Gridded Precipitation Datasets and Gauge Precipitation Products for Driving Hydrological Models in the Dead Sea Region, Jordan

Abstract

The consistency of hydrological process modeling depends on reliable parameters and available long-term gauge data, which are frequently restricted within the Dead Sea/Jordan regions. This paper proposes a novel method of utilizing six satellite-based and reanalysis precipitation datasets, which are assessed, evaluated, and corrected, particularly for the cases of ungauged basins and poorly monitored regions, for the first time. Due to natural processes, catchments fluctuate dramatically annually and seasonally, making this a challenge. This variability, which is significantly impacted by topo-geomorphological and climatic variables within the basins themselves, leads to increased uncertainty in models and significant restrictions in terms of runoff forecasting. However, quality evaluations and bias corrections should be conducted before the application of satellite data. Moreover, the hydrological HEC-HMS model was utilized to predict the runoff under different loss methods. Furthermore, this loss method was used with an integrated model that might be efficiently employed when designing hydraulic structures requiring high reliability in predicting peak flows. The models’ performance was evaluated using R-squared (R²), the root mean square error (RMSE), the mean absolute error (MAE), and Nash–Sutcliffe efficiency (NSE). In addition, these statistical metrics were implemented to quantitatively evaluate the data quality based on the observed data collected between 2015 and 2020. The results show that AgERA5 exhibited better agreement with the gauge precipitation data than other reanalysis precipitation and satellite-based datasets. The results demonstrate that the data quality of these products could be affected by observational bias, the spatial scale, and the retrieval method. Moreover, the SC loss method demonstrated satisfactory values for the R², RMSE, NSE, and bias compared to the IC and GA loss, indicating its effectiveness in predicting peak flows and designing hydraulic structures that require high reliability. Overall, the study suggests that AgERA5 can provide better precipitation estimates for hydrological modeling in the Dead Sea region in Jordan. Moreover, integrating the SC, IC, and GA loss methods in hydraulic structure design can enhance prediction accuracy and reliability.

1. Introduction

Hydrological catastrophic events, such as typhoons, floods, droughts, hurricanes, earthquakes, and landslides, are natural hazards that can cause damage to human lives and property [1] and lead to the collapse of infrastructure and communication networks [2]. The impact of human activities and climate change on land use may modify the patterns of severe rainfall and subsequent flooding, increasing the variability of these phenomena [3,4,5]. Some studies have shown that flash flooding has become a regular phenomenon in South Asian countries [6,7] and is considered the most prevalent and destructive natural disaster on the planet [8]. The frequency of extreme occurrences is increasing, and crop loss is occurring due to global climate change [9]. Effective and improved policy formulation is required to promote farmers’ livelihoods. As a result, flash flood risk assessment, prediction mapping, monitoring, and vulnerability analysis can be utilized as a proactive management tool, and their repercussions are critical for low-lying locations [10,11,12]. In this context, effective flash flood vulnerability mapping has been recognized as the most relevant and necessary way to identify flash flood vulnerability zones for future decision-making processes [6,13,14].

Additionally, various factors, which change based on geography and geophysical background, cause flash floods. As a result, when flash flood-induced vulnerability mapping is performed utilizing multi-criteria analyses rather than solely criterion-based flash flood-prone zoning, the outcomes become much more trustworthy, legitimate, and permissible [14,15].

The use of hydraulic and hydrological models to assess flood risk is frequent; however, the scarcity of input data in unmonitored areas increases the uncertainty of the results. Satellite-based and reanalysis-based precipitation can estimate input parameters [16]. Conceptual models have numerous advantages in terms of applications, particularly in developing-country watersheds, where input and calibration data are not always available and/or accessible to hydrological model users. One of the advantages observed above is reducing the number of user input data and calibration parameters.

Because of their simplicity, these conceptual models are widely applicable to a wide range of watersheds worldwide. However, the hydrologic simulation methodology used by these models presents challenges with uncertainties, making robust parameter estimates unfeasible.

The rainfall–runoff analysis tool developed by the United States Army Corps of Engineers (HEC) is widely used around the world [17], as is continuous simulation [18,19]. By utilizing various precipitation loss methods [19], such as initial and constant (IC), SCS curve number (SC), and Green and Ampt (GA), the HEC-HMS model may be employed to investigate urban floods, flood frequency, flood warning systems, and the efficacy of spillways and detention ponds across a watershed [20]. Numerous studies [20,21,22,23,24,25] explain that selecting a loss method that calculates the runoff volume and estimating the model parameters are crucial in setting up the HEC-HMS [19]. Derdour [26], for example, accomplished a study in arid environments and discovered that the SCS curve number loss approach outperformed the Green and Ampt methods. Zelelew and Melesse [24], on the other hand, compared two loss method combinations, namely the SCS curve number and the initial and constant methods, with two transformation methods and discovered that the model set containing the initial and constant loss method and an SCS unit hydrograph was the best combination for Ethiopian arid catchment. Furthermore, the best loss approach for runoff simulation varies from catchment to catchment. As a result, selecting the most efficient loss method for a specific catchment is critical for accurate runoff prediction.

1.1. Literature Review Related to Flooding in Jordan

Jordan is a small Arab country in Southwest Asia that is semi-arid. It is located in the Northern and Eastern hemispheres of the Earth amid the rocky desert of the northern Arabian Peninsula. Because of the growth in the population and unrestrained urbanization, the region is subject to heavy rain events, and a flash flood occurred on 25 October 2018. A total of 21 people were killed in two separate places, and a bridge collapsed into the Dead Sea (DS). However, several scientific researchers have utilized various models to propose a flash flood hydrological model in various locations in Jordan. For instance, Momani et al. [27] suggested models that can be used to anticipate the monthly rainfall for the decade to come to assist decision-makers in establishing priorities for water demand management at the Amman airport station. Shaded and Almasri [28] demonstrated that integrating a GIS (geographic information system) with the Soil Conservation Service Curve Number (SCS-CN) technique provides a powerful tool for estimating runoff volumes in West Bank catchments representing Palestine’s arid to semi-arid catchments. Abushandi and Merkel [29] combined a re-adjusted satellite-derived rainfall dataset (GSMaP_MVK+) to predict the exact position of the rainfall storm to provide an innovative structure for rainfall–runoff model applications in the Wadi Dhuliel desert catchments. The performance of IHACRES had some issues. Odeh et al. [30] promoted utilizing an integrated strategy that included remote sensing, a geographic information system, and hydrologic response units to hydrologically simulate a heterogeneous catchment in the Wadi Zerka Ma’in catchment area northeast of the Dead Sea. The average rainfall in the studied area fell from 275 mm/year to 100 mm/year over the last 30 years, but the temperature rose from 24.8 to 26.8 °C. These changes in the climate had a substantial impact on the study region’s hydrological cycle, decreasing Zerka Ma’in River runoff and increasing evapotranspiration. As a result, groundwater recharge in the catchment declined at the same time. Ries et al. [31] utilized hydrometeorological observations, soil moisture measurements, and soil texture to identify significant correlations between event rainfall and runoff volumes and to propose promising options for assessing and managing surface runoff as a water resource in the Dead Sea and east of Jerusalem. Arabeyyat et al. [32] employed an ANN (artificial neural network) and NARX (nonlinear autoregressive exogenous) input model to simulate and predict rainfall quantities in Jordan’s semi-arid regions. The combined application of two delay inputs and eight neurons produces the best training for the ANN, according to the calculated mean squared error (MSE). Givati et al. [33] predicted future Jordan River discharges utilizing nineteen daily regional climate models (RCMs) from the CORDEX project and the GR6J rainfall–runoff model. His investigation’s conclusions could have far-reaching ramifications for the region. Alhasanat [34] examined the risks of probable flash flood hazards in Wadi Mousa and determined the number of flows for flash flood hazards, as well as constructed floodplain zone maps using average annual rainfall and average annual evapotranspiration by utilizing the Unit Hydrograph method. According to the runoff calculations, only rainfall events over 22 mm within 24 h would result in runoff. Scharifi et al. [35] investigated flood scenarios and the impact of climate change in the Al Hasa basin using runoff data from 1990 to 2016 and geological and soil maps based on curve number, unit hydrograph, and time of concentration methods. The outcomes of the chosen approaches are acceptable approximations. However, The time of concentration approach, on the other hand, is the most valuable because it considers all optimum variables while ignoring the impacts of external variables. To mitigate the impact of flash floods in Jordan’s Dead Sea, Gökçekuş et al. [36] recommended a flash flood risk mitigation plan to be executed by municipalities, provincial executives, and authorities using rainfall data and DEM by employing 2D HEC-RAS modeling based on unsteady flow analyses for generating flooding risk maps for undertaking spatial planning considering flash floods. Utilizing daily precipitation potential evapotranspiration and runoff data, Abdulla and Al-shurafat [37] proposed rainfall–runoff modeling for semi-arid and international regions connected in the Yarmouk River Basin, the results of which could be used by water departments to further enhance Yarmouk River Basin water resource management. Shawaqfah et al. [38] proposed a study mapping flash flood potential and risk level in Jordan’s Amman Zarqa basin applying Geographic Information Systems (GIS) tools and the potential index of flash flood; results revealed that the slope and land use weights in the used equations were the most influential parameters in this study. The potential threat level for all scenarios was evaluated, and the results revealed that the study region would be subjected to a medium risk level. Islaih et al. [39] utilized the hydrologic modeling Soil Conservation Services (SCSs) technique and the Watershed Modeling System model (WMS 11) to evaluate the consequences of climate change on flash floods in the Zarqa main region. Peak discharges for the thunderstorm on 25 October 2018 were 102.94, 126.66, and 146.7 m³/s for sub-basin 1, 2, and 3, respectively. Abdelal et al. [40] studied hydrological evaluation and flood control system management implications. A paucity of runoff measurements and low-resolution rainfall and topography data in Petra, Jordan, hampered the study. From 2019 to 2020, rainfall data were utilized by WMS (Watershed Modeling System) for watershed delineation and HEC-HMS for runoff simulation. The methodology and criteria provided apply to similar dry and semi-arid mountainous environments prone to flash floods. Ali and Alshraifat [41] proposed a study that utilized GIS, AHP (Analytical Hierarchy Process), and DEM (Digital Elevation Model) to predict floods in the Wadi Zarqa Ma’in basin. According to the findings, 34% of the basin is prone to flooding during the fall season due to heavy rains and an inability to cover vegetation. It was also revealed that the basin was prone to flooding with the same severity during the winter season, reaching 19% in the high inclination region, characterized by restricted rainfall infiltration and penetration. The study proposed using field surveys supplemented by a Global Positioning System device to assess the natural and human explicates that may be considered when assessing the likelihood of flooding. AlMahasneh et al. [42] utilized the GIS-Rational model to produce a potential flood danger severity map in Jordan using rainfall gauging and intensity duration frequency (IDF) stations, Lulc, and soil type. The study provided consistent data on flood hazard classifications across the country to ensure the effective execution of flood management policies and flood mitigation activities. In addition, the study highlighted the advantages of GIS technology in the construction of models and parameterization. A. Hawamdeh [43], predicted flood flow in Wadi Wala, Jordan, utilizing an Artificial Neural Network (ANN) and a comprehensive historical record of meteorological data from 1980 to 2018. The developed models accurately predicted flood flow over the watershed. Unami, K. [44] proposed a study investigating the dynamics of rainfall–runoff events in a desolate Jordan Rift Valley catchment. The produced upper and lower limiting rainfall–runoff models with fractional derivatives are evaluated in a system–theoretic framework by a pair of exogenous input (ARX models) with linear autoregressive models employing time series rainfall and runoff data. Aqnouy et al. [45] combined six spatial layers to generate a flash flood susceptibility map for Aqaba City and investigate its impact on land use/land cover (LULC). These layers included rainfall, elevation, slope, stream order (distance to stream), soil, and LULC. These layers were processed using GIS tools and MCA (multi-criteria analysis). The studies revealed that rivers, canyons, and flat low altitudes are especially vulnerable to flash floods in urban and agricultural areas. Furthermore, steep and ridge slopes and upper-stream high altitudes were determined to be less vulnerable to flash flood risks.

Understanding the impact of climate change on the Al Hasa basin using runoff data from 1990 to 2016 and acceptable approximations further enhance Yarmouk River Basin water resource management, which are both studied by apply investigating rainfall and runoff data and upper-stream high altitudes.

1.2. Research Gap and Study Objectives

Recently, climate change is leading to more severe extreme weather events worldwide. This trend will increase water-related disasters, including floods and droughts. The Mediterranean region is anticipated to face growing exposure to flash floods. This is attributed to the projected rise in hydrologic extremes and rapid population growth in the area. Hence, the development of a flood impact reduction model is crucial. It is an essential tool for mitigating stormwater runoff and minimizing its consequences.

Moreover, it provides an advantageous structure for contemplating future land use and urban planning in the study region. However, due to the lack of reliable and extensive records of streamflow observations, creating a model in poorly or ungauged basins involves significant challenges. As a result, re-analysis-based precipitation and satellite-based data are valuable alternatives to existing data for hydrometeorological research in areas with sparse or inaccurate observational data. However, it is essential to carefully evaluate these precipitation products’ applicability before using them in particular basins due to their inherent flaws that vary based on climate zones, seasonal cycles, and land surface characteristics. According to the authors’ review, The performance of runoff modeling based on precipitation loss approaches employing event-based modeling in the Dead Sea (DS) region has not received much attention. The novelty of this study is to emphasize the utilization of reanalysis-based and satellite-based precipitation as an alternative within poorly gauged or ungauged and poorly monitored regions, where it is challenging because the natural processes that occur within catchments change dramatically seasonally and annually. This particular variant, heavily influenced by climatic and topo-geomorphological variables within a basin, leads to greater model uncertainty and a significant restriction for runoff forecasting. To overcome this restriction, the “Predictions in Ungauged Basins” effort provides several studies that use evaluation, correction, and spatial calibration methodologies to improve runoff forecasting performance. Process-based models significantly improve when remote sensing data replicates and generate complex hydrological processes.

The research objectives were to perform a corrective model to improve the quality of the precipitation product and to thoroughly assess the performance of satellite-based and reanalysis-based precipitation as input for a rainfall–stream flow hydrological model for the entire study period. Then, utilizing various scenarios of precipitation loss methods using HEC-HMS calibrated by the gauge observed, the applicability of the best precipitation products and actual daily precipitation are investigated in the hydrological simulation. Our approach is superior to calibrated techniques in that it eliminates the impact of different model parameter settings on simulation outcomes. It enables us to assess the benefits and limitations of hydrological simulation and assess the benefits and limitations of hydrological simulations.

2. Material and Method

There are two aspects to this research. Precipitation product evaluation: the first section evaluates the potential use of satellite-based precipitation (CHIRPS (CHI), NOAA_CDR_PERSIANN (NCP), and NOAA CPC CMORPH (NCC)) and reanalysis-based precipitation (ERA-AG (ERA), MERRA-2 (MER), and NOAA CPC DAILY GLOBAL(NCD). The best-selected data are adjusted. The selected and adjusted SPD is evaluated in the second step (runoff simulation evaluation). Then, the actual daily precipitation to be used drives the hydrological models by utilizing different scenarios of precipitation loss methods, namely: IC (initial and constant), SC (SCS curve number), and GA (Green and Ampt loss), and the accuracy and applicability of the runoff simulation results are evaluated. The proposed analytical process used in this paper is illustrated in Figure 1.

2.1. Study Area and Data Used Description

Jordan is located in Asia at 31.9277° N latitude and 35.8793° E Longitude. The Dead Sea (DS) is the lowest elevation on the continent, with a surface level that is currently 433 m below mean sea level situated in the geological depression of the DS Basin (DSB) at 31.3333° N latitude and 35.4999° E longitude (Figure 2a). A terminal hypersaline water body with a Ca-chloride brine composition makes up the lake.

Flash floods caused by torrential rains are frequently caused by surface water. They could be catastrophic and lead to infrastructural damage. On 25 October 2018, two distinct locations saw the deaths of 21 individuals, and a bridge collapsed due to flash floods. Incisions into weak mud deposits are where the energy released during such cataclysmic occurrences dissipates. Jordan is susceptible to numerous risks, including natural disasters. The severity and frequency of Jordan’s other significant hazards, such as flash floods and drought, are predicted to worsen due to climate change [26]. This situation puts Jordan’s economic and social development in danger in several ways. Jordan has, since 2018, experienced unique shocks of catastrophic localized flash floods. Although they do not happen often, they pose a very significant threat to the nation’s ecosystems, infrastructure, and people. According to the General Directorate of Civil Defense, sites of disruptive flash flooding have been statistically documented. (refer to Table S1 as Supplementary Material).

The Mediterranean and Saharan desert climate zones are both included in the DS watershed. As stated by [46], the northern and central-western DS watershed is distinguished by hot/warm summer (Mediterranean climate). At the same time, the southern and eastern regions experience hot semi-arid to hyper-arid desert climates. The watershed experiences its heaviest precipitation between December and February. The rainy season lasts from October to May [47,48]. Rainfall is infrequent during the summer (June to September), especially when substantial atmospheric subsidence predominates in the area. The Ministry of Water & Irrigation reports that the average rainfall varies greatly, with lowland areas receiving 100 mm of rain annually and highland areas receiving 450 mm, as indicated in Figure 2b. 22 °C is the average yearly temperature (Figure 2c). Two weather stations established in various locations within the research area provide meteorological data for the area.

Furthermore, the Jordan River and the Yarmouk River [49,50,51], several tiny tributaries, freshwater and saltwater springs, and runoff (through dry rivers, i.e., Wadis) serve as the primary sources of water for the modern DS. The three main surface basins in the eastern DS region are three significant surface basins: Wadi Al Hasa and Wadi Zerka Ma’in catchments. There are elevations between −415 m and 1320 m. The Wadi, formerly discharged straight into the DS, as it did so in the 1960s at a DS level of roughly −395 m. Since then, the discharge levels have decreased simultaneously, with the DS level dropping by roughly 20 m, as per Ref. [52]. As a result, AL Rawashdeh et al. [52] observed that as a result, the sea surface area of DS shrunk from 934.26 km² in 1973 to 640.62 km² in 2004. Additionally, the drop-off in water surface elevations (WSE) has led to the older coastal sediments being cut.

Furthermore, the soil types are complex. The main soil types (Figure 3a) are 80% of Xerochrept, which is a moderately developed soil and has a high content of clay in its layers, which makes it suitable for the runoff after saturation; 17% Torriorthent, which is very weakly developed; and 3% Camborthid, which has an aridic (dry) moisture regime with weak soil development. According to its permeability and infiltration, each soil type was categorized into its corresponding hydrological soil group, according to information and descriptions in the National Engineering Handbook published by the U.S. Department of Agriculture’s Natural Resources Conservation Service (USDA-NRCS, 2009). It is separated into the following groups: A, B, C, and D, which represent the soil’s texture, the minimum rate of infiltration, and the different types of cover that are explained in (Table S2 as Supplemental Material). Based on the data gathered, the distribution of the hydrological soil group in the DS area is as follows: 80% of soil group D, 17% of soil group C/D, and 3% of soil group A, which is calculated based on the extracted (Table S3 as Supplementary Material) for the soil group map. The extracted land use land cover (Figure 3b) from Landsat 8 satellite images for the DS region is classified as 55% open space, 3% water bodies, 2% agriculture, and 40% of low residential density. According to the land use, the assigned curve number for soil group A is 77, group C is 90, and group D is 92. By multiplying the soil group type % by the associated curve number, the computed curve number for each basin is obtained. According to the General Directorate of Civil Defense, sites of disruptive flash flooding have been statistically documented. At the same time, the three main surface basins in the eastern DS region are significant. Wadi Al Hasa and Wadi Zerka Ma’in the catchments had soil type A.

2.2. Dataset

2.2.1. Ground-Based Gauge Precipitation Data

The daily rainfall data and flood events were employed in the proposed study. From 2011 to 2022, the Ministry of Water and Irrigation published the observed daily rainfall data at gauge stations in the DS region. (

Table 1. Information regarding the selected stations.

Station ID	Station Name	Latitude [N°]	Longitude [E°]	Elevation [m]
1	Khanzira (taiybat el-karak)	31.057	35.601	997
2	Aiy	31.133	35.640	898
3	Mountain_nibo	31.764	35.751	791
4	Madaba	31.716	35.796	799
5	Ma’in	31.679	35.736	865
6	Mushaqqar evap. St	31.787	35.804	859
7	Hisban	31.805	35.812	875
8	Rabba_evap	31.274	35.742	958
9	Mazar	31.058	35.697	1278
10	Qasr	31.319	35.744	940
11	Sirfa	31.325	35.657	870
12	Karak	31.184	35.703	1031
13	Ain_al-bsas	31.197	35.696	720
14	Ghores-safi	31.050	35.501	−343

). The stations range in elevation from 343 to 1278 m, most of which are in the middle and lower latitudes (Figure 2a).

A tipping bucket rain gauge was used to measure the rainfall at a height of 0.3 m above ground level. The specifications of the rain gauge are listed in Table S4 as a part of the Supplementary Material.

2.2.2. Satellite-Based Precipitation Data (SPD)

A climate engine (Cloud Computing of Climate and Remote Sensing Data) was used to extract the spatial resolution of the rainfall data from 1979 to 2022 due to the short duration of station rainfall data at the DS region. Reanalysis has numerous uses in atmospheric sciences, not the least of which are operational weather centers, where it is employed to evaluate forecast error anomalies and assimilation capabilities. Reanalysis has numerous uses in atmospheric sciences. Not the least of which are operational weather centers, which are employed to evaluate forecast error anomalies, track the development of assimilation capabilities and modeling, and assess the effects of observing system changes. This study selected reanalysis-based precipitation (ERA, MER, NCD) and satellite-based precipitation (CHI, NCP, and NCC), the selection was made due to the lack of gauge stations in the DS region. The detailed SPD is summarized in

Table 2. Significant characteristics of SPD used in the study (https://climateengine.com/, accessed on 17 January 2023).

Products	Resolution	Period
Reanalysis precipitation dataset
ERA-AG (ERA)	9600 m (1/10-deg)	1979–present
MERRA-2(MER)	9600 m (1/10-deg)	1980-present
NOAA CPC DAILY GLOBAL(NCD)	5500 m	1979–present
Satellite precipitation dataset
CHIRPS(CHI)	4800 m (1/20-deg)	1981–present
NOAA_CDR_PERSIANN(NCP)	2400 m (1/4-deg)	1983–present
NOAA CPC CMORPH(NCC)	2500 m	1998–present

. The fifth generation of atmospheric reanalysis is known as ERA5 (ERA). The FGGE project launched atmospheric reanalysis activities in 1979. In general, succeeding atmospheric reanalysis has profited from continuous model improvement and offered improved horizontal resolution, more complex schemes, and benefits. A retrospective examination of second-generation modern-era research and applications is known as MERRA 2(MER). The Climate Prediction Center’s (CPC) Global Precipitation Time Series contains time series charts of daily precipitation data and accumulated precipitation compared to typical accumulated amounts for numerous locations worldwide. NOAA CPC DAILY GLOBAL (NCD) Climate Prediction Center (CPC) Global Precipitation Time Series provides time series charts showing observations of daily precipitation and accumulated precipitation compared to normal accumulated amounts for various stations around the world. CHIRPS (CHI) New land-only climatic database for precipitation, obtained from the University of California, Santa Barbara’s (UCSB) Climate Hazards Group. A daily, quasi-global precipitation product called NOAA_CDR_PERSIANN (NCP) covers the years 1982 through 2020. In total, 60° S to 60° N and 0° to 360° longitude are covered with a 0.25° spatial resolution. NOAA CPC NCC CMORPH bias-rectified CMORPH satellite precipitation estimates are generated on an 8 km x 8 km grid over the entire globe domain from 60 deg S to 60 deg N at 30 min intervals starting on 1 January 1998. This formal version (Version 1) of bias-corrected CMORPH is manually prepared once a month at a lag of three to four months due to the latency of some input data sets. This study considers the time scale and accumulated precipitation compared to typical accumulated amounts for numerous locations worldwide.

2.3. Correction of Satellite-Derived Rainfall

Due to inadequate parameterization procedures, the rainfall/precipitation (R/P) reported by SPD is either exaggerated or underestimated. The bias caused by locally prominent atmospheric components is the term used to describe this underestimating or overestimation. When employing gauged R/P data for bias correction, the estimated R/P values can be improved. According to earlier works, several approaches have been developed based on Measure-Correlate-Predict, Linear Adaptation, Cumulative Distribution Function, and Modulated Output Statistics [53,54,55,56,57,58,59,60].

By applying the Measure-Correlate-Predict (MCP) approach to identify a correction factor or scaling factor, the bias in estimating R/P using gauged data can be decreased [60]. The mathematical equation of MCP is presented in Equation (1).

According to earlier works, several approaches have been developed based on Measure-Correlate-Predict, Linear Adaptation, Cumulative Distribution Function, and Modulated Output Statistic Estimating.

$$R_{\mathit{ce},i}=\frac{\overline{R_m}}{\overline{R_e}}\times R_{e,i}$$

(1)

The correct estimated rainfall data are represented by s${\mathrm{R}}_{\mathrm{ce},\mathrm{i}}$, the mean gauged rainfall data are represented by $R_m$, the mean estimated R/P data are represented by SPP and $R_e$, and the estimated R/P data are represented by SPP and $R_{e,i}$.

Another method for rectifying the estimated (R/P) supplied by SPPs is linear adaptation (LA). Equation (2) shows the line of best fit between the estimated and observed GHI, which is then subtracted from $R_e$ = $R_m$; the path leading to Equation (3). In this paper, this approach is referred to as LA1a.

$$R_{e,i}=m_1{R}_{m,i}+c_1$$

(2)

$$R_{\mathit{ne},i}=R_{e,i}-\left[+c_1\right]$$

(3)

where $m_1$ is the slope and $c_1$ is the intercept, which is estimated using Equation (2).

By generating a linear fit between $R_{\mathit{ne},i}$ and $R_{e,i}$. As shown in Equation (4), to obtain the slope and intercept, the correction made using gauged data can be expanded to non-overlapping years. The time series of $R_{\mathit{ce},i}$ data are found using Equation (5). This approach, known as LA2, is used in

$$R_{\mathit{ne},i}=m_2{R}_{e,i}+c_2$$

(4)

$$R_{\mathit{ce},i}=m_2{R}_{e,i}+c_2$$

(5)

where the intercept ($c_2$) and slope ($m_2$) are determined using Equation (1).

By establishing a linear relationship between gauged and estimated R/P data, as shown in Equation (6), the bias correction based on gauged data can also be carried out. Using Equation (7), the slope and gradient of the best-fit line are utilized to obtain the corrected time series; this technique is referred to as LA3 in this study.

$$R_{m,i}=m_3{R}_{e,i}+c_3$$

(6)

$$R_{\mathit{ce},i}=m_3{R}_{e,i}+c_3$$

(7)

where $m_3$ is the slope and $c_3$ is the intercept, which is estimated using Equation (3).

To quantitatively evaluate the data quality of different precipitation products in this paper, three statistical metrics, including the R-Squared (R² or the coefficient of determination), root mean square error (RMSE), and the mean absolute error (MAE), are used. The expressions of the statistical metrics used in the current study are presented in Equations (8)–(10).

• Coefficient of determination (R²)

$$R^2=1-\frac{\sum _{i=1}^n{\left(a_{a,i}-a_{p,i}\right)}^2}{\sum _{i=1}^n{\left(a_{p,i}-a_{a,\mathit{ave}}\right)}^2 }$$

(8)

• Root mean square error (RMSE)

$$\mathit{RMSE}=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(a_{a,i}-a_{p,i}\right)}^2}$$

(9)

• Mean absolute error (MAE)

$$\mathit{MAE}=\frac{1}{n}\sum _{i=1}^n\left|a_{a,i}-a_{p,i}\right|$$

(10)

where $a_{a,i}$ is the observed value, $a_{a,\mathit{ave}}$ is the observed mean, and $a_{p,i}$ is the simulated value.

2.4. Hydraulic Model (HEC-HMS Model)

The hydrologic model assists with comprehending, predicting, and managing water resources by providing a simplified representation of an actual hydrologic system [61]. Hydrological models are an essential tool for managing and planning water resources. Locally, urbanization and industrialization significantly impact hydrologic systems, as does the rapid increase in the worldwide population. Multiple water demands must therefore be considered when planning development and managing various water supplies. On the other hand, obtaining gauge discharge data has always been challenging because measurements cannot be taken at various points along the river [62].

To address as many challenges as possible, including water supply for large river basins, flood hydrology, and small urban river flow, the United States Army Corps of Engineers developed HEC-HMS. Several research projects can use HMS hydrographs [16,63,64,65,66,67]. Extreme weather events (such as floods and droughts), rainfall–runoff models, streamflow modeling, and agriculture water ungauged basins at various regional and national scales have been the focus of water resource study. The HEC-HMS model was found to be suitable for streamflow simulation in ungauged basins and analysis of runoff processes for water resource management and development [67,68]. In this study, the precipitation–runoff processes of dendritic watershed systems were simulated using HEC-HMS 4.10 [69]. The conceptual HEC-HMS hydrological model simulates runoff and is semi-distributed. Daily precipitation, the basin’s runoff flow (for validation and calibration), and geographical data about the basin are required to produce the simulated runoff as output [19]. The HEC-HMS model configuration comprises a basin model, a meteorological model, control parameters, and input data (time series data) [60]. Numerous techniques (including deficiency and constant, exponential, Green and Ampt, SCS curve number, initial and constant, Smith Parlange, and Soil Moisture Ac—counting—SMA) were used to simutlate infiltration losses. HEC-HMS creates a continuous stream flow record for the sub-basin from the direct runoff and base flow data. Direct runoff is transformed into stream flow using a user-selected transform mechanism. The transform options include the Clark unit hydrograph, kinematic wave, Mod-Clark, SCS unit hydrograph, Snyder unit hydrograph, user-specified graph, and user-specified unit hydrograph.

Using actual precipitation (A) and the ERA dataset (E), the SCS unit hydrograph (HU) method will be utilized to calculate the hydrologic loss rate in this study. Initial and constant (IC), SCS curve number (SC), and Green and Ampt (GA) loss methods will also be used, namely: SC-A, IC-A, GA-A, SC-E, IC-E, and GA-E, which were evaluated based on the observed runoff data.

2.4.1. Initial and Constant (IC) Loss Method

A simplified loss method, the initial and constant (IC) method, is appropriate for catchments with limited data related to the soil. This loss approach may be estimated using just two parameters: constant rate and the initial loss [19]. Initial estimates for these two parameters were obtained based on the type of soil and the use of the property. The following are the general equations (Equations (11)–(13)) [19] for the initial and constant loss methods. Initial estimates for these two parameters were obtained based on the type of soil and the use of the property.

$${\mathit{pe}}_t=0 \mathit{if} \sum \mathit{pi}<\mathit{Ia}$$

(11)

$${\mathit{pe}}_t=p_t-f_c \mathit{if} \sum \mathit{pi}>\mathit{Ia} \mathit{and} \mathit{pt}>\mathit{fc}$$

(12)

$${\mathit{pe}}_t=0 \mathit{if} \sum \mathit{pi}>\mathit{Ia} \mathrm{and} \mathit{pt}<\mathit{fc}$$

(13)

where $f$ is the highest possible rate of precipitation loss, $\mathit{Ia}$ is the beginning loss, and $\mathit{pi}$ is the depth of the initial precipitation.

The initial loss rate ranges from 2.54 mm to 5.08, and the considered value in this study is 3.81 mm. The constant rate value for each basin was assigned based on soil group type; for soil group (A), the value is 9.65 mm/hr, group (B) is 3.81 mm/hr, group (C) is 2.54 mm/hr, and group (D) is 0.025 mm/hr.

2.4.2. SCS Curve Number (SC) Loss Method

The SCS curve number (SC) approach, which estimates excess precipitation as a function of soil cover, cumulative precipitation, antecedent moisture condition, and land use [41], is another straightforward and well-liked loss method. Curve numbers (C.N) and starting abstraction are the only two factors for this approach that need to be estimated [40]. The area’s various land use classifications were considered while calculating the curve number as a weighted value [38]. In addition, when calculating the curve number, the antecedent moisture condition and hydrological soil group must also be considered applicable to the implementation of the SCS Runoff C.N mathematical Equation (14):

$$Q=\frac{{\left(P-0.2S\right)}^2}{P+0.8S}$$

(14)

where $S$ stands for the potential maximum retention amount, $P$ stands for the quantity of rainfall, and $Q$ stands for the amount of surface runoff. Through the hydrological component known as curve number (C.N.), the maximum retention possibility is calculated as follows:

$$S=\left(\frac{25400}{\mathit{CN}}\right)-254$$

(15)

2.4.3. Green and Ampt (GA) Loss Method

A conceptual loss method called Green and Amp (GA) loss is utilized to calculate the loss in allowable surfaces [41]. To estimate this method, several factors are needed, including initial loss, hydraulic conductivity, wetting front suction, and volume moisture deficit. By consulting the literature [37,40], these parameters were approximated. Below is provided Equation (16) (the general equation for the Green and Ampt loss approach) [40]. The Green–Ampt Equation (17) is represented in its fundamental form as follows:

$$f\left(\mathit{xt}\right)=k\left(1+\frac{∆\theta (\phi +h0}{F\left(t\right)}\right)$$

(16)

where $t$ indicates the time, $k$ indicates the saturated hydraulic conductivity, $∆\theta$ indicates the soil capacitance (defined as the difference between the saturated and initial moisture content), $\phi$ indicates the soil suction head, $h0$ indicates the depth of ponded water, and $F\left(t\right)$ indicates the cumulative infiltration derived from:

$$F\left(t\right)-∆\theta \left(\phi +h0\right)\mathit{ln}\left(1+\frac{F\left(t\right)}{∆\theta (\phi +h0}\right)=\mathit{Kt}$$

(17)

USDA (The United States Department of Agriculture) determined soil parameters based on soil type, as illustrated in

Table 3. USDA soil types for the GA Method, ‘Green–Ampt infiltration parameters from soils data).

USDA Soil Type	Suction (mm)	Hydraulic Conductivity (mm/hr)	Porosity (Fraction)
Clay	316.3	0.3	0.385
Silty Clay	292.2	0.5	0.423
Sandy Clay	239	0.6	0.321
Clay Loam	208.8	1	0.309
Silty Clay Loam	273	1	0.432
Sandy Clay Loam	218.5	1.5	0.33
Silt Loam	166.8	3.4	0.486
Loam	88.9	7.6	0.434
Sandy Loam	110.1	10.9	0.412
Loamy Sand	61.3	29.9	0.401
Sand	49.5	117.8	0.417

.

For soil group type A, sand, the suction value is 49.5 mm, the hydraulic conductivity value is 117.8 mm/hr, and the porosity value is 0.417. For soil group type D, clay, the suction value is 316.3 mm, the hydraulic conductivity value is 0.3 mm/hr, and the porosity value is 0.385. The parameters mentioned above were calculated for each basin based on their soil type group, as illustrated in Table S3 of the Supplementary Material, by multiplying their soil type percentage by the parameter value.

2.4.4. SCS Unit Hydrograph Method Transformation Method

The transformation loss is calculated using the SCS unit hydrograph approach, which only needs one parameter for each sub-basin: “The lag time.” The standard lag is the interval of time between the centroid of the peak discharges of the ensuing hydrograph and precipitation mass [70]. A lag time determination is required as an input for the transform procedure. Equation (18) illustrates the link between the lag time ($T\mathrm{lag}$) and the time of concentration ($T\mathrm{C}$) that was developed by the SCS. The concentration time is calculated using Equation (19) of the Giannotti formula. The time of concentration and the lag time are to be computed for each sub-basin.

$$T\mathrm{lag}=0.6T\mathrm{C}$$

(18)

$$\mathit{TC}=\frac{4\sqrt{A}+1.5L}{0.8\sqrt{H}}$$

(19)

where $A$ indicates the size of the watershed (in km²), $L$ indicates the length of the main channel (in km), and $H$ indicates the difference between the mean basin elevation and the outflow height (in m).

2.4.5. Model Calibration

The hydrological simulation requires sensitivity analysis and calibration. The effectiveness of hydrological simulation can be increased by using sensitivity analyses to identify the parameters that significantly impact the simulation. Parameter calibration is the methodical process of changing the model parameter values to bring the simulation results closer to the observed gauge data [61]. Curve number (CN); initial abstraction (i); lag time (TL); GA, conductivity; GA, suction; IC, constant rate; and IC, initial loss parameters were the seven parameters proposed for the calibration procedure. To increase the disparity between the simulated and observed discharges, the observed peak discharges in the DS region can be utilized.

The following is the calibration procedure: The model is initially constructed using the findings from Section 2.4.3. The calibration is then repeated until all three parameters can no longer be increased before the findings are evaluated using R², RMSE, NSE, and BIAS. NSE (Nash–Sutcliffe efficiency coefficient) shows how far the simulated and observed values deviate from one another. NSE has a range of −1 to negative infinity. The simulated results are more similar to the observed values when the NSE value is 1. Equation (20) was used to calculate the NSE values.

$$\mathit{NSE}=1-{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}(\mathrm{Qi},\mathrm{obs}-\mathrm{Qi},\mathrm{sim})2}{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}(\mathrm{Qi},\mathrm{obs}-\mathrm{Qobs})2}}$$

(20)

where $\mathit{Qi},\mathit{obs}$ is the observed discharge at time t = i and $\mathit{Qi},\mathit{sim}$ is the simulated discharge at time t = i, $N$ is the total number of observations, and $\mathit{Qi},\mathit{obs}$ is the average observed discharge.

A systematic error that leads to an incorrect evaluation of the effect or interaction is known as bias. This demonstrates how well the gauge mean and mean estimate agree. Equation (21) was used to determine the bias value. No units exist for bias.

$$\mathit{BIAS}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}(\mathrm{Si}-\mathrm{Gi})}{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}(\mathrm{Gi})} \ast 100\mathrm{\%}$$

(21)

• $\mathit{Gi}$= the gauged observed precipitation;
• $\mathit{Si}$ = the precipitation;
• $N$ = the number of observations.

3. Results and Discussion

3.1. Gauge-Observed Data and Comparison of Multi-Precipitation Products

The daily scale (ERA, MER, CHI, NCD, NCP, and NCC) defines the SPD products. They are first compared to actual observed daily rainfall from 2015 to 2020, as illustrated in Figures S1–S14 in the Supplementary Material. In addition, the computed maximum daily precipitation compared to the maximum observed daily rainfall in one year at fourteen gauge-observed stations within the DS region is illustrated in Figure 4 and summarized below.

• MER dataset shows closer results to observed daily rainfall at stations 1, 2, 6, 7, 11, 12, and 13, which have higher elevations values ranging from 720 m to 1031 m while overestimating the rainfall at station 14, which is a low laying region (−343 m) during the flood event in the 2018 year. ERA shows satisfactory results to the observed rainfall at stations 1, 2, 5, 6, 10, 13 (From 720 m to 997 m above sea level), and 14 (elevation −343 m) while underestimating the rainfall at stations 8, 11, and 12 (elevations range from 870 m to 1031 m).
• NCC overestimated values of precipitations at stations 3, 4, 5, 6, 8, 10, 11, 12, 13 (elevations range from 720 m to 997 m), and 14 (elevation −343 m) compared to other SPD products during the same year while showing closer results at stations 1 and 2.
• CHI overestimated the rainfall at stations 3, 6, 8, and 10 (elevations range from 791 m to 958 m) and underestimated the rainfall at stations 1, 2, 5, and 11 (elevations range from 865 m to 997 m), while showing closer results at stations 4 and 12 (elevations range from 799 m to 1031 m). No records were obtained at low-laying regions at station 14.
• NCP overestimated the rainfall at station 3 (elevation 791 m) and underestimated the rainfall at stations 1, 2, 5, 7, 8, 9, 10, 11, 12, and 13 (elevations range from 720 m to 997 m) while showing closer results at station 14, which is a low laying region.
• NCD underestimate the rainfall at stations 1, 2, 5, 8, 11, 12 (elevations range from 720 m to 997 m), and 14 (elevation −343 m) while showing closer results at stations 3, 4, 6, 10, and 13 (elevations range from 720 m to 940 m) and defined by the daily scale (ERA, MER, CHI, NCD, NCP, and NCC) are first compared to actual observed daily rainfall during.

The daily scale data of NCC, CHI, NCD, and NCP in all observed gauged stations show an unsatisfactory correlation and unimodal pattern compared with the observed gauged stations. In contrast, ERA and MER are satisfactory in stations (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12). The most significant differences between the mentioned dataset above and the observed rainfall related to sub-regions and other climatic and geographical conditions influence the precision and reliability of the precipitation estimates. For example, at station 5, the observed rainfall was 46.70 mm when the flood occurred on 25 October 2018. ERA and MER show satisfactory values of daily precipitation of 19.85 mm and 24.84 mm, respectively, compared to CHI, NCP, NCC, ERA, MER, and NCD values. In contrast, ar, 0, 0, 0, 22.41, 12.94, and 0 mm, at the same date as shown in the plotted Figure S5 of the Supplementary Material for daily precipitation.

The statistical comparison of the RMSE, MAE, and R² is illustrated in

Table 4. Statistical parameters using daily data for all stations.

Index	Stations	CHI	NCP	NCC	ERA	MER	NCD
R2	1	0.0128	0.0001	0.0010	0.2959	0.2436	0.0011
	2	0.0097	0.0017	0.0504	0.1842	0.2059	0.0021
	3	0.0001	0.0005	0.0004	0.0205	0.0094	0.0005
	4	0.0088	0.0001	0.0001	0.2093	0.2041	0.0002
	5	0.0006	0.0002	0.0000	0.2897	0.2428	0.0035
	6	0.0025	0.0002	0.0001	0.2450	0.3409	0.0026
	7	0.0001	0.0002	0.0005	0.1761	0.1614	0.0017
	8	0.0000	0.0004	0.0007	0.1656	0.0395	0.0003
	9	0.0068	0.0000	0.0004	0.1263	0.1550	0.0000
	10	0.0044	0.0004	0.0000	0.1553	0.0514	0.0024
	11	0.0529	0.0012	0.0037	0.3349	0.2953	0.0046
	12	0.0002	0.0015	0.0002	0.0624	0.0517	0.0624
	13	0.0023	0.0008	0.0000	0.2142	0.0675	0.0026
	14	*	0.0006	0.0000	0.0527	0.0084	0.0007
MAE	1	2.4692	2.0927	7.8004	1.6657	2.1658	1.9406
	2	2.5395	2.0502	7.7580	1.6644	2.2392	2.0432
	3	3.8406	7.2165	0.7985	0.7308	0.8670	0.2847
	4	1.3159	1.2653	3.9978	0.8880	0.8300	1.3162
	5	2.6315	2.1287	5.7794	1.7202	1.7539	2.3566
	6	3.0224	2.4491	5.3111	1.9364	1.8386	2.5073
	7	1.1800	4.8563	0.9970	1.0257	1.4239	0.8087
	8	1.2428	0.9702	5.8520	0.7004	1.2934	0.8594
	9	1.0530	5.1641	0.7527	0.7968	0.8651	0.6670
	10	1.2052	5.0776	0.8573	1.2416	1.0538	0.7283
	11	2.6307	2.3895	31.5003	2.0227	2.4297	2.3711
	12	1.1279	6.8138	0.8344	1.2380	0.8344	0.7641
	13	1.2765	8.4793	1.0012	1.5160	1.2185	0.9162
	14	0.6292	7.0299	0.3436	1.0516	0.3320	0.1725
RMSE	1	7.5671	6.3320	17.3343	5.1610	6.3773	6.2036
	2	7.5790	6.0280	17.2056	4.9846	6.5600	5.9703
	3	18.0985	17.7391	2.6568	2.6054	3.0793	1.7870
	4	5.6834	4.6049	19.9921	3.6348	3.6529	4.8046
	5	8.2431	5.9609	26.8721	4.7061	4.8637	6.3182
	6	10.2740	7.5212	18.7156	6.0717	5.8204	7.5424
	7	3.8533	27.4403	3.1879	3.2210	4.4489	3.5217
	8	4.6760	3.2764	13.3343	2.6765	4.6429	3.4948
	9	4.0999	15.3034	3.7760	3.8355	3.9101	3.8450
	10	4.0950	15.8287	3.1781	4.8067	3.7544	3.5066
	11	7.3518	6.8238	64.0178	5.5463	6.5331	6.7854
	12	4.7042	17.1864	4.2736	5.2527	4.2736	4.4394
	13	4.5020	4.5020	18.6226	3.5809	5.0441	4.3093
	14	2.5185	17.5149	1.3263	4.4845	1.4296	1.1470

* For station gauge number 14, no CHRIPS (CHI), no available data.

, respectively. Higher than 0.5 [71], R² scores are considered acceptable. Additionally, the obtained values of R² (Table 4) at most of the gauge stations for CHI, NCP, NCC, and NCD are closer to zero, which indicates unsatisfactory values for predictive models. Moreover, R² values at stations 1, 2, 5, 6, and 11 for ERA and MAE range from 0.2 to 0.4; corrections of ERA and MAE improve R² values.

• The obtained values of MAE (Table 4) for CHI, NCPP, NCC, and NCD at most stations are higher than one, which indicates a poor agreement with the observed data, while MAE values for ERA and MER at stations 3, 4, 7 and 8 are less than one, which indicates an acceptable value. Corrections for MER and ERA data improve the values of MAE.
• RMSE values (Table 4) are higher than 1 for SPD products. This demonstrates that the modifications can significantly minimize the overestimation of the SPD products, and those precipitation products are unable to actually reflect the actual precipitation incidence.
• NCP, NCC, and NCD overestimate the precipitation, especially for NCD, which shows inferior performance for prediction purposes, and the data still need to be calibrated, as mentioned in several previous studies [72,73,74,75]. The results show that the applicability of the CHI in the DS region is not as good in arid regions. For practical flood modeling and forecasting, such hydrological models may be calibrated on a broader scale thanks to ERA rainfall, suggesting its potential as a substitute for observations in data-limited regions of the DS region [67]. Jiang et al. [68] also provided a reference for using ERA in hydrological applications. In the DS region, MER fared better than ERA precipitation products, but it still has significant ambiguities [76] and deserves consideration from data developers and users [77].

This demonstrates that the modifications can significantly minimize the overestimation of the SPD products, and those precipitation products are unable to adequately reflect the actual precipitation incidence.

3.2. Error Correction

The findings of the examinations of several precipitation products show that MER performs best when compared to other datasets. In contrast, ERA quality is good and highly correlated with observed gauge data. Correcting the ERA and MER datasets, the Measure-Correlate-Predict (MCP) and Linear Adaptation (LA), LA1, and LA2 methods were used. The best-fit line’s slope (m, m1, m2) and intercept (c, c1, c2) were calculated, which serve as illustrations for proportional systematic error and constant systematic error for each gauge station, as shown in Table S5 and on scatter plots (Figure S15), to evaluate the ERA and MER datasets’ correction quality quantitatively. For instance, Figure 5 illustrates the contrast between the observed rainfall at Basin 5 during the flood year event and the corrected ERA and MER datasets. Before and following adjustment, the R² for daily precipitation for ERA and MER to the observed data was calculated and tabulated in Table S6 of the Supplementary Material.

The calculated R² for the corrected ERA at gauge stations 2, 4, and 12 were 0.81, 0.79, and 0.94, respectively, while corrected MER were 0.50, 0.77, and 0.56, respectively. The findings demonstrate that the correction quality which significantly increased at the gauge stations listed, is of the best quality, and outperforms the corrected MER. In contrast, the best-fit line’s slope (m, m1, m2) and intercept (c, c1, c2), serve as illustrations for proportional systematic error and constant systematic error for each gauge station, as shown in Table S5 and on scatter plots (Figure S15).

3.3. Hydrological Simulation Evaluation

3.3.1. HEC-HMS Model

All basin characteristics required for hydrological analysis have been successfully generated by integrating ArcGIS, QGIS, and SAGA tools [77]. Basin parameters can be automatically extracted to generate an HEC-HMS model using the SAGA plug, sophisticated software that can be used to define natural watersheds.

Table 5. Hydrological parameters of basins for DS area.

ID	Basin-AREA-(km2)	Upper Stream Elev. (m)	Downstream Elev. (m)	Length of Stream (Km)	H (m)	Slope
1	141.71	−193.96	−360.5	9.71	166.54	1.71%
2	167.08	700.65	−374.5	31.29	1075.15	3.44%
3	131.64	531.26	−398	23.05	929.26	4.03%
4	159.99	449.07	−394.5	12.57	843.57	6.71%
5	239.95	745.45	−397	38.65	1142.45	2.96%
6	63.88	830.88	800.5	3.45	30.38	0.88%
7	596.64	591.05	−395.5	45.56	986.55	2.17%
8	96.34	783.62	−385.65	17.65	1169.27	6.62%
9	178.26	790.1	−398.36	24.78	1188.46	4.80%
10	226.75	1180.49	−397	50.61	1577.49	3.12%
11	257.58	694.56	−381	24.46	1075.56	4.40%
12	507.08	1055.31	−382.5	24.73	1437.81	5.81%
13	107.04	661.43	39.5	10.7	621.93	5.81%
14	330.58	1119.2	893.52	26	225.68	0.87%
15	707.27	1169.13	559.5	50.78	609.63	1.20%

shows the basin parameters that were determined, including basin area, stream length, minimum and maximum elevations for streams, and slopes. Figure 6 shows how different watersheds are represented across the watershed.

CN is the most widely used [28,29,40,43]. Because it has one parameter (the curve number), which varies with soil type, land use, surface condition, and antecedent moisture condition, it is predictable, easy to grasp, and stable.

Table 6. CN, GA, and IC methods parameters.

Basin	CN						IC
	CN	Retention S	Initial Abstraction I = 0.2*S	Tc (Min.)	Tlag (Min.)	Initial Rate (mm)	Constant Rate (mm/hr)
1	90.92	25.37	5.07	361.4	216.84	3.81	1.44
2	91.52	23.53	4.71	225.61	135.37	3.81	1.26
3	91.52	23.53	4.71	197.97	118.78	3.81	1.26
4	91.62	23.23	4.65	179.33	107.6	3.81	1.08
5	90.8	25.74	5.15	266.14	159.69	3.81	2.01
6	90.72	25.98	5.2	505.5	303.3	3.81	2.68
7	91.57	23.38	4.68	396.48	237.89	3.81	1.17
8	91.43	23.81	4.76	144.19	86.52	3.81	1.24
9	91.43	23.81	4.76	197.05	118.23	3.81	1.24
10	91.38	23.96	4.79	257.09	154.25	3.81	1.33
11	91.43	23.81	4.76	230.71	138.42	3.81	1.24
12	91.48	23.66	4.73	251.52	150.91	3.81	1.15
13	91.5	23.6	4.72	172.74	103.65	3.81	1.12
14	91.5	23.6	4.72	557.78	334.67	3.81	1.12
15	91.5	23.6	4.72	554.49	332.7	3.81	1.12
Basin	GA
	Suction (mm)	Hydraulic Conductivity (mm/hr)	Porosity (Fraction)	Initial Content	Saturated Content
1	207.29	9.61	0.34	0.07	0.27
2	218.81	3.66	0.33	0.07	0.26
3	218.81	3.66	0.33	0.07	0.26
4	216.76	3.75	0.33	0.07	0.26
5	219.28	6.91	0.33	0.07	0.26
6	235.21	2.94	0.32	0.06	0.26
7	217.79	3.71	0.33	0.07	0.26
8	215.89	4.88	0.33	0.07	0.27
9	215.89	4.88	0.33	0.07	0.27
10	216.92	4.84	0.33	0.07	0.26
11	215.89	4.88	0.33	0.07	0.27
12	214.87	4.93	0.33	0.07	0.27
13	214.46	4.94	0.33	0.07	0.27
14	214.46	4.94	0.33	0.07	0.27
15	214.46	4.94	0.33	0.07	0.27

shows values for curve numbers (CN), the time of concentration, and the lag time.

The GA parameters, including the soil’s hydraulic conductivity, suction, porosity, and initial moisture content, and the IC method parameters, including initial rate and constant rate, were obtained based on the soil type map (Figure 4), as shown in Table 6.

CN obtained values ranging from 90 to 91 due to 85% of the soil being type D, mostly clay and salty soils. Maximum time of concentration and lag time values obtained at station 14 of 557.78 min and 334.67, respectively, a maximum area of 330.58 km² and the lowest difference height of elevation value of 225.68 m. While the minimum time of concentration and lag time values obtained at Station 8 of 144.19 min and 86.52 min, respectively, have the lowest area of 96.34 km² and the highest difference height of elevation value of 1169.27 m. Initial rate ranged from 2.54 mm to 5.08 mm. The suction values range from 207.29 to 235.21 mm due to 85% of soil being type D, mostly clay and salty soils.

The selected year of 2018 was when the historical flash flood event occurred after heavy rainfall, and the first such rain occurred after the end of the summer season on 25 October 2018. The records were collected for peak discharge for most of the gauge stations within the study area. After running the initial simulation with HEC-HMS, we produced

Table 7. Simulated (actual and ERA data set), observed, and optimized peak discharge.

BS.	Simulated Peak Discharge (m3/s)						Calibrated Peak Discharge (m3/s)			Obs. Runoff
	SC-A	SC-E	IC-A	IC-E	GA-A	GA-E	SC-O	IC-O	GA-O
1	56.40	35.80	55.80	37.60	29.6	7.8	56.70	56.70	47.5	120.00
2	66.60	66.60	65.80	44.40	54	28.6	66.70	66.90	56.2	120.00
3	37.60	30.00	38.60	30.40	26.9	14.6	25.20	19.60	24.1	25.20
4	63.80	40.60	63.20	42.80	51.5	27.1	63.80	64.00	53.9	120.00
5	95.40	60.60	93.20	34.20	62.6	7.7	90.30	88.60	80.6	120.00
6	25.40	16.10	24.50	16.30	21.5	11.8	25.70	5.20	21.3	120.00
7	237.80	151.40	235.80	159.50	192.4	101.7	180.30	96.50	125.2	120.00
8	52.10	40.60	52.60	40.70	42.5	31.2	53.20	53.00	46.2	60.00
9	96.80	75.40	97.30	97.30	78.5	57.8	97.40	19.70	35.6	60.00
10	123.10	92.00	123.40	95.30	100.1	73.7	62.50	79.00	70.3	35.90
11	65.20	39.50	64.80	41.10	38.5	10.3	43.60	13.30	13.3	41.70
12	128.30	73.30	127.50	75.60	75.2	16.3	85.70	88.30	94.8	78.30
13	27.10	15.50	26.90	16.00	15.9	3.4	18.10	16.70	19.5	16.50
14	83.70	47.80	83.20	49.30	49	10.6	56.00	59.90	62.4	71.00
15	179.00	102.30	178.00	105.40	104.8	22.7	118.40	112.00	132.9	109.20

, which showed how using various precipitation loss techniques, we were able to simulate (using the actual and ERA data set) and observe peak discharge for the event year 2018 differently.

The obtained simulated peak discharge at basin 5 for SC-A, SC-E, IC-A, IC-E, GA-A, and GA-E are 95.40, 60.60, 93.20, 34.20, 62.2, and 7.7 m³/s, respectively; however, the observed peak discharge is about 120.00 m³/s on 25 October 2018. SCA has a closer result of 95.40 m³/s to observed data 120.00 m³/s (Figure 7) and closer to the calculated peak discharge in Islaih et al. [39] study at the same basin. The GA simulated model underestimates the peak discharge at basin five compared to SCN and IC, which are lower than the observed runoff; the same observations were obtained at basins 1, 2, 4, 6, 7, 8, and 9. While at basins 11, 12, 13, 14, and 15, the simulated peak discharge for actual precipitation is higher than the simulated ERA and observed.

ERA data set showed closer peak discharge results than observed runoff by utilizing the SC loss method at Basins 1, 2, 4, 5, 6, and 7. In contrast, the IC loss method obtained satisfactory results at Basins 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, and 15, in addition to acceptable results of the GA loss method at basins 1, 2, 4, 6 and 7.

The supplementary figures for the other basins demonstrate that the SCS curve number (SC) loss approach produced the best findings for peak discharge compared to observed runoff.

3.3.2. Model Calibration

Hydrologists concur that it is impossible to create a singular modeling structure, give it a singular parameter set, and then determine the worldwide optimal simulator of all processes in a river basin using a singular objective function. This is true despite criticism of the uniformity idea. More than three decades of research have established that it is challenging to assign model residuals a sufficient formal error structure and identify a particular statistical measure better suited for fitting model outputs to observations. It is impossible to create a statistically correct fitting function due to the inconsistent interaction of uncertainties and errors across all modeling aspects [78].

According to Figure 8, the calibration aims to identify the variables whose fluctuation significantly alters the model’s outputs. The measured runoff of each gauge station is employed to increase the difference between the simulated and observed discharge hydrograph for calibrating the generated simulation in the current study. CN (Curve Number), IA (Initial Abstraction), LT (Lag Time), GA Conductivity (C), GA Suction (S), IC Constant Rate (CR), and IC-Initial Loss (IL) factors are included in our suggested study. The corresponding calibration parameters for each basin are shown in Table S7 of the supporting documentation. The optimum peak discharge values for the DS region are shown in the corresponding calibration parameters for each basin are shown in Table S7 of the supporting documentation; Figure 8 of the same document.

Following the calibration, we obtained Table 7 and Figure 9, which illustrated the discrepancy between the simulated and actual hydrographs near the outlet of the basin. Peak discharges that were seen and those simulated at Basin 11 are 41.70 and 43.60 m³/s, respectively; in Basin 8, they are 60 and 53.20 m³/s, respectively. Additionally, in Basin 5 are 120 and 95.40 m³/s, respectively, while high deviation was obtained in Basins 1, 2, and 6. Figure 9 indicates that the simulated hydrograph is very close to the observed hydrographs at basins 1 and 5.

The obtained peak values after SC and IC models calibration are closer to each other than GA calibrated model, as illustrated in Figure 10; parameter calibration improved peak discharge values to be closer to observed data.

The R², RMSE, Nash–Sutcliffe efficiency coefficient (NSE), and bias approaches are used to assess the performance of the HEC-HMS model. R² indicates the percentage of variance the model can account, indicating how closely the predicted values match the actual values. The model performs better with a higher R² value.

As basin outlet high deviation was obtained in Basins 1, 2, and 6 than GA calibrated model, as illustrated in Figure 10; parameter calibration improved peak discharge valueswith aOne of the best overall indicators of model effectiveness is the RMSE, which quantifies the mean difference between observed and predicted values [79]. Lower RMSE valuesLower RMSE values indicate better accuracy. The NSE scales from minus infinity to one and measures the skill of the estimates with the gauge mean. Negative values show that the gauge mean is a better estimate, zero shows that the gauge mean is is as good as the estimate, and one shows that the gauge and satellite-based data are perfectly matched. The Bias reveals the degree of agreement between the gauge and mean estimates. There are no units in NSE or Bias. Lower RMSE values values indicate better accuracy.

The obtained R² values for simulated and optimized peaks illustrated in Table S8 of the Supplementary Material show higher values than 0.5 for SC-A, SC-O, IC-A, IC-O, GA-O (all basins), and SC-E. (1, 2, 4, 5, 6, 7), IC-E(1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14 and 15), GA-A(1, 2, 6, 7 and 12) and GA-E(1, 2, 4, 6 and 7) indicate satisfactory performance. While the results of SC-E(3, 8, 9, 10, 11, 12, 13, 14 and 15), IC-E(10 and 12), GA-A(3, 4, 5, 8, 9, 10, 11, 13, 14 and 15), and GA-E(3, 4, 5, 8, 9, 10, 11, 13, 14 and 15) are less than 0.5, which indicated unsatisfactory performance. For R² values obtained higher than 0.8, SC-A(1,2,4,5,6,7,14), SC-E(2), SC-O(1, 2, 4, 5, 6 and 7), IC-A(11, 15), IC-E(2, 5, 4, 6 and 7), IC-O(11, 13, 14 and 15), which are closer to 1, indicate the accuracy of the model. SC loss method revealed higher values of R² with an average of 0.75 compared to IC and GA loss methods with an average of 0.73 and 0.29, respectively. The ERA dataset obtained satisfactory performance by utilizing the IC loss method, with average R² values of 0.67. At the same time, GA had a poor performance, with average R² values of 0.29 and 0.2 when using actual perception (AP) and the ERA dataset €.

The obtained RMSE values for simulated and optimized peaks illustrated in Table S8 Supplementary Material. show lower values less than 0.50 for SC-A(4, 5, and 9), SC-E(2), SC-O(2,3,4,5 and 14), IC-A(4, 5, 12), IC-A(14), IC-O(2, 4, 5, 7, 13, 13 and 15) and GA-O(5, 7, 13, 14 and 15), which indicate a satisfactory performance compared to remaining models. RMSE values in calibrated models were improved to be more accurate.

The obtained NSE values for simulated and optimized peaks illustrated in Table S8 Supplementary Material show negative values SC-A(7, 10, 13 and 15), SC-E(3, 7, 8, 9, 10, 11, 12, 13, 14, and 15), IC-A(2, 7, 9, 10, 13 and 15), IC-E(2 and 9), IC-O(6 and 11), GA-A(2, 3, 5, 7, 8, 9, 10, 11, 13, 14 and 15), GA-E (all basins) and GA-O(9 and 11) indicate that a better approximation is mean. While the values obtained equal or close to zero for SC-A(11), SC-O(11), IC-A(3 and 11), IC-O(11), and GA-E(1 and 6) indicate that the mean is as good as the estimate. Higher values of NSE than 0.8 for SC-A(5 and 9), SC-O(5), IC-O(15), and GA-O (7 and 14) indicate a perfect match between simulated and observed data.SC calibrated model revealed higher values of NSE with an average of 0.61 compared to IC and GA loss methods with averages of 0.55 and 0.54, respectively.

The obtained BIAS values for simulated and optimized peaks illustrated in Table S8 Supplementary Material show lower values of less than −15% for IC-A(1, 2, 4, and 8), IC-E(1, 2, 3, 4, 5, 6, 8, 9, 10 and 14), IC-O(1, 3, 4, 9, 10 and 11), GA-A(1, 2, 4, 5, 6, 8, 12, 13 14 and 15), GA-E(1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14 and 15) and GA-O (1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13 and 15) indicate that the models are overestimated. While the values obtained higher than 15% for IC-A(3, 9, 10, 11, 12, 13, 14 and 8), IC-E(7), IC-O(13, 14 and 15) and GA-A(7, 10 and 11) indicate that the models are underestimated.

Moreover, the BIAS values range from −15% to 15 for SC-A, SC-E, SC-O(all basins), IC-A (5 and 8), IC-E(12, 13, 14 and 15), IC-O(2, 5, 7, 8 and 12), GA-A(3 and 9), GA-E(7) and GA-O(7, 13 and 14) indicate a good model. The SC loss method revealed good values of BIAS, with an average of 0.31 compared to IC and GA loss methods with an average of 8.83 and −43.62, respectively. Furthermore, the GA infiltration equation has some limitations when used to describe infiltration during steady and erratic rainfall episodes. This model merely approximates reality by assuming that soil water movement is a wetting front and that diffusion has no impact. Contrary to what most GA infiltration models predict, the soil profile is not always uniform. It is difficult to assess saturated hydraulic conductivity in the model; therefore, the model results are more likely to be sensitive when it is, and the model results are more likely to be sensitive when utilized. Every event occurring at a microscale must be considered, but this does not always lead to better prediction; instead, it adds to the number of unknowable parameters, increasing the unwarranted risk of model uncertainty [80].

This discrepancy may be partly because the mean actual rainfall (AR) and ERA dataset (E) values used for the simulation were estimated based on the poorly reported spatial distribution of rainfall within the DS region. The spatial distribution of rainfall over time significantly impacts how much rain falls and how much runoff occurs. The parameter optimization method may have run into problems because of insufficient rainfall data and inaccurate streamflow observations, leading to simulation responses that were different from the observed. Hydrographs observed and simulated demonstrated that the model did not perform as expected for several peak flow events. Peak discharge measurement and recording must be carefully supervised due to the discrepancy in peak flow estimations if better-quality data and more representative samples could be used in future models. Comparing the SC loss approach to the IC and GA loss, satisfactory R2, RMSE, NSE, and BIAS values were found. Consequently, hydraulic modeling may apply this loss method efficiently with satisfactory performance by utilizing the IC loss method, with average R2 values of 0.67. At the same time, revealing the saturated hydraulic conductivity in the model is considered due to the iR2, RMSE, NSE, and BIAS values.

4. Conclusions

Precipitation is the primary mechanism driving hydrological processes and the main output flow in the atmospheric process. Accurate precipitation measurements are essential for modeling the hydrologic cycle of a basin, comprehending water balance, and forecasting extreme weather and natural disasters (such as floods and landslides). Jordan is vulnerable to a variety of natural disaster dangers. Without a doubt, the impact of climate change is most likely leading to other significant risks in Jordan more frequent and severe, especially for the DS region, where flash floods occurred in 2018. The applicability of CHI, NCP, NCC and NCD, ERA, and MER in the DS region was first assessed in this study. To rectify the deviation in the precipitation products (ERA and MER), a correction model is subsequently constructed based on correlations between the precipitation products and observations. The hydrological runoff simulation for actual rainfall (AR) and ERA dataset (E) data was completed, calibrated, and evaluated under various scenarios of precipitation loss methodologies. The following are the primary conclusions:

The quality of satellite-based precipitation products at a daily time scale is inferior to reanalysis-based precipitation products. NCP, NCC, and NCD all overestimate the amount of precipitation, but NCD does p only when forecasting tooorly. CHI overestimates precipitation. The meteorological and topographical circumstances in sub-regions, which impact the accuracy and dependability of precipitation estimates and are a crucial cause of the differences between observed rainfall and NCC, CHI, NCD, and NCP data.

• The ERA performed best compared to other dataset products for precipitation, while the MER performed well. Additionally, the variation from the observation is higher for all the other precipitation products. The best at capturing actual precipitation is ERA.
• An ERA and MER-based correction approach for precipitation data was put forth. These techniques separately corrected the precipitation data for the chosen years, significantly increasing the accuracy of the data. R² was calculated to evaluate the accuracy of selected datasets’ corrections. The findings demonstrate that ed. The quality of ERA correction has significantly increased at the gauge stations listed, is of the best grade, and outperforms corrected MER.
• R², RMSE, Nash–Sutcliffe efficiency coefficient (NSE), and bias approaches were used to assess the performance of the nine HEC-HMS models.
• SC loss method revealed higher values of R² with an average of 0.75 compared to IC and GA loss methods with an average of 0.73 and 0.29, respectively. The ERA dataset obtained satisfactory performance by utilizing the IC loss method with average R² values of 0.67. At the same time, GA revealed a poor performance with average R² values of 0.29 and 0.2 using actual perception (AP) and ERA dataset (E).
• The obtained RMSE values are less than 0.50 for SC-A(4, 5 and 9), SC-E(2), SC-O(2, 3, 4, 5 and 14), IC-A(4, 5, 12), IC-A(14), IC-O(2, 4, 5, 7, 13, 13 and 15) and GA-O(5, 7, 13, 14 and 15), which indicate a satisfactory performance compared to remaining models. RMSE values in calibrated models were improved to be more accurate.
• Higher values of NSE than 0.8 for SC-A(5 and 9), SC-O(5), IC-O(15), and GA-O(7 and 14) imply that the simulated and observed data perfectly correspond to one other. SC-calibrated model revealed higher values of NSE, with an average of 0.61 compared to IC and GA loss methods with averages of 0.55 and 0.54, respectively.
• SC loss method revealed good values of BIAS with an average of 0.31 compared to IC and GA loss methods with an average of 8.83 and −43.62, respectively. The GA model has a significant benefit over the CN model in that itconsiders the temporal fluctuation of the excess intensity of rainfall [81]. In future research, a proposed integrated model of SC, IC, and GA models is to be used to analytically establish linkages between them so that the beneficial qualities of integrated models can be considered for application.

In conclusion, reanalysis precipitation products modeled by ERA have been extensively employed in hydrological models. However, observational bias, spatial scale, and retrieval method invariably impact the data quality of these products. To maximize the findings of the hydrological simulations and make the water cycle process in the basin and more precise, additional in-depth research on the regional variations in the various precipitation products and the applicability of hydrological simulations is required. Compared to IC and GA loss, the SC loss approach produced acceptable R², RMSE, NSE, and BIAS values. Consequently, these loss approaches with combined SC, IC, and GA models might be employed successfully in building hydraulic systems that demand high reliability in peak flow prediction. Precipitation is the primary mechanism driving hydrological processes and the main output flow in the atmospheric process only when forecasting meteorological and topographical circumstances in sub-regions. The quality of ERA correction has significantly increased at the gauge stations list satisfactory performance by utilizing the IC loss method with average R2 values of 0.67.