## 3 Collocation and Evaluation Methodology
### Evaluation Methodology  
To quantitatively compare the cloud mask results, three validation scores (i.e., Probability of Detection (_POD_), False-Alarm Ratio (_FAR_), and Hit Rate (_HR_)) were employed to analyze the statistics of the agreement between the two systems. The definitions are given by [PERSON] et al. (2018):  
\[PODcld = \frac{a}{a+c} \tag{1}\] \[PODclr = \frac{d}{b+d}\] (2) \[FARcld = \frac{b}{a+b}\] (3) \[FARclr = \frac{c}{c+d}\] (4) \[HR = \frac{a+d}{a+b+c+d} \tag{5}\]  
where \(a\) and \(d\) represent the numbers of collocated samples that are all identified as cloudy and clear, respectively, by both AGRI and MODIS; \(b\) represents the number of matched samples determined as cloudy by AGRI but clear by MODIS; \(c\) represents the number of collocated samples classified as clear by AGRI but cloudy by MODIS. Note that the categories of \"probably cloudy\" and \"probably clear\" scenes are not included in the statistics here (i.e., only the pixels that classified as \"cloudy\" or \"clear\" by both AGRI and MODIS are considered here for comparison). _PODcld_ and _PODclr_ represent the efficiency of the AGRI cloud mask algorithm for detecting the cloudy and clear condition, respectively. The higher the _POD_ value, the higher the efficiency. _FARcld_ and _FARclr_ indicate that the AGRI cloud mask algorithm misjudged collocated samples as \"cloudy\" and \"clear\", respectively. The _HR_ or accuracy represents the overall efficiency of the AGRI cloud mask algorithm. Specifically, _HR_ represents the identification accuracy of AGRI's cloud mask when only the detection results of cloud-sky and clear-sky conditions are compared, without considering the detection results of probably cloudy and probably clear conditions. At the extremes, there are two cases: (1) if the AGRI cloud mask agrees perfectly with MODIS, the _POD_ and the _HR_ will be one, and the _FAR_ will be zero, while (2) no agreement results in the _POD_ and the _HR_ being zero, and the _FAR_ being one.  
To quantitatively compare _CTH_, similar to [PERSON] et al. (2018), four parameters (i.e., Standard Deviation (_STD_), Mean Absolute Error (_MAE_), Mean Bias Error (_MBE_), and Correlation Coefficient (_CC_)) were used to quantify the _CTH_ statistics of differences between AGRI and MODIS.  
\[STD=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\bigl{(}\Delta x_{i}-\overline{\Delta x} \bigr{)}^{2}} \tag{6}\]  
\[MAE=\frac{1}{N}\sum_{i=1}^{N}\lvert\Delta x_{i}\rvert \tag{7}\]  
\[MBE=\frac{1}{N}\sum_{i=1}^{N}\Delta x_{i} \tag{8}\]  
\[CC=\frac{\sum_{i=1}^{N}[(x_{Ai}-\overline{x_{A}})(x_{Mi}-\overline{x_{M}})]}{ \sqrt{\sum_{i=1}^{N}(x_{Ai}-\overline{x_{A}})^{2}}\sqrt{\sum_{i=1}^{N}(x_{Mi}- \overline{x_{M}})^{2}}} \tag{9}\]where \(x_{Ai}\) and \(x_{Mi}\) represent the AGRI CTH and MODIS CTH, respectively, and \(N\) represents the numbers of collocated samples. \(\Delta x_{i}=x_{Ai}-x_{Mi}\), \(\overline{\Delta x}=\frac{1}{N}\sum_{i}^{N}\Delta x_{i}\), \(\overline{x_{A}}=\frac{1}{N}\sum_{i=1}^{N}x_{Ai}\), \(\overline{x_{M}}=\frac{1}{N}\sum_{i=1}^{N}x_{Mi}\).  
Either one, or several 1-km pixel-level MODIS CTH retrievals can fall within a single 4-km AGRI CTH retrieval. Therefore, similar to [PERSON] et al. [36], it was the distance weighted averaged MODIS CTH that was compared to the AGRI products within the AGRI 4-km FOV.  
\[CTH=\frac{\sum_{i=1}^{N}\biggl{[}\biggl{(}1-\frac{r_{i}^{2}}{R^{2}}\biggr{)} CTH_{i}\biggr{]}}{\sum_{i=1}^{N}\biggl{[}\biggl{(}1-\frac{r_{i}^{2}}{R^{2}} \biggr{)}\biggr{]}} \tag{10}\]