## 4 Data and Methodology
### Methodology
#### 4.2.2 Categorical Technique  
Another assessment technique of satellite estimation/model forecast is using a contingency table that reflects the frequency of \"Yes\" and \"No\" of the satellite estimation/forecast model (see Table 3).  
A dichotomous estimates says, \"Yes, an event will happen\", or \"No, the event will not happen\". By using this table for daily precipitation, a set of statistical indices are shown as follows:  
Probability of detection (POD) responds to the question of what fraction of the observed \"Yes\" events was correctly estimated/forecasted. The perfect score is \(1\).  
\[POD=\frac{a}{a+c} \tag{7}\]  
False alarm ratio (FAR) deals with the question of what fraction of the estimated/forecasted \"Yes\" events did not occur. The ideal score is \(0\).  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & & \multicolumn{2}{l}{**Satellite/Model**} & \\ \hline \multirow{4}{*}{**Rain-Gauge**} & \multirow{2}{*}{**Yes**} & **Yes** & **No** & **total** \\ \cline{3-4}  & & **Yes** & **Hits (a)** & **Misses (c)** & **a + c** \\  & **No** & **False alarms (b)** & **Correct negative (d)** & **b + d** \\  & total & **a + b** & **c + d** & **total** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Contingency table to evaluate precipitation occurrence by satellite products.  
\[FAR=\ \frac{b}{a+b} \tag{8}\]  
Critical success index (CSI) or threat score (TS), answers the question of how well the estimated/forecasted \"Yes\" events corresponded to the observed \"Yes\" events. The perfect score is 1.  
\[CSI=\ \frac{a}{a+b+c} \tag{9}\]  
Accuracy (fraction correct) measures the fraction of correct estimates/forecasts and its perfect score is 1.  
\[Accuracy=\ \frac{a+d}{total} \tag{10}\]  
Bias (frequency bias) answers the question of how the estimated/forecasted frequency of \"Yes\" events compared to the observed frequency of \"Yes\" events. Range of values is 0 to \(\infty\) with a perfect score of 1.  
\[Bias=\ \frac{a+b}{a+c} \tag{11}\]  
Probability of false detection (POFD) deals with the question of what fraction of observed \"No\" events were incorrectly estimated/forecasted as \"Yes\". The range varies from 0 to 1 and the perfect score is 0.  
\[POFD=\ \frac{b}{d+b} \tag{12}\]  
Success ratio (SR) responds to the question of what fraction of estimated/forecasted \"Yes\" events was correctly observed. The range is 0 to 1 and the perfect score is 1.  
\[SR=\frac{b}{a+b} \tag{13}\]  
Equitable threat score (ETS) or Gilbert skill score, answers the question of how well the estimated/forecasted \"Yes\" events corresponded to the observed \"Yes\" events. The range is \(-1/3\) to 1 and the perfect score is 1. For rare events, the minimum ETS value is near 0, while the absolute minimum is obtained if the event has a climatological frequency of 0.5, and there are no hits. If the score goes below 0 then the chance forecast is preferred to the actual forecast, and the forecast is said to be unskilled.  
\[ETS=\ \frac{a-a_{random}}{a+b+c-a_{random}} \tag{14}\]  
Odds ratio (OR) deals with the ratio of the odds of \"yes\" estimates/forecasts being correct over the odds of \"Yes\" estimates/forecasts being wrong. Odds ratio range is 0 to \(\infty\), 0 indicates no skill and the perfect score is \(\infty\).  
\[OR=\frac{a*d}{c*b} \tag{15}\]  
Hanssen and [PERSON] discriminant (HK) or true skill statistic (TSS) covers the question of how well the estimates/forecast separated the \"Yes\" events from the \"No\" events. The range is \(-1\) to 1, while 0 indicates no skill and 1 is the perfect score [35; 36; 37].  
\[TSS=\ \frac{a}{a+c}-\ \frac{b}{b+d} \tag{16}\]  
\[ORSS=\ \frac{a*d-c*b}{a*d+c*b} \tag{17}\]  
where \(a\) represents the number of times that observed rain is correctly detected, \(b\) is the number of times that rain is detected but not observed, \(c\) is the number of times that observed rain is not detected, \(d\) is the number of times that observed and estimated did not occur and _total_ is the sample size and \[a_{random}=\ \frac{(a+c)*(a+\ b)}{total} \tag{18}\]