*A.2. Variable Importance Calculated from the RF Models*

Figure A1 shows the normalized relative variable importance calculated from the RF models for the two schemes. The normalization was done by sum to 100%. Daily variable importance of step 2 in S1 were averaged before normalization.

**Figure A1.** Normalized relative variable importance calculated from the RF models of two steps (step 1 and step 2) for scheme 1 (S1), the orange bar; and scheme 2(S2), the blue bar, for daytime (**a**–**c**) and nighttime (**d**–**f**).

#### *A.3. Two Scheme Combination (SC) Methods of Daytime*

In Section 4.1, the upper quartile of cloudy sky LST was close to the lower quartile of clear sky LST for most in situ stations in the daytime. We used the AMSR2 BT to select the dates of daytime high

and low LSTs. First, all of the eight daytime AMSR2 BTs listed in Table 1 were aggregated to 1 km as a MODIS grid using bilinear resampling. Temporal correlations of AMSR2 BTs and in situ data at the 10 stations were performed over all-weather conditions in summer; we selected 10V, which showed the highest correlation, as the reference variable (Table A3). The 75th percentile (i.e., upper quartile) value of 1 km AMSR2 BT 10V was then calculated over the summer study periods (July–August, 2013–2018) for each pixel. Finally, the LSTs developed from S2 were used for days when the BT of AMSR2 10V was over the 75th percentile, and S1 was used for days when the BT of AMSR2 10V was below the 75th percentile, based on the results in Section 4.4.


**Table A3.** The temporal correlation (Pearson correlation coefficient; R) results between eight AMSR2 BTs and the 1 km bias-corrected in situ LSTs during July and August from 2013 to 2018 for the 10 stations in daytime. Refer to Figure 1 for station numbers.
