Soil Erodibility Factor K

The soil erodibility factor *K* represents the susceptibility of soil to erosion under standard plot conditions. Soil erodibility is scaled from 0–1, depending on the soil texture, e.g., high values are used for silt to fine sand and low values for coarse sand due to its resistance to erosion. To calculate soil erodibility factor *K*, ref [32] has proposed a relationship shown in Equation (3) that considers the soil textural information, organic matter, information about the soil structure, and permeability. Although Equation (3) is based on the soil data of regional conditions in the United States, in many studies outside the United States researchers have used Equation (3) for soil erodibility factor calculations [25].

$$K = \frac{0.1317 \left[2.1 \times 10^{-4} M^{1.14} (12 - a) + 3.25(b - 2) + 2.5(c - 3)\right]}{100} \tag{3}$$

where *M* is a parameter based upon soil texture and estimated using Equation (4) as adopted from [33], *a* is the organic matter content (%), *b* is a code related to soil structure (1 for very fine granular, 2 for fine granular, 3 for coarse granular, 4 for massive), and *c* is a code related to soil permeability (1 to 6, fast to very slow draining characteristics).

$$M = (\mathbf{m}\_{\rm silt} + \mathbf{m}\_{\rm vfs}) \times \left(100 - \mathbf{m}\_{\rm clay}\right) \tag{4}$$

where mclay is a fraction of clay contents with particle size <0.002 mm, msilt is a fraction of silt contents with particle size ranging from 0.002 to 0.05 mm, and mvfs is a fraction of very fine sand contents with particle size ranging from 0.05 to 0.1 mm. All fractions are expressed as a percentage.

Soil maps help to define the codes related to soil structure and soil permeability. Soil erodibility can also be identified based on the regional studies, e.g., reference [34] have reported the erodibility factor *K* values for the Potohar region, Pakistan. In Pakistan, the Soil Survey of Pakistan and the Geological Survey of Pakistan prepare maps that can be used to define erodibility classes. Moreover, some satellite products are also available at a coarser scale for harmonized soil type information. Satellite data of different soil fractions are also available on 250 m grid resolution. However, the erodibility factor for the current study was calculated using the soil texture information extracted from the Food and Agriculture Organization (FAO) soil datasets (www.fao.org, accessed on 23 May 2019). Soil erodibility values were assigned based on the texture and organic matter of the soil. Three soil layers were extracted from the FAO soil database. Soil classes were identified from clay loam to loam with organic matter of more than 2% because the soils in the catchment are very rich in organic carbon. The values assigned for clay loam and loam were 0.26 and 0.28, respectively.
