*3.2. Breakpoint Analysis*

A shift linear analysis method [42,73] was used to identify the breakpoint in the albedo time series. The idea behind this method is determining the point where the slope changes significantly in the time series before and after the point. The calculation method is as follows:

$$\mathbf{A}\_{\mathbf{i}} = \begin{cases} \mathbf{b}\_1 + \mathbf{k}\_1 \mathbf{t}\_{\mathbf{i}} & \mathbf{t}\_{\mathbf{i}} < \mathbf{b}\_3 \\\ \mathbf{b}\_2 + \mathbf{k}\_2 \mathbf{t}\_{\mathbf{i}} & \mathbf{t}\_{\mathbf{i}} \ge \mathbf{b}\_3 \end{cases} \tag{1}$$

where Ai denotes the albedo in the ith year; ti denotes the ith year; and b1, b2, b3, k1 and k2 are the fitted parameters. Among them, k1 and k2 represent the slopes of the fitted line, b1 and b2 represent the fitted intercepts, and b3 represents the breakpoint position.

The Chow test which is generally used to detect changes in time series was applied to test the significance in this study and the formula is expressed as follows:

$$\mathbf{F} = \frac{\mathbf{S}\_1 - \mathbf{S}\_2 - \mathbf{S}\_3}{\mathbf{S}\_2 + \mathbf{S}\_3} \cdot \frac{\mathbf{N}\_1 + \mathbf{N}\_2 - 2\mathbf{c}}{\mathbf{c}} \tag{2}$$

where S1 = ∑n i=1 (Ai − Aˆ i) 2 indicates the sum of square errors of the time series. For the former N1 number of the time series, S2 = ∑ N1 i=1 (Ai − Aˆ i) 2 indicates the sum of square errors of the former time series, and S3 = ∑ N2 i=1 (Ai − Aˆ i) 2 indicates the sum of square errors of the latter N2 number of the time series. c is the number of the estimated parameter in the whole time series.

#### *3.3. Interannual Variation Rate Calculation*

A simple linear regression model was used to calculate the interannual variation rate. Using the albedo time series as an example, the interannual variation rate of each pixel is equal to the slope of the trend line via the least-squares regression of the multiyear value in each pixel. The calculation for the slope is as follows:

$$\mathbf{K}\_{\mathbf{A}} = (\mathbf{n} \times \sum\_{i=1}^{n} \mathbf{i} \times \mathbf{A}\_{i} - (\sum\_{i=1}^{n} \mathbf{i})(\sum\_{i=1}^{n} \mathbf{A}\_{i})) / (\mathbf{n} \times \sum\_{i=1}^{n} \mathbf{i}^{2} - (\sum\_{i=1}^{n} \mathbf{i})^{2}) \tag{3}$$

where KA represents the interannual variation rate of albedo, n represents the number of years, i denotes the ith year, and Ai denotes the albedo value in the ith year. A positive slope value indicates an increasing trend, while a negative slope indicates a decreasing trend.

The significance of the calculated tendency is determined by an F test. The calculation formula is expressed as follows:

$$\mathbf{F} = \mathbf{R} \times (\mathbf{n} - \mathbf{2}) / \mathbf{Q} \tag{4}$$

where Q = ∑ni=<sup>1</sup> (Ai − Aˆ i)2 indicates the sum of square errors, and R = ∑ni=<sup>1</sup> (Aˆ i − A)<sup>2</sup> represents the regressed square sum. Ai denotes the albedo value in the ith year, A ˆ i denotes the albedo regression value in the ith year, A denotes the mean albedo value across all years, and n denotes the number of years.

This method has also been applied to the calculation of interannual variation rates for vegetation and urbanization, where KV and KU represent the interannual variation rate of vegetation and urbanization, respectively.
