TABLE 2.

Verification metrics list. All metrics are calculated across time (using index i, where N is the total number of times in the dataset), separately at each spatial location (grid cell).

Statistical index	Equation	Range	Perfect value
Bias (subtractive)	$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}A=\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\left({\mathrm{R}\mathrm{F}}_i-{\mathrm{R}\mathrm{S}}_i\right)$	−∞ to ∞	0
Root mean squared error (RMSE)	$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{N}\sum {\left({\mathrm{R}\mathrm{F}}_i-{\mathrm{R}\mathrm{S}}_i\right)}^2}$	0 to ∞	0
Pearson's correlation coefficient (r)	$r=\frac{\sum \left({\mathrm{R}\mathrm{F}}_i-\stackrel{-}{\stackrel{-}{\mathrm{R}\mathrm{F}}}\right)\left({\mathrm{R}\mathrm{S}}_i-\stackrel{-}{\stackrel{-}{\mathrm{R}\mathrm{S}}}\right)}{\sqrt{\sum {\left({\mathrm{R}\mathrm{F}}_i-\stackrel{-}{\stackrel{-}{\mathrm{R}\mathrm{F}}}\right)}^2\sum {\left({\mathrm{R}\mathrm{S}}_i-\stackrel{-}{\stackrel{-}{\mathrm{R}\mathrm{S}}}\right)}^2}}$	−1 to 1	1
Accuracy (A); Proportion Correct	$A=\frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}+\mathrm{T}\mathrm{N}}$	0 to 1	1
Threat score (TS); Critical success Index	$\mathrm{T}\mathrm{S}=\frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}}$	0 to 1	1
False alarm rate (FAR)	$\mathrm{F}\mathrm{A}\mathrm{R}=\frac{\mathrm{F}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}$	0 to 1	0
Probability of detection (POD)	$\mathrm{P}\mathrm{O}\mathrm{D}=\frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}$	0 to 1	1
Brier score (BS)	$\mathrm{B}\mathrm{S}=\frac{1}{N}\sum {\left(F_i-O_i\right)}^2$	0 1	0

Abbreviations: $F_i$, the probability that was forecast on day $i$; $\text{FN}$, false negative, missed event (event was not forecast but did occur in observation); $\text{FP}$, false positive, false alarm (event was forecast, but did not occur in observation); $O_i$, The actual outcome that was observed on day $i$; ${\text{RF}}_i$, rainfall forecast from NWM (unit: Mm day⁻¹) on day $i$; ${\text{RS}}_i$, Rainfall observation from satellite (unit: Mm day⁻¹) on day $i$; TN, True negative, correct negative (event was not forecast and did not occur in observation); $\mathrm{TP}$, True positive, hit (event was forecast and occurred in observations).