## 4 Results
### SST Coefficients of COMS/MI  
Figure 4 shows the differences between the estimated SST and in situ SST as a function of in situ SST for the algorithms of OSI SAF and the present study for daytime and nighttime data. One of significant features of the present formulations can be found at low range of SST, especially of less than 10 \({}^{\circ}\)C. As mentioned earlier in Figure 4a,b, the OSI SAF algorithms resulted in high overestimation of low SSTs. Although this might be related to the unequal distribution of matchup data that are concentrated around 30 \({}^{\circ}\)C as shown in Figures 3 and 4, the overestimation should be reduced though the selection of regionally appropriate formulation. By contrast, the MCSST and NLSST formulation of this study do not reveal such significant overestimation problems at low SST range (Figure 4d-f). Regardless of daytime and nighttime, MCSSTs showed near-zero bias in most range of in situ temperature ranges (Figure 4c,d). This implies that the present MCSST algorithm can contribute to solving the trend of overestimation at low temperature range. In case of NLSST as shown in Figure 4e,f, there were slight overestimations at low temperature range (<10 \({}^{\circ}\)C) because very cold and dry atmospheric conditions were not sufficiently reflected in the estimation of coefficients. The other capability of NLSST algorithm can be detected from the errors with insignificant biases at high temperature ranges of greater than 25 \({}^{\circ}\)C, which improves the slight underestimation of MCSSTs (<0.2 \({}^{\circ}\)C) as shown in Figure 4d,f. The NLSST approaches seem to reduce the nonlinear effect of water vapor at high temperature [17, 41]. Figure 3: (**a**) Spatial distribution of the number of matchup points between COMS and in situ measurements in bins of 2\({}^{\circ}\)\(\times\) 2\({}^{\circ}\) and the histograms of the matchups with respect to (**b**) month, (**c**) local time (hour), (**d**) latitude (\({}^{\circ}\)N), and (**e**) in situ temperature (\({}^{\circ}\)C) for the period from April 2011 to March 2015. Values in last two columns in Table 3 represent the RMSE and bias errors of the previously-known SST equations of MCSST and NLSST using the split window or the triple window. The RMSEs range from 0.29 \({}^{\circ}\)C to 0.71 \({}^{\circ}\)C depending on algorithm and time. Although the two equations of [49] had the smallest errors, they were rejected based on the results of [PERSON] et al. [22]. The MCSST and NLSST algorithms of the present study, the Equations (1) and (2), show the RMSEs of about 0.67 \({}^{\circ}\)C and 0.58 \({}^{\circ}\)C for daytime data and 0.79 \({}^{\circ}\)C and 0.71 \({}^{\circ}\)C for nighttime data, respectively (Table 4). These errors are relatively high of about 0.03 \({}^{\circ}\)C (day) and 0.08 \({}^{\circ}\)C (night) as compared with those of the algorithms in [20]. However, the estimated NLSST of OSI SAF exhibited large scatters of the differences especially at low SST range of less than about 10 \({}^{\circ}\)C. In addition, the NLSST errors of daytime OSI SAF presented a tendency of overestimation in that they were positive at low temperatures of about 0.5 \({}^{\circ}\)C-1.5 \({}^{\circ}\)C as shown in the Figure 4a. Such overestimation of SST seem to be amplified as the water temperature decreases from 15 \({}^{\circ}\)C to 5 \({}^{\circ}\)C. The estimated OSI SAF NLSSTs exhibited much more positive RMS errors in the nighttime, amounting to 1.8 \({}^{\circ}\)C at a range of low SST about 5 \({}^{\circ}\)C, than those in the daytime. Figure 4: Distributions of NLSST errors of OSI SAF during the (**a**) daytime and (**b**) nighttime, MCSST errors during the (**c**) daytime and (**d**) nighttime, and NLSST errors in the (**e**) daytime and (**f**) nighttime as a function of the in situ SST (\({}^{\circ}\)C). The color represents the percentage of the data to the total number of matchup points in each bin; error bars represent the standard deviation of SST errors of each interval.