL = 0.10. The objective function was 2.684 for set 1 and 0.002 for set 2. 4. Discussion The performance metrics of the reservoir operation demonstrated the effectiveness of the proposed hedging rules from the start of the Castanhão operation to 2012. They successfully satisfied the water demand while adhering to the stakeholders' rationing ratio requirements (Table 2 ). This effectiveness was achieved despite the model simplicity and the prevalence of drought conditions (Fig. 3 ), which ranged from mild to extreme during most of the study period (Table 1 ). Nevertheless, the hedging policies obtained have certain limitations. First, they were defined using estimated inflow data, which were adjusted via regionalization. Second, water balance calculations (Eq. 8) suffer from uncertainties due to data scarcity and technical difficulties with on-site measurements, although we did not observe any significant errors. During the entire simulation period, both water transfer proposals, using their respective optimized decision variables, satisfied the priority demand (human and livestock consumption) (Fig. 6 ). Decreasing the total demand (which encompasses agricultural uses) at the study site will not impose failures in the proposed hedging rules. Thus, the recent decision from COGERH and water users to allocate 17 m³/s from the Castanhão reservoir during the second half of 2025 would not be seen as a risk for the proposed rules (COGERH 2025 ), as they would inherently protect this supply. The analysis of set 1 revealed a paradoxical behavior. Warning storage remained below the S1 trigger for almost the entire rainy season (Fig. 5 ), which is a conservative stance that may improve assurance during severe droughts (Gomes et al. 2022 ). Despite this, in 45% of the simulations (SMAP inflow), the R1 transfers were greater than the stakeholder-adjusted total demand (D’), indicating an inefficiency. Therefore, the rules (Equations 4–5) require adjustments. They must be modified to enforce the maximum water transfer at the adjusted demand to prevent over-delivery, similar to Eq. 7. In contrast, the decision variables for set 2 produced a warning storage that was consistently higher than that of set 1, remaining above the S1 and S2 triggers for most of the simulations (Fig. 5 ). This can be explained by two factors: first, for SPI3 values above − 0.49, R2 transfers are constrained to the minimum of D' and the total demand multiplied by a reduction factor (Fig. 6 ). This resulted in smaller monthly water releases, thus conserving reservoir storage and increasing WS. Furthermore, the α 3 values for set 2 were consistently lower than those for set 1 (Table 3 ). Because α 3 is applied when SPI3 is negative, a lower α 3 value reduces the drought penalty. This resulted in an increase in the (1 + α 3 • SPI3) factor, leading to a higher WS estimation. In contrast, when evaluated using the on-site (measured) inflow data, the proposed hedging rules failed to satisfy water demand under one set of decision variables during the simulated months in 2021 and 2022. A key limitation is that the SMAP inflow data presupposes hydrological similarities between catchments (Gui et al. 2019 ). This assumption is problematic because similarity does not ensure identical behavior, potentially leading to overestimated inflows. This may be evident in 2021, where Fig. 4 a shows that the measured inflows were significantly lower than the SMAP estimated inflows (Fig. 4 c). This overestimation by SMAP likely explains why the WS values in 2021 were so low (often below the S2 trigger) (Fig. 7 a-b). In 2022, however, the measured inflow and inflow estimated by Eq. 1 were in strong agreement (Fig. 4 b) and were similar to the SMAP values (Fig. 4 c). This improved alignment in 2022 may be attributed to favorable hydrological conditions (consistently positive SPI3 values) during that period, which contributed to higher WS values (above the S2 trigger) (Fig. 7 c-d) (Hazbavi et al. 2018 ). In 2021, the warning storage dropping below the S2 trigger pushed R1 to significantly low values (due to the α 2 factor), although these values were still above the priority demand requirements (Fig. 8 ). Mild to extreme drought conditions also pushed R2 values below the D' requirements, but for 50% of the simulated period. In 2022, even with higher WS values (between S1 and S2) and better precipitation conditions, R1 failed to satisfy water demand because of its simplicity and sole dependence on the α 1 factor. With R2 transfers, on the other hand, there was no failure during the entire simulation. This finding suggests that for adaptive hedging in data-scarce drylands, the calculation method (i.e., the rule itself) is more critical than the disposal of on-site inflow measurements. Therefore, operating rules optimized using simulated data (e.g., regionalization or Eq. 1 ) may be effective in satisfying water demands and stakeholder requirements, even when integrated with a simple drought index and in the presence of data uncertainties. Previous hydrological modeling supports these conclusions. For instance, Rottler et al. ( 2024 ), when developing a hydrological forecasting system for the study site based on satellite monitoring and hydrological modeling, observed that it was possible to estimate storage volumes for all reservoirs in Ceará. This was achievable even for reservoirs with no prior information, despite uncertainties arising from the model components. Similarly, Karamouz and Araghinejad ( 2008 ) proposed hedging rules for long-term decisions in a dryland reservoir in Iran based on estimated water availability, drought indices, and inflow forecasts. They demonstrated that this operational framework significantly mitigated drought damage in the study area. 5. Conclusions This study proposed a simple hedging rule for a data-scarce dryland that is adaptive to drought conditions and incorporates the rationing ratio requirements defined by stakeholders. By developing optimized rules using estimated inflow and testing them against on-site measurements, this study suggests that hedging rules can be effectively applied even in the face of data uncertainty. The principal findings are summarized as follows: Drought impacts can be mitigated by triggering early water shortages using a dynamic warning storage that considers both reservoir storage and a drought index (SPI3). For adaptive hedging in data-scarce drylands, the method used to define the operating rule is more critical than the disposal of on-site inflow data. The SPI3 index proved to be an effective input for the operating rules, demonstrating its effectiveness in guiding water transfers to satisfy the demands. Declarations Competing Interests The authors have no relevant financial interests to disclose. Ethics statement The authors have addressed the issue of plagiarism, and this article is free of any concerns. Funding The present study was supported through the National Council for Scientific and Technological Development – CNPq (#307680/2023-1) and the Brazilian Federal Agency for Support and Evaluation of Graduate Education – CAPES (#88887.007807/2024-00). Authors Contributions A. J. A. Toné: Conceptualization; Formal analysis; Investigation; Methodology; Validation; Writing – original draft. D. A. C. Cid: Writing – review and editing. A. C. Costa: Formal analysis; supervision; Writing – review and editing. C. J. P. A. Toné: Data curation; software. M. U. G. Barros: Data curation. I. E. Lima Neto: Formal analysis; supervision; Writing – review and editing; Project administration. 7. Acknowledgments The authors thank the Water Resources Managament Company of Ceará (COGERH) for supporting the field surveys and providing the data used in this study. Data availability statement All essential data are provided in the paper. References Aboutalebi Mahyar BH, Omid A (2015) Optimal Monthly Reservoir Operation Rules for Hydropower Generation Derived with SVR-NSGAII. J Water Resour Plan Manag 141:04015029. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000553 Ahana BS, Nguyen BQ, Kantoush SA et al (2025) Influence of existing reservoirs on the propagation from meteorological to hydrological extremes under climate change in the Ruzizi river basin: historical assessment and future projection. 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Environ Rev 19:333–349. https://doi.org/10.1139/a11-013 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 09 Feb, 2026 Reviewers invited by journal 05 Feb, 2026 Editor invited by journal 03 Feb, 2026 Editor assigned by journal 29 Jan, 2026 First submitted to journal 29 Jan, 2026 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-8725090","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":586473315,"identity":"455ff85f-be00-463b-a427-9cf3a651a9e6","order_by":0,"name":"Arthur Jordan de Azevedo Toné","email":"","orcid":"","institution":"IFCE: Instituto Federal de Educacao Ciencia e Tecnologia do Ceara","correspondingAuthor":false,"prefix":"","firstName":"Arthur","middleName":"Jordan de Azevedo","lastName":"Toné","suffix":""},{"id":586473316,"identity":"c5262b07-efee-4543-87c8-206937b4b15f","order_by":1,"name":"Daniel Antônio Camelo Cid","email":"","orcid":"","institution":"FUNCEME","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"Antônio Camelo","lastName":"Cid","suffix":""},{"id":586473317,"identity":"2555071c-9179-4878-9ad0-794d87754d1d","order_by":2,"name":"Alexandre Cunha Costa","email":"","orcid":"","institution":"UNILAB: Universidade da Integracao Internacional da Lusofonia Afro-Brasileira","correspondingAuthor":false,"prefix":"","firstName":"Alexandre","middleName":"Cunha","lastName":"Costa","suffix":""},{"id":586473318,"identity":"f4a80155-0b1b-482b-ae09-70d665ff8538","order_by":3,"name":"Caio J. di Pedro A. Toné","email":"","orcid":"","institution":"Ecole des Mines de Paris: Mines Paris - PSL","correspondingAuthor":false,"prefix":"","firstName":"Caio","middleName":"J. di Pedro A.","lastName":"Toné","suffix":""},{"id":586473319,"identity":"d60c3aa1-abc2-4aba-a33d-d53ef5079d4c","order_by":4,"name":"Mário Ubirajara G. Barros","email":"","orcid":"","institution":"COGERH","correspondingAuthor":false,"prefix":"","firstName":"Mário","middleName":"Ubirajara G.","lastName":"Barros","suffix":""},{"id":586473320,"identity":"e9f2289e-c2e2-4d57-8047-87d69ca0dcc0","order_by":5,"name":"Iran Eduardo Lima Neto","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBACNhDxgY0hAUwzMBwgTgvjDIgWxhlEaQEBZh6StPBJH3722KbMJo+/gcew4QfDnXzCDuNLMzfOOZdWLHGAx7Cxh+GZZQNBLTwMZtK5bYcTGw7wmD9mYDhsQNgWHvZv0pZt/xPnA21pJlILj5k0Y9uBxA2kaCmT7DmXnLjxMFthY4/BM8Ja5HvYt0n8KLNLnHe8eWPDj4o7hLUgADOIIEXDKBgFo2AUjALcAACypTdXVNkIvgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8612-5848","institution":"Federal University of Ceara: Universidade Federal do Ceara","correspondingAuthor":true,"prefix":"","firstName":"Iran","middleName":"Eduardo Lima","lastName":"Neto","suffix":""}],"badges":[],"createdAt":"2026-01-28 20:54:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8725090/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8725090/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103049112,"identity":"a320897b-9d4b-4585-934d-cf5fb7778b2c","added_by":"auto","created_at":"2026-02-20 07:32:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":176724,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of the study site in the Brazilian semi-arid region. The river reach simulated by the river-aquifer model is indicated in red\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/a9be0a9ce14090a9c65aaff1.png"},{"id":102318561,"identity":"d5455240-24a5-4a74-9a5d-4b4b99a16a80","added_by":"auto","created_at":"2026-02-10 13:18:53","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":72709,"visible":true,"origin":"","legend":"\u003cp\u003eMethodological flowchart applied in the definition of the hedging rules for the Castanhão Reservoir\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/356f3d2dba7d1377f23da1ed.jpeg"},{"id":104779037,"identity":"3cc8a479-b5b7-4430-a3ae-2f3b80d21ccb","added_by":"auto","created_at":"2026-03-17 07:29:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":69158,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly SPI3 from the beginning of Castanhão reservoir operation until 2022\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/b1d9df91c70027f01932ce3a.png"},{"id":102397281,"identity":"ff39982a-2226-4a28-91c5-e97f48367cfb","added_by":"auto","created_at":"2026-02-11 10:14:53","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":124253,"visible":true,"origin":"","legend":"\u003cp\u003eInflow data for optimizinghedging rules in 2021 (a), 2022 (b) and 2004-2012 (c)\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/9ff4d6db043ba36529765192.png"},{"id":102318566,"identity":"18c5096c-25f5-4a68-a6bb-248f75a00d45","added_by":"auto","created_at":"2026-02-10 13:18:53","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":86426,"visible":true,"origin":"","legend":"\u003cp\u003eComparison between warning storage (WS) and hedging triggers (S1 and S2) for decision variables sets 1 (a) and 2 (b)\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/6ff629e61804a7741e6a9b0c.png"},{"id":102318568,"identity":"4f48b92e-055d-4fdf-9c3f-4a185a7623d9","added_by":"auto","created_at":"2026-02-10 13:18:53","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":169683,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of water transfers for decision sets 1 (R1) and 2 (R2) with the adjusted total demand (D') (a) and the resulting storage volume variation for both sets (b)\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/983ba0ee7e980fed45133905.png"},{"id":102318565,"identity":"450e4853-f1a5-433e-8053-4b9d2b26bf3b","added_by":"auto","created_at":"2026-02-10 13:18:53","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":126274,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of warning storage (WS) against hedging triggers (S1 and S2) for both decision variable sets. Subplots show: (a) set 1 in 2021; (b) set 2 in 2021; (c) set 1 in 2022; and (d) set 2 in 2022\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/2d9a571fef613a2af08a165d.png"},{"id":102318567,"identity":"95ba96d0-79fe-4ad9-b822-c8d56b0b0b2d","added_by":"auto","created_at":"2026-02-10 13:18:53","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":66913,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of water transfers for decision sets 1 (R1) and 2 (R2) with the adjusted total demand (D') in 2021 (a) and 2022 (b)\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/6756e347e5aa062308beaada.png"},{"id":104783659,"identity":"f9e9a7d6-b794-4d41-8da6-796ef307327f","added_by":"auto","created_at":"2026-03-17 08:03:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1625867,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8725090/v1/464ef109-48f9-40d5-8e85-da5f74eeb50c.pdf"}],"financialInterests":"","formattedTitle":"Adaptive hedging rules for a data-scarce dryland reservoir: integrating simple drought index, water user participation, and short-term hydrological monitoring","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eRecent climate changes in dryland regions have shown higher warming rates and declining precipitation, extending the duration of dry periods (Daramola and Xu \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The rapid negative impacts of meteorological droughts on subsurface and surface water supplies in drylands shorten early warning times, highlighting the need for adaptive management to reduce the effects of climate variability on water scarcity in the region (Ahana et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). An effective drought management framework requires risk reduction strategies and tools. Two common strategies for long- and short-term water vulnerability mitigation are the construction of reservoirs and the implementation of demand restrictions through the regulation of river and groundwater exploitation (Cid et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Akram \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Drought indices serve as decision support tools, and there is extensive literature on their use in drought monitoring and triggering mitigation measures based on onsite conditions. While the utility of any single index can be limited depending on the type of drought being analyzed, their primary advantages are the straightforward interpretation of their values and their role in drought contingency planning (Zargar et al. \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2011\u003c/span\u003ea, Zaniolo et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, Gon\u0026ccedil;alves et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs reservoirs are typically the only water source available in drylands (Lopes and Freitas \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), effective reservoir operation during periods of drought can mitigate the imbalance between planned demand and water availability through reasonable allocation. Known as hedging, this policy is driven by the idea of accepting minor present shortages to prevent critical future shortages and is implemented through rationing factors and rule curves (Tu Ming-Yen et al. 2008; Luo et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Numerical approaches have been used to define optimal hedging rules, as the decision to ration water must account for the complexity of water allocation in data-scarce regions. Optimization models proposed in the literature for drylands seek to identify optimal solutions by optimizing an objective function that either diminishes the maximum extent of a single-period deficit in the system or enhances the economic benefits. These solutions are normally hedging triggers or indicators of when and by how much to hedge. They are selected by comparing and ranking the system performance (i.e., reducing failures in satisfying demand) against the metrics of vulnerability, reliability, and resilience (Shih and ReVelle \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Neelakantan and Sasireka \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Ashrafi and Dariane \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Hong et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn this context, Cid et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) proposed a collaborative model that optimizes hedging rules to meet the rationing frequencies defined by water allocation agents. The numerical approach is based on the discrete hedging rule for a monthly reservoir proposed by Shih and ReVelle (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1995\u003c/span\u003e) and does not assess monthly drought conditions using a drought index. Tributary flow series were obtained using a soil moisture accounting procedure that was adjusted via regionalization. This approach relies on the implicit assumption that catchments with similar characteristics exhibit similar hydrological behaviors. However, this assumption can be problematic because these catchments, although similar, are not identical (Guo et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eChang et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) developed a numerical framework to determine the minimal reservoir water level required to satisfy water users during different drought events. This hedging trigger is useful for drought mitigation because future operating policies can be made suitable for specific emergence conditions. The model requires long-term meteorological and hydrological information for its applicability, particularly for inflow and drought assessments, as it integrates three drought indices (the streamflow drought index (SDI), standardized precipitation index (SPI), and relative moisture index (RMI)). This extensive data requirement can limit its use in data-scarce drylands (Kumar et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Similar to the framework of Cid et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), in which water users define temporal allocation values based on reservoir storage conditions, the model also depends on previous optimal operation decisions to define the hedging policy.\u003c/p\u003e \u003cp\u003eBeshavard et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), on the other hand, proposed a numerical hedging model that calculates rationing ratios and rule curves linked to a warning storage based on a drought index (SDI). The model advances the state of the art by allowing earlier rationing responses to identified drought periods, and its application is simple in data-scarce areas. Notwithstanding, hedging policies are not only numerical issues, and they are more likely to be effective when the numerical model is united with a collaborative approach, where rationing ratios and acceptable risks are built together with water users (Sandoval-Solis et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eNumerous studies have employed multi-objective genetic algorithms, specifically the NSGA-II, to propose optimal operation rules. Ahmadianfar et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) utilized this method to define a hedging rule capable of gradually changing the rationing factors across operation zones in a dryland reservoir in southern Iran. In the Brazilian semi-arid region, Gomes et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) applied NSGA-II to design an operation rule that balances the stakeholder water supply with acceptable water quality standards. In another study, Karnatapu et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) derived optimal rules for a generic dryland reservoir in India, addressing both water supply and hydropower generation, and found better performance metrics with the proposed rules than with the standard operating policy. Based on these results, the authors suggested that NSGA-II is suitable for optimizing the operation rules in any reservoir with limited water availability.\u003c/p\u003e \u003cp\u003eNevertheless, few studies have proposed an adaptive operational policy for a multi-use dryland reservoir that can deal with the rapid impacts of climate change on streamflow (Mujere et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Coulibaly et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Furthermore, existing operation policies rarely integrate water user participation, short-term field-measured hydrological monitoring, and early rationing based on a simple drought index simultaneously. Moreover, few approaches have proposed a hedging rule based on a water balance that considers river-aquifer dynamics, an important feature of dryland hydrology, coupled with a multi-objective genetic algorithm (NSGA-II) to find optimal decision variables. Thus, the objectives of this study are as follows: (1) to develop a hedging rule for a data-scarce dryland reservoir that seeks to balance the complexity of water allocation, drought assessment, and dryland hydrological processes while maintaining operational simplicity; (2) to evaluate the performance of the proposed hedging rules using simulated and measured inflow data; and (3) to provide insight into the requirements for the development of hedging rules in dryland reservoirs.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1. Study site\u003c/h2\u003e\n\u003cp\u003eThe study site is a multi-use reservoir in the Middle Jaguaribe sub-basin in the Brazilian semiarid region (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The Castanh\u0026atilde;o Reservoir has a surface area of 325 km\u003csup\u003e2\u003c/sup\u003e and a storage capacity of 6.7\u0026nbsp;billion m\u003csup\u003e3\u003c/sup\u003e, with depths exceeding 60 m in certain areas (Arantes et al. \u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e; Lima Neto \u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e). The catchment area is 45,309 km\u003csup\u003e2\u003c/sup\u003e, and the rainfall regime is concentrated from January to May and only for a few days, ranging from 500 to 900 mm/year. During the dry season, potential evaporation rates throughout the year may exceed rainfall values by up to four times. These meteorological conditions, combined with shallow soils over crystalline geological formations, have resulted in extensive dry periods with minimal baseflow and streamflow within a few months (De Ara\u0026uacute;jo and Medeiros \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Raulino et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eThe Castanh\u0026atilde;o Reservoir experiences high variability in storage and inflow. For instance, following occasional floods in 2008, it reached 96% of its total storage capacity. However, during the subsequent severe drought (2012\u0026ndash;2018), its volume plummeted to just 2%, significantly increasing water treatment costs. In recent years, the reservoir has recovered to more than 30% of its capacity (Lima Neto \u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e). No significant inflow, on the other hand, is observed during the dry season, such that reservoir management policies to satisfy human supply and other demands are defined during the rainy season (Molisani et al. \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2. Dataset\u003c/h2\u003e\n\u003cp\u003eFor the study site, monthly rainfall data were obtained from the National Hydrometeorological Network of the National Water and Sanitation Agency (ANA), and evaporation data were sourced from a regional study by ANA (\u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e) on dryland reservoirs in Brazil. This study also provides the total demand used in the operation model (D\u0026thinsp;=\u0026thinsp;18.85 m\u003csup\u003e3\u003c/sup\u003e/s).\u003c/p\u003e\n\u003cp\u003eThe elevation-area-volume curve of the Castanh\u0026atilde;o Reservoir was obtained from the Cear\u0026aacute; Hydrological Portal of the Cear\u0026aacute; Foundation of Meteorology and Water Resources (FUNCEME). Recognizing that improved inflow data can enhance hedging rules (Neelakantan and Sasireka \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e), we conducted field measurements to obtain these data. In the first half of 2021, the inflow at the entrance of the Castanh\u0026atilde;o Reservoir was measured using a SonTek RiverSurveyor M9 ADCP. Because of technical difficulties at this site, we could not perform daily measurements. Therefore, in 2022, monitoring was relocated to a gauge approximately 21 km upstream of the Jaguaribe River. At this new location, the ANA provided daily inflow and river stage data, which were used to forecast the inflow at the Castanh\u0026atilde;o Reservoir entrance. The daily flow volume was defined as the total 24-hour discharge derived from the ANA records. We also used monthly inflow data generated for the study site using a soil moisture accounting procedure (SMAP) and later adjusted via regionalization by the Federal University of Cear\u0026aacute; (UFC) and COGERH (2013) to propose the hedging policies. This inflow series data spans the period from January 1912 to December 2012.\u003c/p\u003e\n\u003cp\u003eWe estimated the streamflow into the study site during the first semester of 2022 using the river routing equation proposed by Ton\u0026eacute; et al. (\u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e) for dryland and data-scarce catchments. This numerical model requires few parameters and estimates river-aquifer dynamics, such as aquifer recharge and hyporheic flow. The outflow from a river reach is calculated as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$$\\:{\\text{O}}_{\\text{t}+\\varDelta\\:\\text{t}}=\\frac{1}{1-\\text{X}}(\\frac{{\\text{V}}_{\\text{t}}}{\\text{K}}{)}^{\\frac{1}{{\\gamma\\:}\\text{m}}}-\\frac{\\text{X}\\bullet\\:{\\text{Q}}_{\\text{t}}+{\\pi\\:}+{\\mu\\:}+{\\Omega\\:}+{\\delta\\:}}{1-\\text{X}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere O\u003csub\u003et+\u0026Delta;t\u003c/sub\u003e is the outflow (m\u0026sup3;/s), V\u003csub\u003et\u003c/sub\u003e is the volume (m\u0026sup3;), X is a weighting factor, K is the storage constant (s), and \u0026gamma; and m are calibrated exponents. According to Ton\u0026eacute; et al. (\u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e), for the 21 km river reach between the Jaguaribe gauge and the study site, exponent m is set to 1.6. Exponent \u0026gamma; is set to 0.9 when the river stage is equal to or below the mean river head at the measurement location, and 0.5 when it is higher. Additionally, the model accounts for direct in-river flux (\u0026pi;), sub-catchment runoff (\u0026micro;), and river-aquifer interaction (Ω), with all terms expressed in m\u0026sup3;/s. A detailed description of the steps required to calculate each term in Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e are provided in Ton\u0026eacute; et al. (\u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eIn addition to the previously described data, Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e requires the determination of geometric, sub-catchment, and hydrogeological parameters. The geometric parameters were derived as follows: the channel length, river slope, and sub-catchment area were obtained from the Copernicus GLO-30 digital elevation model (DEM) using the QGIS raster analysis tool. The other parameters (perimeter, area, hydraulic radius, and top width) were derived from river stage measurements, assuming a triangular cross-section of the river. We assumed a constant top width because no flow beyond the main channel was considered in this study. The sub-catchment curve number (assuming type 2 soil moisture) was provided by ANA (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). The hydrogeological parameters were obtained separately. The aquifer width and hydraulic conductivity of the alluvium were obtained from surveys conducted by the Brazilian Geological Service (CPRM) (2014, 2015). The hydraulic conductivity of the riverbed was calculated using Hazen's method, which was applied to the riverbed grain size data from Wiegand (\u003cspan class=\"CitationRef\"\u003e2009\u003c/span\u003e) for the Jaguaribe River.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3. Drought index\u003c/h2\u003e\n\u003cp\u003eThis study used the SPI, which is commonly adopted in operational models in drylands. The SPI is calculated by dividing the difference between precipitation and its long-term mean by the standard deviation (Faye \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). The criteria for identifying drought events are SPI values that are continuously negative and equal to or below \u0026minus;\u0026thinsp;1.0 for any time scale (McKee et al. \u003cspan class=\"CitationRef\"\u003e1993\u003c/span\u003e). A major advantage of the index is that it relies only on precipitation data and can be calculated for different timescales, allowing for adaptable drought analysis and hydrological monitoring (Zargar et al. \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eTo implement adaptive reservoir operations on short time scales, it is necessary to address the rapid and significant impact of climate change on streamflow in drylands (Swain et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Saedi et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Werede et al. \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e). Since intermittent streamflow patterns are best characterized by SPI values at the 2\u0026ndash;6-month scale (Mishra and Desai \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e), this study calculated the SPI on a 3-month time scale (SPI3) using historical precipitation records from the study site, as described in the Dataset section. Although evaporation driven by higher temperatures plays an important role in trends toward drier conditions, suggesting the utility of drought indices that consider potential evapotranspiration, such as the Standardized Precipitation Evapotranspiration Index (SPEI), the SPI3 and SPEI3 showed significant agreement at the study site based on historical data from 1980 to 2019 (Tomasella et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eHowever, De Ara\u0026uacute;jo J\u0026uacute;nior et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e observed that the SPI failed to capture reservoir storage fluctuations in another reservoir in the Brazilian semiarid region because of the time lag between precipitation and water volume variations. Nevertheless, other studies have suggested its utility in this region. Recently, Gon\u0026ccedil;alves et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) evaluated several drought indices for the Castanh\u0026atilde;o Reservoir based on six criteria: treatability, robustness, transparency, sophistication, dimensionality, and extensibility. Their findings indicated that the SPI outperformed other indices by identifying more drought events. Given the rapid impact of meteorological droughts on surface water in drylands (Ahana et al. \u003cspan class=\"CitationRef\"\u003e2025\u003c/span\u003e), we selected the SPI to identify these events. The rationale is to start rationing earlier, owing to the application of a drought index, than conventional operation rules that rely solely on the actual reservoir storage. The SPI classification adapted to the study site is presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSPI classification for water management at the study site (Santos \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Gon\u0026ccedil;alves et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSPI values\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eClassification\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026ge;\u0026thinsp;2.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExtreme rainfall\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.49 to 1.99\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSevere rainfall\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.99 to 1.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModerate rainfall\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.49 to 0.99\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eWeak rainfall\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.49 to 0.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAlmost normal\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.99 to -0.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMild drought\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.49 to -1.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModerate drought\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.99 to -1.50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSevere drought\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026le; -2.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExtreme drought\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e2.4. Operation rules\u003c/h2\u003e\n\u003cp\u003eThe operating rules are defined based on the reservoir storage and rationing ratios established by the water allocation agents. These ratios were established through a stakeholder consultation process conducted by Cid et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e), wherein participants defined the values for the Castanh\u0026atilde;o Reservoir corresponding to various drought scenarios. The resulting consensus values are listed in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. In this study, each drought condition will be assessed using SPI values (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). One of the conditions to be optimized is that the operation rules must meet the consensus rationing ratios for each drought state (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e); otherwise, there will be a failure in the system performance.\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eStakeholder consensus on rationing ratios at the study site under different drought conditions.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth colspan=\"5\" align=\"left\"\u003e\n\u003cp\u003eDrought state\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eCastanh\u0026atilde;o\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAlmost normal\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMild drought\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eModerate drought\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSevere drought\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExtreme drought\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSPI3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026gt; -0.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0.99 to -0.49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.49 to\u003c/p\u003e\n\u003cp\u003e-1.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1.99 to -1.50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u0026le; -2.00\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRationing ratios\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.95\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eReservoir storage is divided into three zones defined by monthly upper (S1) and lower (S2) trigger volumes. Typically, these thresholds determine the water allocation ratio based on the storage and inflow at the beginning of each operational period. To address the impacts of climate change in drylands, we adopted a monthly dynamic warning storage (WS\u003csub\u003et\u003c/sub\u003e) proposed by Beshavard et al. (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). In this study, this parameter integrates the 3-month SPI to enable earlier rationing measures. Specifically, this mechanism ensures that rationing is triggered if the SPI3 indicates a drought condition, even when the observed reservoir storage (S\u003csub\u003et\u003c/sub\u003e) remains high.\u003c/p\u003e\n\u003cp\u003eWS\u003csub\u003et\u003c/sub\u003e = S\u003csub\u003et\u003c/sub\u003e \u0026bull; (1\u0026thinsp;+\u0026thinsp;\u0026alpha;\u003csub\u003e3\u003c/sub\u003e \u0026bull; SPI3) (2)\u003c/p\u003e\n\u003cp\u003eIn other words, when the SPI3 is positive, the warning storage remains equal to the current monthly storage. However, when SPI3 is negative, the warning storage is effectively reduced by a factor derived from the product of the SPI3 value and an optimized monthly coefficient \u0026alpha;\u003csub\u003e3\u003c/sub\u003e ranging from 0 to 1 (see next section). Consequently, even if the actual reservoir storage is near or above the upper S1 trigger, the reduced warning storage forces early rationing to mitigate the impact of future droughts on the water supply.\u003c/p\u003e\n\u003cp\u003eIn this study, we compare two water allocation rules. For both, the total demand considered encompasses priority demands (human and livestock consumption) and non-priority demands (irrigation). This total demand is adjusted using stakeholder ratios depending on the drought conditions identified by SPI3 values (D\u0026rsquo;= Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e factors \u0026bull; D). Rule 1 is a standard three-zone policy. If the WS (Eq.\u0026nbsp;2) and inflow are above the upper trigger (S1), no rationing is applied to the demand. If it is between the S1 and S2 triggers, the demand is rationed using a fixed coefficient, \u0026alpha;\u003csub\u003e1\u003c/sub\u003e. If it is below the lower trigger (S2), demand is rationed by a fixed coefficient \u0026alpha;\u003csub\u003e2\u003c/sub\u003e (Eq.\u0026nbsp;3\u0026ndash;5), as follows:\u003c/p\u003e\n\u003cp\u003eIf S\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;WS\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e then R\u003csub\u003et\u003c/sub\u003e = D\u0026rsquo; (3)\u003c/p\u003e\n\u003cp\u003eIf S\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;WS\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e \u0026lt; S\u003csub\u003e1\u003c/sub\u003e then R\u003csub\u003et\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026alpha;\u003csub\u003e1\u003c/sub\u003e \u0026bull; D\u0026rsquo; (4)\u003c/p\u003e\n\u003cp\u003eIf WS\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e \u0026lt; S\u003csub\u003e2\u003c/sub\u003e then R\u003csub\u003et\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026alpha;\u003csub\u003e2\u003c/sub\u003e \u0026bull; D\u0026rsquo; (5)\u003c/p\u003e\n\u003cp\u003eRule 2 is similar to Rule 1 and was adapted from Cid et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) to consider WS (Eq.\u0026nbsp;2). It also releases D\u0026rsquo; when the warning storage (Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) and inflow exceed S1 (Eq.\u0026nbsp;6). However, in the other two zones, both rationing coefficients (\u0026alpha;\u003csub\u003e1\u003c/sub\u003e and \u0026alpha;\u003csub\u003e2\u003c/sub\u003e) can be used to calculate water allocation, and coefficient \u0026beta; is considered to reduce R\u003csub\u003et\u003c/sub\u003e when the SPI3 value is above \u0026minus;\u0026thinsp;0.49 (from \u0026ldquo;almost normal\u0026rdquo; to \u0026ldquo;extreme rainfall\u0026rdquo; conditions) (Eq.\u0026nbsp;7).\u003c/p\u003e\n\u003cp\u003eIf S\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;WS\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e then R\u003csub\u003et\u003c/sub\u003e = D\u0026rsquo; (6)\u003c/p\u003e\n\u003cp\u003eIf S\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;WS\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e then R\u003csub\u003et\u003c/sub\u003e = min(D\u0026rsquo;; D \u0026bull; (1\u0026thinsp;+\u0026thinsp;\u0026beta;) \u0026bull; (1 \u0026ndash; y\u003csub\u003e1,t\u003c/sub\u003e \u0026bull; \u0026alpha;\u003csub\u003e1\u003c/sub\u003e \u0026ndash; y\u003csub\u003e2,t\u003c/sub\u003e \u0026bull; (\u0026alpha;\u003csub\u003e2\u003c/sub\u003e - \u0026alpha;\u003csub\u003e1\u003c/sub\u003e))) (7)\u003c/p\u003e\n\u003cp\u003eWhere Q\u003csub\u003et\u003c/sub\u003e is the monthly inflow (m\u0026sup3;), R\u003csub\u003et\u003c/sub\u003e is the monthly water release (m\u0026sup3;), and \u0026beta; is a monthly coefficient, respectively. The variable y\u003csub\u003e1,t\u003c/sub\u003e is a binary indicator equal to 1 if the warning storage (WS\u003csub\u003et\u003c/sub\u003e) is below trigger S1 during month t, and 0 otherwise; similarly, y\u003csub\u003e2,t\u003c/sub\u003e is equal to 1 if WS\u003csub\u003et\u003c/sub\u003e is below trigger S2, and 0 otherwise.\u003c/p\u003e\n\u003cp\u003eTo propose an operating curve that divides the reservoir storage into three zones, we used a multiobjective genetic algorithm, NSGA-II, to calculate the decision variables (Deb et al. \u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e) (see next section). This tool was selected based on its demonstrated effectiveness in estimating optimal monthly operational rules in previous studies (Chang et al. \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e; Aboutalebi Mahyar et al. 2015; Gomes et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). These variables were calculated using an inflow dataset that included the historical period from the start of the Castanh\u0026atilde;o Reservoir\u0026rsquo;s operation until 2012 (SMAP-estimated) and inflow data from the rainy seasons in the first halves of 2021 and 2022 (see Dataset section). The genetic algorithm estimated two sets of optimized decision values: the first, considering Equations 3\u0026ndash;5 for monthly water release (R1), and the second, considering Equations 6\u0026ndash;7 for monthly water release (R2).\u003c/p\u003e\n\u003cp\u003eThe necessary restrictions for the operation rules are as follows: for reservoir storage, the condition is Smin\u0026thinsp;\u0026le;\u0026thinsp;S2\u0026thinsp;\u0026lt;\u0026thinsp;S1\u0026thinsp;\u0026le;\u0026thinsp;Smax, where Smax is the maximum storage volume of the Castanh\u0026atilde;o reservoir (6700 hm\u0026sup3;) and Smin is the minimum volume required to meet priority demand (58.1 hm\u0026sup3;) (ANA \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e); for the rationing coefficients, the constraints are 0\u0026thinsp;\u0026lt;\u0026thinsp;\u0026alpha;\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026alpha;\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1 and 0\u0026thinsp;\u0026lt;\u0026thinsp;\u0026beta;\u0026thinsp;\u0026lt;\u0026thinsp;1. An additional constraint is introduced to prevent the S1 and S2 trigger values from being too close, which is necessary for effective rule operation. This constraint is defined as S1 \u0026ge; (1\u0026thinsp;+\u0026thinsp;\u0026gamma;) \u0026sdot; S2, with the coefficient \u0026gamma; restricted to the range [0.3, 1.0].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e2.5. Operation simulation\u003c/h2\u003e\n\u003cp\u003eTo determine the reservoir storage (S\u003csub\u003et\u003c/sub\u003e) at the end of each monthly time step (t), we applied the following water balance equation:\u003c/p\u003e\n\u003cp\u003eS\u003csub\u003et+1\u003c/sub\u003e = S\u003csub\u003et\u003c/sub\u003e \u0026ndash; E\u003csub\u003et\u003c/sub\u003e + Q\u003csub\u003et\u003c/sub\u003e \u0026ndash; Spill\u003csub\u003et\u003c/sub\u003e \u0026ndash; Inf\u003csub\u003et\u003c/sub\u003e \u0026ndash; R\u003csub\u003et\u003c/sub\u003e (8)\u003c/p\u003e\n\u003cp\u003eThe variables E\u003csub\u003et\u003c/sub\u003e, Inf\u003csub\u003et\u003c/sub\u003e, and Spill\u003csub\u003et\u003c/sub\u003e represent the monthly evaporation, monthly infiltration, and spill volumes (m\u0026sup3;), respectively. The spill volume is determined as follows: if the storage at the end of the month, S\u003csub\u003et+1\u003c/sub\u003e, is greater than the maximum capacity, Smax, then the spill is the excess volume (Spill\u003csub\u003et\u003c/sub\u003e = S\u003csub\u003et+1\u003c/sub\u003e \u0026minus; Smax). Otherwise, Spill\u003csub\u003et\u003c/sub\u003e = 0. Monthly infiltration was considered zero in the study site.\u003c/p\u003e\n\u003cp\u003eWith the rationing ratios already established in consultation with water agents (\"how much to hedge\"), the focus now shifts to optimizing the operating rules. This optimization must provide simple rules for operators to implement, but these rules must also be robust enough to handle the impacts of climate change on water supply deficits (Neelakantan and Sasireka \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e; Şen \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Raulino et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). The first goal, robustness against climate change, is achieved using storage triggers and warning storage linked to the SPI3 drought index, as described previously. This mechanism determines \"when to hedge\" to conserve water and reduce socioeconomic impacts. The second goal, simplicity, is intended to facilitate the development and execution of drought preparedness plans.\u003c/p\u003e\n\u003cp\u003eTherefore, to optimize the operating rules, we aimed to minimize the total water supply deficit. This was achieved by minimizing the modified shortage index (MSI) (Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e), proposed by Hsu and Cheng (\u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e) for a region experiencing extreme hydrological variability. For this optimization, we employed NSGA-II to determine the optimal values for 39 decision variables, encoded as a single chromosome string. These variables were the 24 monthly reservoir triggers (S1 and S2), 12 monthly \u0026alpha;\u003csub\u003e3\u003c/sub\u003e coefficients for the warning storage calculation, and three rationing coefficients (\u0026alpha;\u003csub\u003e1\u003c/sub\u003e, \u0026alpha;\u003csub\u003e2\u003c/sub\u003e, and \u0026beta;).\u003c/p\u003e\n\u003cp\u003eNSGA-II generates a random population of size N. Following the selection, crossover, and mutation processes, the algorithm categorizes different individuals according to their level of non-domination within the population. The operation is repeated until a defined stopping criterion is met. To minimize the computational time required for simulation, we set this criterion to 100 generations. Although this implies that the calculated decision variables may not guarantee the global optimum, they provide satisfactory solutions that meet the objectives and restrictions defined in this study. In each generation, the objective function for each individual was calculated, and the decision variables were evaluated against the restrictions and performance metrics (see the next section). This iterative process continued until the final generation, which determined the optimal values for the decision variables.\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$$\\:\\text{O}\\text{B}\\text{J}=\\text{M}\\text{S}\\text{I}=\\frac{100}{\\text{n}}\\bullet\\:\\sum\\:_{\\text{t}=1}^{\\text{n}}{\\left(\\frac{{\\text{T}\\text{S}}_{\\text{t}}}{{\\text{T}\\text{D}}_{\\text{t}}}\\right)}^{2}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere n is the total number of simulated months, TS\u003csub\u003et\u003c/sub\u003e is the shortage during month t (the difference between D\u0026rsquo; and monthly water release), and TD\u003csub\u003et\u003c/sub\u003e is the D\u0026rsquo; demand during month t.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003e2.6. Evaluation of operation rules\u003c/h2\u003e\n\u003cp\u003eWe evaluated the effectiveness of the hedging rules using the following performance measures: time-based reliability, volumetric reliability, resilience, and vulnerability. These indicators are described in detail by McMahon et al. (\u003cspan class=\"CitationRef\"\u003e2006\u003c/span\u003e) and are presented as follows.\u003c/p\u003e\n\u003cp\u003e1. Time-based reliability (REL\u003csub\u003et\u003c/sub\u003e): For a monthly simulation, it is the number of months in which the total demand is fully satisfied (N\u003csub\u003es\u003c/sub\u003e) divided by the total amount of months (n). The REL\u003csub\u003et\u003c/sub\u003e value is restricted to the range |0.0,1.0].\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$$\\:{\\text{R}\\text{E}\\text{L}}_{\\text{t}}=\\frac{{\\text{N}}_{\\text{s}}}{\\text{n}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2. Volumetric reliability (REL\u003csub\u003ev\u003c/sub\u003e): Similarly, this is the volume of water transferred to meet demand, divided by the amount of volume of water demanded over the simulation period. The REL\u003csub\u003ev\u003c/sub\u003e value is also restricted to the range |0.0,1.0].\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ4\" class=\"mathdisplay\"\u003e$$\\:{\\text{R}\\text{E}\\text{L}}_{\\text{v}}=1-\\frac{{\\sum\\:}_{\\text{i}=1}^{\\text{n}}\\left({\\text{T}\\text{S}}_{\\text{i}}\\right)}{\\sum\\:_{\\text{i}=1}^{\\text{n}}{\\text{D}}_{\\text{i}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e3. Resilience (RES): This indicates the speed at which a reservoir system recovers from a failure state. It is calculated as the number of consecutive failure events (f\u003csub\u003es\u003c/sub\u003e) divided by the total number of months in which the system was in a state of failure (f\u003csub\u003ed\u003c/sub\u003e). The RES value is restricted to the range [0.0,1.0].\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ5\" class=\"mathdisplay\"\u003e$$\\:\\text{R}\\text{E}\\text{S}=\\frac{{\\text{f}}_{\\text{s}}}{{\\text{f}}_{\\text{d}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e4. Vulnerability (VUL): It is an indicator of the severity of failure in volumetric terms during its occurrence. The VUL value is also restricted to the range |0.0,1.0].\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ6\" class=\"mathdisplay\"\u003e$$\\:\\text{V}\\text{U}\\text{L}=\\frac{\\sum\\:_{\\text{i}=1}^{{\\text{f}}_{\\text{d}}}\\frac{{\\text{T}\\text{S}}_{\\text{i}}}{{\\text{D}}_{\\text{i}}}}{{\\text{f}}_{\\text{d}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe genetic algorithm was constrained to find solutions (decision variables) that satisfy the following performance criteria: REL\u003csub\u003et,v\u003c/sub\u003e \u0026ge; 0.95 and VUL\u0026thinsp;\u0026le;\u0026thinsp;0.1, as the RES value requires careful interpretation. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the methodological flowchart of this study, which is valid for each water allocation rule.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe SPI3 values required to calculate the warning storage were compiled for the 228-month period from the start of the Castanh\u0026atilde;o Reservoir\u0026rsquo;s operation (January 2004) to the measurements at the Jaguaribe River gauge (2022) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In this timeframe, while annual rainfall varied widely (366.2 to 2438.1 mm), SPI3 values were predominantly negative (67% of the time), with 47% of values falling below \u0026minus;\u0026thinsp;0.5 (mild to extreme drought). This was most evident during the 2012\u0026ndash;2016 drought, the region's most severe in the last century, when reservoir storage experienced declines of up to 80% (FUNCEME 2026), and 68% of SPI3 values were below \u0026minus;\u0026thinsp;0.5. Critically, the SPI3 values in our study period showed a significant decreasing trend (P-value\u0026thinsp;\u0026lt;\u0026thinsp;0.009) compared to the two earlier periods (1985\u0026ndash;2003 and 1966\u0026ndash;1984), which is consistent with the global trend of increasing drought frequency in drylands (Hazbavi et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Satoh et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRegarding streamflow, the maximum observed value in 2021 was 31.81 m\u0026sup3;/s at the entrance of the Castanh\u0026atilde;o reservoir and 483.19 m\u0026sup3;/s at the Jaguaribe gauge in 2022. The inflow values estimated with SMAP (2004\u0026ndash;2012) varied from 0 to 475 m\u0026sup3;/s, whereas those from Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (2022) varied from 0 to 561.77 m\u0026sup3;/s. These four series are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and their values are similar to those observed in previous studies on the Jaguaribe River (Costa et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003eb indicates greater peak flows at the end of the 21 km river reach compared with the observed streamflow at its beginning. This suggests that groundwater fluxes (such as hyporheic flow) and sub-catchment runoff contribute to the water balance of the Castanh\u0026atilde;o Reservoir.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the optimized α\u003csub\u003e3\u003c/sub\u003e values for decision variable sets 1 and 2, respectively. This coefficient is used to calculate the warning storage, which determines the monthly water release.\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\u003eOptimized α\u003csub\u003e3\u003c/sub\u003e values for warning storage estimation in each set of decision variables.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"12\" nameend=\"c13\" namest=\"c2\"\u003e \u003cp\u003eMonths\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\u003eSets\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eJan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFeb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eApr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eJun\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eJul\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAug\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eSep\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eOct\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNov\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003eDec\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.32\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\u003eThroughout the simulation, the monthly warning storage was calculated using α\u003csub\u003e3\u003c/sub\u003e, SPI3, and S\u003csub\u003et\u003c/sub\u003e (Eq.\u0026nbsp;8) and then compared against the optimized triggers S1 and S2. This SPI3-based mechanism enabled early rationing to mitigate the impacts of future droughts. This effect is visualized in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e, which plots the mean monthly WS against the S1 and S2 triggers for the 2004\u0026ndash;2012 SMAP inflow period. Figures\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-b illustrate WS values falling below the S1 trigger, even during the rainy season. The water rationing coefficients derived from the optimization were α\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.96 and α\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.61 for set 1, and α\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.13, α\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.12, and β\u0026thinsp;=\u0026thinsp;0.14 for set 2, respectively.\u003c/p\u003e \u003cp\u003eFour performance parameters (REL\u003csub\u003et\u003c/sub\u003e, REL\u003csub\u003ev\u003c/sub\u003e, RES, and VUL) were used to evaluate the drought-informed operating rules (set 1 and set 2) for the reservoir. Using the SMAP inflow data, the simulation indicated satisfactory performance for both rules, which was attributed to the water transfer volumes (R1 and R2) based on the optimized S1/S2 triggers and monthly WS variation. Specifically, set 1 experienced four months of failure, yielding REL\u003csub\u003et\u003c/sub\u003e = 0.96, REL\u003csub\u003ev\u003c/sub\u003e = 0.99, RES\u0026thinsp;=\u0026thinsp;0, and VUL\u0026thinsp;=\u0026thinsp;0.10; set 2 performed with only one failure, resulting in REL\u003csub\u003et\u003c/sub\u003e = 0.98, REL\u003csub\u003ev\u003c/sub\u003e = 0.99, RES\u0026thinsp;=\u0026thinsp;0, and VUL\u0026thinsp;=\u0026thinsp;0.08. In the first set, the objective function (Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e9\u003c/span\u003e) was 0.096; for the second set, it was 0.008. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e compares the water releases from R1 and R2 with the total demand, alongside the resulting variation in the storage volume for each set. The monthly variations in water demand (also shown in the figure) result from the application of the stakeholder rationing ratios (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), which are selected based on the SPI3 value for each month (D\u0026rsquo;). There was no significant variation between the storage volumes in either set, as these values were significantly greater than the water release.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen applied to the measured inflow data, the operating rules produced performance metrics that differed significantly based on the water transfer equation (R1 and R2) and drought index. The SPI3 values between March and June of 2021 were consistently negative (-1.08, -0.58, -0.54, and \u0026minus;\u0026thinsp;0.36, respectively), corresponding to moderate to mild drought (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), whereas they were positive in almost all the first half of 2022 and negative only in April (-0.20). In 2021 (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-b), the continuous drought pushed the warning storage below the S2 trigger, which significantly reduced the R1 value, whereas the R2 transfer was able to maintain itself above the required demand in March and June (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003ea). Consequently, R1 experienced system failures in all months except April, even when the rationing ratios were applied to the total demand, whereas R2 experienced two failures. This exception was possible because the warning storage was slightly higher than the S2 trigger. The performance metrics for set 1 were REL\u003csub\u003et\u003c/sub\u003e = 0.25, REL\u003csub\u003ev\u003c/sub\u003e = 0.74, RES\u0026thinsp;=\u0026thinsp;0.67, and VUL\u0026thinsp;=\u0026thinsp;0.35. Set 2 yielded REL\u003csub\u003et\u003c/sub\u003e = 0.50, REL\u003csub\u003ev\u003c/sub\u003e = 0.96, RES\u0026thinsp;=\u0026thinsp;0.5, and VUL\u0026thinsp;=\u0026thinsp;0.08. The objective function was 9.109 for set 1 and 0.310 for set 2.\u003c/p\u003e \u003cp\u003eIn 2022, the consistently positive SPI3 values maintained a constant monthly demand throughout the first half of the year (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003eb). These precipitation conditions kept the warning storage above the S2 trigger during the simulation, except in January for R1 and February for R2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ec-d). The system operation with set 1 decision variables (R1) failed during the entire simulation period, even though R1 values were close to the demand required, whereas there was no failure with set 2 parameters (R2). This condition improved the performance metrics for set 2 compared to those in 2021. For set 2, REL\u003csub\u003et\u003c/sub\u003e = 1.0 and REL\u003csub\u003ev\u003c/sub\u003e = 1.0, and it was not possible to calculate RES and VUL. For set 1, failure in all months dropped REL\u003csub\u003et\u003c/sub\u003e to zero; the other metrics were REL\u003csub\u003ev\u003c/sub\u003e = 0.90, RES\u0026thinsp;=\u0026thinsp;0.83, and VUL\u0026thinsp;=\u0026thinsp;0.10. The objective function was 2.684 for set 1 and 0.002 for set 2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe performance metrics of the reservoir operation demonstrated the effectiveness of the proposed hedging rules from the start of the Castanh\u0026atilde;o operation to 2012. They successfully satisfied the water demand while adhering to the stakeholders' rationing ratio requirements (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This effectiveness was achieved despite the model simplicity and the prevalence of drought conditions (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e), which ranged from mild to extreme during most of the study period (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Nevertheless, the hedging policies obtained have certain limitations. First, they were defined using estimated inflow data, which were adjusted via regionalization. Second, water balance calculations (Eq.\u0026nbsp;8) suffer from uncertainties due to data scarcity and technical difficulties with on-site measurements, although we did not observe any significant errors.\u003c/p\u003e \u003cp\u003eDuring the entire simulation period, both water transfer proposals, using their respective optimized decision variables, satisfied the priority demand (human and livestock consumption) (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Decreasing the total demand (which encompasses agricultural uses) at the study site will not impose failures in the proposed hedging rules. Thus, the recent decision from COGERH and water users to allocate 17 m\u0026sup3;/s from the Castanh\u0026atilde;o reservoir during the second half of 2025 would not be seen as a risk for the proposed rules (COGERH \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), as they would inherently protect this supply. The analysis of set 1 revealed a paradoxical behavior. Warning storage remained below the S1 trigger for almost the entire rainy season (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e), which is a conservative stance that may improve assurance during severe droughts (Gomes et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Despite this, in 45% of the simulations (SMAP inflow), the R1 transfers were greater than the stakeholder-adjusted total demand (D\u0026rsquo;), indicating an inefficiency. Therefore, the rules (Equations 4\u0026ndash;5) require adjustments. They must be modified to enforce the maximum water transfer at the adjusted demand to prevent over-delivery, similar to Eq.\u0026nbsp;7.\u003c/p\u003e \u003cp\u003eIn contrast, the decision variables for set 2 produced a warning storage that was consistently higher than that of set 1, remaining above the S1 and S2 triggers for most of the simulations (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e). This can be explained by two factors: first, for SPI3 values above \u0026minus;\u0026thinsp;0.49, R2 transfers are constrained to the minimum of D' and the total demand multiplied by a reduction factor (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e). This resulted in smaller monthly water releases, thus conserving reservoir storage and increasing WS. Furthermore, the α\u003csub\u003e3\u003c/sub\u003e values for set 2 were consistently lower than those for set 1 (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Because α\u003csub\u003e3\u003c/sub\u003e is applied when SPI3 is negative, a lower α\u003csub\u003e3\u003c/sub\u003e value reduces the drought penalty. This resulted in an increase in the (1\u0026thinsp;+\u0026thinsp;α\u003csub\u003e3\u003c/sub\u003e \u0026bull; SPI3) factor, leading to a higher WS estimation.\u003c/p\u003e \u003cp\u003eIn contrast, when evaluated using the on-site (measured) inflow data, the proposed hedging rules failed to satisfy water demand under one set of decision variables during the simulated months in 2021 and 2022. A key limitation is that the SMAP inflow data presupposes hydrological similarities between catchments (Gui et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This assumption is problematic because similarity does not ensure identical behavior, potentially leading to overestimated inflows. This may be evident in 2021, where Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003ea shows that the measured inflows were significantly lower than the SMAP estimated inflows (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). This overestimation by SMAP likely explains why the WS values in 2021 were so low (often below the S2 trigger) (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-b). In 2022, however, the measured inflow and inflow estimated by Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e were in strong agreement (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003eb) and were similar to the SMAP values (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). This improved alignment in 2022 may be attributed to favorable hydrological conditions (consistently positive SPI3 values) during that period, which contributed to higher WS values (above the S2 trigger) (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ec-d) (Hazbavi et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn 2021, the warning storage dropping below the S2 trigger pushed R1 to significantly low values (due to the α\u003csub\u003e2\u003c/sub\u003e factor), although these values were still above the priority demand requirements (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003e). Mild to extreme drought conditions also pushed R2 values below the D' requirements, but for 50% of the simulated period. In 2022, even with higher WS values (between S1 and S2) and better precipitation conditions, R1 failed to satisfy water demand because of its simplicity and sole dependence on the α\u003csub\u003e1\u003c/sub\u003e factor. With R2 transfers, on the other hand, there was no failure during the entire simulation. This finding suggests that for adaptive hedging in data-scarce drylands, the calculation method (i.e., the rule itself) is more critical than the disposal of on-site inflow measurements. Therefore, operating rules optimized using simulated data (e.g., regionalization or Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) may be effective in satisfying water demands and stakeholder requirements, even when integrated with a simple drought index and in the presence of data uncertainties.\u003c/p\u003e \u003cp\u003ePrevious hydrological modeling supports these conclusions. For instance, Rottler et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), when developing a hydrological forecasting system for the study site based on satellite monitoring and hydrological modeling, observed that it was possible to estimate storage volumes for all reservoirs in Cear\u0026aacute;. This was achievable even for reservoirs with no prior information, despite uncertainties arising from the model components. Similarly, Karamouz and Araghinejad (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) proposed hedging rules for long-term decisions in a dryland reservoir in Iran based on estimated water availability, drought indices, and inflow forecasts. They demonstrated that this operational framework significantly mitigated drought damage in the study area.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study proposed a simple hedging rule for a data-scarce dryland that is adaptive to drought conditions and incorporates the rationing ratio requirements defined by stakeholders. By developing optimized rules using estimated inflow and testing them against on-site measurements, this study suggests that hedging rules can be effectively applied even in the face of data uncertainty. The principal findings are summarized as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eDrought impacts can be mitigated by triggering early water shortages using a dynamic warning storage that considers both reservoir storage and a drought index (SPI3).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFor adaptive hedging in data-scarce drylands, the method used to define the operating rule is more critical than the disposal of on-site inflow data.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe SPI3 index proved to be an effective input for the operating rules, demonstrating its effectiveness in guiding water transfers to satisfy the demands.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors have no relevant financial interests to disclose.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eEthics statement\u003c/h2\u003e \u003cp\u003eThe authors have addressed the issue of plagiarism, and this article is free of any concerns.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe present study was supported through the National Council for Scientific and Technological Development \u0026ndash; CNPq (#307680/2023-1) and the Brazilian Federal Agency for Support and Evaluation of Graduate Education \u0026ndash; CAPES (#88887.007807/2024-00).\u003c/p\u003e\u003ch2\u003eAuthors Contributions\u003c/h2\u003e \u003cp\u003eA. J. A. Ton\u0026eacute;: Conceptualization; Formal analysis; Investigation; Methodology; Validation; Writing \u0026ndash; original draft. D. A. C. Cid: Writing \u0026ndash; review and editing. A. C. Costa: Formal analysis; supervision; Writing \u0026ndash; review and editing. C. J. P. A. Ton\u0026eacute;: Data curation; software. M. U. G. Barros: Data curation. I. E. Lima Neto: Formal analysis; supervision; Writing \u0026ndash; review and editing; Project administration.\u003c/p\u003e\u003ch2\u003e7. Acknowledgments\u003c/h2\u003e \u003cp\u003eThe authors thank the Water Resources Managament Company of Cear\u0026aacute; (COGERH) for supporting the field surveys and providing the data used in this study.\u003c/p\u003e\u003ch2\u003eData availability statement\u003c/h2\u003e \u003cp\u003eAll essential data are provided in the paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAboutalebi Mahyar BH, Omid A (2015) Optimal Monthly Reservoir Operation Rules for Hydropower Generation Derived with SVR-NSGAII. 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Environ Rev 19:333\u0026ndash;349. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1139/a11-013\u003c/span\u003e\u003cspan address=\"10.1139/a11-013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"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":"Reservoir operation, hedging rules, early rationing system, water allocation","lastPublishedDoi":"10.21203/rs.3.rs-8725090/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8725090/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA numerical hedging model for a dryland reservoir, featuring an early rationing system based on the identification of drought events, is presented. Key advantages include the optimization of decision variables (trigger volumes and rationing coefficients) using a genetic algorithm (NSGA-II), integration of water user participation, water allocation connected with drought assessments through a simple drought index, streamflow prediction based on river-aquifer dynamics, and the use of short-term field-measured hydrological data. The results show that the proposed hedging rule maintained system vulnerability below 10% using both simulated and measured inflow data, and the objective function (the modified shortage index) was successfully optimized even when early rationing occurred during the rainy season. The quantitative analysis suggests that for adaptive hedging in data-scarce drylands, the calculation method (the rule itself) is more critical than the availability of onsite inflow measurements. Therefore, operating rules for a dryland reservoir optimized using simulated data may be effective in satisfying water demands and stakeholder requirements, even when integrated with a simple drought index and in the presence of data uncertainties.\u003c/p\u003e","manuscriptTitle":"Adaptive hedging rules for a data-scarce dryland reservoir: integrating simple drought index, water user participation, and short-term hydrological monitoring","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-10 13:18:48","doi":"10.21203/rs.3.rs-8725090/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-02-09T07:17:01+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-05T15:52:01+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Water Resources Management","date":"2026-02-03T15:29:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-30T00:24:11+00:00","index":"","fulltext":""},{"type":"submitted","content":"Water Resources Management","date":"2026-01-29T05:58:04+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":"2cfbb288-1943-47e1-89cc-83203b8fb50e","owner":[],"postedDate":"February 10th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-02-10T13:18:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-10 13:18:48","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8725090","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8725090","identity":"rs-8725090","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}