Table 2 Evaluation metrics for comparing the performance. The thresholds are set as 1 and 4  mm which are commonly used. Notation. Let N represent the number of pixels, while \(f_i\) and \(p_i\) denote the true observations and the predicted radar frames, respectively. \(MAX_{f}\) represents the maximum rainfall intensity. TP, TN, FP, and FN stand for true positives, true negatives, false positives, and false negatives, respectively, between \(f_{i}^{\theta }\) and \(p_{i}^{\theta }\). \(N_x\) and \(N_y\) represent the sums of the x-grid and y-grid divided by the number of neighboring grid cells, denoted by r.

From: Self-clustered GAN for precipitation nowcasting

\(\text {MSE} = \frac{1}{N} \sum _{i=1}^{N} (f_i - p_i)^2,\)

\(\text {PSNR} = 10 \log \left( \frac{{\text {MAX}_{f}}^2}{\text {MSE}} \right) ,\)

\(\text {CSI} = \frac{\text {TP}}{\text {TP}+\text {FP}+\text {FN}},\)

\(\text {ETS} = \frac{\text {TP}-\frac{1}{N}(\text {TP}+\text {FP})(\text {TP}+\text {FN})}{\text {TP}+\text {FN}+\text {FP}-\frac{1}{N}(\text {TP}+\text {FP})(\text {TP}+\text {FN})},\)

\(\text {HSS}= \frac{2(TP\times TN - FN \times FP)}{FN^{2} + FP^{2}+2(TP\times TN) + (TP+TN)(FN+FP)},\)

\(\text {FSS}_r = 1 - \frac{\text {FBS}_r}{\text {FBS}_r^{\text {ref}}},\)

\(\quad \text {FBS}_r = \frac{1}{N_{x}N_{y}} \sum _{i=1}^{N_{x}} \sum _{j=1}^{N_y} [f_{(i,j)} - p_{(i,j)}]^2,\)

\(\quad \text {FBS}_r^{\text {ref}} = \frac{1}{N_{x}N_{y}}\left[ \sum _{i=1}^{N_{x}}\sum _{j=1}^{N_y} f_{(i,j)}^{2} + \sum _{i=1}^{N_{x}} \sum _{j=1}^{N_y} p_{(i,j)}^{2} \right] .\)

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