*3.3. Snow Albedo Feedback*

Snow albedo feedback estimation based on the block bootstrap test is explained in detail with an example trial, according to the method introduced previously (Section 2.2). Specifically, following Step 1, it takes 27 times of random choice before all the 14 blocks of data are picked. Details of each pick are displayed in Table 1. Specifically, Pick ID represents the count of each pick, while Block ID is the block of data of the corresponding year. During the experiment, it is not until the occurrence of Block 15 (the 27th pick) that all 14 blocks of the original dataset are included. Thus, 27 blocks with 324 data are contained in the newly generated dataset.

Following Step 2, snow albedo feedback can be quantified based on the newly picked dataset. Scatterplot of the 324 Δ*Gs*(*t*,*R*) and Δ*T*(*t*,*R*) data are shown in Figure 6a. Colors of the dots represent the frequency of their occurrence (corresponding to Table 2). The dash line is the least square fit of the 324 data, i.e., snow albedo feedback strength of this trial.

**Figure 6.** Snow albedo feedback estimations over the North Extratropical Land during 2003–2016 from the block bootstrap test: (**a**) an example of one test (Scatterplot of monthly snow albedo radiative forcing anomalies (Δ*Gs*(*t*,*R*)) versus surface air temperature anomalies (Δ*T*(*t*,*R*)), dots with different colors represent their frequency, and the least square fit coefficient suggests the magnitude of snow albedo feedback); and (**b**) probability density function of snow albedo feedback estimations from the 10,000 tests.

Following Step 3, the mean snow albedo feedback and the 95% confidence level can be estimated after repeating the experiment for 10,000 times. The histogram of the 10,000 snow albedo feedback is shown in Figure 6b. The value of the red line refers to the mean snow albedo feedback, in our case, 0.18 ± 0.08 W·m−2· ◦C−<sup>1</sup> over the NEL during 2003–2016. This implies that as surface albedo decreases in association with 1 ◦C temperature increase, snow albedo feedback would cause an increase of 0.18 ± 0.08 W·m−<sup>2</sup> in the net shortwave radiation at TOA, averaged over the NEL.

By rescaling the NEL result with product of two factors: the ratio of the NEL area to the global area and the ratio of annual mean surface air temperature change of the NEL to global mean change [56], global snow albedo feedback can be scaled as 0.04 ± 0.02 W·m−2· ◦C−1. However, due to the limited sample amount, the result may be subjected to substantial uncertainty.


**Table 1.** Every Pick of the example test.

**Table 2.** Frequency of each block of data based on the example test.

