**2. Materials and methods**

#### **2.1 Study area**

Lake Ol Bolossat catchment is located on latitude 00 090 S and longitude 360 260 E in Nyandarua County, Central Province of Kenya. The lake with an area of 43.3 km<sup>2</sup> lies at an average altitude of 2340 m above sea level in a wedge shaped rift valley floor sloping eastwards and northwards [32] and forms the headwaters of Ewaso Narok River which is the major tributary of Ewaso Ng'iro North River (see **Figure 1**).

The region enjoys favourable climate for most periods of the year, with temperatures ranging between 10° and 28°C. The climate is sub-humid and is strongly influenced by local topography of the surrounding central highlands with mean

**Figure 1.** *Flow chart analysis of soil loss.*

annual rainfall of 980 mm and increases southwards and westwards. Rainfall is bimodal, with long peaks between April and June and the shorter peaks between October and November [32].

The areas is dominated by small holder mixed farmers who grow crops and rear livestock on parcels of land ranging from 1 to 4 hectares. Nearly 60% of the families own less than 2 ha of land. Since they have free access to pasture around the lake, most of them own more livestock than their 2-ha plots can support. The human population density in the lake basin and the lake's watershed is approximately 202 per km<sup>2</sup> [33].

#### **2.2 Data sources**

Different data sources were referred to analyse the soil loss in the study area. A digital elevation model (DEM) with 90-meter resolution developed by NASA was used to calculate the slope length and slope gradient of the study area. The land cover classification map for 2014 was used for the analysis of crop management factor (C-value) while a soil map made by Centre for Training and Integrated Research in ASAL Development (CETRAD) was used in the analysis of soil erodibility factor (K-value).

Analysis of soil erosivity factor (R-value) was derived from annual rainfall data for different rainfall stations in the catchment which was obtained from CETRAD database. Conservation practices factor (P-value) was derived from land use types aligned to specified slope of the study area. The estimation of soil loss was then done by map overlays, pixel by pixel which enabled accurate multiplication of USLE parameters.

#### **2.3 Methodology**

The universal soil loss equation (USLE), developed by [23], was employed to assess the amount of soil loss in Lake Ol Bolossat Catchment. The USLE was applied in GIS based on the flow chart shown in **Figure 2**.

Mathematically the equation is denoted as:

$$A(\text{tons}/\text{ha}/yr) = \text{RX}XXLXSXCXP} \tag{1}$$

Where A is the mean annual soil loss, R is the rainfall erosivity factor, K is the soil erodibility factor, L is the slope length factor, S is the slope steepness factor, C is the crop management factor and P is the erosion control practice or land management factor. The analysis of each process factors of USLE was derived procedurally as illustrated in **Figure 2**.

#### *2.3.1 Rainfall erosivity factor (R)*

There are three equations which have been used to derive R-factor in different parts of the world [30] namely;

$$R = \text{9.28} \\ XP \quad \text{- 8838} \\ \tag{2}$$

Mean annual erosivity (KE > 25) where P is mean annual precipitation.

$$R = 0.276 \text{XPX130} \tag{3}$$

*Spatial Soil Loss Assessment Using USLE in Lake Ol Bolossat Catchment DOI: http://dx.doi.org/10.5772/intechopen.112129*

**Figure 2.** *Rainfall erosivity factor.*

Mean annual EI30, where P is mean annual precipitation.

$$R = 0.\text{5XP (in US unit) and } R = 0.\text{5XPX1.73 (in Metric unit)}\tag{4}$$

The study noted that the Eq. (2) is applicable in Peninsular Malaysia while the Eq. (3) requires I30 factor which is difficult to calculate. Eq. (4) is applicable in humid and sub-humid areas with mean annual rainfall of between 900 mm and 1700 mm [30]. This equation Eq. (4) was applied in this study where it was integrated into Arc GIS 10.3 software to derive R-factor. The rainfall data was obtained from CETRAD database. Average annual rainfall for at least twenty years was computed for ten weather stations in the catchment with respective rainfall erosivity factor using Arc GIS 10.3 [e.g., **Table 1** and **Figure 3**).

## *2.3.2 Soil erodibility factor (K)*

Bizuwerk et al. [30] defines Soil Erodibility Factor (K) as mean annual rainfall soil loss per unit of R for a standard condition of bare soil, recently tilled up-and-down with slope with no conservation practices and on a slope of 50 and 22 m length. Hellden [34] in [30] developed a USLE for humid and sub-humid highlands condition by adapting different sources and proposed the K values of the soil based on their colour. This soil classification was adopted for the study and modified according to four soil types found in the area. Soil map was obtained from CETRAD database.


*The rainfall stations were selected based on their proximity to the study area. Where there was no rainfall station existing near the study area, another station was selected and then extrapolation of data was carefully done in order to have the most representative rainfall data.*

#### **Table 1.**

*Computation of rainfall erosivity factor (R Factor) for the study area.*

**Figure 3.** *Soil erodibility factor.*

However, the soil data were in their geomorphologic names but not their colour and hence an attempt was made to match the soil names with their colour referring to World Reference Bureau (WRB) classification. The k value was then computed using Arc GIS 10.3 and results presented in raster format as shown in **Figure 4**.

*Spatial Soil Loss Assessment Using USLE in Lake Ol Bolossat Catchment DOI: http://dx.doi.org/10.5772/intechopen.112129*

**Figure 4.** *LS factor.*

#### *2.3.3 Slope length and slope steepness factors (LS)*

Wischmeier and Smith [23] noted that slope length and slope steepness can be used in a single index to express the ratio of soil loss using the following equation.

$$LS = (X/22.1)^m \left( 0.065 + 0.045S + 0.0065S^2 \right) \tag{5}$$

Where X = slope length (m) and S = slope gradient (%).

The values of X and S were derived from DEM. To calculate the X value, Flow Accumulation was derived from the DEM after conducting FILL and Flow Direction processes in Arc GIS 10.3

<sup>X</sup> <sup>¼</sup> Flow accumulation<sup>∗</sup> ð Þ Cell value

By substituting X value, LS equation was:

$$\text{LS} = \left(\text{Flow accumulation} \ast \text{Cell value} / 22.1\right)^{\text{m}} \left(0.065 + 0.045 \,\text{S} + 0.006 \,\text{S} \,\text{S}^2\right)^{\text{m}}$$

Moreover slope (%) was directly calculated from the DEM using the same software. The value of m varies from 0.2–0.5 depending on the slope as shown in **Table 2** [23]. The result of LS factor analysis is shown in the **Figure 5**.


*The slope for the study area ranged from less than 1%–5% and therefore the m-value (slope length) ranged from 0.2 to 0.5 (dimensionless).*

*Source: Bizuwerk et al. [30].*
