The annual soil erosion can be assessed by computing average rainfall, R, K, LS, C and P factors and using Equation 1:

$\text{Annual Soil Loss}=R\times K\times LS\times C\times P$(1)

Factor details in above formula are depicted in below mentioned table ( Table 3 ):

In order to calculate Rainfall Erosivity (R Factor), annual average rainfall data is used which was obtained from three meteorological stations (Chilas, Astore and Skardu) situated in Gilgit working under Pakistan Metrology Department. The point data was further computed by Inverse Distance Weighted (IDW) of ArcGIS. To calculate R-Factor, we used Lambordi methodology, which is as follows:

$R=1.03\times P$(2)

here ‘R’ indicates rainfall erosivity (MJ mm/ha/h/year) & ‘P’ represent annual rainfall (mm).

With regards to soil erodibility, there are various geological factors i.e. soil texture, organic matter content of soil, partical permeability, and soil size as described by Renard and Ferreira (1993) . For calculating K-Factor, world soil data was taken from “Harmonized World Soil Database Viewer version 2.0” collaboratively created by Food and Agriculture Organization of the United Nations (FAO) and International Institute for Applied Systems Analysis (IIASA). Thereafter, K factor of each above mentioned soils were computed through following Equations (3) to (7) as suggested by Williams et al., (1995):

$K_{usle}=f_{csand}\times f_{cl\text{-}si}\times f_{orgc}\times f_{hisand}$(3)

$f_{csand}=\left(0.2+0.3\times \exp \left(-0.256\times m_s\left(1-\frac{m_{silt}}{100}\right)\right)\right)$(4)

$f_{cl-si}={\left(\frac{m_{silt}}{m_c+m_{silt}}\right)}^{0.3}$(5)

$f_{orgc}=\left(1-\frac{0.25\times orgc}{orgc+\exp \left(3.72-2.95\times orgc\right)}\right)$(6)

$f_{hisand}=\left(1-\frac{0.7\times \left(1-\frac{m_s}{100}\right)}{\left(1-\frac{m_s}{100}\right)+\exp \left(-5.51+22.9\times \left(1-\frac{m_s}{100}\right)\right)}\right)$(7)

In this framework,

$K_{usle}$ indicates the amount of erodibility,

$m_s$ indicates the percentage of sand,

$m_{silt}$ indicates the percentage of silt,

$m_c$ indicates the percentage of clay,

$f_{orgc}$ is a factor that declines the K values with high organic carbon content in soil,

$orgc$ indicates the organic carbon content,

$f_{csand}$ is a factor that decreases the K indicator with high coarse-sand content and proliferations it for soils with little sand, in soils,

$f_{cl\text{-}si}$ gives little soil erodibility factors with high clay-to-silt ratios, and,

$f_{hisand}$ declines the K value for soils with tremendously high sand content.

The topographic factor (LS Factor) comprises of two factors slope length and steepness. These factors are calculated individually first DEM data which was taken from Open Topography ( https://portal.opentopography.org/datasets ). DEM is then utilized to calculate flow accumulation. The data is then inserted in Raster Calculation function of ArcGIS using Equation (8) as recommended by Moore and Burch (1986) to calculate LS Factor.

$LS={\left(\frac{\text{Flow accumulation}\times \text{Cell size}}{22.13}\right)}^{0.4}\times {\left(\frac{\text{Sin}\text{Slope}\varnothing \times 0.01745}{0.0896}\right)}^{1.3}$(8)

For crop management factor (C Factor), NDVI is used (Ahmad et al., 1988). NDVI shows a relationship among parts having specific type of vegetation and those which are barren. NDVI data is taken through Landsat-8 data which was taken from USGS website ( https://earthexplorer.usgs.gov/ ). Bands 4 and 5 of LANDSAT 8 data are then used to calculate NDVI and consequent C Factor through Equations (9) and (10) ( Durigon et al., 2014 ).

$\text{NDVI}=\frac{\text{NIR}-\text{Red}}{\text{NIR}+\text{Red}}$(9)

$C\text{factor}=\frac{-\text{NDVI}+1}{2}$(10)

The last factor i.e. Conservation practice Factor (P Factor) is calculated based on types of cropping technique dominant in the study area ( Wischmeier & Smith, 1978 ; Renard et al., 1993 ).

The mean annual rainfall in study region is between 698 - 1331 mm per year as shown in Figure 2 . This data was taken from Pakistan Meteorological Department stations (Chilas, Astore and Skardu) situated in the study area. This data was then inserted in the Lambordi equation (Equation (2)) ( Isikwue et al., 2015 ) in the raster calculator and R Factor map ( Figure 3 ) was generated that shows wide variation in the study region ranging from 1371.96 MJ mm/ha/h/year – 718.949 MJ mm/ha/h/year. The central and eastern region exhibit highest values whereas the western region shows the lowest value of R Factor.

Related study area conducted by Ganasri et al. (2016) in Nethravathi Basin, projected rainfall erosivity factor from 2948.16 to 4711.4 expressed as MJ mm/ha/h/year. Another paper by Sidi Almouctar et al. (2021) in Niger (Maradi Region) stated that the average rainfall-erosivity value was 822.3 MJ mm/ha/h/year. Khan et al. (2023) reported the values of R ranging from 456 to 695 MJ mm/ha/h/year in District Swat of Khyber Pakhtunkhwa province of Pakistan.

It has been observed that soil erosion rate is highly controlled by precipitation cycle received in the study area, meaning that area having higher precipitation cycle will have higher soil erosion and vice versa ( Jain et al., 2001 ; Dabral et al., 2008 ). Therefore, it can be seen that areas mentioned in Table 4 and study area i.e. Baltistan Division, Pakistan have relatively high R factor. Lower R factor value in Maradi Region i.e. 0.011 is due to the fact that Northern part of the area is dry and has lower annual average rainfall compared to south Maradi Region. Variation in R factor values in different parts of the world has linkages with inconsistent soil erosion rate observed across the globe.

Data from world soil data base was inserted in ArcGIS and study area was clipped, wherein following three types of soils along with thick sheets of Glaciers were

found: Orthic Acrisols, Lithosols, Eutric Cambisols. $f_{orgc}$, $f_{csand}$, $f_{cl\text{-}si}$ and $f_{hisand}$ of each soil type was calculated through the Equations (4) to (7) and K Factor then calculated from Equation (3). Accordingly, K Factor was then inserted in ArcGIS and relevant map was generated which is at Figure 4 . Details of the soil are also given in Table 4 .

This corroborates the findings of Waseem et al. (2023) who have calculated the rate of erosion of the soil in the Jhelum River watershed (Azad Jammu and Kashmir, AJ&K, Pakistan). They suggested that heavy rainfall and steep slopes together results in significant erosion runoff. Ganasri et al. (2016) also reported that if the steepness increases the erosion also increases. K values ranging from 0.131 to 0.156 in Jhelum area of Pakistan.

LS Factor can be determined by slope length and its steepness. These factors directly impact the rate of erosion of the soil. If the steepness increases the erosion also increases ( Ganasri & Ramesh, 2016 ). For LS, we first used Digital Elevation Model (DEM) data to determine slope length and then steepness was calculated. Topographic Factor was then calculated by inserting both these factors in Equation 8( Moore & Burch, 1986 ). The values lf LS factor computed were in the range of 0 to 176.998 ( Figure 5 ).

Ganasri et al. (2016) reported LS values ranged from 0 - 1240 in the Nethravathi Basin which is quite higher than the present values. Similarly, during estimation of soil erosion risk in Kerala, India Prasannakumar et al. (2012) reported LS Factor values ranged from 0 - 22.90 which is much lower than the present value. In the present study high LS Value (47.199 - 176.997) were observed in higher altitude mostly covered with glaciers. These areas experienced high rate of soil erosion by water due to abrupt slope gradient and high precipitation rate ( Ansari & Tayfur, 2023 ). Lower LS values were found in areas around water bodies.

In order to calculate NDVI, LANDSAT 8 data of area was acquired from ( https://earthexplorer.usgs.gov/ ). Data was then inserted in ARCGIS and NDVI was calculated by using Equation (9). NDVI values ranged from 1.0 to 0.414068 ( Figure 6 ). C Factor was calculated through Equation (10), where values ranging from 0.0 - 0.707034 were obtained ( Figure 7 ).

Belasri and Lakhouili (2016) reported C-Factor ranged from 0.0 to 1.0 in Morocco, Prasannakumar et al. (2012) suggested C factor ranged from 0.3 to 1.5 in Kerala, India. The values of C in the present study was little higher as compared to other studies.

High value of C factor has been observed on the northern part of study area which is on high altitude and mostly covered with glaciers ( Waseem et al., 2023 ). Furthermore, due to high altitude and land steepness, crop management and agricultural practice is difficult in said area. According to different reports variable C-Factors were reported. The studies mentioned above depicted that high values have been observed in areas having high altitude and water bodies.

Table 5 was taken as reference in order to calculate P Factor. Values normally obtained varies from zero to one, where zero represents area where low soil erosion rate will be observed and one denotes area having high rate of soil erosion rate. P factor also depends upon type of cropping practice being followed in the study area. Using slope data calculated earlier during LS, P-factor ranging from 0.10 to 0.20 was obtained ( Figure 8 ). High P factor shows that area needs good cropping practices in order to reduce the risk of soil erosion ( Joshi et al., 2023 ).

Source: Korean Institute of Construction Technology, 1992.

Research papers similar to same region has also observed various that is 0.1 to 1 in Minab, Iran ( Azimi Sardari et al., 2019 ) and 0.55 to 1 in Nepal ( Joshi et al., 2023 ).

After obtaining all the factors, annual soil erosion was calculated on ARCGIS using RUSLE Model equation and annual average value of 6.68279 tons/hectare/year was obtained. Classification Statistics is shown in Table 6 .

The ASL values was classified ( Table 7 ) depending on erosion intensity (low to high) and map was generated which is at Figure 9 .

Milentijević et al. (2021) reported ASL in Bačka ranges situated in Serbia from 0.0 - 28.6 tons/hectare/year, with an average value of 0.007022 tons/hectare/year. Further, ASL from 0.0 - 38.09 tons/hectare/year and average annual soil loss rate of 2.2 tons/hectare/year was observed in Dijo watershed area, Ethiopia ( Bekele & Gemi, 2021 ).