*3.4. Contribution Analysis*

Urbanization and vegetation are two main factors that affect variations in albedo. In our study, the annual variation rate of albedo in each pixel is expressed by the contributions of vegetation (V), urbanization (U), and other factors (Δ) (formula (5)).

$$\mathbf{K}\_{\mathbf{A}} = \mathbf{C}(\mathbf{V}) + \mathbf{C}(\mathbf{U}) + \mathbf{C}(\boldsymbol{\Delta}) \tag{5}$$

where KA represents the interannual variation rate of albedo. C(V), C(U), and C(Δ) represent the contributions of vegetation, urbanization, and other factors to the interannual variation rate of albedo, respectively. The vegetation contribution calculation method [74] is as follows:

$$\mathbf{C}(\mathbf{V}) = \frac{\partial \mathbf{A}}{\partial \mathbf{V}} \times \mathbf{K}\_{\mathbf{V}} \tag{6}$$

KV represents the slope of the linear regression line for the multiyear EVI time series. A denotes albedo, V denotes EVI, and *∂*A*∂*V (S(V)) represents the sensitivity of albedo to EVI. This sensitivity term was derived as a partial derivative via the multiple regression of albedo on EVI and DMSP/OLS. Positive and negative values of this sensitivity term reflect the positive and negative correlations between the analyzed factors and albedo, respectively. The magnitude of the absolute value of the sensitivity coefficient indicates whether the relationship between the factors and albedo is strong or weak (the greater the value, the stronger the relationship). The contribution of urbanization (C(U)) can also be calculated via the sensitivity of albedo to urbanization(S(U)) and KU in the same way.

Due to the spatial differences in the contribution intensity from vegetation and urbanization in different regions, the relative contribution percentage of vegetation, urbanization, and other factors to changes in albedo can be expressed with the following equation [44]:

$$P(\text{V}) = \frac{|\text{C}(\text{V})|}{|\text{C}(\text{V})| + |\text{C}(\text{U})| + |\text{C}(\text{A})|} \times 100\% \tag{7}$$

$$P(\mathcal{U}) = \frac{|\mathcal{C}(\mathcal{U})|}{|\mathcal{C}(\mathcal{V})| + |\mathcal{C}(\mathcal{U})| + |\mathcal{C}(\Lambda)|} \times 100\% \tag{8}$$

$$\text{P(A)=100} - \text{P(V)} - \text{P(U)} \tag{9}$$

where, <sup>P</sup>(V), P(U) and P(Δ) represent the relative contribution percentage of vegetation, urbanization, and other factors, respectively.
