## 2 Materials and Methods
### Landscape Metrics Analysis  
The use of landscape metrics is a utile method for estimating the relationships between spatial patterns and spatial processes [44]. The analyses of the pattern changes through time enable the correlation between landscape patterns and the soil loss rates. In order to investigate the relationship between the landscape metrics for land cover and the watershed soil erosion, landscape metrics were calculated at the class level using FRAGSTAT software (version 4.2.1) for the years 2010 and 2020.  
The most commonly used metrics are Number of Patches (_NP_), Patch Density (_PD_), Edge Density (_ED_), Largest Patch Index (_LPI_), Percentage of Landscape (_%PLAND_), Euclidean Nearest Neighbor Distance Area-Weighted Mean (ENN_AM), and Splitting Index (SPLIT) metrics. These selected metrics have been frequently used in previous studies in order to assess the links between land cover patterns and soil erosion [45; 46].  
* Number of Patches is the number of patches per unit area: \[NP=\sum_{i=1}^{n}P_{i}\] (21) where \(P_{i}\) is a patch of type \(i\).
* Patch Density is the number of patches of a corresponding patch type (class) per unit area: \[PD=\left(\frac{n}{A}\right)\times 10,000\times 100\] (22) where \(A\) is the area of a certain landscape type (m\({}^{2}\)), \(n\) is the number of patches, and 10,000 \(\times\) 100 is the number of patches per 100 hectares. The higher the _PD_, the higher the degree of landscape fragmentation.
* Edge Density is the total length of all edge segments per hectare for the considered landscape: \[ED=\frac{E}{A}\times 10,000\] (23) where \(E\) is the total length of an edge in a landscape (m) and \(A\) is the total landscape area (m\({}^{2}\)).
* Largest Patch Index is the percentage of the landscape in the largest patch (%): \[LPI=\frac{\max\left(a_{ij}\right)}{A}\times 100\] (24) where \(a_{ij}\) is the area of patch \(ij\) and \(A\) is the total landscape area.  
LPI is almost 0 when the largest patch in the landscape is too small; however, it equals 100 when the whole landscape consists of a single patch. In other words, the largest patch covers 100% of the landscape.  
* Percentage of Landscape measures the extent percentage of each land cover class comprised of a particular patch type: \[PLAND_{i}=\frac{\sum_{j=1}^{n}a_{ij}}{A}\times 100\] (25) where \(a_{ij}\) is the area of patch \(j\) for the \(i\)th land cover class and \(A\) is the total landscape area.  
PLAND_ is almost zero when the corresponding land cover class is occasionally present in the landscape and approaches 100 when only a single patch of the corresponding land cover type still exists.
* Euclidean Nearest Neighbor Distance Area-Weighted Mean (ENN_AM) is the shortest straight-line distance (m) between a focal patch and its nearest neighbor of the same class.
* Splitting Index is the number of patches obtained by subdividing the landscape into equal-sized patches based on the effective mesh size.  
These metrics indicate the degrees of fragmentation for different land cover types and change images. According to these metrics, the multiple linear regression (MLR) approach was used in order to correlate soil erosion loss and landscape patterns.