*4.2. Evaluation of Two Schemes Using Clear Sky LSTs*

Figure 5 shows the results of the first (upper) and second (lower) validations for summer daytime and nighttime for Scheme 1(S1). The R<sup>2</sup> values for estimating 10 km daytime and nighttime LSTs were 0.82 and 0.85, respectively, in the first validation. The RMSE values have a daytime LST of 1.40 ◦C and a nighttime LST of 0.95 ◦C. Considering their similar nRMSE, the main reason for the RMSE difference between daytime and nighttime is likely the range difference in the temperature distribution. In the second validation, the R<sup>2</sup> (RMSE) values for estimating 10 km daytime and nighttime LSTs were 0.79 (1.55 ◦C) and 0.88 (1.14 ◦C), respectively. The accuracy of the two RF-based validations corresponds to the MODIS LST validation error of 1–2 K [53–55]. In particular, the second validation results were similar to the first validation in terms of accuracy (i.e., R<sup>2</sup> and nRMSE), even with a separate validation dataset by date. These results imply that the constructed 2-step RF-based model is robust for humid areas where clouds often cover most regions in summer. However, since we performed both validations using the MODIS clear sky LSTs, the effect of clouds was not considered. Thus, accuracy assessment using in situ LST data under cloudy conditions was needed.

**Figure 5.** Density scatter plots between the estimated and 10 km moderate-resolution imaging spectroradiometer (MODIS) LSTs for scheme 1(S1) from two validation results for daytime and nighttime. The color ramp from blue to red corresponds to increasing point density. Black dashed lines show the regression line and red solid lines represent the line of identity (y = x).

Figure 6 shows the validation results of the second step for Scheme 1, using clear sky MODIS LSTs estimated with the bilinear resampling (Bilinear), the lapse rate approach (Lapse rate), and the proposed RF-based algorithm (RF) among the different land covers. RF outperformed the other two techniques with higher correlation and lower RMSE in most land covers for both daytime and nighttime. For daytime, RF showed R<sup>2</sup> of 0.6–0.8 and RMSE of 1.6–3.0 ◦C with some variation according to land cover. This accuracy is considered significant with an average range value of RMSE similar to approximately 2.0 K, which is the target accuracy in several daytime LST retrieval studies [56–58]. The reason why urban areas showed lower performance than other land covers might be that the relatively high LSTs in urban areas were not accurately simulated when downscaling 10 km LST to 1 km, considering the fact that RF underestimated the downscaled LSTs (mean bias: −1.5 ◦C, not shown). Moreover, it has been reported that MODIS daytime LSTs in urban areas have relatively high uncertainty [16,59]. Note that the RF outperformed the lapse rate approach, which assumes the dependency of cloudy LSTs only on the altitude for all land covers in the daytime [12]. The RF appears to simulate the surface thermal heterogeneity well in daytime, using not only Elev, but also the Imp and ACPs—MAST, YAST, and theta—as input variables.

**Figure 6.** Model performance of three downscaling approaches (bilinear resampling (bilinear), lapse rate, and random forest (RF)) in the second step for scheme 1 by land cover for daytime (**a**) and nighttime (**b**).

For nighttime, the RF model returned highly accurate results, with R2~0.8 to 0.9 and RMSE < 1.5 ◦C with some variations by land cover. The lapse rate approach showed worse performance than the other two methods for most land cover types. Duan et al. used an average lapse rate of 6.5 K/km for both day and night [12]. However, the lapse rate could be applied to the air temperature of the troposphere, not the LSTs, which implies that the LST difference by altitude does not seem to be significant on the local scale. Interestingly, the bilinear and RF models did not show much difference for nighttime, where RF showed slightly better performance than the bilinear interpolation in terms of R<sup>2</sup> and RMSE for most land covers. This suggests that the nighttime LST is thermal-homogenous enough for bilinear interpolation to achieve good results.

Table 2 summarizes the results of the first and second validations for a 1 km clear sky LST estimation in S2. The first validation showed excellent performance resulting in R<sup>2</sup> > 0.9 and RMSE < 1 ◦C for both daytime and nighttime. The second validation, however, dividing samples by date, yielded relatively low accuracy, which is possibly due to the daily LST variations. It is not surprising that the prediction performance of S2 by time over humid areas in the summer would be less accurate than the first validation, because clouds covered most areas for specific days, which might not have been trained well. In particular, cloudy areas in the summer daytime have an LST range different from

clear sky areas (Figure 4); therefore, S2-based 1 km LSTs need further investigation using in situ data under cloudy conditions.


**Table 2.** The two validation results of the 1 km LST estimation from scheme 2(S2) for daytime and nighttime.
