# Rainfall-flow Modeling Using a Global Conceptual Model: Case of the Beni Bahdel Watershed (Northwest of Algeria)

## Abstract

Rainfall-flow modeling remains necessary, even essential, to understand the dynamics of a watershed and to solve problems related to the disruption of hydrological regimes. It has been proven effective by providing solutions to many water-related problems, such as sizing and management of structures, and flood forecasting. Global hydrological models can simulate the transformation of rainfall data into flows on natural basins for many practical applications in the field of water resource management. Our study aims to evaluate the reliability of one of these models, that of Rural Engineering 'GR' at three time steps: annual (GR1A), monthly (GR2M), and daily (GR4J), which will be applied to the Beni Bahdel watershed with an area of 1040 km², one of the sub-basins of Northwestern Algeria. The input parameters are precipitation and potential evapotranspiration (PET), and the output parameters are flows. The results obtained, both in calibration and validations, are encouraging, where the evaluation criteria taken into consideration, namely the Nash criterion and the correlation coefficient, exceeded 70% and 0.80 respectively. The study could be a decision-making tool for the simulation of flows, and be very useful for future hydraulic developments in the study area.

## 1 Introduction

In a context where climate change is topical (Barnett 2001; PNUD-FEM 2003; Puget et al. 2010; Khezazna 2017; GIEC 2018), the problem of water resource management is increased, especially in countries impacted by water deficit, such as those in the Maghreb (Agoumi et al. 1999; Kettab 2001; Boudjadja et al. 2003; Bouanani 2004; Medejerab and Henia 2011; Hamlet 2014). Algeria, like other semi-arid countries, has been affected by severe droughts since the mid-1970s (Tardy and Probst 1992; Laborde 1993; Ait Mouhoub 1998; Khaldi 2005; Ed-Daoudi 2014). This water stress, which lasted until the early 2000s, intensified from east to west of the country (Matari et al.1999; Meddi and Meddi 2009). This climate variability has had a significant impact on the hydrological cycle and water resources; indeed, the research established in this direction has shown that the basins of the northwest were much more affected and that this disruption of hydro-climatic behavior led to a reduction in runoff of around 70% (Meddi and Hubert 2003; Ghenim et al. 2010). Thus, the question of assessing surface water resources has long been a major challenge for the country, following the climate hazard and the ever-increasing need for drinking water supply for the population (Kettab 2001; Benblidia and Thivet 2010; Otmane 2019). Over the past two decades, the Tafna basin, of which our study basin is a part, has been the subject of several studies, some seeking to analyze and characterize the rain-flow relationship through wet and dry periods (Meddi et al. 2007; Belarbi 2010; Ghenim et al. 2010; Belarbi et al. 2017), while others have studied the liquid-solid flow relationship, especially during flood periods where more than 90% of solid transport occurs (Terfous et al. 2003; Bouanani 2004; Megnounif 2007; Ghenim 2008; Kazi Tani et al. 2017; Bouguerra and Bouanani 2019; Kazi Tani et al. 2020; Diaf and Gnenim 2021).

All this research, and many other studies, are the basis for a better understanding of the dynamics of the water cycle, and the materials and compounds it conveys at the watershed scale. In addition, the use of hydrological models such as rain-flow models, has gradually become necessary, with the aim of better predicting and reproducing liquid flows from rainfall measurements (Nascimento 1995; Ambroise 1999; Bakreti 2014). This approach has proven to be essential over the years and climate change scenarios have emerged, which, combined with global conceptual or semi-distributed physical models, have made it possible to anticipate future changes by 2050, up to 2100, of average and extreme precipitation and their impact on the hydrological cycle (Zettam et al. 2017; Mami 2020). This being so, and with a view to providing decision-makers with a management tool allowing the estimation or forecasting of flows for a hydraulic development study, we performed rain-flow modeling to simulate flows as a function of precipitation availability. To do this, we opted for the class of global conceptual hydrological models with tanks for rural engineering "GR", designed respectively for annual (GR1A), monthly (GR2M), and daily (GR4J) time steps and which we applied to our study region, the Beni Bahdel watershed (1040 km^{2}), a sub-basin of the Tafna, located in the northwest of Algeria. Developed by Cemagref since the 1980s, models for rural engineering have used various versions in order to prove their performance (Edijatno and Michel 1989; Edijatno 1991; Kabouya and Michel 1991; Makhlouf and Michel 1994; Nascimento 1995; Edijatno et al. 1999; Perrin 2000; Perrin 2002; Perrin et al. 2003; Mouelhi 2003; Mouelhi et al. 2006b). They have been tested on watersheds ranging from less than 10 km² to more than 100,000 km², and with various climatic contexts (Andreassian et al. 2006; Perrin et al. 2007). Indeed, these models are parsimonious (few parameters to calibrate) and take into account the chronological succession of phenomena on the one hand, and the influence of parameters such as evapotranspiration, soil humidity, and external exchanges on the other hand (Perrin et al. 2001). The input variables are limited to rainfall, evapotranspiration, and flow series only. The objective of the modeling consists of an optimization of the parameters characterizing the model through the improvement of adjustment criteria in order to achieve a robust and reliable rainfall-runoff simulation. At the end of this study, the results obtained were satisfactory and go in the same direction as those already found for neighboring basins of the Tafna or the Macta (Bouanani et al. 2011; Djellouli et al. 2015; Gherissi et al. 2017; Zennaki et al. 2020). The results can be used as a decision support and as a prevention tool against natural disasters.

## 2 Materials and methods

### 2.1 Study area

With an area of 1040 km², the Beni Bahdel watershed is part of the large Tafna watershed located in northwestern Algeria (Figure 1). The basin has an elongated shape and is particularly faulted and well drained by the wadi Sebdou. More than 50% of the basin is located at an altitude exceeding 1200 m, the topography is quite strong and is characterized by a very strong sensitivity to water erosion on slopes exceeding 15°.

Figure 1 Location map of study area**.**

The wadi length is 50 km; it originated in the ridges which culminate at 1465 m and passed through many ramifications dug in the very carbonated Jurassic ground. These ramifications join the plain of Sebdou at 900 m in the Plio-Quaternary alluvium (Figure 2). The wadi then follows its course in a deep valley and digs into marl limestone, limestone, and Dolomites from the Jurassic ground to the outlet of the basin, where it meets wadi Khemis on its left bank before flowing into the Beni Bahdel dam with a capacity of 63 million m^{3}. The most dominant plant formations are scrubland, rangelands, and extensive crops. The region is characterized by a semi-arid climate and the basin receives an average of 430 mm annually, generating an average flow of 30 mm/year for the observation period from September 2000 to August 2019, with a run-off coefficient of 7%, thus reflecting the intervention of several factors in the irregularity and the weakness of the water supplies such as the climatic characteristics, the configuration of the catchment area, the discontinuous vegetal cover, and the presence of well karstified geologic formations.

Figure 2 Geology of Beni Bahdel watershed.

### 2.2 Hydro-climatic context

The hydrological regime is very irregular, and we can distinguish two climatic periods: a period corresponding to the dry months of the year (June, July, August) and another for the remaining nine months, in which the months of October to April are considered as the wettest of the year, and where flows are abundant with a maximum flow of 1.8 m^{3}/s recorded in February (Figure 3). The evolution of monthly rainfall accumulations and their corresponding runoff relating to the study period (Figure 4) shows a first, fairly significant increase in precipitation from the months of September through January. Indeed, the rains that occurred in autumn and winter were very intense and totaled 248 mm, which corresponds to 58% of the annual percentage of precipitation. From February, the increase in the rainfall regime continues until May, but with a break in the slope of the accumulation curve, indicating a drop in the contribution for the spring season. This second phase accumulates 168 mm of rain, corresponding to 39% of the total annual precipitation. Runoff, on the other hand, has progressed steadily since the first rains of autumn through December, when a cumulative of 9 mm corresponding to 30% of the annual runoff is recorded in this phase. During the second half of winter through to the first months of spring, there is a break in the hydrometric cumulation curve. These will increase further to reach 15 mm, a contribution of 51%.

Figure 3 Mean monthly basin-averaged rainfall and flow during the observation period (2000/01 - 2018/19).

Figure 4 Cumulative periodogram of the mean monthly rainfall and flow series during the observation period (2000/01-2018/19).

It should be noted that if we observe the variation of the average daily flows (Figure 5), the wadi Sebdou is characterized by a succession of very pronounced floods during the wet period of the hydrological year. They appear from October through November, with exceptional peaks of 4 m^{3}/s and 5.47 m^{3}/s respectively, to continue in winter (the wettest season) where they were much more frequent in the months of January and February with daily peaks exceeding 3 m^{3}/s. The floods seem to subside in March with exceptional daily flows of 2 m^{3}/s and more. We can conclude that the hydrological response of the study basin during the two decades of observation strongly depends on the intensity of the rains, stormy and intense in autumn, and very abundant in winter. Spring was also characterized by a relatively high flow due to intense rainfall during this season, and that the soil was saturated following the heavy rainfall of winter. It should be noted that the flows are influenced by the karst character of the basin, which favors the infiltration of water in autumn after a dry season concomitant with high evaporation. Indeed, autumn, with a cumulative rainfall of 130 mm, recorded an average flow of 0.80 m^{3}/s, while spring, which had a total of 120 mm of precipitation, recorded a flow of 1.20 m^{3}/s, which shows a value much higher than that of autumn. The filling of groundwater during the period of high water effectively ensures the support of surface runoff during the summer season, which has ensured up to 13% of the total annual runoff during this dry season of the year.

Figure 5 Mean daily basin-averaged flow during the observation period (2000/01 - 2018/19).

### 2.3 Data availability

The observed data used in the present work, namely the daily, monthly, and annual values of rainfall, flow, and temperature, are those provided by the National Agency for Water Resources. They were recorded at the hydrometric gauging station located at the Beni Bahdel dam (Table 1). The potential evapotranspiration, an input component of the models, is calculated using the Thornthwaite method (1948) for the annual and monthly model, and by the formula of Oudin (2004) for the daily model. The structure of the GR1A, GR2M, and GR4J models, their characteristics, and their operating principle are described in detail on the CEMAGREF website (Perrin et al. 2007).

Table 1 Summary of data from the Beni Bahdel hydrometric gauging station.

Station | Code | Latitude | Longitude | Altitude (m) | Observation period | Mean temperature (°C) | Mean annual rainfall (mm) |

Beni Bahdel | 160402 | 34°43’55” N | 1°31’46” W | 665 | 2000/01 − 2018/19 | 17 | 430 |

### 2.4 Model evaluation criteria

The current version of the annual time step model (GR1A) is that proposed by Mouelhi et al. (2006a), and the one designed for the monthly model (GR2M) is that proposed by Mouelhi et al. (2006b), while for the daily model (GR4J), the version of Perrin et al. (2003) is presented here. Calibration consists of determining the optimized parameters from the various commonly used quality criteria. Two evaluation criteria, including coefficient of correlation (*R*, Equation 1), and the Nash–Sutcliffe coefficient (*NS*, Equation 2), were used to evaluate the efficiency of the models developed, as follows:

(1) |

(2) |

Where:

n |
= | total number of observations, |

= | observations values, | |

= | prediction values, | |

= | average of observed flows, and | |

= | average of simulated flows. |

The coefficient of correlation (*R*) is defined as the degree of correlation between observed and predicted values.

The Nash-Sutcliffe coefficient measures the efficiency of the model by relating the goodness-of-fit of the model to the variance of the measured data; Nash-Sutcliffe efficiencies can range from −∞ to 1. An efficiency of 1 corresponds to a perfect match of modeled discharge to the observed data. An efficiency of 0 indicates that the model predictions are as accurate as the mean of the observed data, whereas an efficiency less than zero (−∞ < NS < 0) occurs when the observed mean is a better predictor than the model. Besides, due to frequent use of this coefficient, it is known that when values between 0.6 and 0.8 are generated, the model performs reasonably well. A value between 0.8 and 0.9 indicates that the model performs well, and a value between 0.9 and 1 indicates that the model performs extremely well (Nash and Sutcliffe 1970).

The validation of the model aims to check whether the calibrated model correctly simulates a series of reference data not used during the calibration. Thus, to ensure an appreciable quality of the model, we seek to improve the values of the criteria of adjustment, translating the performances of the simulations.

## 3 Description of the three models

### 3.1 The annual model GR1A

The structure of the annual GR1A model sums up to a simple equation, the flow *Q _{k }*of the year

*k*is proportional to the rainfall

*P*of the same year, with a flow coefficient dependent on

_{k}*P*, the rainfall

_{k}*P*

_{k-1}of the year

*k*-1 and the average annual potential evapotranspiration

*E*. The model is formulated by Equation 3.

(3) |

Where:

Q_{k} |
= | annual flow corresponding to year k, |

P and_{k} P_{k-1} |
= | annual rainfall of the year (k) and (k-1), respectively, |

E |
= | average annual potential evapotranspiration, and |

X |
= | GR1A model parameter. |

The model has only one optimizable parameter, the dimensionless parameter *X*. It reflects the influence of an opening of the basin on the non-atmospheric outside environment (for example exchange with deep aquifers or with adjacent basins): if *X* is greater than 1, the system loses water, otherwise it's a water supply. Over a large sample of watersheds, the median of *X* is 0.7 and a 90% confidence interval is given by [0.13; 3.5] (Perrin et al. 2007).

### 3.2 The monthly model GR2M

The Rural Engineering model with a monthly time step and two parameters (GR2M), consists of a reservoir controlling the production function and characterized by its maximum capacity, and a "gravity water" reservoir governing the transfer function with a capacity of 60 mm.

The former is intended to reproduce hydrological processes in soils and their interfaces, while the second reflects transfer of water to the river, notably groundwater exchanges. At each modeling time step, precipitation is channeled either towards the soil reservoir by infiltration, or directly towards the routing reservoir as surface flows. This model uses two optimizable parameters: *X1* and *X2*, where *X1* (mm) represents the maximum capacity of the production tank, and *X2* the underground exchanges coefficient (Figure 6). If *X2* is greater than 1, there is a water supply from the outside of the basin; otherwise, there is a loss.

*P _{1}: excess rain; P_{2}: percolation of the production reservoir*

*S*

_{k}and R_{k}: level of the production and routing reservoir at the start of the time step, respectivelyFigure 6 Pattern of the GR2M model (Perrin et al. 2007).

For this new version of the GR2M model, the introduction of the parameter allows the correction of possible biases in the climatic and discharge time series. Mouelhi et al. (2006b) also indicated that this parameter allows a better representation of lateral water exchanges between the underground part of any topographic basin and its external environment (through permeable geological layers). On a large sample of watersheds (Perrin et al. 2003), the values of the parameters obtained are given in Table 2.

Table 2 Parameter values of the GR2M model.

Parameter | Median | 90% Confidence Interval |

X1 (mm) |
380 | 140 − 2640 |

X2 |
0.92 | 0.21 − 1.31 |

### 3.3 The daily model GR4J

GR4J’s daily model structure combines a production reservoir and a routing reservoir, unit hydrographs, and a function of opening to the non-atmospheric outside environment allowing the simulation of the hydrological behavior of the basin (Figure 7). The GR4J model has some common functions with the GR2M model (for example, the production function is linked to the ground reservoir). Its routing module is, however, more sophisticated than at the monthly time step. The GR4J model has only four parameters to calibrate, *X1*: production tank capacity (mm); *X2*: underground exchange coefficient (mm); *X3*: one day capacity of the routing tank (mm); and *X4*: unit hydrograph base time.

*P _{n}, E_{n}: rainfall and net evapotranspiration*

*S*

_{k},R_{k}: contents of the production and routing reservoir at the beginning of month k*Es: amount of water withdrawn from the production reservoir*

*Q9, Q1: output flow from the two hydrographs HU1 and HU2*

*Qd, Qr: drainage flows from Q9 and Q1*

Figure 7 Diagram of the structure of the GR4J model

This model has the distinction of introducing two-unit hydrographs for routing storage, with the first unit hydrograph (UH1) giving a direct runoff from a part (10%) of effective runoff. The other part, (90%) which reaches the routing storage through unit routing through the second unit hydrograph (HU2) with base time *X4*. On a large sample of watersheds, Perrin et al. (2007) obtained the values given in Table 3.

Table 3 Value of GR4J model parameters obtained on a large watershed sample.

Parameter | Median | 90% Confidence Interval |

X1 (mm) |
350 | 100 − 1200 |

X2 (mm) |
0 | -5 − 3 |

X3 (mm) |
90 | 20 − 300 |

X4 (days) |
1.7 | 1.1 − 2.9 |

## 4 Results and discussion

The calibration of the models was obtained after several simulations of the rain-flow series. Indeed, these were obtained by changing a set of the optimizable parameters specific to each of the three models, until having optimal values of the coefficients of determination and the Nash criterion (Table 4).

Table 4 Results of the calibration model performance.

Model | Parameters | Model Evaluation Criteria | Calibration Period | ||

Nash | Balance | Coefficient of Correlation (R) |
|||

GR1A | X = 1.07 |
82% | 90% | 0.92 | 1984/85 − 2009/10 |

GR2M | X1 = 2368 X2 = 0.84 |
72.2% | 98.2% | 0.85 | 01/01/2000 − 31/12/2015 |

GR4J | X1 = 148.4 X2 = -0.2X3 = 54.6 X4 = 1.92 |
74.7% | 75.3% | 0.82 | 01/01/2015 − 31/12/2016 |

### 4.1 Model GR1A

For the GR1A annual model, and according to the evapotranspiration correction coefficient (*X*=1.07>1), the basin seems to lose water during this observation period. It also reflects the exchanges with the deep aquifers of the Jurassic karstic limestone massifs. Indeed, the karstic nature of the study basin suggests that the global “aquifer-wadi” system is characterized by groundwater recharge throughout the wadi. The value of the Nash criterion of 82%, the correlation coefficient of 0.92, and the balance of 90% confirm the concordance between the two curves representing the observed and simulated flows (Figure 8), with the exception of the year 2008 (very rainy) where we see an underestimation of the annual flows by the model. This is due to the high floods recorded during this year generating exceptional flows, which thus feed the deep aquifers due to the karstic nature of the basin. In fact, after a succession of three climatically dry years with very low flows, the stream is fed only by the emptying of groundwater or by exchanges with the other basins, which makes the observed flow higher than the simulated flow.

Figure 8 Calibration of the GR1A model, (a) Visualization of the calibration quality, and (b) Correlation between observed and predicted values.

### 4.2 Model GR2M

For the GR2M monthly model, the variability of the flow is greater than that of the annual, following the introduction of the parameter *X2* (coefficient of underground exchanges) thus allowing to better reflect the hydrological behavior of the basin by associating a production reservoir and a routing reservoir. The values found for the parameters specific to the model respect the bounds of the confidence interval, and the positive value of *X2* indicates that the model simulates a water supply from neighboring basins. In fact, the karstic nature of the basin promotes underground exchanges through the supply of aquifers. The evaluation criteria (Nash criterion of 72.2%, correlation coefficient *R* = 0.85, and the fairly balanced assessment of 98.2%) allow us to say that the model is well calibrated. The general pattern of the curve of the simulated flows approximates that of the flows observed in the basin (Figure 9a). It should be noted that during flood periods, the model globally overestimates the flows, as is the case in May 2002 or June 2008, but it sometimes happens that there is an underestimation of the observed flows, such as in March 2012 and June 2013. This distinction is mainly due to the interdependence of several factors such as soil moisture and infiltration capacity, geology and the influence of the underlying aquifers that act as reservoirs returning a late hydrological response, and the strong spatio-temporal heterogeneity of precipitation that allows supporting or not supporting the runoff. The correlation between the observed flows and those simulated (Figure 9b) is acceptable with an *R* coefficient of 0.85, except for a few scattered points which are above or below the regression line, and where the flows are therefore either overestimated or underestimated. These differences are the result of a few extreme events that generally occur during the dry period of the year, when the soil is dry, rainfall is scarce, and the water supply is done only by emptying aquifers or by exchanges with other adjacent basins.

Figure 9 Calibration of the GR2M model (a) Visualization of the calibration quality, and (b) Correlation between observed and predicted values.

Under these conditions, the flow is slow to reach its maximum because of the late response of the basin. Indeed, the slow response is due to the karstic formations and the fault network that characterize the study basin. The observed results (Figures 10a and b) relating to the strong fluctuations in the level of the production reservoir and the routing reservoir, show that a significant exchange of groundwater takes place in the adjacent formations and that flows are delayed at the outlet of the basin following the significant losses upstream by infiltration due to the karst character of the watershed.

Figure 10 Monthly variation (a) of the level *S* of the production reservoir, and (b) of the level *R* of the routing reservoir.

### 4.3 Model GR4J

For the daily GR4J model, the flow variability is much more important than the annual and monthly one, following the introduction of new parameters such as the parameter *X3* (one-day capacity of the routing reservoir), and the parameter* X4* (base time of the unit hydrograph). The four optimization parameters respect the confidence interval bounds. The value of the exchange parameter (*X2*) is negative, so the model simulates water loss. With a Nash criterion equal to 74.7%, a correlation coefficient *R* = 0.82 (Figure 11b), and a fairly balanced balance equal to 75.3%, we can assume that these results reflect the ability of the model to represent the flows observed under better conditions.

The shape of the observed/simulated flow curves (Figure 11a) reproduces the rainfall sequences, as well as the flood episodes, well. We sometimes witness an overestimation of the observed flows certainly due to the hydrological response of the basin which, following its karstic character, causes the flows to reach the outlet late, as is the case on 06/02/2015 where the observed flow is 0.24 mm/d, and the simulated flow is 0.88 mm/d with zero precipitation. In addition, an underestimation should be highlighted, for example, on 06/04/2016 when we recorded a rainfall of 21.5 mm and where the simulated flow was 0.84 mm/d, and the observed flow was 1.14 mm/d. This explains why the water in the river comes from another basin following violent summer storms.

Figure 11 Calibration of the GR4J daily model (a) Visualization of the calibration quality, and (b) Correlation between observed and predicted values.

The amplitude of the variations at the level of the production reservoir and that of the routing (Figures 12a and b) clearly attest to the effect of underground exchanges in the karstic aquifer on daily flows.

Figure 12 Daily variation (a) of the level *S* of the production reservoir, and (b) of the level* R* of the routing reservoir.

The validation relates to the application of the model on a time series of data which were not used during calibration. The validation test (Table 5) shows that modeling gives fairly significant results for the three time steps. Indeed, the analysis of the hydrographs relating to the simulated flows and those observed (Figures 13a, b and c) reflect a good similarity between the two variables. The graphs corresponding to the correlations (simulated *Q* –observed *Q*) confirm this observation with correlation coefficients exceeding 0.80.

Table 5 Results of the validation model performance.

Model | Parameters | Model Evaluation Criteria | Validation Period | ||

Nash | Balance | R | |||

GR1A | X = 1.11 |
71.3% | 107.3% | 0.93 | 2010/11 − 2019/20 |

GR2M | X1 = 837.1 X2 = 1 |
73.4% | 100.7% | 0.85 | 1/1/2016 − 31/8/2021 |

GR4J | X1 = 298.8 X2 = -4.4X3 = 85.6 X4 = 1.92 |
72.8% | 72.1% | 0.91 | 1/1/2017 − 31/12/2017 |

Figure 13 Quality of validation and correlation between observed and simulated values (a) GR1A, (b) GR2M, and (c) GR4J.

To give reliability to our study, we presented the work of other authors on GR hydrological modeling (Table 6). The use of these models for Mediterranean basins of the same climatic context, gave powerful results that confirm the relevance of the comparison with our study basin.

Table 6 Calibration results and validation of the 'GR' model on three basins of the Tafna.

Tafna Basin (NW Algeria) |
Time step | Parameters | Calibration | Validation (R) | ||

Nash (%) | Balance (%) | Coefficient of correlation (R) | ||||

wadi Boumessaoud (Medane 2012) | GR1A | X1=1.32 |
75.5 | 105.2 | 0.89 | 0.95 |

GR2M | X1=148.4 |
77.2 | 96.9 | 0.88 | 0.72 | |

X2=0.47 |
||||||

GR4J | X1=298.8 |
76.7 | 101 | 0.84 | 0.772 | |

X2=-4.02 |
||||||

X3=20.09 |
||||||

X4=2.89 |
||||||

wadi Boukiou (Berrezoug 2016) | GR1A | X1=0.92 |
87.5 | 97.5 | 0.93 | 0.84 |

GR2M | X1=148.4 |
84.5 | 120.9 | 0.94 | 0.92 | |

X2=0.64 |
||||||

GR4J | X1=336.8 |
71.9 | 79.5 | 0.83 | 0.85 | |

X2=-0.8 |
||||||

X3=20.3 |
||||||

X4=2.75 |
||||||

wadi Lakhdar (Gherissi et al. 2017) | GR2M | X1=287.4 |
87.9 | 83.5 | 0.91 | 0.47 |

X2=0.82 |
||||||

GR4J | X1=215.2 |
88.2 | 105.4 | 0.86 | 0.75 | |

X2=-5.8 |
||||||

X3=65 |
||||||

X4=2.41 |

## 5 Conclusion

Global conceptual models developed over more than two decades have proven their effectiveness in reproducing flows from rainfall data alone. This will further strengthen the efforts made in the management of water resources, which have become so scarce in semi-arid environments, and will also help to prevent natural disasters, mainly due to climate change. Rainfall-flow modeling using the Rural Engineering model applied to the Beni Bahdel watershed for annual (GR1A), monthly (GR2M), and daily (GR4J) time steps gave quite significant and representative results. Indeed, during the calibration and validation periods, the evaluation criteria used to assess the quality of the hydrological simulation of the basin gave very acceptable values, i.e., more than 70% for the Nash criterion, and more than 0.8 for the correlation coefficient. We were thus able to determine the optimization parameters corresponding to each of the three models; in particular, those associated with the production and routing reservoirs, as well as the underground exchange coefficient characteristic of the water supply and losses in the basin. These have been interpreted as being the consequence of the important circulations of groundwater towards the supply of deep aquifers all along the wadi, thus reflecting the karstic character of the basin. At the end of this study, we can say that the conceptual model "GR”, given its parsimonious nature and its performance in flow simulation, continues to be used in Mediterranean basins with a semi-arid climate.

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