**3. Spatial quantification of soil loss**

The extent of soil erosion estimation is a complex interactions between Geology, topography, climate, soil, land use and land cover. RUSLE approach was selected to predict protracted average annual soil loss rates in an area (**Figures 2** and **3**). In this model, five major parameters were utilized to quantify soil erosion loss in Eastern Hindu Kush region. The mathematical expression of RUSLE model is given in the following equation:

$$\mathbf{A} = \mathbf{R} \times \mathbf{K} \times \mathbf{L} \times \mathbf{S} \times \mathbf{C} \times \mathbf{P} \tag{1}$$

Where,

A = Soil loss per unit area (tons/ha/yr.).

R = Rainfall-runoff erosivity factor (index) (MJ/hectare mm/yr.).

K = Soil erodibility factor (tons/ha/yr).


*Spatial Quantification of Soil Erosion Using Rusle Approach: A Study of Eastern Hindu… DOI: http://dx.doi.org/10.5772/intechopen.112346*

#### **3.1 Rainfall-runoff Erosivity factor (R)**

Rainfall-Runoff erosivity (R) quantifies the impact of raindrop on the surface and the rate of runoff likely to take place after a rain event. This factor is well-defined as the mean annual sum of individual or specific storm event energy (E), and also the maximum 30 min rainfall intensity for a specific storm event as described by [13, 18]. In order to estimate the accurate R factor, it is recommended to observe at least 20 to 30 years of rainfall data to accommodate climatic variation. The R factor determines the erosivity by rainfall at a specific region based on the intensity and amount of rainfall. It basically represents the impact of rainfall intensity on soil erosion. The rainfall-runoff erosivity was estimated by the following equation used by many researchers on areas where similar topographic and atmospheric conditions prevail [19, 20].

$$\mathbf{R} = \mathbf{0}.\mathbf{0}\mathbf{5} \times \mathbf{P}.\tag{2}$$

Where,

R = Rainfall Erosivity Factor, P = Mean Annual Rainfall in (mm).

#### **3.2 Soil Erodibility factor (K)**

The K factor is a quantitative measurement of the erodibility of a particular type of soil. It can be also described as a measure of the susceptibility of soil particles towards detachment and transportation by rainfall intensity and runoff. Soil texture, soil structure, soil permeability and the organic matter are the main soil properties influencing K factor. The soil erodibility factor for every particular soil is defined as the rate of erosion per unit erosion index from a standard unit plot of 22.13 m long slope length having 9% of slope gradient [21]. It represents the rate of soil loss per rainfall erosivity index (R).

On the basis of data availability, following equation was used to estimate the soil erodibility of soil given by Wischmeier and Smith [18].

$$\mathbf{K} = \mathbf{Fcsand}^\* \text{ Fsi} - \text{cl}^\* \mathbf{Fogc}^\* \mathbf{Fhisand}^\* \mathbf{0.1317}. \tag{3}$$

Where,

$$\text{Fcsand} = \left[ \mathbf{0.2} + \mathbf{0.3} \cdot \exp\left( -\mathbf{0.0256} \,\text{SAN} \left( \mathbf{1} - \frac{\text{SIL}}{\text{100}} \right) \right) \right]. \tag{4}$$

$$Fsi - cl = \left(\frac{\text{SIL}}{\text{CLA} + \text{SIL}}\right) \text{0.3.} \tag{5}$$

$$\text{Forgc} = \left( 1.0 - \frac{0.25C}{C + \exp\{3.72 - 2.95C\}} \right). \tag{6}$$

$$\text{Fhisand} = \left( 1.0 - \frac{0.70 \text{SNI}}{\text{SNI} + \exp\{5.51 + 22.95 \text{SNI}\}} \right). \tag{7}$$

Where, C is the organic carbon content, SIL, CLA and SAN are % silt, clay and sand, respectively, SN1 is sand content which is obtained by subtracting it from 1 and dividing by 100, Fcsand = gives a low soil erodibility factor for soil with coarse sand

and a high value for soil with little sand content, Fsi-cl gives a low soil erodibility factor with high clay to silt ration, Forgc is the factor that reduces soil erodibility for soil with high organic content, Fhisand is the factor that reduces soil erodibility for soil with extremely high sand content.

#### **3.3 Slope length and slope steepness factor (LS)**

The Slope length or Steepness factor (LS) is the output of two individual factors combined together i.e. Slope length factor (L) and a Slope gradient factor (S), both of these factors are delineated from the ALOS PALSAR DEM. The LS factor proves to be an important parameter in the modeling of soil erosion.

The L factor depicts impact of slope on soil erosion. When the length of slope increases, erosion of soil will also increase. Whereas, the S factor represents impact of slope gradient on erosion. The rate of soil loss increases with increasing slope steepness more than it does with length of slope. The LS factor depicts erodibility because of slope steepness and length. It signifies the influence of topography, specifically slope features, on soil erosion. Hence, proving it to be directly proportional to the soil erosion e.g., an increase in slope steepness and length marks an increase in the LS factor.

The LS factor was calculated from after generating the flow direction and flow accumulation grids in ArcMap 10.5 by using Arc Hydro toolset.

$$L = \left(\frac{\lambda}{22.13}\right)^{\text{m}}.\tag{8}$$

Where, L = Slope length factor, λ = Slope length (m), m = Slope-length exponent

$$m = \frac{F}{1 + F'}.\tag{9}$$

$$\frac{\sin\,\\$/0.0896}{\\$\,(\sin\,\\$)0.8+0.56}.\tag{10}$$

Where, F = Ratio of rill erosion to inter-rill erosion, *β* = Slope angle (°). In ArcMap, *L* was calculated by the following equation,

$$\mathbf{L} = \frac{\left(\text{flow}\_{\text{acc}} + \text{625}\right)^{(m+1)} - \text{flow}\_{\text{acc}}^{(m+1)}}{2\mathbf{5}^{(m+2)} \* \text{22.13}^m} \tag{11}$$

*S* ¼ *Con Tan* ðð Þ ð Þ slope ∗ 0*:*01745 < 0*:*09 , 10 ð Þ *:*8 ∗ Sin slop ð ∗ 0*:*01745Þ þ 0*:*03 , ð16*:*8 ∗ Sin slop ð ∗ 0*:*01745Þ � 0*:*5ÞÞ

For Slope gradient factor,

$$S = \text{Con}((\text{Tan}(\text{slope} \ast 0.01745) < 0.09), (10.8 \ast \text{Sim}(\text{slope} \ast 0.01745) + 0.03), \quad \text{(12)})$$

$$(16.8 \ast \text{Sim}(\text{slope} \ast 0.01745) - 0.5))$$

Final LS Factor,

$$\mathbf{L}\mathbf{S} = \mathbf{L}^\*\mathbf{S}.\tag{13}$$

.

*Spatial Quantification of Soil Erosion Using Rusle Approach: A Study of Eastern Hindu… DOI: http://dx.doi.org/10.5772/intechopen.112346*

#### **3.4 Cover management factor (C)**

Cover management factor (C) is used for estimation cropping impact and other managing practices on soil erosion. After topography, vegetation is considered the 2nd most vital aspect that helps in minimizing the risk of soil erosion. Different types of land use and land cover intercepts precipitation and increasing infiltration rates and also helps in the reduction of rainfall impact on ground by reducing its energy before hitting the ground.

In the study area, Global land cover data was used to generate a C-factor map. It was generated by modifying the dataset in a raster-based GIS environment. The shape file was then modified in ArcGIS by merging all the attributes of same grid codes of land cover type. The C values were assigned by reviewing the literature of comparable model usage in the areas having similar prevailing climatic conditions as my study area.

### **3.5 Erosion control practice management factor (P)**

Erosion support practice factor (P) indicates the rate of soil loss according to different land cover management practices. This factor accounts for the control practices which reduces the rate of erosion caused by runoff and their influence on runoff concentration, runoff velocity, drainage patterns. P factor also accounts for the hydraulic forces exerted on soil by runoff. Land treatment in the form of contouring, strip cropping and terracing are the precautionary measures taken to prevent erosion. The precautionary measures or any control practices that are being used to minimize the impact of various factors on erosion contributes in the calculation of P factor.

The extent of soil erosion can be predicted by estimating the complex interactions between Geology, topography, climate, soil, land use and land cover. This empirical based technique is used globally to predict protracted average annual soil loss rates in an area. In this model, five major parameters are calculated to measure the soil erosion rates in a specific region (**Figure 3**). The work flow the Study is given below.
