Water erosion mapping using several erosivity factors in the Macta Basin (North-West of Algeria)

The quantification of the water erosion using empirical models has been applied for several regions around the world. Indeed, the model proposed by Wischmeier and Smith also called RUSLE model remains the most used approach. The main purpose of this work is to produce a soil losses vulnerability map of the Macta Basin and to determine its water erosivity potential, taking into account four rainfall erosivity indices that have been widely applied in the Mediterranean regions namely: Arnoldus index, MFI Modified Fournier Index, Roose index and Rango-Arnoldus index. The calculation of soil losses with the RUSLE model gives respectively the values: 7.94, 13.98, 12.5 and 20.6 t ha -1 year -1 . By comparing with other basins of the same characteristics, we note a good correlation.


Introduction
The water erosion process at the catchment scale is characterized by three phases, namely: the tearing phase, the transport phase and the deposit or sedimentation phase. Downstream of the watershed, the storage capacity of the dams is reduced under the siltation effect, this is the case of the Fergoug dam in the wilaya of Mascara (North West of Algeria). Upstream of the watershed, there will be land losses, which causes a drop in agricultural production. The and losses vary from country to other but many work show that erosion is accelerated in the Maghreb countries. In Algeria, and like most semi-arid zones, the consequences of water erosion are disastrous, offering a naked landscape and crisscrossed by an intense ravine, particularly in mountainous regions with a dense hydrographic network. The operational dams are therefore threatened, especially in the west of Algeria, given that 47% of all of its land is affected (Kouri, 1993;Gomer, 1992;Touaïbia, 2000). In Morocco, cumulative annual land losses are estimated at 100 million tons (Heusch, 1970). In Tunisia, water erosion totals 8.5 million hectares which represents 52% of the total country area (Cormary and Masson, 1964). The intensity of water erosion depends on the climatic conditions, hence the rains erosivity, the slope which acts directly on the kinetic energy of the runoff, the cover land which absorbs the energy kinetics of the raindrops and increases the soil resistance against erosion, and finally soil erodibility which is closely related to the texture and soil structure. To estimate and quantify water erosion, several scientific approaches are proposed in the literature. The simplest empirical models are applied only for sufficiently large spatiotemporal scales. More elaborate mechanistic models that estimate the spatial distribution of solid fluxes for each meteorological event. However, the availability and the quality of data required to estimate the risk of water erosion remains a real challenge especially in large ungauged catchments, but with the rapid development of GIS tools, empirical models have become more effective approaches and thus constitute a better decision-making tool. Empirical models are hydrological models based on mathematical laws applied and validated in the laboratory or on experimental fields. The simplest and most widely used model, which relates soil loss to rainfall or runoff is governed by the Universal Soil Loss Equation (USLE) and carried out by (Wischmeier and Smith 1965;1978). The modified version of the model, proposed by (Williams, 1975), estimates the solid transport of each storm by taking into account the volume of runoff instead of the rain erosivity (Djoukbala et al, 2018). In this work we are interested in the mapping of the vulnerability to water erosion expressed in soil losses in the Macta Basin. A parametric investigation of the erosivity is thus carried out using four empirical formulas dedicated to Mediterranean semiarid catchments with ephemeral streams called also Wadis, to estimate their effects. The Macta Basin is characterized by a long period of drought, over the period 1930-2002, from which annual rainfall recorded a drop of around 40% on average (Meddi et al, 2009), adding the predominance of silt and clayey-sandy textures. The consequences of water erosion are manifested by the siltation of the Fergoug dam located downstream of the Macta Basin. The mapping of areas with high water erosion requiring development has become essential to minimize the rate of siltation.

Study area
Located in the North-West of Algeria, the Macta Basin extends over an area close to 14400 km 2 . It is limited to the North by the Mediterranean Sea, to the South by the Oran highlands, to the East by the Cheliff Zahrez region and to the West by the Tafna catchment and the Oran coast (Fig. 1 El Ma at an altitude of 1100 m and travels 172 km in the south-east direction. It is formed by the confluence of three Wadis: Melrir, Hounet and Sahouet which join at the point named Trois Rivières (Fig. 1).
The Macta Basin is subject to the semiarid climate characterized by a cold winter and hot summer, it undergoes the Mediterranean influence in the North and the continental conditions in the South from where the precipitations are irregular in space and in time.
The northern borders where the marshes are located and the southern limits of the Macta Basin are characterized by low slopes which vary between 0 and 9%. Upstream of the marshes, most of the areas have steep slopes between 40 to 58%. To the east, the slopes range between 18 and 47%, while in the West the slopes are moderate and do not exceed 27% (Fig. 2). The relief of the Macta Basin is characterized by the existence of plains interspersed with massifs: -Low coastal plain: It is separated from the sea by a band of dune and has altitudes below 9 m. We notice the presence of water bodies, marshes and more or less humid steppes. Upstream, the plain extends to the southeast through the valleys of the Wadis of Sig and Habra. According to Strahler (1952), the hypsometric curve can give indications on the dynamic equilibrium state of the watershed. The shape of the hypsometric curve ( Fig. 2) shows that the Macta Basin is an erosive basin which presents non-equilibrium (young) stage. All the collated data were used to estimate the parameters defied below of the Revised Universal Soil Loss Equation.

Data collection
Data processing was carried out with the ArcGis V.10.4 geographic information system.

RUSLE model factors
The model proposed by Wischmeier and Smith (1965;1978) is the most commonly used for the quantification of soil losses. This model requires available data on the watershed such as topography, soils, rainfall, landcover, cropping systems and erosion control practices. The Universal Soil Loss Equation (USLE) is written as follows: where A is the annual soil loss rate (t ha -1 year -1 ); R is the rainfall erosivity factor expressed in Mega-Joule mm ha -1 hour -1 year -1 ; K is the soil erodibility factor (t ha hour -1 ha -1 MJ -1 mm -1 ); LS is a dimensionless factor that represents the slope (S in %) and the length of the slope (L in m); C is dimensionless factor of plant cover and cropping practices; P is a dimensionless factor related to land use and the conservation practices.

Rainfall erosivity indices
In the literature, several authors have proposed a variety of rainfall erosivity indices. In this study we are mainly interested in four indices such as: 1) Erosivity index of Arnoldus, 2) Modified Fournier Index, 3) Roose's erosivity index and Rango-Arnoldus index:

Arnoldus Index
The Arnoldus formula (Arnoldus, 1980) translates a linear regression with the Modified Fournier Index according to equation (2). This combination has been tested and applied in the regions of West Africa. (2)

Modified Fournier Index (MFI)
The (MFI) index proposed by Arnoldus (1980), consists of using the sum of the Fournier indices for the twelve months of the year, it is the sum of the ratio of the squares of the average monthly rainfall and the average annual rainfall. (3)

Roose erosivity index
Roose's work (Roose, 1981), for over than 20 years of measurements, led to the proposal of simple empirical relationships, linking the erosivity index to the average annual rainfall Pan for the same period such as: The value of (a) is around 0.1 to 0.12 in northwestern Algeria (Morsli et al, 2004).

Rango-Arnoldus index
An alternative formula, that involves monthly and annual precipitation to determine the R factor, are proposed by Arnoldus (Rango and Arnoldus, 1987). It has been applied by several authors for the quantification of erosion in the Maghreb regions is presented in the form: where

R4
is in [MJ mm ha -1 hour -1 year -1 ] Pi and Prepresents respectively the monthly and mean annual rainfall in [mm]

Soil erodibility factor (K)
This factor reflects the resistance of a soil to water erosion. The K factor depends on several properties of the soil in particular; the percentage of sand, silt and clay and also the content of organic matter and permeability. Based on Global Harmonized Soil data version 1.2, one can establish the map of soil properties in the study area. The value of the soil erodibility is calculated using the formula proposed by (Neitsch et al, 2011).
where decreases the value of K in case of high coarse sand content and increases it in case of fine sand soil; − decreases the value of K for soils with a high ratio of clay to silt; decreases the value of K for soils with high organic matter content; ℎ decreases the value of K for soils with a very high sand content.
Each parameter is given as: where is the percentage of sand content in where the particle diameter is between 0.05 and 2 mm; is the percentage of silt content with particle diameters between 0.002 and 0.05 mm; is the percentage of the clay content whose particle diameters are less than 0.002 mm; is the percentage of organic carbon content.

Land cover factor (C)
The land cover plays an important role in soil protection, land losses decrease with the increase in the landcover rate. Many studies have been proposed to estimate the C factor using the Normalized Vegetation Difference Index (NDVI) (Lin et al., 2002;Wang et al., 2002). Knowing that the vegetation absorbs a significant part of the solar radiation in the red band and it reflects it to the maximum in the near infrared band, this index is determined as follows: where: PIR -Numerical value of the same pixel in the near infrared band (between 0.55 and 0.68µm); R -Numerical value of the same pixel in the red band (between 0.73 and 1.1 µm).
The NDVI value varies between -1 and +1; negative values correspond to surfaces other than plant cover, such as snow, water or clouds for which the reflectance in the red band is greater than that of the near infrared. For bare soils, the reflectance being roughly of the same order of magnitude in the red and the near infrared where the NDVI is close to zero. On the other hand, the plant formations, have positive NDVI values, generally between 0.4 and 0.7. The highest values correspond to very dense plant cover. NDVI data are obtained from the Landsat-8 satellite.
To estimate the C factor, several authors have developed regressions with NDVI (Karaburun, 2010;Ouallali et al, 2016). Since our study area is located in the North-West of Algeria, it is more convenient to select the regression proposed by (Toumi et al, 2013) given as:

Topographic factor (LS)
The slope plays a crucial role in the process of uprooting, transport and sediments deposition. Runoff increases with the slope increasing. Several formulas allow the evaluation of the LS factor from the DEM, such as that of Kalman (1967), David (1987) and Mitasova et al. (1996). In our case, we use the formula of (Wischmeier and Smith, 1978) given by:

Soil conservation practices factor (P)
The P-factor takes into account anti-erosion practices and cultivation techniques used to reduce the runoff effect and erosion. Among these techniques, we find contour farming, the laying of grassy strips between two cultivation areas, natural or artificial mulching, and the laying of cover crops. Based on the work of (Roose, 1994), the P value is determined from the following Table 1. Results and discussion:

R-erosivity factor
The erosivity maps generated from the rainfall data of the 42 stations, and using the four empirical formulas give the same erosivity distribution. They thus show that the values of the R1, R2, R3 and R4 factors in the Macta Basin vary from 9.54 (Arnoldus) to 73 (Rango-Arnoldus) MJ mmha -1 hour -1 year -1 ( Table 2). The high values are recorded at the eastern and western of the basin borders, while the southern areas indicate lower values (Fig. 5). It can thus be seen that erosivity is directly related to the precipitation (Fig. 3a), both distribution are well correlated.
The erosivity indices Rare distributed in the Macta Basin into four classes, R1, R2, R3 and R4. With the exception of the Roose index, the other approaches show that the high erosivity class has a low percentage (Table 2), (R1 6.01%, R2 6.49%, R3 18.36%, R4 6.92%). The low erosivity classes also occupy small areas (R1 8.52%, R2 8.45%, R3 8.51%, R4 8.55%  6a indicates the classification of soils in the Macta Basin, one can see that grazing areas dominate the surface of the basin. The spatial distribution of the erodibility classified into four groups (Fig. 6b) indicates that the soil K-erodibility factor in the Macta Basin ranges from 0.0138 to 0.0227 t ha hour MJ -1 ha -1 mm -1 . Almost half of the basin surface (58.35%) has a low K index (0.013) Table 3.

C-landcover factor
Using the NDVI map (Fig. 7a), the spatial distribution of the C-landcover factor of the Macta Basin is generated using ArcGIS software. The values of C factor observed over the entire study area vary from 0.09 to 1.8. More than 60% of the area of the basin has very low vegetation cover, 8% of the area has a C index less than 0.5. Values below 0.5 refer to dense forests, dense scrubland or matorral and arboriculture. Values between 0.5 and 0.9 are assigned to areas covered with sparse forests. Values tending to 1 are related to bare soil and harvested cropland (Table 4).

LS-slope factor
Erosion has been shown to increase exponentially with the degree and length of slope inclination represented by the LS factor. The length L and the slope S are very decisive parameters in the erosion process. Thus, the transport accelerates downward due to the increase in the kinetic energy of the runoff. In the Macta Basin, the distribution of the LS factor has been classified into five groups (Table 5). The highest values of LS are noticed from upstream to downstream and show a southwest-northeast orientation; they are mainly concentrated in the eastern side of the Macta Basin (Fig. 8). The LS low values are observed in the plain, this corresponds to 1) low altitude areas, concentrated mainly in the western part of the basin, 2) plain areas such as the plains of Ghris, Sidi Bel Abbes and of Mohammadia and 3) to the floodplains of Wadi Mekerra and Wadi El Hammam.

P-Occupation factor
The P-factor takes into account control practices that reduce the erosion potential of runoff in terms of its concentration, velocity and hydraulic forces applied on the soil surface. Support practices include contour tillage, strip-cropping on the contour, and terrace systems. Table 6 summarizes the P values in hectares and in [%].
It can be seen that the maximum values coincide with those of the steep slopes following the southwestnortheast orientation (Fig. 9).

RUSLE Soil loss
The average annual soil losses in the Macta Basin have been calculated with the RUSLE model using the four empirical erosivity formulas discussed above. The erosivity factors are calculated from rainfall data from 42 stations over 45 years . The vector product of the five factors is produced using ArcGIS software and gives a spatial resolution matrix of 30 m x 30 m. These are the four maps showing average soil losses in [t ha -1 year -1 ] (Fig. 10). The soil loss classes are summarized in Table 7, from which the mean values are respectively; 7.94, 13.98, 12.5 and 20.6 t ha -1 year -1 . We notice that the model calculated based on R1 Arnoldus indices, underestimates the value of RUSLE, on the other hand the RUSLE obtained by R4 Rango-Arnoldus indices overestimates the soil losses. The results obtained with the R2 (MFIindices) and R3 (Roose index) show a good correlation with other Algerian basins with similar climatic and environmental characteristics and extracted from the literature, such as 1) the Wadi Mina 11.2 t ha -1 year -1 (Benchettouh et al., 2017); 2) Wadi Boumahdane basin of 11.18 t ha -1 year -1 (Bouguerra et al., 2017); 3) basin of the Wadi Sahouat between 12 and 16 t ha -1 year -1 (Toubal et al., 2018) and 4) Wadi Gazouana between 9.65 and 11.33 t ha -1 year -1 (Djoukbala et al., 2018).

Conclusion
This study focuses on the estimation of soil losses by water erosion in the Macta Basin located in northwest Algeria using the Revised Universal Soil Loss RUSLE model proposed by Wischmeier and Smith. The spatial distribution of the soil losses is thus parameterized using four empirical erosivity factors; (Arnoldus, MFI, Roose and Rango-Arnoldus) and indicates an average values of 7.94, 13.98, 12.5 and 20.6 t ha -1 year -1 respectively. With the exception of the value calculated using Rango-Arnoldus indices (20.6 t ha -1 year -1) and by comparing with other similar Algerian basins, the calculated results are in good agreement. These results also show that about 0.21% of the surface of the watershed has a higher erosion rate, greater than 5 (t ha -1 year -1 ), observed on the hills and lands characterized by steep slopes of the catchment. This explains the severity of the soil degradation especially upstream of the Macta Basin due to the lithology, aggressive climate but also unfavourable land use. Erosion maps, obtained from the four erosivity approaches, provide useful information for selecting suitable areas for planning conservation and preservation works. The modeling of soil loss remains an investigation subject given the complexity of natural phenomena and the non-linearity of the relationships between the intervening variables. However, the use of empirical models is still part of the decision-making tools. It thus has several advantages in terms of mitigating risk with perimeters protection and also to predict soil protection scenarios by planning intervention works to fight against the phenomenon of water erosion.