The Use of the HEC-HMS Model to Improve Regionalized Hydrological Modeling and Its Application to the Cheliff Basin, Algeria

GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 THE USE OF THE HEC-HMS MODEL TO IMPROVE REGIONALIZED HYDROLOGICAL MODELING AND ITS APPLICATION TO THE CHELIFF BASIN, ALGERIA Noureddine MAKHLOUFI1,2, Yamina ELMEDDAHI1,2 Alper BABA3 , Orhan GÜNDÜZ4 1 Hassiba Ben Bouali University, Faculty of Civil Engineering and Architecture, Department of Hydraulics, 02000 Chlef, Algeria 2 Hassiba Ben Bouali University, Vegetal Chemistry – Water-Energy Laboratory (LCV2E), 02000 Chlef, Algeria 3 Izmir Institute of Technology, Faculty of Engineering, Department of International Water Resources, Izmir, Turkey 4 Izmir Institute of Technology, Faculty of Engineering, Department of Environmental Engineering, Izmir, Turkey E-mail: [email protected] ABSTRACT Hydrological modeling is an effective tool for predicting the hydrological response of watersheds in order to develop appropriate water resource management strategies. Various modeling techniques are available to simulate rainfall-runoff processes in ungauged basins, including regionalization of hydrologic model parameters. Regionalization by spatial proximity (SP) and physical similarity (PS) were chosen for this study to be used with Hydrologic Modeling System (HEC-HMS), which is semi-distributed hydrological model, to evaluate the performance of the model in simulating sub-basin flows as well as the applicability of averaging methods in the case of ungauged sub-basins. Eight sub-basins belonging to the large Cheliff watershed were selected using available data from the period 2007 to 2012. In order to perform a controlled regionalization, one of the eight sub-basins (Wadi Tikzal) was assumed to be ungauged, and five sub-basins were selected to be donors by the (SP) regionalization method and five others by the (PS) regionalization. The results were compared to the original gauged sub-basin series. The performance analysis was carried out through the Nash-Sutclife Efficiency (NSE), the coefficient of determination (R2) and the root mean squared error (RMSE). The results of the simulation are generally satisfactory for wadi Tikzal sub-basin. The model adequately simulated the flows in the other sub-basins, during both calibration and validation phases. The results obtained showed that the regionalization methods used in this study, with the arithmetic mean and the inverse distance weighting (IDW), yielded good results with NSE and R2 values exceeding 0.75 and RMSE values were close to 0.20. The arithmetic mean gave higher results compared to the IDW method, the mean of NSE between the two methods is 0.68 for the arithmetic mean and 0.65 for IDW, and R2 of 0.69 for the arithmetic mean and 0.65 for IDW. The obtained results demonstrate that the regionalization by spatial proximity and physical similarity, using the HECHMS hydrological model can be effectively used to predict streamflow in ungauged watersheds, leading to effective water resources management, which enriches the literature regarding the flows regionalization, averaging methods and HEC-HMS performance, in ungauged sub-basins and especially in the northern Algerian region. Keywords: Arithmetic mean; Cheliff basin; HEC-HMS; Inverse distance weighting; Physical similarity; Regionalization; Spatial proximity. 243 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 1 INTRODUCTION Researchers face a major challenge in dealing with streamflow simulation at ungauged basins due to nonexistence of calibration data. Streamflow regionalization, also known as streamflow prediction in ungauged catchments, is an indispensable tool in watershed management, infrastructure control and water availability for multiple uses [1]. Indeed, many regions of the world do not have flow data to calibrate simulation model’s parameters due to high operational costs of stations or large gaps in data records. In addition, changes in watershed characteristics as a result of urbanization make flow forecasting in ungauged basins a challenging task in hydrology [2]. Hence, the concept of regionalization is applied in hydrological modeling such that runoff time series in the ungauged catchment are predicted by the use of the hydrological model parameters calibrated in the gauged catchment(s), called donor(s) [3]. Among many modeling techniques available for simulating rainfall-runoff processes in ungauged basins, the method of predicting runoff in ungauged basins by transferring information from gauged basins (donors) to ungauged ones that is known as the regionalization of hydrological model parameters is one of the most powerful techniques to predict flows [4, 5]. In general, regionalization methods fall into three main categories; similarity-based methods, regression-based methods and hydrological signature methods. The similarity-based methods are categorized into spatial proximity methods and physical similarity methods. The spatial proximity methods assume that geographically close watersheds have similar hydrological behavior [6] where the level of proximity is typically measured though the Euclidean distance. The physical similarity methods, on the other hand, consider that watersheds with similar physical characteristics respond to a precipitation event in a hydrologically similar way [7, 8, 9]. The normalized distance between two points in an N-dimensional space defines similarity, such that each dimension represents a sub-basin descriptor, such as elevation, soil type and land use. The egression-based methods relate the model parameters to the physical and climatic characteristics of the watershed by regression functions and assume that the relationship is transferable from gauged to ungauged basins [10]. Finally, the hydrological signature methods consider the hydrological signatures of watersheds which are represented by static indicators such as average streamflow, flood frequency etc., and dynamic indicators such as baseflow index, flow change rate etc [11]. There have been numerous studies conducted previously on ungauged watershed predictions and particularly since the launch of the Predictions in Ungauged Basins (PUB) initiative by the International Association of Hydrological Sciences in 2003. These studies multiply and extend to several regions of the world. Many studies have applied and compared regionalization methods for various regions in combination with a wide range of hydrological models [12, 13, 14]. Several techniques were applied in different regions, and thus many conclusions were drawn claiming that studies in specific regions and the choice of certain hydrological models influence the performance of regionalization methods e.g. [12, 15, 16, 17, 18, 19, 20]. For both spatial proximity and physical similarity methods, it was proven by many authors that regionalization using multiple donors could lead to significantly improved results compared to using a single donor [7, 18]. To average the generated hydrographs, there are many implementations of multi-donor averaging, but the two most commonly known approaches are the arithmetic average and inverse distance weighting (IDW) methods. Various studies have applied the HEC-HMS model for different purposes in several Algerian watersheds with specific soil and climatic conditions. Derdour et al [21] used the HEC-HMS hydrological model to predict surface runoff in a semi-arid area in the Ksour Mountains of Ain Sefra, southwestern Algeria. Mokhtari et al [22] predicted the hydrological response of the Wadi Cheliff-Ghrib watershed to climate and land use change scenarios by applying the HEC-HMS model. Allali et al [23] conducted a comparative study of two approaches, using the SCS unit hydrograph and CLARK unit hydrograph transformation methods of the HEC-HMS model to simulate the peak flow and surface runoff in the Ouahrane basin. In addition, Haddad [24] applied the HEC-HMS model to the Oued El Hachem watershed for modeling extreme rainfall-runoff events. On the other hand, and despite the problem of availability of data in several Algerian basins due to a large number of the lack or poor quality of data, there are few research studies dealing with the regionalization methods. For example, Zamoum et al [25] used the GR2M model to provide continuous monthly streamflow information in ungauged catchments in northern Algeria by using two classification techniques: principal component analysis (PCA) and self-organizing maps (SOM). Ammari et al [26] used a simple entropy-based method for discharge simulations in gauged and ungauged river sites in the coastal Algerian watershed. Based on this premise, streamflow prediction in ungauged basins is especially challenging and no previous study was conducted in the Cheliff basin, with an area of about 44000 km2 drained by the cheliff river which is considered the most important river in Algeria and extends over 700 km. To this end and given the importance of 244 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 regionalization in the region of Algeria and to enrich the literature by a study of regionalization in this semi-arid zone, this present study aims to employ two methods of the regionalization, by spatial proximity and by physical similarity, using the arithmetic mean and the inverse distance weighting (IDW) approaches to obtain the flows in the ungauged sub-basin from multi-donor. The HEC-HMS hydrological model was used for the transfer of flows from five gauged sub-basins in Cheliff basin (Northern Algeria) to a pseudo ungauged sub-basin. The obtained results were compared with the real flow series of the pseudo ungauged sub-basin to test the effectiveness of the implemented approach. 2 STUDY AREA Located in northern Algeria, the Cheliff basin is circumscribed within the chains of the Atlas Tellien parallel to the Mediterranean coast. It consists of three parts (upper and middle cheliff with 10930 km2, lower cheliff and the mina of 13150 km2 and the upstream Boughzoul with 19990 km2). It is located between 0°12' and 3°87' East meridians and between 33°91' and 36°58' North latitudes. It covers three sub-regions, Cheliff upstream of Boughzoul, Upper and Middle Cheliff and Lower Cheliff and Mina. It is limited to the north by the Mediterranean Sea, to the south by the high plains, to the east by the Algiers basin and to the west by the Oran basin. The precipitation in the basin is highly variable with a decreasing trend in the north-south and east-west directions [27]. The eight sub-basins studied within this study are located in the Upper and Middle Cheliff of elongated shape and very dense hydrographic flow (Figure 1). Figure 1. Location of the study area and studied sub-basins !( !( !( !( !( !( !( !( !( !( !( !(!( !(!( !( !(!( !(!( !( !( !( !( #* #* #* #* #* #* #* #*011514 011801 011905 012301 012201 012004 011715 011601 w. zeddine 0119 w. tikzal 0120 011906 011605 011901 w. sly 0123 w. ebda 0118 012007 012001 w. ouahrane 0122 012318 012309 012304 w. harreza 0117 012218 012201 w. harbil 0115 w. deurdeur 0116 011715 011702 011512 011509 011804 011803 011606 011603 011601 2°50'0"E 2°50'0"E 2°40'0"E 2°40'0"E 2°30'0"E 2°30'0"E 2°20'0"E 2°20'0"E 2°10'0"E 2°10'0"E 2°0'0"E 2°0'0"E 1°50'0"E 1°50'0"E 1°40'0"E 1°40'0"E 1°30'0"E 1°30'0"E 1°20'0"E 1°20'0"E 1°10'0"E 1°10'0"E 1°0'0"E 1°0'0"E 36°20'0"N 36°20'0"N 36°10'0"N 36°10'0"N 36°0'0"N 36°0'0"N 35°50'0"N 35°50'0"N 35°40'0"N 35°40'0"N . 15°0'0"E 15°0'0"E 10°0'0"E 10°0'0"E 5°0'0"E 5°0'0"E 0°0'0" 0°0'0" 5°0'0"W 5°0'0"W 10°0'0"W 10°0'0"W 40°0'0"N 40°0'0"N 35°0'0"N 35°0'0"N 30°0'0"N 30°0'0"N 25°0'0"N 25°0'0"N 20°0'0"N 20°0'0"N ALGERIA Legend Gauged sub-basin Ungauged sub-basin !(Rainfall station # *Runoff station . . 15°0'0"E 15°0'0"E 10°0'0"E 10°0'0"E 5°0'0"E 5°0'0"E 0°0'0" 0°0'0" 5°0'0"W 5°0'0"W 10°0'0"W 10°0'0"W 40°0'0"N 40°0'0"N 35°0'0"N 35°0'0"N 30°0'0"N 30°0'0"N 25°0'0"N 25°0'0"N 20°0'0"N 20°0'0"N 3°20'0"E 3°20'0"E 2°30'0"E 2°30'0"E 1°40'0"E 1°40'0"E 0°50'0"E 0°50'0"E 0°0'0" 0°0'0" 36°40'0"N 36°40'0"N 35°50'0"N 35°50'0"N 35°0'0"N 35°0'0"N 34°10'0"N 34°10'0"N Legend DEM.tif ValueHigh : 1942 Low : 4 Legend World_Countries__Generalized_ W. sly 0123 sub-basin name and code 012201 station code 010 20 30 405Kilometers 245 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 3 DATA AND METHODOLOGY 3.1 Data The period from 2007 to 2012 was chosen so as to have a duration covering all the stations with the smallest gaps present in the series of the region, we therefore chose 26 stations while trying to maintain geographical distribution throughout the study area. Table 1. Characteristics of the stations used (Source ANRH, Algeria) Sub-basin Station Code Station Type Station name X (m) Y (m) Z (m) W. Harbil 011509 Rainfall Medea secteur 478010.84 4013328.66 935 011512 Rainfall Ain Sultan 439017.34 4009581.38 285 011514 Rainfall/Runoff Djenane B-Ouadah 449021.74 4008687.01 336 W. Deurdeur 011601 Rainfall/Runoff Marabout Blanc 433426.31 3999655.06 358 011603 Rainfall Bordj Elamir AEK 433951.74 3969592.79 1074 011606 Rainfall Sidi Mokerfi 437321.24 3991601.55 447 W. Harreza 011702 Rainfall Arib cheliff 413954.07 4016184.92 246 011715 Rainfall/Runoff El ababsa 417311.00 4002046.94 320 011718 Rainfall Harreza BGE 418805.93 4005515.18 312 W. Ebda 011801 Rainfall/Runoff Arib Ebda 413449.57 4019401.08 280 011803 Rainfall Sidi Medjahed 425903.56 4020829.64 850 011804 Rainfall Ain Defla 408451.47 4013695.89 271 W. Zeddine 011605 Rainfall Thniet el had 412557.08 3969995.72 1162 011901 Rainfall El touaibia 404261.20 3997469.23 376 011905 Runoff Bir ouled tahar 392159.37 4010104.75 331 011906 Rainfall Rouina mines 395150.25 4008085.03 343 W. Tikzal 012001 Rainfall El abadia 380853.85 4012119.23 158 012004 Rainfall/Runoff Tikzal 388770.83 4005865.68 215 012007 Rainfall Bir saf saf 375186.60 4008237.86 166 W. Ouahrane 012201 Rainfall/Runoff Ouled fares 341490.70 4011118.12 116 012218 Rainfall Domaine si tayeb 335957.07 4003437.22 84 012221 Rainfall Medjadja 353419.22 4012948.51 188 W. Sly 012301 Runoff Ouled Ben AEK 344798.05 3989147.23 260 012304 Rainfall Souk El had 368456.80 3957438.33 550 012309 Rainfall Oued Sly 338434.90 3997733.37 95 012318 Rainfall Sidi Yakoub BGE 347745.10 3982598.30 272 3.2 Methodology The eight sub-basins studied are located in the upper and middle cheliff part of north-west Algeria, whose areas vary from 592 to 1432 km2. These are Oued Ouhrane (code 0122), Oued Sly (code 0123), Oued Deurdeur (code 0116), Oued Ebda (code 0118), Oued Harbil (code 0115), Oued Harreza (code 0117), Oued Tikzal (code 0120), Oued Zeddine (code 0119). These sub-basins all discharge towards wadi Cheliff. This region is characterized by a semi-arid to arid climate. The study was designed as three steps. In the first step, the calibration of the model was made for all sub-basins in the study area. The flow series and model parameters were then estimated. The flow series and model parameters are estimated by optimization trials where the peak weighted RMSE objective function available in HEC-HMS was chosen. After that, a group-based watershed classification was conducted before regionalization, in that it defined homogeneous areas with common characteristics. Then, the regionalized flows were obtained from five donor sub-basins to the target, using two methods: spatial proximity and physical similarity. Later the 246 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 hydrograph averaging concept by regionalizing the parameters of the donor sub-basin and transferring them to the target sub-basin, or by obtaining a hydrograph directly by averaging the regionalized parameters from the donor sub-basins to the target sub-basin (parameter averaging) was performed. Afterwards, the Arithmetic Mean and the Inverse Distance Weighting IDW methods were applied to estimate streamflow in the ungauged basin. After that, a comparison was made between the gauged sub-basin and the regionalized one. The flowchart given in Figure 2 illustrates the three steps carried out. Figure 3 gives hydrological modeling process used in flow series estimation. Figure 2. Overall flowchart of the regionalization procedure: Wadi Tikzal is the receiver sub-basin. (P1 to P5) and (Q1 to Q5) are the model parameters and the flows series of the donor sub-basins. QT-1 to QT-5 are the flows series of the receiver sub-basin using the model parameters of the donor sub-basins 3.3 HEC-HMS model description The HEC-HMS model created by the United State Army Corps for Engineers (USACE) is used to model the flows for the selected sub-basins. It belongs to the category of physically based distributed models designed to simulate the rainfall-runoff processes. HEC-HMS can be used to simulate a single watershed or multiple hydrologically connected watersheds in humid, tropical, subtropical and arid zones. The HEC-HMS model requires multiple inputs as digital elevation model (DEM), soil type, land use and weather data [23, 28]. The area of the basin and many hydrological elements like junctions and sinks needs to be defined to the model. For the loss method, the deficit and constant method was chosen and the SCS unit hydrograph was selected for the transform method. For the baseflow method, the recession baseflow approach was used in this study. The deficit and constant loss method takes into account continuous changes in moisture content. It is used in combination with canopy and surface methods, the first will extract water from the ground by the potential evapotranspiration calculated in the meteorological model, and the second will retain water on the soil surface. The Soil Conservation Service (SCS) unit hydrograph method allows a curvilinear unit hydrograph to be defined, where the percentage of unit runoff that occurs before peak flow is defined. It estimates the Unit Hydrograph peak discharge Up (Eq. 1) and the time of peak Tp (Eq. 2). 𝑈𝑝=𝐶𝐴 𝑇𝑝 (1) 𝑇𝑝=∆𝑡 2+𝑡𝑙𝑎𝑔 (2) 247 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 where Up is the unit hydrograph peak, A is the watershed area, C=2.08 is the conversion constant, Tp is the time of the peak, Δt is the excess precipitation duration, tlag is the basin lag and is equal to 60% of the time of concentration Tc. After an event, the channel flow recedes exponentially and the recession baseflow method approximates this typical behavior observed in watersheds. This method is used for both event and continuous simulation. Figure 3. Hydrological modeling process For the spatial proximity, the Euclidean distance between the sub-basin’s centroids was calculated using the equation 3. 𝑑=√(𝑋𝐺−𝑋𝑈)2+(𝑌𝐺−𝑌𝑈)2 (3) where d is the distance between the centroids and (XG, YG) and (XU, YU), which correspond to the coordinates of the centroids of the gauged and ungauged watersheds [13]. The similar sub-basins are defined on the basis of the calculation of a similarity index θ, which can be calculated using the formula given in equation 4 [29]. 𝜃=∑|𝐶𝐷𝑖𝐺−𝐶𝐷𝑖𝑈| ∆𝐶𝐷𝑖 𝐾 𝑖=1 (4) where CDi are the values of the descriptor i for a gauged basin (G) and the ungauged basin (U), k is the number of physical descriptors taken into account, and ΔCDi is the range of values available for the physical descriptor (i), that is the maximum value minus the minimum value. The smallest similarity index indicates the most similarity to the donor basin [13]. The morphological descriptors used for this study were given in Table 2. 248 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 Table 2. The morphological descriptors used in this study Descriptor Symbol Unit Sub-basin surface A km2 Minimum altitude Zmin M Maximum altitude Zmax M Specific elevation DS M Compactness index KG - Overall slope index Ig m/km Length of the equivalent rectangle L Km Equivalent rectangle width L Km Average precipitation Pmean mm Maximum precipitation Pmax mm Minimum precipitation Pmin mm The objective Peak-Weighted RMSE function was used to improve the quality of the optimized parameters. These parameters are shown in Table 3. Table 3. Parameters calibrated for each sub-basin N° Parameters Unit 1 Deficit and Constant-Constant rate mm/hr 2 Deficit and Constant-Initial Deficit Mm 3 Deficit and Constant-Maximum Deficit Mm 4 SCS Unit Hydrograph-Lag time Min 5 Simple canopy-Initial Storage % 6 Simple canopy-Max Storage Mm 7 Simple surface-Initial Storage % 8 Simple surface-Max Storage Mm 9 Recession-Initial discharge M3/s 10 Recession-Ratio to peak - 11 Recession-Recession Constant - 3.4 Performance criteria analysis To evaluate the performance of the hydrological model, three criteria were used: the Nash-Sutcliffe Efficiency (NSE), the coefficient of determination (R2) and the root mean square error (RMSE). The NSE (Eq. 5) was used in many studies to evaluate the performance of hydrological models. A value of NSE=1 indicates a perfect fit between simulated and observed data [30]. 𝑁𝑆𝐸=1−[∑(𝑄𝑜𝑏𝑠,𝑖−𝑄𝑠𝑖𝑚,𝑖)2 𝑛 𝑖=1 ∑(𝑄𝑜𝑏𝑠,𝑖−𝑄𝑜𝑏𝑠        )2 𝑛 𝑖=1 ] (5) where Qobs,i is the observed discharge, Qsim,i is the simulated discharge, Qobs is the mean observed discharge. The coefficient of determination R2 (Eq. 6) is used to determine the fit of the simulated data to the observed data. 𝑅2=[ [∑(𝑄𝑜𝑏𝑠,𝑖−𝑄𝑜𝑏𝑠        ) 𝑛 𝑖=1 𝑥(𝑄𝑠𝑖𝑚,𝑖−𝑄𝑠𝑖𝑚        )]2 √∑(𝑄𝑜𝑏𝑠,𝑖−𝑄𝑜𝑏𝑠        ) 𝑛 𝑖=1 2𝑥√∑(𝑄𝑠𝑖𝑚,𝑖−𝑄𝑠𝑖𝑚        ) 𝑛 𝑖=1 2]2 (6) 249 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 where Qobs,i and Qsim,i are the observed and simulated discharge, respectively. Qobs and Qsim are the mean observed and the mean simulated discharge, respectively. The RMSE (Eq. 7) is used to compute the mean magnitude of the error between the observed and the simulated values based on squared differences, in which the largest deviations contribute the most. RMSE=0 indicates a perfect fit between the simulated and the observed data. 𝑅𝑀𝑆𝐸=[∑(𝑄𝑜𝑏𝑠,−𝑄𝑠𝑖𝑚,𝑖)2 𝑛 𝑖=1 𝑁]1/2 (7) where Qobs,i is the observed discharge, Qsim,i is the simulated discharge, N is the number of data points that have been observed. 4 RESULTS AND DISCUSSIONS The results obtained will be discussed taking into account the values of the performance criteria for calibration and validation as well as the quality of the streamflow series results transferred from the donor sub-basins to the receiving sub-basin. A comparison with previous studies will be made. 4.1 Calibration and validation of the HEC-HMS model for all sub-basins The main objective of the rainfall-runoff modeling step by the HEC-HMS model for all the sub-basins is to verify the applicability of this model in this zone and therefore to ensure that the regionalization study can be performed. The optimized parameters, their values, and the simulation results (calibration and validation) of the HEC-HMS model for all basins are presented in Tables 4 and 5, respectively. Table 4. Parameters calibrated values for each sub-basin (P1 to P5 and PT) Parameters W. Harreza W. Ouahrane W. Zeddine W. Tikzal W. Deurdeur W. Harbil W. Ebda W. Sly 1 5.44 6.56 4.49 5.26 5.02 5.9 5.15 5.84 2 1.19 2.44 1.17 0.83 1.07 1.16 0.83 1.05 3 1.2 10.05 2.17 2.44 1.62 1.51 1.07 1.12 4 1100 1700 1800 1800 2000 2000 1832 1600 5 0.1 4.23 0.59 0.4 0.048 0.23 0.28 0.26 6 0.08 16.85 0.61 0.23 0.92 0.22 0.31 0.9 7 0.07 2.31 0.39 0.21 0.6 0.18 0.23 0.46 8 1.13 6.07 0.85 0.7 1.42 1.2 1.24 1.39 9 0.2 0.2 0.3 0.1 0.1 0.3 0.3 0.3 10 0.1 0.5 0.8 0.7 0.9 0.8 0.8 0.8 11 0.4 0.6 0.2 0.5 0.1 0.1 0.6 0.3 Table 5. Results of efficiency coefficients of all sub-basins modeling Efficiency coefficients W. Harreza W. Ouahrane W. Zeddine W. Tikzal W. Deurdeur W. Harbil W. Ebda W. Sly Calibration Phase NSE 0.71 0.79 0.64 0.61 0.61 0.63 0.62 0.65 R2 0.71 0.79 0.64 0.60 0.61 0.65 0.63 0.66 RMSE 0.50 0.50 0.60 0.60 0.60 0.60 0.60 0.60 Validation Phase NSE 0.77 0.73 0.67 0.77 0.61 0.63 0.63 0.64 R2 0.76 0.74 0.67 0.76 0.61 0.63 0.64 0.64 RMSE 0.50 0.50 0.60 0.50 0.60 0.60 0.60 0.60 250 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 The results show several performance rates for the eight sub-basins from satisfactory to good results with good values of the averages of the coefficients. Nash-Sutcliffe criterion was calculated as 0.66 in the calibration phase and 0.68 for the validation phase whereas R2 was found to be 0.66 in the calibration phase and 0.68 for the validation phase. The RMSE values were 0.58 in calibration phase and 0.56 in the validation phase. The maximum of the NSE coefficient is recorded for wadi Ouahrane with 0.79 in the calibration phase and for wadi Tikzal with 0.77 in the validation phase. Better values were recorded for the three coefficients in the validation phase than in the calibration phase, due to the quality of the data which is good in the validation period, then the calibration period has some estimated values of discharges, however there is good consistency between the series of precipitation and the series of discharges in the validation phase. This implies that the HEC-HMS model can be well calibrated for this region and for the set of sub-basins chosen, and that shows its capability to reproduce streamflows. Consequently, the second step of the study, which is the regionalization of the parameters for the ungauged sub-basin, can be carried out. These results in calibration stage are in agreement with several studies on the region, such as [23] and [24]. In addition to that, these results are in harmony with other studies worldwide, such as [31, 32]. The hydrographs of observed and simulated streamflow for all sub-basins are shown in Figures 4 and 5 for the calibration and validation phases, respectively. To assess the performance of the model more precisely, a critique can be used on each phase of the hydrograph, as the rising part, the descending part, the base flow and the peak flows. The figures show that the model reproduces the shape of the observed hydrographs in a satisfactory manner. The simulated peak flows are underestimated by the model for both calibration and validation stage. The average value of precipitation from the rainfall stations used could have given an underestimate of the simulated hydrographs. HEC-HMS does not consider the slope as a parameter, this could have led to a higher peak in the hydrograph. There is no important delay in the simulation of the rising or the descending parts of all the hydrographs, this can be explained by the good quantification of the interception losses by the model and the good optimization of the lag time. To begin the process of regionalizing the parameters of the HEC-HMS hydrological model from the donor subbasins to the receiving sub-basin, we proceeded to classify the donor sub-basins by the two similarity methods (SP and PS). Table 6 gives the classification of the sub-basins for the two similarity methods. The sub-basin with the smallest index (d), for the spatial proximity and the smallest index (θ), for the physical similarity, is judged to be the most similar to the receiver sub-basin. Table 6. Classification of the sub-basins for the similarity Class Spatial proximity Physical similarity Sub-bassins Distance from receiver subbasin centroid (d) (km) Sub-bassins Physical similarity index Θ 1 W. Zeddine 28.43 W. Harbil 2.33 2 W. Ebda 29.55 W. Ebda 3.72 3 W. Ouahrane 44.01 W. Deurdeur 3.78 4 W. Harreza 46.09 W. Zeddine 4.42 5 W. sly 46.80 W. Ouahrane 4.53 6 W. Deurdeur 58.84 W. Harreza 4.85 7 W. Harbil 65.38 W. sly 5.73 The spatially closest basins were selected by calculating the Euclidean distance between their centroids and the receiver sub-basin centroid and allowed us to classify the sub-basins in order. Geographically, the closest basin to the ungauged basin (Tikzal sub-basin) is the Zeddine sub-basin and the farthest sub-basin is the Harbil subbasin. The sub-basins taken into consideration for this method are the sub-basins of oued Zeddine, oued Ebda, oued Ouahrane, oued Harreza and oued Sly. To determine the sub-basins similar to the receiving sub-basins by physical similarity, the coefficient θ is calculated so that the most similar basin is the one with the lowest θ. The five most physically similar sub-basins taken for this part of the study are the sub-basins of oued Harbil, oued Ebda, oued Deurdeur, oued Zeddine and oued Ouahrane. 257 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 [12] SALINAS, J.L., G. LAAHA, M. ROGGER, J. PARAJKA, A. VIGLIONE, M. SIVAPALAN & G. BLÖSCHL. Comparative assessment of predictions in ungauged basins – Part 2: Flood and low flow studies. Hydrology and Earth System Sciences. 2013, vol. 17(7), pp. 2637–2652. ISSN 1607-7938. DOI: 10.5194/hess-17-2637-2013 [13] BRETON-DUFOUR, M. Étude de méthodes de régionalisation des paramètres des modèles hydrologiques et application à un bassin versant non-jaugé au Mexique [Study of methods for regionalising hydrological model parameters and application to an ungauged catchment in Mexico]. Montréal, 2017. Doctoral thesis. Université du Quebec, École de technologie supérieure. [14] YANG, X., J. MAGNUSSON, J. RIZZI & C.-Y. XU. Runoff prediction in ungauged catchments in Norway: comparison of regionalization approaches. Hydrology Research. 2018, vol. 49(2), pp. 487–505. ISSN 1998-9563. DOI: 10.2166/nh.2017.071 [15] MERZ, R & G. BLÖSCHL. Regionalisation of catchment model parameters. Journal of Hydrology. 2004, vol. 287(1–4), pp. 95–123. ISSN 0022-1694. DOI: 10.1016/j.jhydrol.2003.09.028 [16] PARAJKA, J., A. VIGLIONE, M. ROGGER, J.L. SALINAS, M. SIVAPALAN & G. BLÖSCHL. Comparative assessment of predictions in ungauged basins – Part 1: Runoff-hydrograph studies. Hydrology and Earth System Sciences. 2013, vol. 17(5), pp. 1783–1795. ISSN: 1607-7938. DOI: 10.5194/hess-171783-2013 [17] REICHL, J.P.C., A.W. WESTERN, N.R. MCINTYRE & F.H.S. CHIEW. Optimization of a similarity measure for estimating ungauged streamflow. Water Resources Research. 2009, vol. 45(10). ISSN 00431397. DOI: 10.1029/2008WR007248 [18] SAMUEL, J., P. COULIBALY & R.A. METCALFE. Estimation of continuous streamflow in Ontario ungauged basins: Comparison of regionalization methods. Journal of Hydrologic Engineering. 2011, vol. 16(5), pp. 447–459. ISSN 1084-0699. DOI: 10.1061/(ASCE)HE.1943-5584.0000338 [19] VIGLIONE, A., J. PARAJKA, M. ROGGER, J.L. SALINAS, G. LAAHA, M. SIVAPALAN & G. BLÖSCHL. Comparative assessment of predictions in ungauged basins – Part 3: Runoff signatures in Austria. Hydrology and Earth System Sciences. 2013, vol. 17(6), pp. 2263–2279. ISSN 1607-7938. DOI: 10.5194/hess-17-2263-2013 [20] POOL, S., D. VIVIROLI & J. SEIBERT. Value of a limited number of discharge observations for improving regionalization: A large‐sample study across the United States. Water Resources Research. 2019, vol. 55(1), pp. 363–377. ISSN 0043-1397. DOI: 10.1029/2018WR023855 [21] DERDOUR, A., A. BOUANANI & K. BABAHAMED. Modelling rainfall runoff relations using HECHMS in a semi-arid region: Case study in Ain Sefra watershed, Ksour Mountains (SW Algeria). Journal of Water and Land Development. 2018, no. 36 (I–III), pp. 45–55. ISSN 1429–7426. DOI: 10.2478/jwld-20180005 [22] MOKHTARI, E.H., B. REMINI & S.A. HAMOUDI. Modelling of the rain-flow by hydrological modelling software system HEC-HMS-watershed’s case of wadi Cheliff-Ghrib, Algeria. Journal of Water and Land Development. 2016, no. 30 (VII–IX), pp. 87–100. ISSN 1429–7426. DOI: 10.1515/jwld-2016-0025 [23] ALLALI, H., Y. ELMEDDAHI, D.-E. MOUDJEBER, H. MAHMOUDI & M.F.A. GOOSEN. Utilizing hydrograph transform methods and a hydrologic modeling system in rainfall-runoff simulation of a semiarid watershed in Algeria in north-west Africa. Desalination and Water Treatment. 2022, vol. 255, pp. 220–228. ISSN 1944-3994. DOI: 10.5004/dwt.2022.28344 [24] HADDAD, A. Extreme Rainfall-Runo Events Modeling Using HEC-HMS Model for Oued El Hachem Watershed, Northern Algeria. Archives of Hydro-Engineering and Environmental Mechanics. 2022, vol. 69(1), pp. 45–57. ISSN 2300-8687. DOI: 10.2478/heem-2022-0004 [25] ZAMOUM, S. & D. SOUAG-GAMANE. Monthly streamflow estimation in ungauged catchments of northern Algeria using regionalization of conceptual model parameters. Arabian Journal of Geosciences. 2019, vol. 12(11), pp. 1–14. ISSN 1866-7511. DOI: 10.1007/s12517-019-4487-9 [26] AMMARI, A., T. MORAMARCO & M. MEDDI. A simple entropy-based method for discharges measurements in gauged and ungauged river sites: the case study of coastal Algerian rivers. Bulletin de l’Institut Scientifique, Section Sciences de la Terre, Rabat. 2017, no. 39, pp. 35–44. ISSN 1114-6834. Available at: http://www.israbat.ac.ma/wp-content/uploads/2017/10/Ammari_et_al_final_Octobre2017.pdf [27] ELMEDDAHI, Y., H. MAHMOUDI, A. ISSAADI, M.F.A. GOOSEN & R. RAGAB. Evaluating the effects of climate change and variability on water resources: A case study of the Cheliff Basin in Algeria. American Journal of Engineering and Applied Sciences. 2016, vol. 9(4), pp. 835–845. ISSN 19417020. DOI: 10.3844/ajeassp.2016.835.845 [28] IBRAHIM-BATHIS, K. & S.A. AHMED. Rainfall-runoff modelling of Doddahalla watershed—an application of HEC-HMS and SCN-CN in ungauged agricultural watershed. Arabian Journal of Geosciences. 2016, vol. 9(3), art. no. 170. ISSN 1866-7511. DOI: 10.1007/s12517-015-2228-2 258 GeoScience Engineering Vol. 69 (2023), No. 2 geoscience.cz pp. 242–258, ISSN 1802-5420 DOI 10.35180/gse-2023-0101 [29] BURN, D.H. & D.B. BOORMAN. Estimation of hydrological parameters at ungauged catchments. Journal of Hydrology. 1993, vol. 143(3–4), pp. 429–454. ISSN 0022-1694. DOI: 10.1016/0022-1694(93)90203-L [30] NASH, J.E. & J.V. SUTCLIFFE. River flow forecasting through conceptual models part I – A discussion of principles. Journal of Hydrology. 1970, vol. 10(3), pp. 282–290. ISSN 0022-1694. DOI: 10.1016/00221694(70)90255-6 [31] HALWATURA, D. & M.M.M. NAJIM. Application of the HEC-HMS model for runoff simulation in a tropical catchment. Environmental Modelling & Software. 2013, vol. 46, pp. 155–162. ISSN 1364-8152. DOI: 10.1016/j.envsoft.2013.03.006 [32] AZMAT, M., M.U. QAMAR, S. AHMED, E. HUSSAIN & M. UMAIR. Application of HEC-HMS for the event and continuous simulation in high altitude scarcely-gauged catchment under changing climate. European water. 2017, no. 57, pp. 77–84. ISSN 1105-7580. Available at: https://www.ewra.net/ew/pdf/EW_2017_57_11.pdf