*2.3.1.3 Soils*

Soil data are a control variable for the erosion process. Its participation in the erosion phenomenon depends on its permeability and the ability to detach and transport its particles. Each soil type will react differently to the attack of rain and shear of runoff, depending on its texture, structure, porosity, and level of organic matter. The Menoua watershed is made up of a mosaic of soils linked to the geological history of the region. They come from basalts, sandy soils, and alluviums. To assess erodibility, we took into account not only the infiltration capacity which, according to Ref. [21], allows us to know the soil runoff potential, but also texture and organic matter content which, according to Ref. [22], have a considerable influence on the sensitivity of soils to erosion. These factors condition the permeability and cohesion of aggregates. According to these criteria, four major classes of soil are thus defined for the Menoua basin. Ferralitic soils, which benefit from good internal drainage form the first class and have a high infiltration capacity. In the second class, we have soils rich in humus and poorly developed soils. They generally have lower percolation and infiltration rates. The third class consists of moderately organic soils, such as poorly drained fine sands, loamy soils, and thin permeable soils. Hydromorphic soils consist of poorly structured and poorly drained heavy clays, which are found in the fourth class. According to these criteria, two major soil classes are defined for the Menoua basin. The first class is made up of ferralitic soils with good internal drainage and very high infiltration capacity. The second class includes hydromorphic soils consisting of moderately organic, poorly drained, and permeable thin soils (**Table 3**).

### *2.3.1.4 Drainage density*

Drainage density is an input parameter into the various soil water erosion models, which represent tools to help implement future soil conservation plans. It is indicative of the infiltration and permeability of the basin. A high drainage density reflects the


**Table 2.** *Landuse distribution.*


#### **Table 3.**

*Soil classification according to their contribution to erosion.*

impermeable lithological nature that favors surface runoff. The hydrographic network of the Menoua basin is of order 6; therefore, very active during the rainfall.

### *2.3.1.5 Climate*

Climate is an important factor that directly or indirectly influences soil erosion [23]. Rainfall in the humid tropics is the most important climatic variable that affects soil erosion. The action of rainfall amplifies the driving forces necessary for the uprooting of soil particles. Rainfall intensity and energy trigger soil erosion. The precipitation map of the Menoua watershed was produced using rainfall data from two meteorological stations (IRAD-Dschang, Djutitsa). These data have undergone interpolation operations (spline interpolation).

The sensitivity factors resulting from these data were rasterized in dimension 10 m\*10 m for a pixel in order to harmonize the spatial resolution. These rasterization operations were carried out using the ESRI software range (ArcGIS© 10.3) at the URCLIEN Research Unit at the Department of Geography of the University of Dschang.

#### *2.3.2 Hierarchical structuring of factors*

Establishing the hierarchical structure consists of classifying the various factors selected according to their degree of influence on soil erosion. To facilitate the task, [16] set up a scale of numerical values (**Table 4**).


**Table 4.** *Scale proposed by Ref. [16].*


*Modeling of Soil Sensitivity to Erosion Using the Analytic Hierarchical Process: A Study… DOI: http://dx.doi.org/10.5772/intechopen.111742*

#### **Table 5.**

*Comparison of factors by the expert.*

#### *2.3.3 Elaboration of binary combinations*

After taking the advice of some researchers and experts on the study of water erosion of soils, the binary combinations, which consist of comparing the factors of erosion with each other within a matrix and assigning to each pair a comparison coefficient were made (**Table 5**).

The values in red are those checked by the expert to materialize the existing links between the factors to be compared. For example, considering the fourth line, the "Slope" indicator is really more important than the "rainfall" factor in the evaluation of the sensitivity of soils of the Menoua watershed to erosion. From this comparison between the different factors, a reciprocal comparison matrix was produced (**Table 7**) by applying the following relationship Eq. (1):

$$A = [aij]\\
with \begin{cases} \quad aii = \mathtt{1}\\\quad aji = \mathtt{1} \end{cases}\\
(reciprealvalue) \tag{1}$$

#### *2.3.4 Determination of the value and the proper vector for each indicator*

The weighting of the criteria makes it possible to reflect the relative importance given to each criterion by the experts. Once the comparison matrix has been obtained, the proper value of each combination and the proper vector corresponding to it are determined. The proper value of each pair comparison is obtained by dividing the numerical importance assigned to the pair by the sum of the numerical degrees of importance of the column. The proper vector indicates the order of priority or the hierarchy of the vulnerability indicators studied. It indicates the relative importance of the indicators. It is estimated by first calculating the sum of the proper values contained in each row of the matrix, then dividing this value by the number of indicators contained in the matrix. The proper vector associated with each factor is the weight assigned to each factor. Calculating the weight of each factor normalizes the comparison matrix so that the sum of all the weights equals 1.

#### *2.3.5 Study of coherence of judgment*

Computed priorities make sense only if the matrix of comparison by pairs is coherent. The evaluation of the coherence of judgments can be made using a Coherence Index (CI). This index measures the logical coherence of judgments of the people consulted. It provides information on consistency in terms of the ordinal importance of indicators to be compared. The estimation of this index is based on the calculation of the proper values of the comparison matrix using the mathematical procedure Eq. (2);

$$IC = (\lambda\_{\text{max}} - n) / (n - 1) \tag{2}$$

such that *λmax* is the maximum proper value of the comparison matrix, obtained by multiplying the total of each column of the comparison matrix by pairs with the relative weight of the indicator of this column, and by adding the results obtained for each column. n is the number of indicators compared in the matrix. The consistency ratio (CR) is then calculated, such as Eq. (3);

$$CR = \frac{IC}{IA} \tag{3}$$

where IA is the random index fixed according to the number of factors (4 in the case of this study). The value of AI was given by Ref. [16], and it is a function of the number of elements compared (**Table 6**).

If CR is less than or equal to 0.1 or 10%, then it is accepted that the weights assigned to the indicators are acceptable and, therefore consistent. If this threshold is exceeded, we are in a situation of inconsistency, then the matrix resulting from the comparisons will have to be reevaluated.

#### *2.3.6 Aggregation of weighted data*

This final stage of the Hierarchical Multi-criteria Analysis (HPA) occurs once the weighting of the landslide assessment factors has been carried out. At this point, it is easy to combine them to obtain an assessment of the sensitivity of the watershed to erosion. The most common and well-known technique of this approach is the weighted linear combination, which integrates all the considered factors into one [24–26]. It consists of multiplying each layer factor by its respective weighting coefficient, and then adding these results to produce a sensitivity index. The mathematical transcription of this combination is expressed as follows Eq. (4);

$$V\_i = \sum\_{j=1}^{5} a\_{j\cdot} a\_{ij} \tag{4}$$


**Table 6.** *Random consistency indices [16].*

*Modeling of Soil Sensitivity to Erosion Using the Analytic Hierarchical Process: A Study… DOI: http://dx.doi.org/10.5772/intechopen.111742*

where *Vi* is the summary index of susceptibility, *ω<sup>j</sup>* is the weight attributed to each indicator, and *aij* is the weighting coefficient evaluating the relative importance of the factors.

This methodology for modeling and mapping soil sensitivity to erosion, which takes into account not only the functioning of the entire system but also the interrelationships between its various factors, is shown diagrammatically in **Figure 2**.

**Figure 2.** *Methodology for mapping soil sensitivity to erosion using the multi-criteria assessment.*
