The following definitions should be used
Mean error
M = \frac{1}{M_w} \sum_{i=1}^n w_i (x_f - x_v)_i |
where the sum of the weights
Root mean square (rms) error
rms = \sqrt {\frac{1}{M_w} \sum_{i=1}^n w_i (x_f - x_v)_i^2 } |
Correlation coefficient between forecast and analysis anomalies
r = \frac{\sum_{i=1}^n w_i (x_f-x_c-M_{f,c})_i (x_v-x_c-M_{v,c})_i}{\sqrt{\left(\sum_{i=1}^n w_i (x_f-x_c-M_{f,c})_i^2 \right) \left(\sum_{i=1}^n w_i (x_v-x_c-M_{v,c})_i^2 \right) }} |
rms vector wind error
rms = \sqrt {\frac{1}{M_w} \sum_{i=1}^n w_i (\vec{V}_f - \vec{V}_v)_i^2 } |
Mean absolute error
MAE = \frac{1}{M_w} \sum_{i=1}^n w_i | x_f - x_v |_i |
rms anomaly
rmsa = \sqrt {\frac{1}{M_w} \sum_{i=1}^n w_i (x - x_c)_i^2 } |
standard deviation of field
sd = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (x - M_x)_i^2 } |
where
M_x = \frac{1}{M_w} \sum_{i=1}^n w_i x_i |
S1 score
S_1 = 100 \frac{\sum_{i=1}^n w_i (e_g)_i}{\sum_{i=1}^n w_i (G_L)_i} |
Where:
