Evaluation of ABCD water balance conceptual model using remote sensing data in ungauged watersheds (a case study: Zarandeh, Iran)

Water balance is an important concern in water resources management and water consumption planning. ABCD water balance conceptual model is a suitable simulation tool due to its simplicity, low input data requirement, and water balance components provision. As the lack of data is a major challenge in many developing countries, IMERG precipitation satellite products and ERA5 temperature reanalysis data were used to obtain the required data for the Zarandeh sub-basin in Neyshabur Northeast Iran. The results were evaluated using four statistical indices including correlation coefficient (R), root mean square error, Nash–Sutcliffe efficiency (NSE), and BIAS. The Results showed that products are reasonably accurate, and there is a high correlation between outputs and observed data. Zarandeh and Baqi stations indicated the highest and lowest correlation of 0.89 and 0.84, respectively. This study aimed to use ABCD model and remote sensing products to determine the water balance. The uncertainties in the model parameters were assessed through Fuzzy numbers. Additionally, the Monte Carlo method was employed to calibrate them based on NSE as an objective function. The results illustrated that the ABCD water balance model is an accurate tool for simulating the surface runoff of the Zarandeh sub-basin with an efficiency coefficient of 0.86. Finally, the model was applied to the Sebi sub-basin in Torbat-e-Heydariyeh, with a moderate performance (NSE = 0.49) showing that the model parameters should be recalibrated in each region. This study indicates that the remote sensing products could be applied as appropriate tools in ungauged basins.


Introduction
In recent decades, dramatic population growth associated with industrial development, and agricultural activities has led to a substantial increase in the exploitation of water resources. Therefore, conscious use of water resources is of great importance (Yaykiran et al. 2019). Water shortage has caused individuals to pay great attention to water consumption with a managerial approach in many parts of the world.
Water scarcity has become a serious crisis that can have both direct and indirect effects on the environment, the economy, health, and even the political, social, and cultural relations of the society. Therefore, appropriate management of water resources is necessary to overcome this issue (Salehi 2022;Sheffield et al. 2018). One of the major concerns in water resources management, decision-making and planning for water consumption in various sectors is water balance, which has attracted enormous attention (Ciampittiello et al. 2021;Iofin 2015). The calculation of water inflow, internal water storage, and output of a hydrological system in a certain time period is called water balance (Wang et al. 2014). The purpose of calculating and denoting water balance is to investigate the input and output components and the amount of water consumption and storage. This is essential for identifying the area capacity development or constraints of surface and groundwater resource exploitation.
Hydrological models are one of the most effective tools for simulating hydrological processes such as water balance. A water balance model could be considered as an equation system that aims to show some aspects of the hydrological cycle. Depending on the aims of the study and the availability of data, modeling can have different levels of complexity. One of the drawbacks of using more complex models over simple models is that they require more data and consume more time for the user to be understood. Furthermore, increasing the complexity of the model does not necessarily improve its accuracy (Devia et al. 2015;Zhang et al. 2002). Distributed/ semi-distributed models are complex and require a considerable amount of data. Therefore, conceptual models have recently received a lot of attention in basin modeling (Anshuman et al. 2019). Thornthwaite (1948) proposed the first conceptual water balance model, comparing potential evapotranspiration (PET) with precipitation. This model has been considered the main idea of many water balance models. Conceptual water balance models use the simplified mathematical concept of a system with a number of interconnected reservoirs to represent the various components of hydrological processes through recharge and discharge. These models are mainly developed to illustrate the hydrological cycle using the association of rainfall-runoff process components with the physical implication conceptually applicable to the basin. Conceptual models are usually integrated and use the same set of parameters for the whole basin. These models are heavily reliant on observational data, and their results depend on the quality of the input data used in the model (Chiew 2010;Jaiswal et al. 2020). The ABCD water balance conceptual model is one of these types of models, which is desirable because of its simplicity and low requirement of input data, and the representation of various water balance components. This model enables to study the groundwater effect on runoff by considering two soil moisture storage layers.
The limitations in observations and recording of information from different basins, as well as the quantitative and qualitative constraints of meteorological data, are one of the major challenges in many developing countries. Therefore, studying and forecasting basins without adequate statistical data have become a challenge for hydrologists, because of their complexity and difficulty, and the significant uncertainties associated with them (Zamoum and Souag-Gamane 2019). Thanks to its advantages of objectivity, timely, economical, and wide coverage, as well as its continuous data and capacity to extend traditional "point" measurements to information about entire areas, remote sensing technology compensates for the lack of meteorological stations . Satellite remote sensing is being used increasingly as a source of complementary data for the in-situ monitoring networks. Satellite-based sensors are now also able to, directly and indirectly, measure almost all components of the hydrological cycle, including precipitation, evaporation, surface water, soil moisture, snow, etc. (Sheffield et al. 2018;Wang and Xie 2018). Al-Lafta et al. (2013) evaluated the performance of the ABCD monthly water balance model for three basins in different parts of the United States. They found that the model was most sensitive to groundwater parameters, and these sources played a crucial role in the formation of total runoff in these basins. In two basins with mild climates (hot and humid), their model performed rather well, but not well enough in snowy areas. Marinou et al. (2017) studied the runoff simulation using the ABCD water balance model in four Eurotas river basins in southeastern Greece. Three sub-basins were studied on daily time-series for one irrigated year, and the fourth sub-basin was studied on monthly time-series over 5 years. The model was calibrated by calculating the Nash-Sutcliffe coefficient (NSE). The model performance in the simulation of runoff in the fourth subbasin is considered good, with a NSE of 0.82 and 0.62 on monthly and daily scales, respectively. Furthermore, the evaluation of the parameters sensitivity analysis showed that in all cases, both runoff generation before soil saturation (parameter A), and the groundwater recharge (parameter C) were recognized as more effective than the PET and soil moisture (parameter B). Wu et al. (2019) used the ABCD model to simulate runoff prediction in the Shinan River Basin and evaluate the application of this model in small and medium-sized catchments in China. For the first time in China, they compared the simulated values with the measured values to evaluate the sensitivity of the four parameters of the ABCD model. Validation indicated a high degree of fit, with the NSE at 0.93 and 0.86 in the flood season and non-flood season, respectively. Also, the role of groundwater recharge in creating total runoff was recognized as the most sensitive parameter of the model. Wang et al. (2020) enhanced the ABCD water balance model by combining temperature-dependent hydrological processes and groundwater evapotranspiration in cold regions with several additional parameters. They proposed a useful hydrological model for groundwater management in the Golmud city on the Tibetan Plateau. The new model was used to regenerate monthly runoff in the previous decades and represented a better performance than other similar models. The results showed a positive correlation between groundwater level in Golmud city and annual runoff in the Golmud River basin; to be more precise, with the increasing streamflow of Golmud River, the groundwater level also increases.
As mentioned earlier, water balance calculation is an important issue in water resources management, especially in areas without sufficient data. Moreover, determining water balance parameters is associated with error and uncertainties. Therefore, using a suitable approach to calculate the water balance in such areas is of paramount importance. While considerable work has been done to analyze model performance, yet the application of satellite products in development of conceptual models has not received sufficient attention. Consequently, the combination of water balance conceptual models and remote sensing techniques can be considered as an approach to assist decision-making at various spatial and temporal intervals. Since there is no record of implementing the ABCD model in Iran, this study aims to develop and evaluate the conceptual model of ABCD monthly water balance in a semi-arid region using ground-based station data and satellite temperature and precipitation products. Also, a fuzzy-probabilistic approach is applied to decrease the uncertainties and to determine the optimal parameters of this model. Accordingly, this study intends to answer the following scientific questions: (1) are the selected satellite products an appropriate representative to be replaced with ground dataset in areas without sufficient data? (2) Does the proposed model have the ability to calculate water balance components and to mitigate their uncertainties in the study area?

Study area
Zarandeh sub-basin is located in the north of the Neyshabur catchment area in Khorasan Razavi province in northeastern Iran, covering an area of 490 km 2 with a semi-arid climate. The height of this sub-basin varies between 1400 and 2900 m a.s.l, respectively. The characteristics of rain gauge, synoptic and hydrometric stations in the study area are presented in Table 1, and Fig. 1 illustrates the location, land use, the stream network of this sub-basin, and the synoptic stations used in this research.
To verify the model, the selected area is the Sebi subbasin located in Torbat-e-heydariyeh-Zaveh which has a semi-arid climate (Fig. 1). The area of this region is equivalent to 1977 km 2 , and the altitude in this area varies between 1250 and 2630 m. Figure 2 illustrates the land use, the stream network of this sub-basin, and the stations used in this research.
The specifications of the rain gauge, synoptic, and hydrometric stations used for this sub-basin are provided in Table 2. As can be seen, seven rain gauge stations have been used inside and outside the area, and the data of the Torbate-Heydariyeh synoptic station was also used as a temperature indicator station in the region. Also, the observational discharge data of the region were obtained from the Sebi hydrometric station.

Datasets
Key steps of the research process are depicted in Fig. 3. Based on this, monthly precipitation, temperature, and discharge data for the stations in Table 1 were obtained for a 16-year statistical period from April 2001 to April 2017. To supplement the missing data in some stations, the data of the adjacent stations that had the highest correlation with the desired station were used.
There is a wide range of satellite precipitation products with different temporal and spatial resolutions. One of these products is dedicated to the Tropical Rainfall Measuring Mission (TRMM), launched in November 1997 to monitor and study tropical rainfall and how it affects the general climate (Yong et al. 2012). Following the success of the TRMM, another project called Global Precipitation Measurement (GPM) was defined and launched in Japan in February 2014. GPM uses the latest and most advanced equipment and sensors and can monitor precipitation in both rain and snow. It has a high spatial resolution of 0.1° × 0.1° and a quasi-global coverage 90° S-90° N latitude (Skofronick-Jackson et al. 2018). In this study, a GPM satellite precipitation product called IMERG was used. The GPM-IMERG V06 Final Run daily precipitation product in the location of the meteorological station was downloaded from http:// apdrc. soest. hawaii. edu/. Additionally, the temperature data were obtained from European Centre for Medium-Range Weather Forecasts (ECMWF). The centre manages one of the largest archives of weather  forecasting data in the world. The fifth generation of ECMWF re-analyzed data, ERA5, published by the Copernicus Climate Change Service (Jiang et al. 2021), was used and evaluated in this study. The spatial resolution of ERA5 temperature data is 0.25° × 0.25°. Like the precipitation product, the temperature product was downloaded from http:// apdrc. soest. hawaii. edu/ according to the position of the synoptic stations.

Evaluation and generalization of satellite products
To analyze the performance of the satellite precipitation products, Pearson correlation coefficient (R), root mean square error (RMSE), Nash-Sutcliffe efficiency coefficient (NSE), and BIAS indices, which can be seen in Eqs.
(1)-(4), were calculated. where x is the value of observed data, y is the value of satellite output, x and y are the averages of observed and satellite values, and n is the number of data, respectively. The area of the study is small, and the stations inside the area and around it are appropriately distributed. Also, the long-term mean annual data of different stations do not differ significantly (values are in the range of 10% compared to the average); therefore, the Thiessen polygon method was used to generalize the temperature and point precipitation data to the whole sub-basin. To achieve this aim, the contribution of each rain gauge and synoptic station of the whole basin was determined first using ArcGIS 10.5 environment. Then, using weighted averaging based on these small areas, the generalized monthly precipitation and temperature values during the statistical period for ground and satellite data were obtained.

ABCD conceptual water balance model
The ABCD conceptual water balance model is a simple, integrated, nonlinear hydrological model for runoff simulation in response to precipitation and PET developed by Thomas in 1981. The model inputs are precipitation and PET, and the final output of the model is the total runoff of the study area. This model shows soil moisture storage, groundwater storage, surface runoff, groundwater discharge, and actual evapotranspiration (AET) (Al-Lafta et al. 2013;Thomas 1981). Figure 4 indicates the conceptual overview of this model. Parameter A denotes the tendency of runoff before the soil is fully saturated, ranging from 0 to 1. Fernandez et al. (2000) perceived that parameter A ranged between 0.95 and 0.99 over large areas of the United States, and the urbanization and deforestation reduce its value. Since there have not been significant urban developments observed in the Zarandeh sub-basin, the value of this parameter is expected to be close to 1. Parameter B is an upper limit for the sum of AET and soil moisture storage in a given month, depending on the ability of the basin to hold water in the upper soil horizon. Parameter B mainly varies between 100 and 1600 mm (Martinez and Gupta 2010). Parameter C controls the water recharge into aquifers which varies between 0 and 1. Parameter D also controls the groundwater discharge to the mainstream rate. When this value is close to 0, it indicates low or no participation of the baseflow (Al-Lafta et al.

2013; Martinez and Gupta 2010).
This model defines two state variables: "Available water (W i )" and "Evaporation opportunity (rate of evaporation) (Y i )". Available water is calculated as follows: where P i is the amount of rainfall per month and SM u,(i−1) is the soil moisture storage in the upper layer in the previous month. The evaporation opportunity is water, which eventually leaves the basin as evapotranspiration, which is defined by two parameters A and B, as follows: The evaporation opportunity is associated with a nonlinear relationship with available water. Evapotranspiration opportunity is the sum of actual evapotranspiration and storage of soil moisture in the upper layer. Topsoil moisture storage and actual evapotranspiration per month are obtained from Eqs. (7) and (8): where SM u,i is the topsoil moisture storage per month, PET i is the potential evapotranspiration per month, and AET i is the actual evapotranspiration per month. The available water for runoff, i.e. (W i − Y i ) is divided by the parameter C into two parts, upper layer runoff, and groundwater recharge: where Q u,i is the upper layer runoff per month and R i is groundwater recharge per month. Using parameter D, the amount of soil moisture storage and runoff in the lower layer per month is calculated as follows: where SM l,i is the lower layer soil moisture storage per month, SM l,i−1 is the lower layer soil moisture storage in the previous month and Q l,i is the lower layer runoff. Finally, the total runoff per month (Q t ) is obtained from the total upper and lower layer runoff (Al-Lafta et al. 2013;Thomas 1981): The Monte Carlo method and triangular Fuzzy numbers were used to estimate the parameters A, B, C, and D. To do so, the range to which each parameter belongs was first determined. Then a triangular Fuzzy number was considered for each parameter according to the interval set. This number was replaced with the probability density function in the Monte Carlo technique, by integrating it into the Cumulative Distribution Function (CDF). Subsequently, by generating a stack of random numbers in the range of 0-1, and applying it to CDF, a number for the desired parameter was obtained. By repeating the process for each parameter, a set of numbers is created for each parameter that together follows the triangular Fuzzy number. These numbers were used to simulate runoff in the ABCD model. To compare the simulated and observed runoff using NSE as an objective function, the optimization was performed in the calibration period and the best answer was identified.

Evaluation of the satellite products
The first fundamental step of the study was to compare the precipitation and temperature values with the observational data at the catchment scale. Table 3 illustrates the evaluation metrics for the IMERG calculated by the comparison of its data with the ground station data. Accordingly, IMERG and the observations provide very similar results in the south and southwest of the basin. As can be seen, the correlation in all stations is higher than about 0.84, with the highest correlation recognized in the Arieh Chaharbagh station in the southeast of the basin. As for the RMSE, the highest estimation error has been in the east of the basin and decreases towards the west and south. In this sense, the lowest value of RMSE is identified in the Zarandeh station. Generally, the NSE indicates the optimal performance of the satellite product in estimating precipitation. Besides, in Table 3, a dry BIAS occurs in the east of the basin; however, the estimated precipitation is more than the observational value moving towards the northwest and southwest of the basin.
Regarding temperature, ERA5 reanalysis performance in Ghuchan and Neyshabur synoptic stations revealed the R and NSE desirable values. Besides, the low error of RMSE, indicates the optimal performance of this product (Table 4). However, this product estimates the temperature values less than the observations due to the negative value of the BIAS.
The temperature and precipitation data from ERA and IMERG were accurate enough for hydrological modeling at the catchments scale. Other studies such as Hamza et al. (2020), Hosseini-Moghari and Tang (2020), Nozarpour et al. (2021), and Nascimento et al. (2021), also showed the good performance of IMERG product in monitoring precipitation with high correlation with the ground data. Therefore, the point precipitation and temperature data were generalized to the entire sub-basin using the Thiessen polygon method. Accordingly, the long-term mean annual rainfall and temperature in this sub-basin of the satellite products are 260.1 mm and 12.7 °C, respectively, and the ground-based stations are 284.5 mm and 14.5 °C. Figure 5 presents the long-term monthly changes in precipitation. As can be seen, the main rainfall occurs from December to May. A glance at the graph provided reveals that there is a good representation of monthly precipitation values in April, May, June, August, September, October, and November, as the differences are small. For July, December, January, and February, it seems that the satellite products estimate less rainfall than the ground data.
To better emphasize the conclusion, long-term variations (minimum, average, and maximum) in the mean monthly temperature of the Zarandeh sub-basin were plotted in Fig. 6. Generally, the satellite product underestimates the temperature data, and this difference is more egregious in winter. Regarding the minimum temperature values, it seems that the snowfall specifically occurs during December-February. Consequently, the peak of runoff flow is expected to occur from February to May.

Simulation and evaluation of ABCD water balance model
In order to calculate the water balance components of the Zarandeh basin, the ABCD monthly water balance model algorithm was implemented and the developed model was performed using ground-based station data and satellite products over a 16-year period from April 2001 to April 2017, and the sub-basin outflow was simulated. The inputs of the ABCD model are precipitation and PET; therefore, the amount of PET was calculated by the Thornthwaite method using data from synoptic stations and ERA5 monthly mean temperature products. The long-term mean annual potential evapotranspiration in sub-basin scale obtained from synoptic stations data and ERA5 temperature products is 819.2 and 748.5 mm, respectively. The figure for potential evaporation is about 2.88 times rainfall in this sub-basin. Consequently, it is expected that a significant amount of the rainfall in this sub-basin is lost due to evaporation during the year.
The long-term mean monthly potential evapotranspiration using ground data and ERA5 products is presented in Fig. 7. As expected, according to Table 4 ERA5 displays a cold BIAS, so the calculated PET values using satellite products are less than PET calculated using synoptic data. Furthermore, turning to long-term maximum monthly temperature from June to September (Fig. 6), the highest value of potential evapotranspiration belongs to the same period (Fig. 7).
Then symmetric triangular Fuzzy numbers for the four parameters of the ABCD model were determined with respect to the available information from their common changes interval (Al-Lafta et al. 2013;Martinez and Gupta 2010). Accordingly, the base of the triangular number was matched to the beginning and end of the change interval. The height of the vertex of the triangular number corresponding to the middle of the interval was determined in a way that the area of these Fuzzy numbers was equal to 1: By integrating the above numbers, each parameter CDF was found. Then a stack of random numbers between 0 and 1 (e.g. 1000 numbers) for each parameter was generated and applied to the CDF, so the different values were obtained for the four parameters. By applying these values, precipitation, and potential evapotranspiration data to the ABCD model, different effluent values were simulated for the Zarandeh sub-basin. The parameters were optimized by comparing the results with the observed discharge rate based on maximizing NSE objective function. The best simulated runoff and the value of the error parameters are shown in Fig. 8 and Table 5, respectively.

Fig. 7
Long-term mean monthly potential evapotranspiration of Zarandeh sub-basin simulation using satellite products is more accurate than ground-based station data in the Zarandeh basin (Fig. 9). Nevertheless, the model is well able to simulate peak discharges in both datasets. Al-Lafta et al. (2013) utilized this model in different catchments with different climates, showing an MSE value of around 8 in mild climate, which could be deemed as intermediate performance of this model in warm and humid areas. Furthermore, they indicated that the model does not work perfectly in snowy areas. Besides, Martinez and Gupta (2010) examined this model in more than 750 catchments showing its good performance in no-snow catchments using NSE and R 2 indices. This could be a confirmation for choosing ABCD model as suitable in the Zarandeh study area with a semi-arid climate. The ABCD model also had a good performance in Vivari basin with NSE of 0.82 on monthly scale (Marinou et al. 2017).
The optimal values of parameters A, B, C, and D are shown in Table 6. Regarding this, the value of parameter A, which is very close to 1, indicates that the propensity to produce runoff before soil saturation is very low due to the existence of agricultural lands and pastures and the lack of urban areas (Fig. 1). Parameter B determines the upper limit of total evapotranspiration and soil moisture storage. The value of zero obtained for parameters C and D using satellite products as model inputs indicate the non-participation of groundwater impact on the simulated runoff for the Zarandeh sub-basin. However, using ground station data as model inputs, parameter C has values between 0 and 1, which indicates the recharge of the lower soil layer. The value of zero obtained for parameter D indicates the ineffectiveness of  soil moisture in the lower layer on the simulated runoff. Soil moisture storage is not able to recharge groundwater; therefore, if there is no plan to use this moisture storage, these resources will be unavailable in the form of evaporation. However, with proper management and knowledge of appropriate methods for the green water storage utilization, e.g., rainfed cultivation, it would be possible to plan for the conventional use of these water resources. Figure 10 presents the amplitude of computational runoff changes considering the model parameters' uncertainty. The use of Fuzzy-probabilistic algorithms makes it possible to deal with these uncertainties. Figure 11 illustrates the comparison of the long-term mean monthly discharge of computational and observational data. As can be seen, the mean temperature and as a consequence, the amount of evapotranspiration is higher during the spring and summer, so the model overestimated the observed discharge. For the cold seasons, when the mean air temperature and evapotranspiration are low, it seems that   Al-Lafta et al. (2013) indicated that the ABCD model works better for lower streamflow periods. Accordingly, in Fig. 11, it can be clearly seen that the difference between the observed and computed runoff has the lowest value between July and November.
Regarding the parameters C and D being 0, the amount of soil moisture in the lower layer and the flow in this layer are also 0. Figure 12 shows the long-term monthly average of water balance components calculated by the ABCD model.
It seems that most of the rainfall in this basin leaks as soil moisture storage which is considered green water storage. Green water storage is the amount of water in the soil profile supplied by rainfall that is available to the plant and eventually becomes inaccessible by evapotranspiration (Schuol et al. 2008); therefore, it is capable to be used by selecting a suitable product for fall rainfed cultivation in the region.

Model verification
To verify the model, the estimated parameters of the ABCD model in the Zarandeh sub-basin have been used in another catchment. It should be noted the desired area for verification should be similar to the Zarandeh sub-basin in terms of climatic conditions. The selected area is the Sebi subbasin located in Torbat-e-Heydariyeh-Zaveh. The existence of urban areas and stone outcrops in this area (Fig. 2) is one of the differences between these two sub-basins.
An 11-year statistical period (April 2001 to April 2012) was considered for the model verification. The coefficients obtained from the model calibration were defined as fixed in the model. The input precipitation and temperature data to the model were downloaded and processed using IMERG and ERA5 products in the location of the rain gauge and synoptic stations in the area. The simulated discharge results for the Sebi sub-basin and the metrics for the model are shown in Fig. 13 and Table 7, respectively.
Investigation and evaluation of the model outputs show its moderate accuracy in the sub-basin. Despite the same climatic conditions, one of the reasons for the reduced accuracy of the model in the verification step is the difference in land use in the Zarandeh and Sebi sub-basins that affects the parameters of the model (Figs. 1, 2). Specific features of the Sebi sub-basin, e.g., the presence of more urban areas than the Zarandeh sub-basin, can be reasons for the medium efficiency of the model in the verification phase. Although the model has identified the runoff pattern adequately, to estimate the runoff with more accuracy it is recommended to calibrate the model parameters separately to apply this model to any region.

Conclusion
Calculating water balance components plays a key role in deciding the consumption, saving, and water resources management in an area. However, in many parts of Iran, hydrological and meteorological observations are not accessible in some areas. This makes it impossible or inaccurate to calculate the water balance for these regions. Furthermore, determining the parameters and coefficients of water balance models has uncertainties. Therefore, this study has made an effort to use remote sensing and the Fuzzy-probabilistic approach as a conceptual model of water balance to calculate water balance components in the Zarandeh sub-basin located in Iran.
IMERG precipitation and ERA5 temperature monthly products were evaluated over 16 years based on ground station data using four statistical indices including R, RMSE, NSE, and BIAS. The results indicate the optimal detection of IMERG precipitation in the region, especially in low altitudes. A slight error and correlation coefficient above 0.99 of the ERA5 re-analysis temperature product indicate a very good performance of this product in this basin.
Finally, the ABCD model was developed using two sets of the ground data and satellite products. The optimal values of its parameters were determined using Fuzzy numbers and the Monte Carlo method and using NSE objective function. The best performance of the model was determined  using satellite products with an efficiency coefficient of 0.86 (Table 5). The verification of the model in the Sebi sub-basin, had a moderate accuracy with an efficiency coefficient of 0.49. Although these two sub-basins have similar climatic conditions, there are a few differences. Therefore, it should be considered that model calibration is required for each region. As discussed in the results, most of the rainfall in the area allocates to soil moisture storage. The parameters C and D of the model are estimated at 0 and the analysis of evapotranspiration results shows high potential in the region. Overall, considering the results and high accuracy of the ABCD model in simulating runoff and peak discharges, this model is a useful tool for applying to arid and semi-arid areas. Furthermore, the model structure with a Fuzzy-probabilistic approach reduces the uncertainty of the parameters and finds their optimal values, and made it a powerful tool for water balance components calculation. The satellite products evaluation results also showed that they can be used in similar areas without ground data. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Data availability statement IMERG V06 Final Run daily precipitation and ERA5 temperature data used during this study are openly available from http:// apdrc. soest. hawaii. edu/. Regarding ground data, due to confidentiality agreements, supporting data can only be made available to bona fide researchers subject to a non-disclosure agreement. Details of the data and how to request access are available from the website of the Islamic Republic of Iran Meteorological Organization (IRIMO) at https:// data. irimo. ir.

Conflict of interests
The authors have no relevant financial or nonfinancial interests to disclose.