*4.3. Spatial Distribution Analysis of All-weather LSTs from Two Schemes*

Figures 7 and 8 show the all-weather average daytime and nighttime 10 km LSTs of S1 from July through August for each year. The overall spatial distribution of the daytime and nighttime LSTs appeared similar, but the range of the daytime LSTs (22.1–34.0 ◦C) was considerably higher than that of the nighttime LSTs (16.0–22.6 ◦C). This is because the differences in heat capacity and evapotranspiration by land type result in a wide range of LSTs in the daytime, affected by incoming solar radiation [22]. Elevation (see Figure 1) yielded a negative spatial relationship with LSTs for both daytime and nighttime, which is consistent with the results of Bertoldi that showed that LST decreases with increasing elevation because of complex factors such as air temperature and vegetation amount [60]. In this study, therefore, the elevation input variable contributes significantly to the LST estimation model. In terms of land cover (see Figure 1), LSTs were relatively low in both the daytime and nighttime in the forested areas, widely distributed in the study area. Meanwhile, the cropland areas showed higher temperature values than in forests, especially for the western part of the study region, which is consistent with the results of Lee et al. [61]. The urban areas also showed relatively high LSTs compared to other landcovers, because of the highly impervious surfaces in both daytime and nighttime [32,62].

The developed 10 km LSTs of S1 also showed a temporal variation over six years (2013–2018). For example, South Korea experienced unprecedented extreme temperatures (i.e., a heatwave) in the summer of 2018 [63], where the developed LSTs show distinctly high-temperature distribution for both daytime and nighttime (Figures 7f and 8f). Furthermore, 10 km LSTs were relatively high at nighttime of summer 2013 (Figure 8a), which is consistent with the analysis of Choi and Lee that showed frequent tropical night events in South Korea in summer 2013 [64]. Overall, the LSTs estimated using S1 on the 10 km scale seem to accurately describe both spatial and temporal patterns of LSTs in summer daytime and nighttime.

Figure 9 shows the mean and variance of the 2013–2018 1 km all-weather LSTs produced by S1 and S2 for summer in both the daytime and nighttime. In the daytime, it should be noted that S2 generally simulated LSTs higher in urban and agricultural areas than S1 (Figure 9a,b). The difference in the estimated LSTs between S1 and S2 might also be due to S2 overestimating the low LSTs under cloudy conditions. The bias of the second validation of daytime was relatively high (~0.16), as shown in Table 2. At nighttime, the S1 and S2 showed similar LST distributions, except urban areas where the S1 LSTs were slightly higher than the S2 ones.

**Figure 7.** Spatial distribution maps of average estimated all-weather 10 km LSTs for scheme 1(S1) during July and August for each year; 2013 (**a**) to 2018 (**f**) for daytime.

**Figure 8.** Spatial distribution maps of average estimated all-weather 10 km LSTs for scheme 1(S1) during July and August for each year; 2013 (**a**) to 2018 (**f**) for nighttime.

**Figure 9.** Spatial distribution maps of average all-weather 1 km LSTs (upper) and the variance (lower) during July and August from 2013 to 2018 produced by the two schemes (S1 and S2) for daytime (**a**,**b**, **e**–**f**) and nighttime (**c**,**d**, **g**–**h**).

Note that the variance of S1 LSTs is quite a lot higher than S2 in most areas in the daytime (Figure 9e–f). The relative variable importance (%) explains this fact as provided by RF (Figure A1). Among the several input variables, only AMSR2 BTs showed temporal changes. In S2, temporally constant variables, such as Lat, YAST, theta, and MAST, played significant roles in the RF model (Figure A1c); therefore, S2 could be relatively limited in simulating the temporal variations of LSTs. In the case of S1, AMSR2 BTs were used only to construct the 10 km LSTs first (step 1), whereas ACPs were used only for step 2. Therefore, S1 could simulate the temporal pattern of daily LSTs accurately by downscaling the proposed 10 km LSTs to 1 km for each day in step 2. At nighttime, S1 and S2 had similar LST variance for most areas (Figure 9g–h). In particular, LSTs in summer nighttime have a distinctly lower variance than those in the daytime (Figure 9e–f), which implies that the nighttime does not show significant temperature changes in summer regardless of weather conditions.

Many previous studies that predicted 1 km cloudy sky LSTs have used auxiliary variables that are indirectly related to LST, such as elevation, latitude, and longitude [12,19]. It should be noted that ACPs (i.e., MAST, YAST, and theta) have been identified as crucial variables by RF for both S1 and S2 (Figure A1). This suggests that ACPs are useful in estimating LSTs for all-weather conditions, due to their characteristics representing the spatial distribution of LSTs, without being affected by clouds.

#### *4.4. Comparison of Two Schemes Using* in Situ *LSTs*

The clear and cloudy sky 1 km LSTs produced from the two schemes were validated (i.e., LOOCV) using the 1 km bias-corrected in situ LSTs measured at the 10 stations (Table 3 for daytime and Table 4 for nighttime). It should be noted that S1 showed negative biases for most stations, which implies that S1 tended to underestimate 1 km LSTs under clear sky conditions. In particular, the RMSE of S1 was relatively high with a large negative bias, especially for stations 5. This might be because the station was located in built-up urban areas, where S1 LSTs were possibly underestimated, as presented in Figure 9. On the other hand, in the case of S2, the bias under clear sky conditions was close to zero and

slightly positive for most stations. Therefore, S2 produced higher accuracy than S1 for high LSTs under clear sky conditions in the daytime.


**Table 3.** The leave one-station out cross-validation (LOOCV) results of the estimated 1 km clear and cloudy sky LSTs from scheme 1 (S1) and scheme 2 (S2) using bias-corrected in situ LSTs at 10 stations during July and August from 2013 to 2018 for daytime. Refer to Figure 1 for station numbers.

**Table 4.** The leave one-station out cross-validation (LOOCV) results of the estimated 1 km clear and cloudy sky LSTs from scheme 1(S1) and scheme 2(S2) using 1 km bias-corrected in situ LSTs for 10 stations during July and August from 2013 to 2018 for nighttime. Refer to Figure 1 for station numbers.


In the daytime under cloudy skies, S1 outperformed S2 for most stations. At stations 2, 3, 4, 8, and 10, S1 exhibited a significant increase in R<sup>2</sup> compared to S2. High temporal correlations of S1 imply the effective simulation of temporal variations of LSTs. Unlike the clear sky conditions, the RMSE of S1 was much smaller compared to S2 for most stations under cloudy skies. One possible reason for the high RMSE in S2 is that low LST values under cloudy areas could be overestimated based on the high bias of the S2 RF model under cloudy sky conditions (see also Figure 9). The RMSEs of S1 (from 2.1 to 3.9 ◦C in summer) for daytime under cloudy skies are comparable to or lower than those from the literature (RMSE of 4.3–8.3 ◦C for four stations in China [65], RMSE of 5.1–5.6 ◦C for two sites in Africa [17], RMSE of 1.8–2.7 ◦C for three stations in North China [30], and RMSE of 3.5–4.4 ◦C for four stations in China [12]), although those studies focused on all seasons, not only summer. It should be noted that Zhou et al. reported that the accuracy of LST estimation under the cloudy sky conditions in summer was lower than the other seasons [26].

Figure 10 represents the temporal distribution of the S1, S2, and in situ LSTs at station 9 for July–August 2017, when the LSTs dynamically changed. In the daytime, extremely high LSTs were well predicted by S2, such as for 13-July and 7-August, as opposed to S1; however, relatively low LSTs were better predicted by S1. It should be noted that there were days when the very high LSTs sharply dropped, such as between 6 July and 7 July, as well as 13 July and 15 July. S1 simulated these

rapid temperature changes better than S2. Furthermore, there were many days with large amounts of precipitation, which resulted in low LSTs (i.e., 10 August and 14 August) in the humid summer. LSTs for such days were also better simulated by S1 with an improved temporal correlation.

**Figure 10.** Time-series of the estimated LSTs for schemes 1(S1) and 2(S2), and 1 km bias-corrected in situ LSTs with daily precipitation at station 9 for (**a**) daytime and (**b**) nighttime during July and August in 2017 (except the missing days due to advanced microwave scanning radiometer (AMSR2) gaps between paths). Daily precipitation data were obtained from automated surface observing systems (ASOSs) operated by the Korea Meteorological Administration.

At nighttime, R<sup>2</sup> was significantly high in both S1 and S2, the RMSE was less than 1 ◦C, and the bias converged to zero for most stations under the clear sky conditions (Table 4). Under cloudy skies, S2 yielded higher R<sup>2</sup> at some stations compared to S1. Nevertheless, both S1 and S2 produced RMSE < 2 ◦C under the cloudy sky conditions, which suggests that the nighttime LSTs are relatively less affected by atmospheric phenomena, such as precipitation and clouds (Figure 10b).

#### *4.5. Two Scheme Combinations*

We further examined the combination of the two schemes (S1 and S2) to improve estimation performance, based on the difference of the LST distribution between clear and cloudy sky conditions, as analyzed in Section 4.1. The LSTs developed from S2 were used for days with relatively high LSTs, whereas S1 was used for days with lower temperatures. Appendix A describes the detailed combination methods of the daytime. For nighttime, the average of S1 and S2 LSTs was used since both schemes resulted in high accuracy [66].

Table 5 shows the results of the LOOCV of all-weather LSTs, as well as of S1, S2, and Scheme combined (SC) models, using bias-corrected in situ LSTs for daytime and nighttime. In the daytime SC, R <sup>2</sup> was relatively high and RMSE was distinctly lower at many stations when compared to S1 and S2. For nighttime, the SC exhibited significantly higher R<sup>2</sup> than did S1 and S2 for several stations, and the RMSE of SC was also generally close to S1 or S2, whichever was lower. The superiority of SC to S1 and S2 is consistent with previous studies' findings that the combination of different models improves performance by overcoming the limitations of each individual model [67]. Therefore, we

propose all-weather LSTs by combining two different schemes with an average R<sup>2</sup> of 0.82 and 0.74 and with RMSE of 2.5 ◦C and 1.4 ◦C for daytime and nighttime, respectively, over the 10 in situ stations.

**Table 5.** The leave one-station out cross-validation (LOOCV) results of the estimated 1 km all-weather LSTs from scheme 1(S1), scheme 2(S2) and scheme combined (SC) using 1 km bias-corrected in situ LSTs at 10 stations during July and August from 2013 to 2018 for daytime. Refer to Figure 1 for station numbers.


## **5. Conclusions**

In this study, we estimated all-weather 1 km MODIS LSTs for daytime and nighttime in South Korea for the humid summer days. We used eight AMSR2 BTs, three ACPs (i.e., MAST, Yast, and theta), and six auxiliary variables for the LST estimations based on RF machine learning. Both clear sky MODIS LSTs and the bias-corrected in situ LSTs under cloud sky conditions were used as a dependent variable to provide the models with the LST characteristics for clear and cloudy skies. We have proposed two schemes: A two- step approach (S1) first estimates 10 km LSTs and then involves the spatial downscaling of LSTs from 10 km to 1 km. S2 is a one-step algorithm that directly estimates the 1 km all-weather LSTs, which we have evaluated using a series of validations. In clear sky daytime, S2 slightly outperformed S1, but in cloudy sky daytime, S1 had an average R<sup>2</sup> of 0.78 and RMSE of 2.6◦C, an improvement when compared to S2 (R<sup>2</sup> of 0.74 and RMSE of 3.8 ◦C) for the bias-corrected 10 in situ stations. At nighttime, S1 and S2 showed no significant difference in performance regardless of cloud conditions. We further examined the combination of the two schemes (S1 and S2) in order to improve estimation performance, producing promising results, with R<sup>2</sup> of 0.82 and 0.74 and with RMSE of 2.5 ◦C and 1.4 ◦C for daytime and nighttime, respectively, over the 10 in situ stations. This study has revealed that the two-step-based S1 was better able to simulate low LSTs in cloudy sky, humid summer daytime conditions (i.e., rainy days) than S2. Moreover, we found that ACPs appear relatively important for the estimation of LSTs in light of spatial variability. To our knowledge, this is the first study to predict all-weather 1 km MODIS LSTs that focuses on humid summer days in great detail. Nevertheless, there is still room for further validation of the constructed LSTs over built-up areas since an insufficient number of in situ stations in urban land cover were used in this study.

Although we have focused this study on South Korea, we believe that the suggested schemes could be successfully used over other regions frequently covered with clouds in humid summer seasons. Recently, new MODIS Aqua LST datasets (MYD21A1D for daytime and MYD21A1N for nighttime) were produced utilizing the ASTER temperature/emissivity separation (TES) technique suitable for hot and humid conditions, although the approach has, thus far, only been tested using a small number of measurements [68]. It is expected that the proposed technique may be used to predict MYD21 LSTs under cloudy sky conditions.

**Author Contributions:** Conceptualization, C.Y.; formal analysis, C.Y. and J.I.; investigation, C.Y. and D.C.; methodology, C.Y., J.I., D.C., N.Y., J.X., and B.B.; supervision, J.I.; validation, C.Y.; writing—original draft, C.Y.; writing—review and editing, J.I., N.Y., J.X., and B.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Korea Meteorological Administration Research and Development Program under Grant KMIPA 2017–7010, by the National Research Foundation of Korea (NRF) (Grants: NRF-2017M1A3A3A02015981; NRF-2016M3C4A7952600; NRF-2018K2A9A2A06023758), by a grant (no. 20009742) of Disaster-Safety Industry Promotion Program funded by Ministry of Interior and Safety (NOIS), Korea, and by the Ministry of Science and ICT (MSIT), Korea (IITP-2020-2018-0-01424). CY was also supported by Global PhD Fellowship Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2018H1A2A1062207).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A**

### *A.1. Before-and after 1 km Bias-corrected in situ LSTs*

Tables A1 and A2 show the relationship between good-quality MODIS LSTs and in situ LSTs before and after bias correction under clear skies, in daytime and nighttime, respectively. In the daytime, before bias correction, the R<sup>2</sup> of the time series data showed a relatively significant range of 0.46–0.76, but the RMSE and bias were quite high. The significant spatial thermal difference within a 1 km grid in the daytime, especially for the summer season, could result in the underestimation of MODIS LSTs when compared to the in situ data [69]. After the bias correction, the RMSE decreased towards 2 ◦C at the 10 stations in which the range of errors were similar to that of the typical MODIS LST validation results (i.e., ~2 K; [59]). The bias converged close to 0, indicating a very slightly negative signal at some stations after correction. For the nighttime, before bias correction, the temporal R<sup>2</sup> was relatively higher than in the daytime for most stations, and the RMSE and bias were significantly lower than the daytime. These results are consistent with previous studies' findings that the MODIS LST validation error is much lower at nighttime than in the daytime [70,71]. After the bias correction, the RMSEs were under 1.5 ◦C and the bias was close to zero for all stations. The reason that the nighttime has a lower bias correction error than the daytime is possibly due to the higher thermal homogeneity in one MODIS grid (i.e., 1 km resolution) at the nighttime without solar shortwave radiation.




**Table A2.** The relationship between clear sky MODIS LSTs and the before-and-after 1 km bias-corrected in situ LSTs during July and August from 2013 to 2018 for the 10 stations at nighttime. Refer to Figure 1 for station numbers.
