# Comparison of SEVIRI-Derived Cloud Occurrence Frequency and Cloud-Top Height with A-Train Data
## 2 Materials and Methods
### Methodology
#### 2.2.3 Validation Methods and Scores  
The statistical validation scores are calculated using the daily and monthly datasets merged from each individual matchup pixel along the matchup track. In the case of cloud occurrence frequency (COF), the SEVIRI parallax-corrected CTH product is used. If CTH data on the corresponding pixel exists, it is assumed to be cloudy, and vice versa. A cloudy pixel from cloud detection can be considered a clear pixel when the simulated radiance does not sufficiently converge to the observed radiance in the CTH retrieval process and also when the error from a different satellite viewing angle is reduced. The CTH are not retrieved over the partly cloudy pixel, thus the partly cloudy pixels are not dealt with in the COF analysis. A binary representation of the results, where cloud cover values of 1 and 0 for cloudy and clear conditions, respectively, are used for each individual pixel. The results are accumulated over the full matchup tracks for each individual month to obtain the scores for COF. It should be noted that the scores are computed by using the matchup data that contain valid CTH values in all three products, CPR, CALIOP, and SEVIRI. For validation with CPR or CALIOP, the mean COF and bias can be computed as  
\[\text{MeanCOF}=\frac{\sum cloudy}{\sum allpixels} \tag{1}\]  
\[\text{bias}=\text{MeanCOF}_{SEVIRI}-\text{MeanCOF}_{ref} \tag{2}\]  
For the other scores, we used the following definitions referring to the notations in the contingency matrix in Table 1[22]. Probability of detection (POD) for both cloudy and cloud-free conditions:  
\[\text{POD}_{cloudy}=\frac{a}{a+b} \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \hline  & **SEVIRI Cloudy** & **SEVIRI Clear** \\ \hline Reference cloudy (CPR or CALIOP) & a: hits & b: misses \\ Reference clear (CPR or CALIOP) & c: false positives & d: correct negatives \\ \hline \hline \end{tabular} Note: CPR: Cloud Profiling Radar; CALIOP: Cloud-Aerosol LiDAR with Orthogonal Polarization.  
\end{table} 
Table 1: Contingency matrix for comparison of Spinning Enhanced Visible and Infrared Imager (SEVIRI) cloud occurrence frequency (COF) with the cloud products from A-Train. \[\text{POD}_{clear}=\frac{d}{c+d} \tag{4}\]  
False alarm ratio (FAR) for both cloudy and cloud-free conditions:  
\[\text{FAR}_{cloudy}=\frac{c}{a+c} \tag{5}\]  
\[\text{FAR}_{clear}=\frac{b}{b+d} \tag{6}\]  
Proportion correct (PC):  
\[\text{PC}=\frac{a+d}{a+b+c+d} \tag{7}\]  
[PERSON]'s skill score (KSS) or True Skill Statistic (TSS):  
\[\text{KSS}=\frac{a\cdot d-b\cdot c}{(a+b)\cdot(c+d)} \tag{8}\]  
The POD and FAR scores estimate the SEVIRI efficiency in determining cloudy or clear conditions. POD (FAR) values are desired to be as high (low) as possible. The PC, which is also known as the accuracy or hit rate, is a condensed measure of the overall efficiency of cloud detection. Finally, the KSS quantity is a counter measure because the PC is heavily influenced by the results for the most common category and can sometimes be misleading. For example, if a case is almost totally cloud-free and all of the few cloudy portions are missed by SEVIRI, the PC score will still be high. The KSS score is more robust: \(1\) very good; \(-1\) very bad. For cloud detection schemes, values above 0.5 show that the scheme is reliable and skilled. Along with quantitative analysis using the statistical scores, qualitative analysis was also conducted to evaluate the cloud detection performance of SEVIRI. The COF distribution in the SEVIRI observation area was analysed, and its seasonal variation and detection tendency over land and ocean was investigated. SEVIRI CTHs were compared with the corresponding measured maximum cloud-top values as interpreted from CPR and CALIOP vertical cloud classification. In the case of CTH, we restricted the number of validation scores to just two, including bias (mean error) and standard deviation (bias-corrected root-mean-square differences).