Zoning of Critical Hubs of Climate Change (Flood-Drought) Using the Hydrologic Engineering Center-Hydrologic Modeling System and Copula Functions Case study: Khorramabad Basin

Zoning of Critical Hubs of Climate Change (Flood-Drought) Using the Hydrologic Engineering Center-Hydrologic Modeling System and Copula Functions Case study: Khorramabad Basin | 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 Zoning of Critical Hubs of Climate Change (Flood-Drought) Using the Hydrologic Engineering Center-Hydrologic Modeling System and Copula Functions Case study: Khorramabad Basin Maryam Robati, Pouriya Najafgholi, Hanieh Nikoomaram, Baharak Motamed Vaziri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5390435/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Climate change is currently the major challenge facing mankind, and this crisis has been the topmost global issue due to the increasing role of human activities and the high sensitivity of human societies to the threats caused by these changes. The climate changes created for humans and nature have led to risks and threats that occur on different spatial and temporal scales. Therefore, adopting policies to deal with climate change will be a critical issue in risk management. Nonetheless, identifying critical hubs in the study area helps improve the risk management process in the ​​risk assessment of climate change consequences, such as floods and droughts. Accordingly, this study mainly aimed to identify such points in the study area according to this principle. As with other parts of the world, the Khorramabad Basin (Lorestan province, Iran) is prone to serious risks in terms of climate change. This area is located as a Class III sub-basin in the Class II Karkheh basin and the Class I basin of the Persian Gulf and the Sea of ​​Oman. In this study, the critical hubs of the desired watershed were identified using the HEC-HMS rainfall simulation model to prioritize the flood-prone sub-basins of the Khorramabad Basin. The sub-basins with a high drought risk were prioritized with the detailed function (copula) statistical method. An important point in this evaluation is the use of Global Precipitation Measurement (GPM) precipitation data as common data in the analyses made in the flood and drought sections. The return rate was also calculated in both methods. The model implementation and statistical analysis revealed that the highest probability of flood occurrence belonged to the flooded part of W990, W1140, and W710 sub-basins, with respective flow volumes and maximum flow rates of 5140.8364 mm and 1389.276 m 3 /s, 539.0018 mm and 383.838 m 3 /s, and 466.8089 mm and 1561.104 m 3 /s, based on the flow volume in all the estimated return periods. In the drought section, the sub-basins W1070, W730, and W610 would be the most critical hubs in terms of drought probability, with return periods of 1.1578, 1.1923, and 1.1976 years, respectively. Climate Change Critical hubs HEC-HMS model Copula function Floods and Droughts Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The climate is a series of atmospheric conditions that determine the air temperature, precipitation, and their changes in a given region. During the last century, the chemical composition of the atmosphere has changed due to the expansion of human industrial activity, population growth, and excessive use of resources, resulting in unprecedented changes in global climate. It is noteworthy that greenhouse gases are the major cause of these changes. Evidence indicates that the earth's temperature has increased dramatically with the increase of greenhouse gases, leading to various consequences, such as effects on the hydrological cycle and, consequently, water resources, and the frequency and severity of drought and flood phenomena (Brunner et al., 2021 ; Rehman et al., 2021 ). Climate change is currently the major challenge facing humans, and this crisis has been the topmost global issue due to the increasing role of human activities and the high sensitivity of human societies to the threats caused by these changes. The climate changes that occurred for humans and nature have led to risks and threats that happen on different spatiotemporal scales. Therefore, adopting policies to deal with climate change will be a critical issue in risk management. Risk management is the prevention, planning, and evaluation process to reduce and minimize the social consequences of crises. It should be acknowledged that identifying critical hubs in the study area helps improve the risk management process in the ​​risk assessment of climate change consequences, such as floods and drought. Accordingly, this study mainly aimed to identify such points in the study area according to this principle (Ackerl et al., 2023 ). As with many parts of the world, Iran is prone to serious risks in terms of climate change consequences and is not prepared for many of these aftermaths. According to the forecasts, Iran's temperature will rise by 2°C until 2030, and downward changes will occur in the runoff of all watersheds by the same year. Such a situation increases the possibility of drought because a 2°C increase in the country's temperature will add about 27 billion m 3 to the evaporation volume and will reduce the volume of underground water supply by about 20%. This type of drought will help flood creation in addition to its destructive effects on drinking water supply and meeting the needs of industries and agriculture. This is because the vegetation will be lost and the water infiltration rate in the ground will decrease with the increase of drought. Besides, the developed impermeable bed will increase the flooding risk after all types of precipitation events. On the other hand, torrential rains occurring in a short period will replace continuous, mild, and long-term rains due to climate changes (Babaian, 2018 ). A report by the World Bank statistics claims that between 80 and 90% of all recorded disasters induced by natural hazards during the past decades have been caused by floods and droughts, affecting 3 billion people worldwide. Rising Earth's temperature increases the moisture content detained by the atmosphere, leading to more severe storms. Paradoxically, however, it also further intensifies drought periods by evaporating water and changing global weather patterns. These changes in the hydrological cycle can be accompanied by more destructive and prolonged droughts and floods that transfer these threats to areas of the globe that have never witnessed them in their memory. It is hardly possible to refer to a region that is not prone to more challenges in managing such crises in the near future. A glance at the average death rate in the areas of natural disasters reveals that almost 60,000 people have lost their lives annually because of these disasters (Pang and Zhang, 2023 ; Veloria et al., 2021 ). Nonetheless, climate change is the major problem of the globe and, consequently, Iran in this century. Therefore, it is of paramount importance to evaluate and predict these changes in the future due to their adverse effects on water resources, the natural environment, and biological, environmental, economic, social, and institutional effects (Mansouri Daneshvar et al., 2019 ; Rahimi et al., 2019 ). As mentioned above, industrial civilization and, consequently, the growth and development of urbanization account for one of the climate change causes. However, it should be borne in mind that the power of nature prevails over mankind, and the effects of these changes, particularly in cities, currently result from the feedback of our actions toward the environment (Wang and Foley, 2021 ). Additionally, the complexity of identifying and predicting urban places with a higher risk of flood and drought occurrence has led to the development of methods and models that encompass more variables to analyze the frequency and magnitude of these two phenomena. In this regard, Sahu et al. ( 2023 ) investigated and compared hydrological models. They believe that hydrological models are simple representations of a hydrological system that help the understanding, managing, forecasting, and behavior of water resources. Hydrological models are a vital component and an essential tool in the field of water resources and environmental planning. According to these authors, urbanization and industrialization significantly influence hydrological processes at the local and global levels, and therefore, planning the development and management of water resources should satisfy several needs in this context. They concluded that the HEC-HMS model showed a higher applicability in the mentioned cases than other hydrological models. Esmaeilpour ( 2023 ) used the HEC-HMS model to simulate runoff and identify sub-basins with high flood potential (Esmaeilpour, 2023 ). The simulation results showed that the flood hydrographs of the sub-basins and the outlet of the basin would be largely influenced by the morphological features and land cover, which were obtained using fuzzy logic. They presented evidence that the sub-basins with a higher flooding risk were located in upstream basins, and the highest flow rate and, consequently, the higher flooding risk belonged to sub-basins W1, W3, W7, W11, and W12, respectively. Liu et al. ( 2021 ) studied flood risk assessment in urban areas of southern Taiwan using HEC-HMS software. The authors aimed to assess the flood risk of urban areas in Kaohsiung City along the Dianbao River based on flood risks and vulnerability. To analyze the risk, they used a rainfall-runoff model (HEC-HMS) to simulate peak discharges in the basin, and the simulated discharges were used as the input for the flood model (FLO-2D). Paudel et al. ( 2019 ) applied the HEC-HMS model for runoff simulation in a case study of the Marsyangdi River basin in Nepal. They concluded that using hydrological models was very useful in assessing and predicting the occurrence of floods. The authors believe that such hydrological models (i.e., the HEC-HMS model) can be used in practical flood analysis applications to implement the simulation process of runoff precipitation more accurately and effectively. Similarly, Hamdan et al. ( 2021 ) employed the HEC-HMS model to estimate runoff values with precipitation volume information to determine the probability of floods. They used a digital elevation map (DEM) and the Hec-geoHMS extension in the framework of GIS software to identify the peak discharge of the Al-Dahim River basin and an earthen dam in Iraq with the simulated precipitation-runoff process. According to Mohammad Umer Nadeem et al. ( 2022 ), floods are on the rise globally as a result of climate change, and this aspect makes them a threat to public security and economic development. Accordingly, they utilized the HEC-HMS hydrological model in the flood risk management of the Hazara watershed in Pakistan to predict the spatiotemporal occurrence of floods to improve the necessary response time in emergencies. Drought has also been investigated in various studies using detailed functions. For instance, Nadari et al. ( 2021 ) analyzed the statistical period duration in drought risk assessment using the copula function approach in a synoptic station in Arak City. They aimed to further develop statistical methods and apply advanced mathematics to study severe phenomena such as drought. For this purpose, they investigated drought with multivariate analysis using SPEI and copula functions and the effect of the statistical period duration on drought risk assessment in the Arak synoptic station. Xiang et al. ( 2020 ) conducted a study on drought risk assessment using the multidimensional copula function approach in arid inland basins of China. They aimed to use the Standard Runaway Index (SRI) with a three-month time scale (SRI-3) to analyze the risk of hydrological drought in two dry river basins with different runoff regimes in northwest China. In a study on drought assessment in Central Asia using the probabilistic copula approach, Zhang et al. ( 2020 ) assessed drought risk in Central Asia within 3 years based on the Standardized Precipitation and Evaporation Index (SPEI). Based on SPEI-3, a drought event is defined through implementation theory. In their study, the multidimensional performance of the copula distribution based on drought risk was comprehensively calculated by sharing drought duration, drought severity, and drought peak variables. Likewise, Yu et al. ( 2021 ) examined principal component analysis (PCA)-based vulnerability and risk analysis based on copula distribution for regional drought risk assessment, aiming at evaluating the effects of drought. As stated by the authors, vulnerability and risk are terms that are generally used to assess drought risk. In their study, PCA was used to generate a general drought vulnerability index (DVI) using multiple socioeconomic indicators and drought frequency analysis based on copula distribution to calculate the drought hazard index (DHI) by considering the occurrence of meteorological drought. Azam et al. ( 2018 ) studied copula-based stochastic simulation for drought risk assessment to evaluate drought risk in South Korea. They reported that meteorological droughts were developing into frequent phenomena in different regions of this country because precipitation remarkably varied spatiotemporally. They estimated the quantiles of four identified homogeneous regions by incorporating the main drought variables (e.g., duration and severity) based on the SPI. In another study, the necessary strategies to reduce flood and drought risks simultaneously were highlighted by Ward et al. ( 2020 ), who mainly aimed to assess the risk of these natural events in an integrated manner. They believe that the occurrence of flood and drought risk has been investigated separately in most studies while floods and droughts are regarded as two sides of the water hydrological cycle. 2. Materials and methods 2.1 The study area In this research, the study area is the Khorramabad Basin located as a Class III sub-basin in the Class II Karkheh basin and the Class I basin of the Persian Gulf and the Sea of Oman. The boundaries and extent of this sub-basin encompass the Zagros Mountain range and include 425 residential areas in its span. Regarding the division situation, the southeast part of this basin can be considered verging the Class II large Karun watershed, and therefore the outlet is toward the center of the Karkheh watershed. With an area of 2481 km 2 , the Khorramabad Basin covers about 16% of the Kashkan basin and is limited to Hashtad Pahlou, Bluman, Remileh, Kouh Sefid, and Azgen mountains. It embraces the Kamalvand, Azna, Tejareh, and Kargah plains. The maximum and minimum heights of the watershed are respectively 2800 m and 1174 m at the outlet (Cham Anjir). Furthermore, the length of the mainstream and the stream network density in the Khorramabad Basin are 94 km and 0.39 km/km 2 , respectively (Fatapour et al., 2023 ). Figure 3 and 4 shows the spatial structure of the main sub-basins and the extent of the urban area in the Khorramabad Basin. To produce a homogeneous and identical comparative value, this collection was produced with the integration and combination of smaller sub-basins using the ArcHydro extension. Due to using an automatic tool for identifying spatial components, the drainage identifier or the hydro identifier was used to identify each component. 2.2 HEC-HMS model The HEC-HMS model is among the most reliable hydrological models for estimating the precipitation-runoff of basins, with wide uses in estimating flood volume and discharge. This model is one of the computerized mathematical models that is used to simulate the hydrological behavior of a watershed (Slamet and Reviana, 2021 ). In this study, the critical flood-prone points of the Khorramabad Basin were identified using this model, which is used for various research purposes, such as water supply projects, urban drainage, flood and flow rate prediction, the effect of land use change, designing dam spillways, flood control studies, and water reservoir system exploitation. In comprehensive watershed management, the control and reduction of flood-induced damage are of particular importance, and to this aim, it is necessary to identify and determine flood-prone areas at the watershed level. Nowadays, many software are available for engineering calculations and water resources. To achieve reliable results, however, engineers need to master the assumptions and calculation steps in the software, and additionally, they require practical experience in using these programs. The HEC-HMS precipitation-runoff simulation model has been developed with an emphasis on Object-Oriented programming logic. This technology provides a natural approach to expressing the problem, breaking down its complexity into comprehensible components, and using the program code to solve the problem (Hamaamin et al., 2022 ; Kassaye et al., 2021 ; Shafiei and Gharari, 2018 ). This model demonstrates the watershed as an integrated system with hydrological components. Each model component simulates an aspect of the precipitation-runoff process within a part of the watershed. In other words, various components are combined for the physical simulation of the watershed, and each component represents one of the factors of precipitation-runoff conversion in the watershed. The final flood hydrograph will be obtained from the combination of the simultaneous effect of the mentioned factors (Yilma and Kebede, 2023 ). 2.3 Detailed functions Drought is an indispensable part of natural disasters. Droughts typically begin gradually without prior warning. This phenomenon is usually developed over time with the passage of many years and, in contrast, has a long treatment process. Drought monitoring and forecasting, especially determining its onset time and duration, is particularly important in water resources management and planning to reduce its harmful consequences. Despite the high demand, it is not simply achievable to develop an algorithm to determine drought prediction through physical or statistical analyses. Another main obstacle to drought statistical analysis is the complexity of the real causes of drought, making its characterization difficult; on the other hand, no precise and comprehensive definition is available for this subject (Li et al., 2023 ; Sobhani et al., 2019 ). In addition, the characteristics of this phenomenon, such as severity and duration, are infinitely correlated, and paying attention to this issue is necessary for the drought assessment analysis. To implement a multivariate analysis, the use of detailed functions (copula), used in this research to determine the critical drought points in the Khorramabad Basin, provides a more complete characterization of drought (Xiao et al., 2019 ). Sklar (1959) was the first to propose the idea of detailed functions to establish links between multivariate distributions with the corresponding univariate marginal distributions. These functions, which develop a multivariate distribution using univariate marginal distributions and can well describe their inter-correlations, have multiple advantages. Some of their merits include no limitation in choosing and using the functions of marginal distributions and structural dependence, usability for more than two variables, separate examination of marginal and structural distributions, and a good depiction of the relationship between two or more variables (Achite et al., 2022 ; Durante and Sempi, 2016 ; Wang et al., 2021 ). In addition to drought analysis, these functions can be used in other analyses, such as floods, storms, and other natural disasters, by establishing correlations between hydrological variables (Liu et al., 2020 ; Nazeri Tahroudi et al., 2021 ). 2.4 Precipitation data Precipitation is a major meteorological element and one of the factors influencing the hydrological cycle. It is necessary for humans and accounts for the main source of freshwater supply for humans, plants, and other living organisms (Veloria et al., 2021 ). An average precipitation of 700–900 mm is estimated on the earth's surface. Nevertheless, changes in global precipitation are such that some areas (e.g., deserts) may have received no types of precipitation for several consecutive years. Precipitation is generally high over seas and oceans, and the precipitation level decreases with moving away from these areas. Based on a rule of thumb, drier weather reduces the confidence in precipitation (Kuttippurath et al., 2021 ). In Iran, diverse climatic and topographic features have led to changes in precipitation levels in different spatiotemporal scales. For this reason, the variability and extreme fluctuation of precipitation are expected in arid and semi-arid areas, including in the plateau of Iran. On the one hand, severe droughts pose heavy damage to the environment and economy of Iran, and torrential rains, on the other hand, lead to destructive floods, which are among the familiar phenomena all over this country. In terms of latitude and proximity to the high-pressure subtropical region, Iran possesses a fluctuating precipitation regime in addition to the shortage of precipitation. Few annual precipitations, severe annual and seasonal fluctuations, short precipitation periods, and precipitations in the form of heavy and sudden showers are considered the conspicuous features of the precipitation regime in this country(Doostan, 2020b ; Mirzaei Hassanlu et al., 2024 ; Sharafi and Mir Karim, 2020 ). Lorestan province and, consequently, the Khorramabad Basin are not exempted from this general rule. Since the province is among the mountainous regions of Iran, the regional precipitation can differ in spatiotemporal distribution because local precipitation can be affected by the local elevation arrangement (Mirhashemi and Hasanvand, 2023 ). In this study, the critical hubs in the flood and drought sections were studied and determined using the GPM precipitation data (obtained from the NASA website) available from September 22, 2002, at 24:00 to October 22, 2022, at 24 as the end of the study period ( https://giovanni.gsfc.nasa.gov/giovanni/ ). These data were used due to their high measurement accuracy vs. incomplete and highly erroneous ground data (Iryani et al., 2023 ). As an important point, the NASA calculations on temperature, as an important factor in the precipitation regime, indicate that the climate has become very acute in the last 20 years (Kheyruri et al., 2024 ). Another reason for choosing this type of data in this study is because many climatic phenomena have occurred in the presented time range. For example, half of the floods in Iran in the last 50 years have occurred in the last 15 years. In the last half century, about 4,000 floods have been recorded in Iran, more than 2,000 of which occurred in the last 15 years. Additionally, the precipitation in Iran reached 50% of previous years and 40% less than the long-term average in recent wet years. These facts reveal that the climate change process and the influence of factors affecting the incidence of floods and droughts have increased in the last few years (Darand and Sohrabi, 2018 ; Doostan, 2020a ; Durante and Sempi, 2016 ; JaliliSadrabad et al., 2023 ; Modarres et al., 2016 ). In this study, the accuracy of GPM data was verified using a comparison with the statistical distribution of observed precipitation in the target area (Santos et al., 2018 ). Based on the analysis of the results, GPM data of the IMERG type are highly accurate in the Khorramabad Basin. In addition, it can be claimed that the average error of the data was 10 mm, suggesting that the average precipitation measured by GPM data differs by about 10 mm from the average actual precipitation. The calculations showed a standard data error of 5 mm, indicating the dispersion of GPM data (about 5 mm) around the average actual precipitation. Furthermore, the correlation coefficient of the data (0.95) discloses the well-correlated GPM data and the reference data. According to the validation results, it can be concluded that the GPM data in the studied watershed are reliable for various purposes, including watershed studies and water resources management. Analysis of results (Flood) 2.5 Arc-Hydro extension and Hec-geoHMS In this part of the study, the details of the inputs of the precipitation-runoff model were extracted using the morphological features of the watershed (morphometry). This procedure has multiple goals, one of which is to determine the geomorphological parameters to specify the hydrological response of the watershed. Morphometry is a study of the physical features and morphological condition of a watershed, which can decisively influence its hydrological characteristics and water regime. Information on the physiographic characteristics of a watershed together with information about the regional weather conditions can produce a relatively accurate image of the quantitative and qualitative functioning of the hydrological system of that watershed (Mahala, 2020 ). The hydrological phenomena that occur in a watershed can be linked to morphometric parameters, including surface area, perimeter, length, distance to the center of gravity of the watershed, height, slope, slope aspect, watershed shape, compactness coefficient, longitudinal profile of the mainstream (net slope and gross slope), drainage density, the bifurcation ratio, and Horton's laws (law of number, law of length, law of area, and law of stream slope) (Harsha et al., 2020 ). Therefore, these parameters influence the flood phenomenon to the hydrological reactions of the watershed to the precipitation that appears as runoff, affecting the severity, weakness, flood flow, and water balance (Loudyi and Kantoush, 2020 ; Ozdemir and Akbas, 2023 ). Table 1 The summarized physiography of the Khorramabad Basin Parameter Symbol Value Watershed area A (m 2 ) 2491931101 Watershed perimeter P (km) 370452.950 Watershed length L (km) 119392.863 Distance to the center of gravity of the watershed L ca (km) 46643.242 Average height of the watershed H (m) 1602.22 Watershed average slope S (Pct) 25.270 Watershed average slope aspect Aspect (Degree) South Watershed form factor FF 0.175 Watershed shape factor SF 5.720 Watershed compactness coefficient C 2.078 Watershed circularity ratio R c 0.232 Watershed elongation ratio R e 0.472 Watershed equivalent rectangle length L (m) 170621.446 Watershed equivalent rectangle width B (m) 14605.029 Form factor L l 9.994 Runoff curve number - 71.859 Watershed drainage density µ(1/km) 0.409 Watershed bifurcation ratio BR 3.103 The law of stream numbers Nu \(\:{\text{N}}_{\text{u}}=(103/3{)}^{4-\text{u}}\) The law of stream length Li (km) \(\:{\text{L}}_{\text{i}}=(886/9)(261/1{)}^{\text{i}-1}\) The law of stream area Ai (km 2 ) \(\:{\text{A}}_{\text{i}}=(243940/5)(168/1{)}^{\text{i}-1}\) The law of stream slope Si (Pct) \(\:{\text{S}}_{\text{i}}=(113/0)(387/0{)}^{\text{i}-1}\) The following indices as Arc-Hydro supplementary primary data can be mentioned to prepare the spatial data of the Khorramabad Basin: - The raster index of the digital elevation model (DEM) of the study area - The stream network index - The land use index of the country - Isohyets of the country 2.6 Implementation of the HEC-HMS model The results were implemented using version 1.4.4 of this model. The result (Fig. 5 ) was obtained by selecting the Hec-geoHMS extension output in the HEC-HMS model and choosing the background schematic images created in the previous steps from the following path. Next, the examined parameters that required redefinition or corrections include the basic coefficient of base flow by the recession method, called Ratio to Peak and Recession Constant (Nazirah et al., 2021 ), the two X and K coefficients in the sub-basin flood routing method, called Muskingum (Ansari et al., 2023 ; Chakraborty and Biswas, 2021 ; Lohpaisankrit et al., 2021 ), the curve number (SCS-CN) hydrograph (Poonia et al., 2021 ; Verma et al., 2022 ) used in the precipitation-runoff model development, and Schneider's unit hydrograph (Rajkumar et al., 2021 ) to prepare the hydrograph of the whole watershed. 2.7 The Decision Support System "DSS" data model for precipitation data In a DSS, the precipitation data were recorded and saved using the DSS database model. The precipitation data were saved according to the 6-hour cumulative nature. The discharge data in five hydrometric stations of the Khorramabad Basin with the related settings were introduced to the mentioned model. These numbers are a 24-hour average. Then, the hypothetical start and end time and simulation steps were reviewed in the content of Control Specifications. According to the observational numbers, the simulation middle time range was a value of 2 h. The peak discharge and the maximum flow volume were calculated in each sub-basin by running the model and according to the target scenario, i.e., identifying the critical hubs of the watershed. Analysis of the results (Drought) 2.8 R-Studio software R-Studio software is considered a graphical interface with R software, which was used in this study for calculations of SPI-based drought risk assessment using detailed functions. This software provides an attractive and flexible environment for users or coders compared to R software (Baral et al., 2023 ; Hussain and Pal, 2023 ; Kassaye et al., 2021 ). For the drought analyses, datasets (precipitation series) were recalled in R-Studio software. To this end, copula and Vine copula packages (Bai et al., 2021 ; Coblenz, 2021 ; Latif and Mustafa, 2020 ) were first extracted to implement the coding process. This recall was performed for all the 39 studied sub-basins according to the Library command in the software environment. It is important to note that the written codes can be viewed more clearly in Notepad. Then, a separate loop was determined for each code to perform all the calculations automatically. The codes can be divided into two parts, the first belonging to drought severity and duration variables, and the second assigning to fit and capability (choosing the most suitable detailed function) and calculations of the return rate. In this study, the detailed functions of Frank (Ekanayake and Perera, 2014 ; Nabaei et al., 2019 ) and combined Joe-Frank detailed functions (Li et al., 2020 ) were selected based on the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) (Achite et al., 2022 ; Ko et al., 2019 ; Li et al., 2020 ; Yu et al., 2021 ). The parameters of detailed functions were calculated using the Log criterion (Achite et al., 2022 ; Azhdari et al., 2020 ; EskandariPour and Soltaninia, 2022 ). To analyze two or more variables of a phenomenon using detailed functions, it is necessary to first identify the univariate distributions of the variables. Accordingly, univariate distributions (e.g., normal, log-normal, exponential, and gamma distributions) were also fitted to the studied data. The most suitable distribution was chosen based on numerical tests of the goodness of fit, i.e. Kolmogorov-Smironov (KS), Anderson- Darling (AD), and chi-square (Deger et al., 2023 ; Hesami Afshar et al., 2016 ; Nomsa Keitumetse and Mengistu Tsidu, 2020 ). In the first two tests, the best distribution is obtained by comparing the empirical and parametric cumulative distribution functions (CDF) (distribution function obtained from the data). However, the chi-square test is directly linked to the frequency such that the empirical frequency and the frequency calculated from the parametric distribution are compared to obtain the difference between them. In this research, the marginal distributions of drought variables were determined using empirical relationships. 3. Discussion and conclusion The climate change phenomenon refers to all long-term changes in weather conditions, and climate change is currently the most critical environmental threat to the planet. The area studied in this research has always been prone to this phenomenon. Khorramabad Basin in Lorestan province is one of the most flood-prone regions of Iran so the incident floods in this watershed have greatly damaged various agricultural sectors, buildings, villages, cities, communication lines, and other sectors in recent years. In addition to the threats caused by floods in this watershed, the study of climate change impacts in recent years shows that the temperature in this region has marked an unusual increase the same as other global regions. With the elevated temperature, decreased precipitation, and increased evapotranspiration, the Khorramabad Basin is threatened by an unprecedented hydrological drought as a climatic phenomenon. Unlike previous investigations, our studies on climate change were conducted in a region where floods and droughts are important and, on the other hand, different residential areas are involved at the time of occurrence. A flood-prone area threatened by the shadow of drought at the same time, while it does not encompass urban and residential areas, will not be a suitable area for the precipitation-runoff model simulation and statistical calculations of drought, producing no suitable output. Thus, such a research project is somewhat insignificant and practically aimless and theoretical. In this study, therefore, 425 residential areas were recognized in 39 sub-basins identified in the Khorramabad Basin, indicating the importance of residential areas in this type of research. Drought and flood are two sides of the same coin, and the studied watershed has always been prone to these two climatic consequences. A major issue in climate change studies is to create a link between these two phenomena. In this research, therefore, a common type of GPM precipitation data was used during a statistical period (2002–2022), and flood simulation and drought analysis were simultaneously studied using detailed functions. Thus, this study tried to consider the aforementioned link by identifying and prioritizing critical hubs of floods and droughts with an emphasis on the return rate of these two phenomena, which is a marked distinctive point compared to previous studies. The flood and drought risk was evaluated individually in most of the past studies, while these two phenomena were analyzed and assessed simultaneously in this research. Since a critical issue in hydrological studies, particularly concerning floods and droughts, is to address the return rate of these two phenomena, this study employed methods for zoning and identifying the critical hubs of floods and droughts. Both emphasize the return rate, and the sub-basins in the study area were also prioritized based on the same criterion, which is completely different from the literature. The results for identifying the critical hubs of floods were analyzed separately in the return periods of 5, 10, 25, 50, 100, 200, 1000, and 10000 years. The identified sub-basins with the highest risk of flooding will be the same in all return rates. Furthermore, the target areas were prioritized to identify the points of drought, with an emphasis on the return period of this phenomenon. Additionally, the results revealed a better condition regarding the threat of drought in the sub-basins with a high risk of flooding, and those with a high risk of drought were not in a good condition in terms of flood incidence and, consequently, precipitation. A crucial principle in the risk management process of natural phenomena is to pay attention to the degree of vulnerability of the study area. In this study, risk assessment methods, such as Bow-Tie, Environmental Impact Assessment (ENVID), Fault Tree Analysis (FTA), and Event Tree Analysis (ETA), can be utilized to fully explain the causes of floods and droughts with an emphasis on resilience. As such, the necessary corrective measures to reduce the vulnerability of the areas can be suggested according to the principle of resilience. 3.1 Floods with specified return periods A basic goal of precipitation-runoff models is to estimate the exact volume and hydrograph shape of floods after precipitation with a specified return period (Al-Hussein et al., 2022 ; Ben Khélifa and Mosbahi, 2022 ). In this study, the instantaneous maximum discharge and flow volume were calculated for all sub-basins according to the return rates of 2, 5, 10, 25, 50, 100, 200, 1000, and 10000 years by running the model and examining the hydrometric statistics. The flood at the outlet and the urban area of the Khorramabad Basin along with the runoff volume is shown in each sub-basin. For example, Figs. 7 , 8 , and 9 depict precipitation flow hydrographs with a return period of 10,000 years. 3.2 Identification of flood critical hubs in the Khorramabad Basin As with other hydrological phenomena, a flood is a random phenomenon that may occur at any time and place. For this reason, it is not usually possible to determine the exact time of the flood, but its occurrence can be predicted according to the hydrological events observed in the past. The HEC-HMS model is among the hydrological models with a very high efficiency in flood warning projects worldwide. In this research, this model was used to simulate the volume and peak flow of floods in the Khorramabad Basin to identify and prioritize the critical hubs during the 20 statistical years (2002–2022) and to explain its steps. Separate data are collected in an integrated set in the modeling process to enable managers or users to implement their scenarios in a tool that has a decision-making environment. According to running the HEC-HMS precipitation-runoff model, the scenario of interest may be recognized based on the areas that are most at risk along the watershed stream network, the location of critical hubs, or flood demonstration in each zone. This study mainly aimed to investigate floods with the mentioned model to identify critical hubs in the Khorramabad Basin. According to the results obtained in the previous stages and the scenario of interest, hydrometric data were provided for the output of the obtained model. The results indicated that the highest probability of flood occurrence belonged to the W990, W1140, and W710 sub-basins, with respective flow volumes and maximum flow rates of 5140.8364 mm and 1389.276 m 3 /s, 539.0018 mm and 383.838 m 3 /s, and 466.8089 mm and 1561.104 m 3 /s, based on the flow volume in all the estimated return periods. The W990 sub-basin includes 12 residential areas, consisting of Jam Kaboud, Jodol Dol, Sarhelt, Gholaman Sofla, Carwash Factory, Cement & Plaster Factory, Biran Plaster Factory, Jazayeri Farm, Sefid Dasht, Gholaman Olya, Hassan Abad, and Sabour villages. 3.3 Drought with specified return periods As mentioned in the flood section, the return period means the time during which a phenomenon (e.g., drought and flood) reoccurs with a given volume or severity (Avsaroglu and Gumus, 2022 ; da Rocha Júnior et al., 2020 ; Kavianpour et al., 2020 ; Mirabbasi et al., 2012 ). In this study, the calculated return period was implemented as a common return period in the (or) mode. The return period in the (or) mode is much stricter than that in the (and) mode. It denotes the time to calculate a phenomenon with two random variables X and Y in a situation where one of these two variables (or both) exceeds its threshold (> 1). Accordingly, drought duration and severity variables (Khan et al., 2021 ; Poonia et al., 2021 ) were analyzed in this study. 3.4 Identification of drought critical hubs Drought is a natural climatic phenomenon that creates various effects on socioeconomic and environmental sectors. The continued drought in a region latently weakens and eventually destroys natural ecosystems in the long term. In the last decade, the tangible drought consequences due to the increased drought frequency and severity in different parts of Iran, such as the Khorramabad Basin, have persuaded planners and managers to seek strategies to deal with this event. Therefore, it is currently necessary to understand the drought behavior in given periods and determine the areas with a higher risk of facing this natural complication in the crisis management process. In this study, the critical hubs in the Khorramabad Basin were identified during a statistical period of 20 years (2002–2022) in the drought section, and the return period of this phenomenon was calculated using the obtained results. To this aim, the drought was analyzed using detailed functions based on the SPI index, and drought severity and duration variables were extracted according to this index. Kendall's correlation coefficient values were considered for these characteristics. Next, marginal distributions were estimated empirically, and then the most appropriate detailed function was selected based on AIC and BIC criteria. To rank the basins, the return period was calculated in two modes: drought severity > 1 or drought duration > 1. The ranking results (Table X) show that the highest risk of flooding belongs to sub-basins W1070, W730, and W610 with return periods of 1.1578, 1.1923, and 1.1976 years, respectively. Moreover, the W1070 sub-basin embraces 35 residential areas comprising, for example, Mian Gol woodcarving, Dinarvand Sofla and Olya, Cheshme Sorkheh, Chenar Khaibari, Deh Bagher, Upper and Lower Anardor, Sorkheh Deh Oliya and Sofla, Cheshmeh Ali, and Gol Ghaleh villages. Table 2 The results of selecting the most appropriate detailed function between the drought severity and duration variables and the return period calculation to prioritize the sub-basins Basin Kendall's correlation coefficient Detailed family 1st parameter 2nd parameter Log-likelihood function AIC BIC Return period {or} Rank W600 0.4346 5 4.6197 0.0000 13.8659 -25.7317 -23.6374 1.2007 5 W610 0.4156 5 4.3133 0.0000 12.5567 -23.1134 -21.0191 1.1976 3 W640 0.4832 5 5.3112 0.0000 17.6810 -33.3620 -31.2676 1.2987 22 W650 0.3803 10 2.7351 0.8786 12.4977 -20.9954 -16.8067 1.2219 6 W660 0.4296 5 4.3811 0.0000 13.3296 -24.6592 -22.5648 1.3801 35 W680 0.4310 5 4.4871 0.0000 13.4308 -24.8615 -22.7672 1.3579 33 W690 0.4086 5 4.2862 0.0000 12.5213 -23.0426 -20.9482 1.2394 8 W700 0.4497 5 4.8026 0.0000 14.9012 -27.8025 -25.7081 1.3900 36 W710 0.4292 5 4.4537 0.0000 13.3451 -24.6901 -22.5958 1.2637 15 W730 0.3828 5 3.8483 0.0000 10.4521 -18.9042 -16.8099 1.1923 2 W740 0.4086 10 2.6199 0.9197 14.1261 -24.2521 -20.0634 1.2659 16 W750 0.4548 5 4.6357 0.0000 14.0692 -26.1385 -24.0441 1.3127 24 W760 0.3726 5 3.5712 0.0000 9.7255 -17.4509 -15.3566 1.2699 19 W780 0.4488 10 2.7606 0.9236 16.4058 -28.8116 -24.6229 1.4155 38 W790 0.4084 10 2.5997 0.9323 15.0017 -26.0034 -21.8147 1.3349 29 W820 0.3939 5 3.7762 0.0000 10.4405 -18.8809 -16.7866 1.3182 26 W830 0.4902 5 5.1903 0.0000 16.7748 -31.5497 -29.4553 1.2502 11 W850 0.4480 5 4.6849 0.0000 14.1280 -26.2560 -24.1617 1.2670 17 W870 0.4210 10 3.2437 0.8638 15.9670 -27.9341 -23.7454 1.3004 23 W880 0.4973 5 5.3932 0.0000 17.8902 -33.7803 -31.6860 1.4293 39 W890 0.3758 5 3.8386 0.0000 10.3494 -18.6988 -16.6044 1.2328 7 W900 0.4299 5 4.3782 0.0000 13.2243 -24.4486 -22.3542 1.1983 4 W920 0.4047 5 4.1469 0.0000 12.0124 -22.0248 -19.9305 1.2810 21 W940 0.3876 10 2.5830 0.9053 13.0803 -22.1606 -17.9719 1.2619 14 W980 0.4303 5 4.2903 0.0000 12.8704 -23.7408 -21.6465 1.3535 31 W990 0.4280 5 4.3150 0.0000 12.8670 -23.7340 -21.6396 1.3541 32 W1000 0.4120 5 4.2268 0.0000 12.3940 -22.7879 -20.6936 1.3283 27 W1010 0.4072 10 2.4563 0.9472 14.7474 -25.4947 -21.3060 1.4027 37 W1020 0.3754 10 2.5169 0.9116 12.5748 -21.1495 -16.9608 1.3486 30 W1050 0.4360 5 4.3821 0.0000 13.3723 -24.7445 -22.6502 1.3316 28 W1060 0.4079 10 2.7107 0.9067 14.2089 -24.4177 -20.2290 1.2458 10 W1070 0.4161 5 4.3565 0.0000 12.7425 -23.4850 -21.3906 1.1578 1 W1080 0.4665 5 4.7944 0.0000 15.0915 -28.1830 -26.0886 1.3153 25 W1090 0.4620 5 4.7748 0.0000 15.1246 -28.2493 -26.1549 1.3640 34 W1100 0.4527 5 4.7600 0.0000 15.0675 -28.1349 -26.0406 1.2680 18 W1110 0.4194 5 4.2872 0.0000 12.7090 -23.4180 -21.3237 1.2612 12 W1120 0.4559 10 3.3497 0.8582 17.0392 -30.0783 -25.8896 1.2796 20 W1130 0.4319 5 4.2961 0.0000 12.5482 -23.0963 -21.0020 1.2613 13 W1140 0.3794 10 2.6421 0.8941 12.8181 -21.6362 -17.4475 1.2415 9 Declarations Funding support The authors also wish to acknowledge the generous financial support provided by the Islamic Azad University, Science and Research Branch, Tehran, which significantly contributed to the advancement of this study's objectives. Declaration of competing interest The authors declare that they have no conflicts of interest regarding the publication of this paper. The research was conducted solely for academic purposes and was not influenced by any external commercial or financial relationships. Author Contribution Author Contributions StatementThe contributions of each author to this manuscript are as follows:1. Maryam Robati (First and Corresponding Author): Data collection, analysis and interpretation of results, and contribution to writing relevant sections of the manuscript.2.Pouriya Najafgholi (Second Author ): Conceptualization and design of the study, methodology, writing the main manuscript text, and coordinating the overall research process.3. Hanieh Nikoomaram (Third Author): Reviewing and editing the manuscript, ensuring scientific accuracy and content integrity.4. Baharak Motamed Vaziry (Fourth Author): Preparing figures and tables, and reviewing and approving the final content and data presentation.All authors confirm that there are no conflicts of interest and that ethical responsibility for the content of the manuscript rests with all authors. Additionally, all authors have reviewed and approved the final version of the MANUSCRIPT. Acknowledgements This article has been extracted from the PhD dissertation in the field of Environmental Science and Engineering, which was approved and defended at the Islamic Azad University, Science and Research Branch, Tehran, Iran. The authors would like to express their sincere gratitude to the esteemed president and the research officials of the Faculty of Natural Resources and Environment at the university. 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Yu et al., 2021)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/af69c14b5ab615781b6d17ca.png"},{"id":70926883,"identity":"31b9a309-902a-42d5-aa10-d77c650e8389","added_by":"auto","created_at":"2024-12-09 09:17:55","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":245608,"visible":true,"origin":"","legend":"\u003cp\u003eLocations of the studied sub-basins in the Class II spatial location of the country (Fatapour et al., 2023)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/8e4ab4d97516619dba5c3f0f.png"},{"id":70926227,"identity":"c26c3722-6289-47e3-8956-2447c4e14d39","added_by":"auto","created_at":"2024-12-09 09:09:55","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":821017,"visible":true,"origin":"","legend":"\u003cp\u003eResidential areas of the Khorramabad Basin\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/aabd5e1d915f4658f259f78e.png"},{"id":70926222,"identity":"b649841b-ce95-4d4d-9099-c1c2743f5777","added_by":"auto","created_at":"2024-12-09 09:09:55","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":216194,"visible":true,"origin":"","legend":"\u003cp\u003eSub-basins of the Khorramabad Basin\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/87638bbe84e66bb35674619e.png"},{"id":70926884,"identity":"7cb3e1b0-4a9f-451a-b81c-4ff60d4be66b","added_by":"auto","created_at":"2024-12-09 09:17:55","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":468296,"visible":true,"origin":"","legend":"\u003cp\u003eExecution of the final model output from the HEC-GeoHMS extension in the HMS model\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/981380762aea1469dd4d7c52.png"},{"id":70928132,"identity":"c96f4a17-738f-4fd0-a036-aeeea7d7fbe4","added_by":"auto","created_at":"2024-12-09 09:25:55","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":123127,"visible":true,"origin":"","legend":"\u003cp\u003eThe precipitation flow hydrograph with a return period of 1000 years in the urban area of the Khorramabad Basin\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/66c890b940d6275334ba8e2c.png"},{"id":70926885,"identity":"daf49ec4-2beb-4b82-badd-4022d90f7597","added_by":"auto","created_at":"2024-12-09 09:17:55","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":133908,"visible":true,"origin":"","legend":"\u003cp\u003eThe precipitation flow hydrograph with a return period of 10,000 years at the outlet of the Khorramabad Basin\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/a2eada7f140af15721e445ba.png"},{"id":70926225,"identity":"f446e74a-3295-4d59-a66e-c0231ae209a9","added_by":"auto","created_at":"2024-12-09 09:09:55","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":72920,"visible":true,"origin":"","legend":"\u003cp\u003eA statistical summary of precipitation flow with a return period of 10,000 years in the urban area of the Khorramabad Basin\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/f8a356c3fcc6606c3cd914a4.png"},{"id":72323487,"identity":"43fb00c1-9d72-40c7-9076-d3b9f77422a7","added_by":"auto","created_at":"2024-12-25 11:01:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3191948,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5390435/v1/6524d5d3-cb7a-43e8-bf09-870a2816fdec.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Zoning of Critical Hubs of Climate Change (Flood-Drought) Using the Hydrologic Engineering Center-Hydrologic Modeling System and Copula Functions Case study: Khorramabad Basin","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe climate is a series of atmospheric conditions that determine the air temperature, precipitation, and their changes in a given region. During the last century, the chemical composition of the atmosphere has changed due to the expansion of human industrial activity, population growth, and excessive use of resources, resulting in unprecedented changes in global climate. It is noteworthy that greenhouse gases are the major cause of these changes. Evidence indicates that the earth's temperature has increased dramatically with the increase of greenhouse gases, leading to various consequences, such as effects on the hydrological cycle and, consequently, water resources, and the frequency and severity of drought and flood phenomena (Brunner et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Rehman et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Climate change is currently the major challenge facing humans, and this crisis has been the topmost global issue due to the increasing role of human activities and the high sensitivity of human societies to the threats caused by these changes. The climate changes that occurred for humans and nature have led to risks and threats that happen on different spatiotemporal scales. Therefore, adopting policies to deal with climate change will be a critical issue in risk management. Risk management is the prevention, planning, and evaluation process to reduce and minimize the social consequences of crises. It should be acknowledged that identifying critical hubs in the study area helps improve the risk management process in the ​​risk assessment of climate change consequences, such as floods and drought. Accordingly, this study mainly aimed to identify such points in the study area according to this principle (Ackerl et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). As with many parts of the world, Iran is prone to serious risks in terms of climate change consequences and is not prepared for many of these aftermaths. According to the forecasts, Iran's temperature will rise by 2\u0026deg;C until 2030, and downward changes will occur in the runoff of all watersheds by the same year. Such a situation increases the possibility of drought because a 2\u0026deg;C increase in the country's temperature will add about 27\u0026nbsp;billion m\u003csup\u003e3\u003c/sup\u003e to the evaporation volume and will reduce the volume of underground water supply by about 20%. This type of drought will help flood creation in addition to its destructive effects on drinking water supply and meeting the needs of industries and agriculture. This is because the vegetation will be lost and the water infiltration rate in the ground will decrease with the increase of drought. Besides, the developed impermeable bed will increase the flooding risk after all types of precipitation events. On the other hand, torrential rains occurring in a short period will replace continuous, mild, and long-term rains due to climate changes (Babaian, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). A report by the World Bank statistics claims that between 80 and 90% of all recorded disasters induced by natural hazards during the past decades have been caused by floods and droughts, affecting 3\u0026nbsp;billion people worldwide. Rising Earth's temperature increases the moisture content detained by the atmosphere, leading to more severe storms. Paradoxically, however, it also further intensifies drought periods by evaporating water and changing global weather patterns. These changes in the hydrological cycle can be accompanied by more destructive and prolonged droughts and floods that transfer these threats to areas of the globe that have never witnessed them in their memory. It is hardly possible to refer to a region that is not prone to more challenges in managing such crises in the near future. A glance at the average death rate in the areas of natural disasters reveals that almost 60,000 people have lost their lives annually because of these disasters (Pang and Zhang, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Veloria et al., \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Nonetheless, climate change is the major problem of the globe and, consequently, Iran in this century. Therefore, it is of paramount importance to evaluate and predict these changes in the future due to their adverse effects on water resources, the natural environment, and biological, environmental, economic, social, and institutional effects (Mansouri Daneshvar et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Rahimi et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs mentioned above, industrial civilization and, consequently, the growth and development of urbanization account for one of the climate change causes. However, it should be borne in mind that the power of nature prevails over mankind, and the effects of these changes, particularly in cities, currently result from the feedback of our actions toward the environment (Wang and Foley, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additionally, the complexity of identifying and predicting urban places with a higher risk of flood and drought occurrence has led to the development of methods and models that encompass more variables to analyze the frequency and magnitude of these two phenomena. In this regard, Sahu et al. (\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) investigated and compared hydrological models. They believe that hydrological models are simple representations of a hydrological system that help the understanding, managing, forecasting, and behavior of water resources. Hydrological models are a vital component and an essential tool in the field of water resources and environmental planning. According to these authors, urbanization and industrialization significantly influence hydrological processes at the local and global levels, and therefore, planning the development and management of water resources should satisfy several needs in this context. They concluded that the HEC-HMS model showed a higher applicability in the mentioned cases than other hydrological models. Esmaeilpour (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) used the HEC-HMS model to simulate runoff and identify sub-basins with high flood potential (Esmaeilpour, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The simulation results showed that the flood hydrographs of the sub-basins and the outlet of the basin would be largely influenced by the morphological features and land cover, which were obtained using fuzzy logic. They presented evidence that the sub-basins with a higher flooding risk were located in upstream basins, and the highest flow rate and, consequently, the higher flooding risk belonged to sub-basins W1, W3, W7, W11, and W12, respectively. Liu et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) studied flood risk assessment in urban areas of southern Taiwan using HEC-HMS software. The authors aimed to assess the flood risk of urban areas in Kaohsiung City along the Dianbao River based on flood risks and vulnerability. To analyze the risk, they used a rainfall-runoff model (HEC-HMS) to simulate peak discharges in the basin, and the simulated discharges were used as the input for the flood model (FLO-2D). Paudel et al. (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) applied the HEC-HMS model for runoff simulation in a case study of the Marsyangdi River basin in Nepal. They concluded that using hydrological models was very useful in assessing and predicting the occurrence of floods. The authors believe that such hydrological models (i.e., the HEC-HMS model) can be used in practical flood analysis applications to implement the simulation process of runoff precipitation more accurately and effectively. Similarly, Hamdan et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) employed the HEC-HMS model to estimate runoff values with precipitation volume information to determine the probability of floods. They used a digital elevation map (DEM) and the Hec-geoHMS extension in the framework of GIS software to identify the peak discharge of the Al-Dahim River basin and an earthen dam in Iraq with the simulated precipitation-runoff process. According to Mohammad Umer Nadeem et al. (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), floods are on the rise globally as a result of climate change, and this aspect makes them a threat to public security and economic development. Accordingly, they utilized the HEC-HMS hydrological model in the flood risk management of the Hazara watershed in Pakistan to predict the spatiotemporal occurrence of floods to improve the necessary response time in emergencies.\u003c/p\u003e \u003cp\u003eDrought has also been investigated in various studies using detailed functions. For instance, Nadari et al. (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) analyzed the statistical period duration in drought risk assessment using the copula function approach in a synoptic station in Arak City. They aimed to further develop statistical methods and apply advanced mathematics to study severe phenomena such as drought. For this purpose, they investigated drought with multivariate analysis using SPEI and copula functions and the effect of the statistical period duration on drought risk assessment in the Arak synoptic station. Xiang et al. (\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) conducted a study on drought risk assessment using the multidimensional copula function approach in arid inland basins of China. They aimed to use the Standard Runaway Index (SRI) with a three-month time scale (SRI-3) to analyze the risk of hydrological drought in two dry river basins with different runoff regimes in northwest China. In a study on drought assessment in Central Asia using the probabilistic copula approach, Zhang et al. (\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) assessed drought risk in Central Asia within 3 years based on the Standardized Precipitation and Evaporation Index (SPEI). Based on SPEI-3, a drought event is defined through implementation theory. In their study, the multidimensional performance of the copula distribution based on drought risk was comprehensively calculated by sharing drought duration, drought severity, and drought peak variables. Likewise, Yu et al. (\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) examined principal component analysis (PCA)-based vulnerability and risk analysis based on copula distribution for regional drought risk assessment, aiming at evaluating the effects of drought. As stated by the authors, vulnerability and risk are terms that are generally used to assess drought risk. In their study, PCA was used to generate a general drought vulnerability index (DVI) using multiple socioeconomic indicators and drought frequency analysis based on copula distribution to calculate the drought hazard index (DHI) by considering the occurrence of meteorological drought. Azam et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) studied copula-based stochastic simulation for drought risk assessment to evaluate drought risk in South Korea. They reported that meteorological droughts were developing into frequent phenomena in different regions of this country because precipitation remarkably varied spatiotemporally. They estimated the quantiles of four identified homogeneous regions by incorporating the main drought variables (e.g., duration and severity) based on the SPI. In another study, the necessary strategies to reduce flood and drought risks simultaneously were highlighted by Ward et al. (\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), who mainly aimed to assess the risk of these natural events in an integrated manner. They believe that the occurrence of flood and drought risk has been investigated separately in most studies while floods and droughts are regarded as two sides of the water hydrological cycle.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 The study area\u003c/h2\u003e\n \u003cp\u003eIn this research, the study area is the Khorramabad Basin located as a Class III sub-basin in the Class II Karkheh basin and the Class I basin of the Persian Gulf and the Sea of Oman. The boundaries and extent of this sub-basin encompass the Zagros Mountain range and include 425 residential areas in its span. Regarding the division situation, the southeast part of this basin can be considered verging the Class II large Karun watershed, and therefore the outlet is toward the center of the Karkheh watershed. With an area of 2481 km\u003csup\u003e2\u003c/sup\u003e, the Khorramabad Basin covers about 16% of the Kashkan basin and is limited to Hashtad Pahlou, Bluman, Remileh, Kouh Sefid, and Azgen mountains. It embraces the Kamalvand, Azna, Tejareh, and Kargah plains. The maximum and minimum heights of the watershed are respectively 2800 m and 1174 m at the outlet (Cham Anjir). Furthermore, the length of the mainstream and the stream network density in the Khorramabad Basin are 94 km and 0.39 km/km\u003csup\u003e2\u003c/sup\u003e, respectively (Fatapour et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows the spatial structure of the main sub-basins and the extent of the urban area in the Khorramabad Basin. To produce a homogeneous and identical comparative value, this collection was produced with the integration and combination of smaller sub-basins using the ArcHydro extension. Due to using an automatic tool for identifying spatial components, the drainage identifier or the hydro identifier was used to identify each component.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 HEC-HMS model\u003c/h2\u003e\n \u003cp\u003eThe HEC-HMS model is among the most reliable hydrological models for estimating the precipitation-runoff of basins, with wide uses in estimating flood volume and discharge. This model is one of the computerized mathematical models that is used to simulate the hydrological behavior of a watershed (Slamet and Reviana, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). In this study, the critical flood-prone points of the Khorramabad Basin were identified using this model, which is used for various research purposes, such as water supply projects, urban drainage, flood and flow rate prediction, the effect of land use change, designing dam spillways, flood control studies, and water reservoir system exploitation. In comprehensive watershed management, the control and reduction of flood-induced damage are of particular importance, and to this aim, it is necessary to identify and determine flood-prone areas at the watershed level. Nowadays, many software are available for engineering calculations and water resources. To achieve reliable results, however, engineers need to master the assumptions and calculation steps in the software, and additionally, they require practical experience in using these programs. The HEC-HMS precipitation-runoff simulation model has been developed with an emphasis on Object-Oriented programming logic. This technology provides a natural approach to expressing the problem, breaking down its complexity into comprehensible components, and using the program code to solve the problem (Hamaamin et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Kassaye et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Shafiei and Gharari, \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). This model demonstrates the watershed as an integrated system with hydrological components. Each model component simulates an aspect of the precipitation-runoff process within a part of the watershed. In other words, various components are combined for the physical simulation of the watershed, and each component represents one of the factors of precipitation-runoff conversion in the watershed. The final flood hydrograph will be obtained from the combination of the simultaneous effect of the mentioned factors (Yilma and Kebede, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Detailed functions\u003c/h2\u003e\n \u003cp\u003eDrought is an indispensable part of natural disasters. Droughts typically begin gradually without prior warning. This phenomenon is usually developed over time with the passage of many years and, in contrast, has a long treatment process. Drought monitoring and forecasting, especially determining its onset time and duration, is particularly important in water resources management and planning to reduce its harmful consequences. Despite the high demand, it is not simply achievable to develop an algorithm to determine drought prediction through physical or statistical analyses. Another main obstacle to drought statistical analysis is the complexity of the real causes of drought, making its characterization difficult; on the other hand, no precise and comprehensive definition is available for this subject (Li et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sobhani et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). In addition, the characteristics of this phenomenon, such as severity and duration, are infinitely correlated, and paying attention to this issue is necessary for the drought assessment analysis. To implement a multivariate analysis, the use of detailed functions (copula), used in this research to determine the critical drought points in the Khorramabad Basin, provides a more complete characterization of drought (Xiao et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). Sklar (1959) was the first to propose the idea of detailed functions to establish links between multivariate distributions with the corresponding univariate marginal distributions. These functions, which develop a multivariate distribution using univariate marginal distributions and can well describe their inter-correlations, have multiple advantages. Some of their merits include no limitation in choosing and using the functions of marginal distributions and structural dependence, usability for more than two variables, separate examination of marginal and structural distributions, and a good depiction of the relationship between two or more variables (Achite et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Durante and Sempi, \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Wang et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). In addition to drought analysis, these functions can be used in other analyses, such as floods, storms, and other natural disasters, by establishing correlations between hydrological variables (Liu et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Nazeri Tahroudi et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 Precipitation data\u003c/h2\u003e\n \u003cp\u003ePrecipitation is a major meteorological element and one of the factors influencing the hydrological cycle. It is necessary for humans and accounts for the main source of freshwater supply for humans, plants, and other living organisms (Veloria et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). An average precipitation of 700\u0026ndash;900 mm is estimated on the earth\u0026apos;s surface. Nevertheless, changes in global precipitation are such that some areas (e.g., deserts) may have received no types of precipitation for several consecutive years. Precipitation is generally high over seas and oceans, and the precipitation level decreases with moving away from these areas. Based on a rule of thumb, drier weather reduces the confidence in precipitation (Kuttippurath et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eIn Iran, diverse climatic and topographic features have led to changes in precipitation levels in different spatiotemporal scales. For this reason, the variability and extreme fluctuation of precipitation are expected in arid and semi-arid areas, including in the plateau of Iran. On the one hand, severe droughts pose heavy damage to the environment and economy of Iran, and torrential rains, on the other hand, lead to destructive floods, which are among the familiar phenomena all over this country. In terms of latitude and proximity to the high-pressure subtropical region, Iran possesses a fluctuating precipitation regime in addition to the shortage of precipitation. Few annual precipitations, severe annual and seasonal fluctuations, short precipitation periods, and precipitations in the form of heavy and sudden showers are considered the conspicuous features of the precipitation regime in this country(Doostan, \u003cspan class=\"CitationRef\"\u003e2020b\u003c/span\u003e; Mirzaei Hassanlu et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e; Sharafi and Mir Karim, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). Lorestan province and, consequently, the Khorramabad Basin are not exempted from this general rule. Since the province is among the mountainous regions of Iran, the regional precipitation can differ in spatiotemporal distribution because local precipitation can be affected by the local elevation arrangement (Mirhashemi and Hasanvand, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eIn this study, the critical hubs in the flood and drought sections were studied and determined using the GPM precipitation data (obtained from the NASA website) available from September 22, 2002, at 24:00 to October 22, 2022, at 24 as the end of the study period (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://giovanni.gsfc.nasa.gov/giovanni/\u003c/span\u003e\u003c/span\u003e). These data were used due to their high measurement accuracy vs. incomplete and highly erroneous ground data (Iryani et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). As an important point, the NASA calculations on temperature, as an important factor in the precipitation regime, indicate that the climate has become very acute in the last 20 years (Kheyruri et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e). Another reason for choosing this type of data in this study is because many climatic phenomena have occurred in the presented time range. For example, half of the floods in Iran in the last 50 years have occurred in the last 15 years. In the last half century, about 4,000 floods have been recorded in Iran, more than 2,000 of which occurred in the last 15 years. Additionally, the precipitation in Iran reached 50% of previous years and 40% less than the long-term average in recent wet years. These facts reveal that the climate change process and the influence of factors affecting the incidence of floods and droughts have increased in the last few years (Darand and Sohrabi, \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e; Doostan, \u003cspan class=\"CitationRef\"\u003e2020a\u003c/span\u003e; Durante and Sempi, \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; JaliliSadrabad et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Modarres et al., \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e). In this study, the accuracy of GPM data was verified using a comparison with the statistical distribution of observed precipitation in the target area (Santos et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). Based on the analysis of the results, GPM data of the IMERG type are highly accurate in the Khorramabad Basin. In addition, it can be claimed that the average error of the data was 10 mm, suggesting that the average precipitation measured by GPM data differs by about 10 mm from the average actual precipitation. The calculations showed a standard data error of 5 mm, indicating the dispersion of GPM data (about 5 mm) around the average actual precipitation. Furthermore, the correlation coefficient of the data (0.95) discloses the well-correlated GPM data and the reference data. According to the validation results, it can be concluded that the GPM data in the studied watershed are reliable for various purposes, including watershed studies and water resources management.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalysis of results (Flood)\u003c/strong\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e2.5 Arc-Hydro extension and Hec-geoHMS\u003c/h2\u003e\n \u003cp\u003eIn this part of the study, the details of the inputs of the precipitation-runoff model were extracted using the morphological features of the watershed (morphometry). This procedure has multiple goals, one of which is to determine the geomorphological parameters to specify the hydrological response of the watershed. Morphometry is a study of the physical features and morphological condition of a watershed, which can decisively influence its hydrological characteristics and water regime. Information on the physiographic characteristics of a watershed together with information about the regional weather conditions can produce a relatively accurate image of the quantitative and qualitative functioning of the hydrological system of that watershed (Mahala, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). The hydrological phenomena that occur in a watershed can be linked to morphometric parameters, including surface area, perimeter, length, distance to the center of gravity of the watershed, height, slope, slope aspect, watershed shape, compactness coefficient, longitudinal profile of the mainstream (net slope and gross slope), drainage density, the bifurcation ratio, and Horton\u0026apos;s laws (law of number, law of length, law of area, and law of stream slope) (Harsha et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). Therefore, these parameters influence the flood phenomenon to the hydrological reactions of the watershed to the precipitation that appears as runoff, affecting the severity, weakness, flood flow, and water balance (Loudyi and Kantoush, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Ozdemir and Akbas, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe summarized physiography of the Khorramabad Basin\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSymbol\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eValue\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\u003eWatershed area\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA (m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2491931101\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed perimeter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eP (km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e370452.950\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL (km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e119392.863\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDistance to the center of gravity of the watershed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL\u003csub\u003eca\u003c/sub\u003e (km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e46643.242\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage height of the watershed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH (m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1602.22\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed average slope\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS (Pct)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.270\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed average slope aspect\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAspect (Degree)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed form factor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.175\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed shape factor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.720\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed compactness coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.078\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed circularity ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.232\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed elongation ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003csub\u003ee\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.472\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed equivalent rectangle length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL (m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e170621.446\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed equivalent rectangle width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eB (m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14605.029\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eForm factor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eL\u003csub\u003el\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.994\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRunoff curve number\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e71.859\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed drainage density\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026micro;(1/km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.409\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWatershed bifurcation ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.103\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe law of stream numbers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNu\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{u}}=(103/3{)}^{4-\\text{u}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe law of stream length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLi (km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{L}}_{\\text{i}}=(886/9)(261/1{)}^{\\text{i}-1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe law of stream area\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAi (km\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{A}}_{\\text{i}}=(243940/5)(168/1{)}^{\\text{i}-1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe law of stream slope\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSi (Pct)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{S}}_{\\text{i}}=(113/0)(387/0{)}^{\\text{i}-1}\\)\u003c/span\u003e\u003c/span\u003e\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\u003eThe following indices as Arc-Hydro supplementary primary data can be mentioned to prepare the spatial data of the Khorramabad Basin:\u003c/p\u003e\n \u003cp\u003e- The raster index of the digital elevation model (DEM) of the study area\u003c/p\u003e\n \u003cp\u003e- The stream network index\u003c/p\u003e\n \u003cp\u003e- The land use index of the country\u003c/p\u003e\n \u003cp\u003e- Isohyets of the country\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e2.6 Implementation of the HEC-HMS model\u003c/h2\u003e\n \u003cp\u003eThe results were implemented using version 1.4.4 of this model. The result (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e) was obtained by selecting the Hec-geoHMS extension output in the HEC-HMS model and choosing the background schematic images created in the previous steps from the following path.\u003c/p\u003e\n \u003cp\u003eNext, the examined parameters that required redefinition or corrections include the basic coefficient of base flow by the recession method, called Ratio to Peak and Recession Constant (Nazirah et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e), the two X and K coefficients in the sub-basin flood routing method, called Muskingum (Ansari et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Chakraborty and Biswas, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lohpaisankrit et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e), the curve number (SCS-CN) hydrograph (Poonia et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Verma et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e) used in the precipitation-runoff model development, and Schneider\u0026apos;s unit hydrograph (Rajkumar et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) to prepare the hydrograph of the whole watershed.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e2.7 The Decision Support System \u0026quot;DSS\u0026quot; data model for precipitation data\u003c/h2\u003e\n \u003cp\u003eIn a DSS, the precipitation data were recorded and saved using the DSS database model. The precipitation data were saved according to the 6-hour cumulative nature. The discharge data in five hydrometric stations of the Khorramabad Basin with the related settings were introduced to the mentioned model. These numbers are a 24-hour average. Then, the hypothetical start and end time and simulation steps were reviewed in the content of Control Specifications. According to the observational numbers, the simulation middle time range was a value of 2 h. The peak discharge and the maximum flow volume were calculated in each sub-basin by running the model and according to the target scenario, i.e., identifying the critical hubs of the watershed.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalysis of the results (Drought)\u003c/strong\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e2.8 R-Studio software\u003c/h2\u003e\n \u003cp\u003eR-Studio software is considered a graphical interface with R software, which was used in this study for calculations of SPI-based drought risk assessment using detailed functions. This software provides an attractive and flexible environment for users or coders compared to R software (Baral et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hussain and Pal, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kassaye et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). For the drought analyses, datasets (precipitation series) were recalled in R-Studio software. To this end, copula and Vine copula packages (Bai et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Coblenz, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Latif and Mustafa, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) were first extracted to implement the coding process. This recall was performed for all the 39 studied sub-basins according to the Library command in the software environment. It is important to note that the written codes can be viewed more clearly in Notepad.\u003c/p\u003e\n \u003cp\u003eThen, a separate loop was determined for each code to perform all the calculations automatically. The codes can be divided into two parts, the first belonging to drought severity and duration variables, and the second assigning to fit and capability (choosing the most suitable detailed function) and calculations of the return rate. In this study, the detailed functions of Frank (Ekanayake and Perera, \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e; Nabaei et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e) and combined Joe-Frank detailed functions (Li et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) were selected based on the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) (Achite et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ko et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e; Li et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Yu et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). The parameters of detailed functions were calculated using the Log criterion (Achite et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Azhdari et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; EskandariPour and Soltaninia, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). To analyze two or more variables of a phenomenon using detailed functions, it is necessary to first identify the univariate distributions of the variables. Accordingly, univariate distributions (e.g., normal, log-normal, exponential, and gamma distributions) were also fitted to the studied data. The most suitable distribution was chosen based on numerical tests of the goodness of fit, i.e. Kolmogorov-Smironov (KS), Anderson- Darling (AD), and chi-square (Deger et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hesami Afshar et al., \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Nomsa Keitumetse and Mengistu Tsidu, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). In the first two tests, the best distribution is obtained by comparing the empirical and parametric cumulative distribution functions (CDF) (distribution function obtained from the data). However, the chi-square test is directly linked to the frequency such that the empirical frequency and the frequency calculated from the parametric distribution are compared to obtain the difference between them. In this research, the marginal distributions of drought variables were determined using empirical relationships.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Discussion and conclusion","content":"\u003cp\u003eThe climate change phenomenon refers to all long-term changes in weather conditions, and climate change is currently the most critical environmental threat to the planet. The area studied in this research has always been prone to this phenomenon. Khorramabad Basin in Lorestan province is one of the most flood-prone regions of Iran so the incident floods in this watershed have greatly damaged various agricultural sectors, buildings, villages, cities, communication lines, and other sectors in recent years. In addition to the threats caused by floods in this watershed, the study of climate change impacts in recent years shows that the temperature in this region has marked an unusual increase the same as other global regions. With the elevated temperature, decreased precipitation, and increased evapotranspiration, the Khorramabad Basin is threatened by an unprecedented hydrological drought as a climatic phenomenon. Unlike previous investigations, our studies on climate change were conducted in a region where floods and droughts are important and, on the other hand, different residential areas are involved at the time of occurrence. A flood-prone area threatened by the shadow of drought at the same time, while it does not encompass urban and residential areas, will not be a suitable area for the precipitation-runoff model simulation and statistical calculations of drought, producing no suitable output. Thus, such a research project is somewhat insignificant and practically aimless and theoretical. In this study, therefore, 425 residential areas were recognized in 39 sub-basins identified in the Khorramabad Basin, indicating the importance of residential areas in this type of research. Drought and flood are two sides of the same coin, and the studied watershed has always been prone to these two climatic consequences. A major issue in climate change studies is to create a link between these two phenomena. In this research, therefore, a common type of GPM precipitation data was used during a statistical period (2002\u0026ndash;2022), and flood simulation and drought analysis were simultaneously studied using detailed functions. Thus, this study tried to consider the aforementioned link by identifying and prioritizing critical hubs of floods and droughts with an emphasis on the return rate of these two phenomena, which is a marked distinctive point compared to previous studies. The flood and drought risk was evaluated individually in most of the past studies, while these two phenomena were analyzed and assessed simultaneously in this research. Since a critical issue in hydrological studies, particularly concerning floods and droughts, is to address the return rate of these two phenomena, this study employed methods for zoning and identifying the critical hubs of floods and droughts. Both emphasize the return rate, and the sub-basins in the study area were also prioritized based on the same criterion, which is completely different from the literature. The results for identifying the critical hubs of floods were analyzed separately in the return periods of 5, 10, 25, 50, 100, 200, 1000, and 10000 years. The identified sub-basins with the highest risk of flooding will be the same in all return rates. Furthermore, the target areas were prioritized to identify the points of drought, with an emphasis on the return period of this phenomenon. Additionally, the results revealed a better condition regarding the threat of drought in the sub-basins with a high risk of flooding, and those with a high risk of drought were not in a good condition in terms of flood incidence and, consequently, precipitation.\u003c/p\u003e\n\u003cp\u003eA crucial principle in the risk management process of natural phenomena is to pay attention to the degree of vulnerability of the study area. In this study, risk assessment methods, such as Bow-Tie, Environmental Impact Assessment (ENVID), Fault Tree Analysis (FTA), and Event Tree Analysis (ETA), can be utilized to fully explain the causes of floods and droughts with an emphasis on resilience. As such, the necessary corrective measures to reduce the vulnerability of the areas can be suggested according to the principle of resilience.\u003c/p\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Floods with specified return periods\u003c/h2\u003e\n \u003cp\u003eA basic goal of precipitation-runoff models is to estimate the exact volume and hydrograph shape of floods after precipitation with a specified return period (Al-Hussein et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ben Kh\u0026eacute;lifa and Mosbahi, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). In this study, the instantaneous maximum discharge and flow volume were calculated for all sub-basins according to the return rates of 2, 5, 10, 25, 50, 100, 200, 1000, and 10000 years by running the model and examining the hydrometric statistics. The flood at the outlet and the urban area of the Khorramabad Basin along with the runoff volume is shown in each sub-basin. For example, Figs. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, and 9 depict precipitation flow hydrographs with a return period of 10,000 years.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Identification of flood critical hubs in the Khorramabad Basin\u003c/h2\u003e\n \u003cp\u003eAs with other hydrological phenomena, a flood is a random phenomenon that may occur at any time and place. For this reason, it is not usually possible to determine the exact time of the flood, but its occurrence can be predicted according to the hydrological events observed in the past. The HEC-HMS model is among the hydrological models with a very high efficiency in flood warning projects worldwide. In this research, this model was used to simulate the volume and peak flow of floods in the Khorramabad Basin to identify and prioritize the critical hubs during the 20 statistical years (2002\u0026ndash;2022) and to explain its steps. Separate data are collected in an integrated set in the modeling process to enable managers or users to implement their scenarios in a tool that has a decision-making environment. According to running the HEC-HMS precipitation-runoff model, the scenario of interest may be recognized based on the areas that are most at risk along the watershed stream network, the location of critical hubs, or flood demonstration in each zone. This study mainly aimed to investigate floods with the mentioned model to identify critical hubs in the Khorramabad Basin. According to the results obtained in the previous stages and the scenario of interest, hydrometric data were provided for the output of the obtained model. The results indicated that the highest probability of flood occurrence belonged to the W990, W1140, and W710 sub-basins, with respective flow volumes and maximum flow rates of 5140.8364 mm and 1389.276 m\u003csup\u003e3\u003c/sup\u003e/s, 539.0018 mm and 383.838 m\u003csup\u003e3\u003c/sup\u003e/s, and 466.8089 mm and 1561.104 m\u003csup\u003e3\u003c/sup\u003e/s, based on the flow volume in all the estimated return periods. The W990 sub-basin includes 12 residential areas, consisting of Jam Kaboud, Jodol Dol, Sarhelt, Gholaman Sofla, Carwash Factory, Cement \u0026amp; Plaster Factory, Biran Plaster Factory, Jazayeri Farm, Sefid Dasht, Gholaman Olya, Hassan Abad, and Sabour villages.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Drought with specified return periods\u003c/h2\u003e\n \u003cp\u003eAs mentioned in the flood section, the return period means the time during which a phenomenon (e.g., drought and flood) reoccurs with a given volume or severity (Avsaroglu and Gumus, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; da Rocha J\u0026uacute;nior et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Kavianpour et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Mirabbasi et al., \u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e). In this study, the calculated return period was implemented as a common return period in the (or) mode. The return period in the (or) mode is much stricter than that in the (and) mode. It denotes the time to calculate a phenomenon with two random variables X and Y in a situation where one of these two variables (or both) exceeds its threshold (\u0026gt;\u0026thinsp;1). Accordingly, drought duration and severity variables (Khan et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Poonia et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) were analyzed in this study.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 Identification of drought critical hubs\u003c/h2\u003e\n \u003cp\u003eDrought is a natural climatic phenomenon that creates various effects on socioeconomic and environmental sectors. The continued drought in a region latently weakens and eventually destroys natural ecosystems in the long term. In the last decade, the tangible drought consequences due to the increased drought frequency and severity in different parts of Iran, such as the Khorramabad Basin, have persuaded planners and managers to seek strategies to deal with this event. Therefore, it is currently necessary to understand the drought behavior in given periods and determine the areas with a higher risk of facing this natural complication in the crisis management process. In this study, the critical hubs in the Khorramabad Basin were identified during a statistical period of 20 years (2002\u0026ndash;2022) in the drought section, and the return period of this phenomenon was calculated using the obtained results. To this aim, the drought was analyzed using detailed functions based on the SPI index, and drought severity and duration variables were extracted according to this index. Kendall\u0026apos;s correlation coefficient values were considered for these characteristics. Next, marginal distributions were estimated empirically, and then the most appropriate detailed function was selected based on AIC and BIC criteria. To rank the basins, the return period was calculated in two modes: drought severity\u0026thinsp;\u0026gt;\u0026thinsp;1 or drought duration\u0026thinsp;\u0026gt;\u0026thinsp;1. The ranking results (Table X) show that the highest risk of flooding belongs to sub-basins W1070, W730, and W610 with return periods of 1.1578, 1.1923, and 1.1976 years, respectively. Moreover, the W1070 sub-basin embraces 35 residential areas comprising, for example, Mian Gol woodcarving, Dinarvand Sofla and Olya, Cheshme Sorkheh, Chenar Khaibari, Deh Bagher, Upper and Lower Anardor, Sorkheh Deh Oliya and Sofla, Cheshmeh Ali, and Gol Ghaleh villages.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe results of selecting the most appropriate detailed function between the drought severity and duration variables and the return period calculation to prioritize the sub-basins\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"10\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBasin\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eKendall\u0026apos;s correlation coefficient\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDetailed family\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1st parameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e2nd parameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLog-likelihood function\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eReturn period {or}\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRank\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\u003eW600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4346\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.6197\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.8659\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-25.7317\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.6374\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW610\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4156\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.5567\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.1134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.0191\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.1976\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW640\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4832\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.3112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17.6810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-33.3620\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-31.2676\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2987\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3803\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7351\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8786\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.4977\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-20.9954\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-16.8067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2219\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4296\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3811\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.3296\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.6592\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.5648\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3801\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW680\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4310\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.4871\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.4308\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.8615\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.7672\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3579\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW690\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.2862\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.5213\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.0426\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-20.9482\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2394\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4497\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.8026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.9012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-27.8025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-25.7081\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4292\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.4537\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.3451\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.6901\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.5958\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2637\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW730\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3828\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.8483\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.4521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-18.9042\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-16.8099\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.1923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW740\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6199\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9197\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.1261\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.2521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-20.0634\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2659\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.6357\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.0692\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-26.1385\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.0441\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3127\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW760\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3726\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.5712\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.7255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-17.4509\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-15.3566\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2699\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW780\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4488\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7606\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9236\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.4058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-28.8116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.6229\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.4155\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW790\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4084\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5997\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9323\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.0017\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-26.0034\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.8147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3349\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW820\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3939\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.7762\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.4405\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-18.8809\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-16.7866\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3182\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW830\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.1903\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.7748\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-31.5497\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-29.4553\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2502\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW850\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4480\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.6849\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.1280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-26.2560\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.1617\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW870\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4210\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.2437\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8638\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.9670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-27.9341\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.7454\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW880\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4973\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.3932\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17.8902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-33.7803\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-31.6860\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.4293\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW890\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.8386\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.3494\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-18.6988\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-16.6044\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2328\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4299\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3782\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.2243\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.4486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.3542\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.1983\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.1469\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.0124\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.0248\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-19.9305\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW940\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3876\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5830\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9053\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.0803\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.1606\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-17.9719\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2619\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW980\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4303\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.2903\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.8704\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.7408\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.6465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3535\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW990\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.8670\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.7340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.6396\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3541\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.2268\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.3940\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.7879\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-20.6936\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3283\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1010\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4072\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4563\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9472\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.7474\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-25.4947\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.3060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.4027\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1020\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3754\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5169\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.5748\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.1495\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-16.9608\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1050\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3821\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.3723\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.7445\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.6502\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3316\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7107\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.2089\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-24.4177\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-20.2290\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2458\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n 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\u003cp\u003e12.5482\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.0963\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.0020\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2613\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW1140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3794\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6421\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8941\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.8181\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-21.6362\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-17.4475\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.2415\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\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"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding support\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors also wish to acknowledge the generous financial support provided by the Islamic Azad University, Science and Research Branch, Tehran, which significantly contributed to the advancement of this study's objectives.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflicts of interest regarding the publication of this paper. The research was conducted solely for academic purposes and was not influenced by any external commercial or financial relationships.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor Contributions StatementThe contributions of each author to this manuscript are as follows:1. Maryam Robati (First and Corresponding Author): Data collection, analysis and interpretation of results, and contribution to writing relevant sections of the manuscript.2.Pouriya Najafgholi (Second Author ): Conceptualization and design of the study, methodology, writing the main manuscript text, and coordinating the overall research process.3. Hanieh Nikoomaram (Third Author): Reviewing and editing the manuscript, ensuring scientific accuracy and content integrity.4. Baharak Motamed Vaziry (Fourth Author): Preparing figures and tables, and reviewing and approving the final content and data presentation.All authors confirm that there are no conflicts of interest and that ethical responsibility for the content of the manuscript rests with all authors. Additionally, all authors have reviewed and approved the final version of the MANUSCRIPT.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003e This article has been extracted from the PhD dissertation in the field of Environmental Science and Engineering, which was approved and defended at the Islamic Azad University, Science and Research Branch, Tehran, Iran. The authors would like to express their sincere gratitude to the esteemed president and the research officials of the Faculty of Natural Resources and Environment at the university. We extend our deep appreciation to the Environmental Science and Engineering Department for providing a supportive environment that allowed dedicated students in the field of climate change to express their views. Additionally, we would like to thank NASA for providing the GPM (Global Precipitation Measurement) data, which was crucial for this research.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAchite, M., Bazrafshan, O., Wałęga, A., Azhdari, Z., Krakauer, N., \u0026amp; Caloiero, T. 2022. Meteorological and hydrological drought risk assessment using multi-dimensional copulas in the wadi ouahrane basin in Algeria. Water, 14(4), 653. \u003c/li\u003e\n\u003cli\u003eAckerl, T., Weldemariam, L. F., Nyasimi, M., \u0026amp; Ayanlade, A. 2023. Climate change risk, resilience, and adaptation among rural farmers in East Africa: A literature review. Regional Sustainability, 4(2), 185-193. \u003c/li\u003e\n\u003cli\u003eAl-Hussein, A. 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Water, 12(2), 421. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Climate Change, Critical hubs, HEC-HMS model, Copula function, Floods and Droughts","lastPublishedDoi":"10.21203/rs.3.rs-5390435/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5390435/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eClimate change is currently the major challenge facing mankind, and this crisis has been the topmost global issue due to the increasing role of human activities and the high sensitivity of human societies to the threats caused by these changes. The climate changes created for humans and nature have led to risks and threats that occur on different spatial and temporal scales. Therefore, adopting policies to deal with climate change will be a critical issue in risk management. Nonetheless, identifying critical hubs in the study area helps improve the risk management process in the ​​risk assessment of climate change consequences, such as floods and droughts. Accordingly, this study mainly aimed to identify such points in the study area according to this principle. As with other parts of the world, the Khorramabad Basin (Lorestan province, Iran) is prone to serious risks in terms of climate change. This area is located as a Class III sub-basin in the Class II Karkheh basin and the Class I basin of the Persian Gulf and the Sea of ​​Oman. In this study, the critical hubs of the desired watershed were identified using the HEC-HMS rainfall simulation model to prioritize the flood-prone sub-basins of the Khorramabad Basin. The sub-basins with a high drought risk were prioritized with the detailed function (copula) statistical method. An important point in this evaluation is the use of Global Precipitation Measurement (GPM) precipitation data as common data in the analyses made in the flood and drought sections. The return rate was also calculated in both methods. The model implementation and statistical analysis revealed that the highest probability of flood occurrence belonged to the flooded part of W990, W1140, and W710 sub-basins, with respective flow volumes and maximum flow rates of 5140.8364 mm and 1389.276 m\u003csup\u003e3\u003c/sup\u003e/s, 539.0018 mm and 383.838 m\u003csup\u003e3\u003c/sup\u003e/s, and 466.8089 mm and 1561.104 m\u003csup\u003e3\u003c/sup\u003e/s, based on the flow volume in all the estimated return periods. In the drought section, the sub-basins W1070, W730, and W610 would be the most critical hubs in terms of drought probability, with return periods of 1.1578, 1.1923, and 1.1976 years, respectively.\u003c/p\u003e","manuscriptTitle":"Zoning of Critical Hubs of Climate Change (Flood-Drought) Using the Hydrologic Engineering Center-Hydrologic Modeling System and Copula Functions Case study: Khorramabad Basin","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-09 09:09:50","doi":"10.21203/rs.3.rs-5390435/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6bfb32fc-ac11-4717-ab20-94d5ee0d4c7b","owner":[],"postedDate":"December 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-25T10:53:19+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-09 09:09:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5390435","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5390435","identity":"rs-5390435","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}