Table 3.

List of the statistical and categorical metrics, used in the present study for the evaluation of precipitation products.

Evaluation Indexes	Describing	Type	Equation	Unit	Range	Optimal value
Mean Absolute Error (MAE)	the average magnitude of the forecast errors	statistical	$\text{MAE}=\frac{\sum _{\text{i}=1}^{\text{N}}\left|{\text{P}}_{\text{i}}-{\text{O}}_{\text{i}}\right|}{\text{N}}$	mm	[0~∞)	0
correlation coefficient (R)	the degree of collinearity between observed precipitation data and the gridded products	statistical	$\text{R}=\frac{\sum _{\text{i}=1}^{\text{N}}\left(\left|{\text{P}}_{\text{i}}-{\overline{\text{P}}}_{\text{i}}\right|\right)\left(\left|{\text{O}}_{\text{i}}-{\overline{\text{O}}}_{\text{i}}\right|\right)}{\sqrt{{\sum _{\text{i}=1}^{\text{N}}\left(\left|{\text{P}}_{\text{i}}-{\overline{\text{P}}}_{\text{i}}\right|\right)}^2}\times \sqrt{\sum _{\text{i}=1}^{\text{N}}{\left(\left|{\text{O}}_{\text{i}}-{\overline{\text{O}}}_{\text{i}}\right|\right)}^2}}$	NA	[-1~1]	1
BIAS score (BIAS)	the ratio of the frequency of forecast events to the frequency of observed events	categorical	$\text{BIAS}=\frac{\text{H}+\text{F}}{\text{H}+\text{M}}$	NA	[0~∞)	1
False Alarm Ratio (FAR)	the fraction of events, detected by the product but not observed	categorical	$\text{FAR}=\frac{\text{F}}{\text{H}+\text{F}}$	NA	[0~1]	0
Probability Of Detection (POD)	the fraction of the observed precipitation events, which were detected by the assessed product	categorical	$\text{POD}=\frac{\text{H}}{\text{H}+\text{M}}$	NA	[0~1]	1
Probability Of False Detection (POFD)	the fraction of the number of the precipitation events detected by the products but not observed by rain gauge stations	categorical	$\text{POFD}=\frac{\text{F}}{\text{F}+\text{C}}$	NA	[0~1]	0
Critical Success Index (CSI)	the proportion of events that were predicted correctly	categorical	$\text{CSI}=\frac{1}{\left(\frac{1}{1-\text{FAR}}\right)+\left(\frac{1}{\text{POD}}\right)-1}$	NA	[0~1]	1
Heidke Skill Score (HSS)	the fractional improvement of the forecast over the standard forecast	categorical	$\text{HSS}=\frac{2\left(\text{HC}-\text{FM}\right)}{\left(\text{H}+\text{M}\right)\left(\text{M}+\text{C}\right)+\left(\text{H}+\text{F}\right)\left(\text{F}+\text{C}\right)}$	NA	[-1~1]	1

Note: N is the number of samples; O_i is the observed precipitation, P_i is the estimated precipitation from the evaluated products, Ō_i and P_i are the average of corresponding data during N events.