Modeling the Rainfall–Runoff Relationship with TOPMODEL in the Wadi El Kebir Watershed
The rainfall–runoff relationship was studied in the Wadi El Kebir watershed, located in Northeastern Algeria, using TOPMODEL (topography based hydrological model). This is a geomorphological and semi-distributed model which is used to predict the hydrological behaviour of watersheds and to calculate the water storage deficit of an aquifer in any location. It uses topographic information of the watershed to predict the extent of contributing areas in the production of runoff.
TOPMODEL was applied with event-based rainfall–runoff modeling where 13 hourly rainfall series were used to predict the discharge at the basin outlet. A digital elevation model (DEM) was also used to define the contours of the basin and to map out the drainage directions and the topographic index.
TOPMODEL was calibrated and validated using the measured discharges and various objective functions such as Nash (Nash-Sutcliffe) and coefficient of determination (R2).
The TOPMODEL results showed a high-performance level. Indeed, after the calibration and validation procedure, the performance of the model oscillates between satisfactory and very good. For the calibration, Nash varied between 0.59 and 0.91, and R2 between 0.66 and 0.91. However, the values of these criteria coefficients were slightly reduced during the validation phase, Nash (0.53 to 0.84) and R2 (0.59 to 0.87). Also, the proposed model shows the weak contribution of groundwater flows in the hydrological response of the study area.
The increased demand for water resources in the world and the improvement in decision-making in terms of flood protection have recently led to the development of hydrological models, in particular those based on rain and flow processes (Perrin 2002; Buytaert et al. 2011). This modeling type has become especially important in developing countries such as Algeria, which lacks sufficient hydrometric stations to control stream flows (Belloum 1993; Touazi and Laborde 2004; Chabour 2012). To develop this modeling type, it is necessary to master the factors affecting hydrological processes (Nourani et al. 2011). Among the factors that govern the generation of streamflow is the watershed topography (Beven and Kirkby 1979; Garambois 2012).
The topography is the main element that controls the hydrological response of the watershed (Lane et al. 2009; Gil and Tobón 2016). It determines the gross drainage area (Wagener and Kollat 2007), the hydraulic characteristics of the soil, (Raghavendra and Mohanty 2012), and many other parameters. The influence of topography on flows has many utilities in hydrological modeling (Beven 2012). In fact, in a hydrological system, soil saturation is reached more easily in zones with low slopes. This allows runoff to be generated more quickly (Kessasra 2017).
Distributed models such as TOPMODEL can directly use the topography to simulate the flow in the catchment (Maréchal 2004). This model aims to reproduce the hydrological behaviour of watersheds in a semi-distributed manner; in particular, the dynamics of areas contributing to surface and subsoil flows (Beven and Kirkby 1979). Therefore, TOPMODEL is able to simulate soil moisture and flow rates which are not only governed by precipitation, but also by the watershed topography (Vincendon et al. 2010). TOPMODEL is the most widely semi-distributed and conceptual model used to simulate runoff in the hydrological system (Beven 1997; Mendicino and Sole 1997). It is one of the first models to use the topographic data explicitly in the model formulation (Beven and Kirkby 1979). It allows extracting topographic information related to the runoff generation (Devi et al. 2015).
Compared with other conceptual hydrological models, the popularity of TOPMODEL comes from its simplified, modifiable, and flexible structure (Beven et al. 2021). It reduces both the data requirements and the number of input parameters (Jeziorska and Niedzielski 2018). These advantages have favoured the application of TOPMODEL to a wide range of watersheds (Nourani et al. 2011). For example, TOPMODEL has been successfully tested in:
- Mediterranean basins: such as Gardond’Anduze (Sempere-Torres 1990), Mont-Lozère (Durand et al. 1992), Avic and Teula (Pinol et al. 1997);
- Temperate wetlands and sub-humid climate: we cite the Buro-borotu watershed in Ivory Coast (Quinn et al. 1991) and Heihejinpen reservoir (China) (Hao et al. 2018); and
- In semi-arid zones, TOPMODEL has been applied to the Karoon Basin in western Iran (Nourani and Mano 2007).
In addition, there are some comparative studies of hydrological models against TOPMODEL which have shown that TOPMODEL is suitable for rainfall–runoff modeling at event or even daily scale (Nourani et al. 2011). These studies have confirmed that despite the few input parameters, TOPMODEL is able to reproduce time series of flows with good accuracy (Saulnier and Datin 2004).
TOPMODEL is based on the concept of variable contributing zones (Ambroise 1999), where the flow occurs from surface flows generated mainly by precipitation (variable contributing area) and also from hypodermic flow from shallow saturated zones according to Darcy’s law (Bireche 2017). The contributing areas are temporarily saturated where precipitation can no longer infiltrate due to subsoil saturation (Lardet and Obled 1994; Taha et al. 1997). In TOPMODEL, the flow modeling at the catchment downstream is based on the theory of hydrological similarity (Xiong and Guo 2004). Topography is expressed quantitatively by the topographic index (or topographic humidity index) (Jeziorska and Niedzielski 2018). This index determines the geographic areas that have similar hydrological behaviour; it mainly depends on the topography (Beven and Kirkby 1979; Obled and Zin 2004; Kessasra 2017). TOPMODEL uses as inputs rainfall data, the DEM of the basin, and a few sets of parameters representing the hydraulic properties of the soil such as the hydraulic conductivity and water reserve in the soil. The advantage of TOPMODEL is that it requires few elements (Beven et al. 1984; Ambroise et al. 1996). Therefore, the model outputs are the discharges at the basin outlet as well as the topographic index map which present the hydrologic similarity classes (Beven 1997).
TOPMODEL software was chosen for this work for several reasons. This work represents the first application of TOPMODEL on an Algerian watershed. Thus, the assessment of water resources in our country suffers from the lack of data regardless of the climatic, hydrological, and hydrogeological data (Belloum 1993; Bouaïchi et al. 2006). This challenge makes it very difficult to apply overly parametric hydrological models such as SWAT (Soil Water Assessment Tool) or moderately parametric models like HEC-HMS (Hydrologic Modeling System). For this, we adopted TOPMODEL as a model that does not require many parameters to study the process of streamflow generation and water storage at groundwater level.
In this study, TOPMODEL was used to simulate the rainfall–runoff relationship and to examine its performance on the Wadi El Kebir basin (Northeastern Algeria), subject to a Mediterranean climate and temporary flow. The simulation was performed with event hydrologic modeling which allows simulating the response of the basin to occasional torrential rains without considering previous conditions, such as antecedent soil moisture and reservoir levels. (Le 2008). Event-based rainfall–runoff modeling is effective in operational flood forecasting (Muhammad et al. 2015). This study also aims to explore the topographic index map to show the spatial distribution of the hydrological response in the study area. The model parameters are calibrated using 7 observed time series of hourly discharges as well as evaluation criteria (Nash and R2). The performance of TOPMODEL on the Wadi El Kebir basin is determined in the validation phase using 6 other observed events.
2 Data and methods
2.1 Study area
The study area was the Wadi El Kebir basin, which is part of the Kebir Rhumel basin (Northeast of Algeria) (Figure 1(a)). It is located between latitudes 36°11’10.03” and 36°32’52.62” North and longitudes 5°25’10.78” and 5°54’50.66” East. Wadi El Kebir is over 53 km in length and drains into an area of about 932 km2.
Figure 1 Location map of the Wadi El-Kebir watershed: (a) General location; (b) Rainfall and gauging stations.
Wadi El Kebir ends at the Beni Haroun dam (Figure 1(a)) which is a very important hydraulic structure in Africa. This dam can store 1 km3 water and ensures the supply of potable water and irrigation for six counties (Chebbah and Kabour 2018). Vegetation in the watershed consists mainly of market gardening and cereal crops with fallow (Figure 2). However, forests represent only 19% of the basin’s surface, the majority of which is cedar and oak. The relief is of the order of 765 m at its highest point and 400 m at the outlet. The average slope of Wadi El Kebir is about 0.6%.
Figure 2 Vegetation map of Wadi El-Kebir catchment.
The Wadi El Kebir basin is subject to a Mediterranean climate, characterized by a hot and dry summer and a mild and humid winter. However, analysis of the annual rainfall and discharge measurements between 1995 and 2013 (Figure 3) shows an irregularity in these two parameters from year to year. The annual average rainfall is around 379 mm, producing about 110 mm of runoff which corresponds to an annual volume of about 102.67 hm3.
The flow in Wadi El Kebir is temporary; it is often dry but can flow from a few days to a few months. The runoff in this wadi is very irregular (Figure 3) and occurs during intense rainfall events. This flow regime characterizes the majority of wadis in Algeria and North Africa (Achite and Ouillon 2007; Maref and Seddini 2018). The interannual variation in discharge (Figure 3) shows that the flow of Wadi El Kebir is not always associated with precipitation. We observe many years of heavy rain (e.g. 1979, 2003, 2004) which generate less flow and vice versa (e.g. 2006 and 2007). The small runoff can be explained by overexploitation of water from the wadi for crop irrigation. However, the high flows come from exceptional floods which are rapid and are characterized by heavy rains (Kerdoud 2006).
Figure 3 Annual variability of total rainfall and runoff in Wadi El-Kebir catchment.
2.2 Model structure
TOPMODEL is a semi-distributed hydrological model used to simulate the rainfall–runoff relationship. This model was presented the first time by Beven and Kirkby (1979). The version used in this work is associated with the ATHYS platform (http://www.athys-soft.org) (HydroSciences Montpellier 2022). It is based on the hydrological similarity principle. It is used to predict the spatial distribution of the water content within the different points of the considered watershed. Hydrological similarity is determined by the topographic index, which is derived from the topography of the basin (Xiong and Guo 2004). It stipulates that all the points on the watershed having the same value of the topographic index present an identical hydrological behaviour in terms of soil moisture and surface saturation (Nourani et al. 2011; Beven 2012). Therefore, TOPMODEL presents the topographic effects on the hydrology of the watershed through a topographic index (Seibert 1999). TOPMODEL is based on three main assumptions:
- The topography contributes to runoff production;
- Rainwater is intercepted at the start of the event in the root zone; and
- The transfer of infiltrated water is done from the unsaturated zone to the saturated zone according to Darcy’s law.
As presented in Figure 4, TOPMODEL conceptualizes the soil column as a set of three reservoirs: root zone, unsaturated zone, and saturated zone (Nourani et al. 2011; Beven 2012; Jeziorska and Niedzielski 2018).
Figure 4 Conceptual diagram of TOPMODEL.
In TOPMODEL we consider that the outlet flow is equal to the sum of the basic flow, which depends on the state of the groundwater and the rapid flow, which depends on the extension of saturated surfaces (Saulnier 1996). The principle is to discretize the basin into elementary surfaces (meshes) using DEM. Each cell is characterized by the drained surface (ai) and the slope (tan βi).
The inflow (m2/s) for mesh i at time t is given by:
|Rit||=||elementary recharges average received by cell i, and|
|ai||=||drained area per unit of contour length.|
Thus, the outflow (m2/s) is expressed by the following formula:
|LR||=||outflow (m2/s), and|
|Tit||=||transmissivity of the soil column given by:|
|z||=||water defecit (m),|
|f||=||parameter of exponential decrease of the hydraulic conductivity (m-1), and|
|K0||=||hydraulic conductivity of the soil at surface saturation.|
K0 controls both the rate of water infiltration into the soil and the percolation of the unsaturated zone towards the water table (Obled and Zin 2004). The water deficit of cell i at time t is zit, and f is the exponential decrease of hydraulic conductivity. We can consider 1/f as a hydrodynamic efficient soil thickness through which the rapid water transfer takes place (Saulnier 1996). In terms of the topographic index τi, the water deficit on cell i at time t is given by:
|=||average of water deficits (m), and|
|=||topographic index over the entire watershed.|
The topographic index τi is given by:
During a timestep Δt, the evolution of the average water deficit is subjected to the fluctuation of the quantity of rainfalls on the unsaturated meshes (Rt), evapotranspiration (Evt), base flow at the outlet (Qb), and the basin area A (km2) as follows:
|Qb||=||base flow at the outlet (m3/s),|
|S||=||retention capacity of the soil tank (mm),|
|Smax||=||maximum water retention capacity of the soil tank; this parameter is in a way the volume of water needed to wet the soil before the event begins (Obled and Zin 2004),|
|ds||=||tank emptying coefficient (days-1), and|
The base flow at the basin outlet is given by the following equation:
All these equations are used to calculate the flow rate at the basin outlet and the state of the soil saturation as a function of four parameters: Smax (mm), K0 (m/h), f (/m), and ds (/d). TOPMODEL has the ability to make distributed predictions without using a large number of parameters (Abhishek 2008).
2.3 Topographic index
The topographic index represents a parameter of the spatial distribution of the excessive runoff generation in the watershed (Nourani et al. 2011). The topographic index helps to determine the effect of topography on the rainfall–runoff process and indicates the spatial distribution of soil moisture and surface saturation (Nourani et al. 2011). To calculate the topographic index, TOPMODEL applies the multiple flow direction algorithm (MD8) developed by Quinn et al. (1991) using DEM. This algorithm can represent the convergence or divergence of the flow path according to geomorphological variation in the basin. Calculation of the topographic index using the MD8 algorithm is therefore very associated with the DEM resolution (Franchini et al. 1996) and it can reproduce more realistic spatial flow models than the D8 algorithm developed by Jenson and Dominique (1988).
The MD8 algorithm is characterized by the distribution of the contributing area to all adjacent cell downslopes (Peng et al. 2008). Figure 5 shows the multiple flow direction algorithm. It suggests that the contour length (L1, L2 and L3) is perpendicular to the flow directions and the flow is shared to adjacent cells by weighting (0.5 weighting for cardinal directions and 0.35 for a diagonal weighting).
Figure 5 Illustration of the multiple flow direction algorithm MD8.
2.4 Model calibration and validation
The purpose of the calibration is to adjust the values of certain parameters to better simulate the hydrological behaviour of the watershed (Madsen 2000). Validation also makes it possible to assess the robustness of the model in the operational domain (Marchandise 2007). Observed data is used in calibration; new observed data, which were not used for calibration, are used in validation of the model (Coustau 2011).
In this work, four parameters are subject to calibration, namely: K0, f, Smax, and ds, by applying both an automatic optimization technique based on the simplex iterative method (Rao 1978) and the objective functions such as Nash and coefficient of determination (R2):
- Nash parameter
- Coefficient of determination (R2)
|Xi||=||calculated N discharge values,|
|Yi||=||observed N discharge values, and|
|=||averages of N calculated and observed discharge values, respectively.|
The Nash and R2 coefficient are the most widely used objective functions to determine the performance of the hydrological forecasting model (Marchandise 2007; Buytaert and Beven 2011; Ferraz et al. 2021). The optimal values of Nash and R2 are both 1. Moriasi et al. (2007) and Thiemig et al. (2013) qualified the criteria of performance level of the hydrological model according to the Nash and R2 values (Table 1).
Table 1 Different performance levels depending on the limits of Nash and R2.
|NSE||Nash ≤ 0.50||0.50 < Nash ≤ 0.65||0.65 < Nash ≤ 0.75||0.75 < Nash ≤ 1|
|R2||R2 ≤ 0.5||0.50 < R2 ≤ 0.70||0.70 < R2 ≤ 0.80||R2 > 0.80|
The calibration and validation procedures were carried out using the observed values of the discharges. Overall, 13 events (rainfall–runoff) were used (Table 2). Seven events were used for model calibration and 6 other events were used for model validation.
Table 2 Main characteristics of the investigated rainfall–runoff events in Wadi El Kebir basin.
|Max rainfall intensity
2.5 Simulation steps
The input data necessary for the operation of TOPMODEL are the hydrological data (rainfall and runoff), topographic data (DEM), and parameters. The rains have been recorded in the two rain gauge stations (100104: Beni Aziz and 100103: Boumalek) and the discharges were observed at the outlet of the basin through a gauging station (100109: Douar Tassadane) (Figure 1(b)). The time step of the rainfall and discharge data varies between 30 min and 1 h (Bouilloud et al. 2010; Nourani et al. 2011; Hao et al. 2018).
Generally, for a TOPMODEL application, the DEM used is 50 m resolution (Figure 6). This spatial resolution was used in several studies (Quinn et al. 1991; Nourani et al. 2011).
Figure 6 DEM of study catchment (using Athys v5.0).
The different stages of the TOPMODEL simulation begin by integrating the DEM of the basin. Using the ATHYS platform, we can delimit the contour of the watershed, discretize the basin into meshes, and derive the drainage directions map (Figure 7).
Figure 7 Drainage direction map of the study catchment (using Athys v5.0).
In the second step, we start with the calibration phase where we used the 7 sets of observed rainfall–runoff data and the initial values of the parameters to be calibrated. The simulation was carried out with event-based rainfall–runoff modeling. This type of modeling is particularly used for the study of storm events such as floods (Gerard 2010) and for understanding detailed hydrologic processes. Thus, a small temporary scale is useful when long term intensive monitoring data is not available, or data are incomplete (Chu and Steinman 2009). As such, we must fix the variation range of each parameter and the number of iterations for the calibration (maximum 500 iterations). However, in the validation phase, the parameter values were fixed, and we used 6 other observed rainfall–runoff datasets. TOPMODEL provides the hydrograph of the calculated discharges and the map of the topographic index, which is used to classify the hydrological similarities, and to deduce the extension of the contributing zones to the runoff production (Maréchal 2004).
3 Results and discussion
In terms of calibration, the performance of TOPMODEL can be evaluated using a numerical comparison (Table 3) or graphs (Figure 8). The results indicate that the model has adequately reproduced the studied events. Encouraging efficiency values were obtained during the calibration phase (Table 3), where the Nash varies between 0.59 and 0.91, and R2 was between 0.66 and 0.91. This result indicates that the performance of the model oscillates between satisfactory and very good.
Table 3 TOPMODEL results with the calibrated parameters and efficiency criterion values.
The graphical comparison between the observed and the calculated hydrograph illustrates only events with extreme values of Nash (min and max) (Figure 8). This comparison shows a good correlation between the two hydrographs. Abhishek (2008) demonstrated that TOPMODEL is relevant in understanding and predicting the hydrological behavior of watershed. Durand et al. (1992) showed in their study that TOPMODEL can successfully simulate discharges in drier catchments. Devi et al. (2015) revealed the capability of TOPMODEL for hydrological modeling in a watershed characterized by shallow soil and moderate topography, as is the case in the study basin.
Table 3 and Figure 8 show that all the maximum discharges calculated by TOPMODEL remain underestimated. In fact, an accurate prediction of runoff requires an accurate recording of precipitation (Beven 2001). The underestimation of peak flows is based on the neglect of the spatial variability of rainfall (Sangati et al. 2009; Maref and Seddini 2018). This is evident in the Wadi El Kebir basin where the rainfall data used in the simulation is provided by only 2 rain gauge stations. This number of stations is insufficient to properly represent the spatial distribution of rainfall in comparison with the area of the study basin (932 km2).
The runoff distribution in the watershed is not only based on topographic information, but also on the spatiotemporal variability of the rainfall over the watershed (Vincendon et al. 2010). The high sensitivity of TOPMODEL to the distribution of precipitation has already been demonstrated (Zehe et al. 2005; Le Lay and Saulnier 2007). The calibration of the parameters indicates that the values of Smax and K0 have the same order of magnitude (Table 3) except for the Smax parameter in the events of 2000-12-24 and 2010-01-10. The average values of these two parameters were 0.99 and 0.05 respectively.
Also, except for the events of 1996-03-09 and 1998-01-20, we can observe small variations in the parameters f and ds where the mean values were 1.84 and 1.10 respectively. The relatively low values of hydraulic conductivity (K0) characterize low soil permeability; the soil in the study basin consists mainly of clay or marl (Kerdoud 2006). This reveals that the runoff generation over the Wadi El Kebir watershed is a Hortonian type (Infiltration Excess Overland Flow). It occurs when the precipitation intensity exceeds the infiltration capacity of the soil (Horton 1933; Coustau 2011). Albergel et al. (2003) revealed that the Hortonian runoff process dominates in Mediterranean basins, especially in flood generation. In general, the hydrological response of the watersheds in these regions is rapid and is directly related to the rainfall intensity (Audard-Vincendon 2010).
Also, the hydraulic conductivity of the soil influences the maximum retention capacity which is determined by the parameter Smax. Thus, Table 3 shows quite low values of Smax, which reflects a slow movement of the water in the soil (Buytaert et al. 2003). Low hydraulic conductivity implies rapid runoff and insignificant subsurface flow, while large conductivity values reflect high infiltration, resulting in a low water volume at the outlet (Sigdel et al. 2011). Marchandise (2007) found that retention capacity is controlled by the hydraulic conductivity of the soil. Therefore, this parameter has a decisive effect on the surface and subsurface flow and the shape of the flow hydrograph (Gil and Tobón 2016).
The topographic index map of the Wadi El Kebir basin is shown in Figure 9. It indicates that the maximum class is around 16.28 to 17.61 and the minimum class is between 4.26 and 5.59. However, the dominant class of the topographic index is between 5.59 and 6.93 (Figure 9). Equal index values of the topographic index characterize areas of similar soil moisture conditions. This indicates that their saturation degree is similar (Burt and Butcher 1985) and in this case they have the same hydrological response characteristics (Fisher and Beven 1996; Xue et al. 2018). The topographic index map (Figure 9) also shows that the high values are associated with flow paths (streams) while the low classes relate to high altitudes (slope). Obviously, the index values gradually increase as the slope decreases.
Figure 9 Topographic index map of Wadi El Kebir catchment.
The high values of the topographic index are associated with low slopes and topographically converging locations, especially downstream of the drainage network (Beven 1997, Seibert 1999, Gil and Tobón 2016). These areas are characterized by a low evacuation capacity and a high saturation capability (Bouilloud et al. 2010). Areas associated with high topographic index tend to be saturated first and then constitute zones that potentially contribute to subsurface and surface runoff (Beven 1997, Gumindoga 2010). Therefore, we can see that the trend of the topographic index of the study basin towards low values reflects a limited contribution of groundwater flow to the runoff generation in the Wadi El Kebir watershed.
The performance of the model in the validation phase is illustrated in Table 4 and Figure 10. It is acceptable, although there is a slight decrease in Nash values (0.53 to 0.84) and R2 values (0.59 to 0.87). However, the model performance is still between satisfactory and very good. In terms of discharge, the model maintained the underestimation of peak flows during the validation.
Table 4 Results of TOPMODEL with efficiency criterion values in the validation phase.
The performance of TOPMODEL to reproduce the hydrological response in a Mediterranean zone has been investigated in this work. TOPMODEL simulates the rainfall–runoff relationships using the variable contributing zones approach to derive the topographic index map with event-based rainfall–runoff modeling.
TOPMODEL has been successfully applied in Wadi El Kebir basin (Northeastern Algeria) where the values of the efficiency criteria (Nash and R2) have indicated that the performance level of this model oscillates between satisfactory and very good in both calibration and validation phases. However, the model systematically underestimates the peak flows because of the spatial heterogeneity of rainfall.
The model parameters remain relatively stable from event to event. In addition, the low values of hydraulic conductivity indicate low soil permeability. This characteristic illustrates that the generation of the runoff over the Wadi El Kebir catchment is directly linked to rainfall intensity. This flow generation is a Hortonian type.
The spatial representation of the topographic index in the study area revealed that high values are associated with stream channels, while low values characterize slopes. Most areas in the Wadi El Kebir basin have a topographic index between 5.59 and 6.93. In addition, areas with the same topographic index are characterized by a similar hydrological response and the degree of soil saturation. Furthermore, the predominance of lower classes in the topographic index indicates a low contribution from groundwater flow.
TOPMODEL can also be applied to identify the mechanism of groundwater flow processes and groundwater level fluctuations. This helps us to properly exploit and mobilize groundwater resources.
Finally, it is recommended to use TOPMODEL in future research and confirm its reliability and relevance for hydrological studies in other Algerian watersheds, as well as in North Africa.
The authors would like to thank anonymous reviewers for their useful beneficial comments which really contributed to improving this paper. We appreciate the editor for their support during the review process. We are also grateful to the National Agency of Hydraulic Resources (ANRH) for providing the hydrological data and the Research Institute for Development (IRD) which is the developer of ATHYS software.
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