Metrics Formula Range
True Positive (TP) \(\frac{\sum_{n=1}^{N}{{(B}_{n}=1)\cap{(S}_{n}=1)}}{N}\times 100\%\) (0, 100) %
False Negative (FN) \(\frac{\sum_{n=1}^{N}{{(B}_{n}=1)\cap{(S}_{n}=0)}}{N}\times 100\%\) (0, 100) %
False Positive (FP) \(\frac{\sum_{n=1}^{N}{{(B}_{n}=0)\cap{(S}_{n}=1)}}{N}\times 100\%\) (0, 100) %
Flood area ratio (RF) \(R_{F}=\frac{\text{Area}_{s}}{\text{Area}_{b}}\) (0, 1)
Mean water depth ratio (RH) \(R_{H}=\frac{\sum_{i=1}^{n}H_{s,i}}{\sum_{i=1}^{n}H_{b,i}}\) (0, 1)
Surface water volume ratio (RV) \(R_{V}=\frac{\sum_{i=1}^{n}{H_{s,i}\times\text{Area}_{s}}}{\sum_{i=1}^{n}{H_{b,i}\times\text{Area}_{b}}}\) (0, 1)
Initial inundation time differences (Tinit) \(T_{\text{init}}=T_{s}-T_{b}\) (-T, +T)
Inundation duration differences (D) \(D=D_{s}-D_{b}\) (-T, +T)
Nash- Sutcliffe Efficiency coefficient (NSE) \(1-\frac{\sum_{n=1}^{N}{(S_{n}-O_{n})}^{2}}{\sum_{n=1}^{N}{(S_{n}-\overset{\overline{}}{O})}^{2}}\) (-inf, 1)
Root Mean Square Error (RMSE) \(\sqrt{\frac{1}{N}\sum_{n=1}^{N}{(S_{n}-O_{n})}^{2}}\) (0, inf)
Correlation Coefficient (CC) \(\frac{\sum_{i=1}^{n}{(o_{i}-\overset{\overline{}}{o})(s_{i}-\overset{\overline{}}{s})}}{\sqrt{\sum_{i=1}^{n}{(s_{i}-\overset{\overline{}}{s})}^{2}}\sqrt{\sum_{i=1}^{n}{(o_{i}-\overset{\overline{}}{o})}^{2}}}\) (0, 1)