The following scores are to be calculated for all parameters against both analysis (except mean sea-level pressure) and observation:

## Wind

### Mandatory:

- rms vector wind error
- mean error of wind speed

## Other parameters

### Mandatory

- Mean error
- Root mean square (rms) error
- Correlation coefficient between forecast and analysis anomalies (not required for obs)
- S1 score (only for MSLP and only against analysis)

### Additional recommended

- mean absolute error
- rms forecast and analysis anomalies (not required for observations)
- standard deviation of forecast and analysis fields (not required for observations)

# Definition

The following definitions should be used

Mean error

where the sum of the weights

\[ S_w = \sum_{i=1}^n w_i \]

Root mean square (rms) error

Correlation coefficient between forecast and analysis anomalies

rms vector wind error

\[ rmse = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (\vec{V}_f - \vec{V}_v)_i^2 } \]Mean absolute error

\[ MAE = \frac{1}{S_w} \sum_{i=1}^n w_i | x_f - x_v |_i \]rms anomaly

\[ rmsa = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (x - x_c)_i^2 } \]standard deviation of field

\[ sd = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (x - M_x)_i^2 } \]where

\[ M_x = \frac{1}{S_w} \sum_{i=1}^n w_i x_i \]S1 score

\[ S1 = 100 \frac{\sum_{i=1}^n w_i (e_g)_i}{\sum_{i=1}^n w_i (G_L)_i} \]

Where:

\( x_f \)
= the forecast value of the parameter in question;
\( x_v \)
= the corresponding verifying value;
\( x_c \)
= the climatological value of the parameter; *n* = the number of grid points or observations in the verification area;
\( M_{f,c} \)
= the mean value over the verification area of the forecast anomalies from climate;
\( M_{v,c} \)
= the mean value over the verification area of the analysed anomalies from climate;
\( \vec{V}_f \)
= the forecast wind vector;
\( \vec{V}_v \)
= the corresponding verifying value;

The differentiation is approximated by differences computed on the verification grid:

\[ e_g = \left ( \left | \frac{\partial}{\partial x}(x_f-x_v)\right | + \left | \frac{\partial}{\partial y}(x_f-x_v)\right | \right ) \] \[ G_L = \max \left ( \left | \frac{\partial x_f}{\partial x}\right | , \left | \frac{\partial x_v}{\partial x}\right | \right) + \max \left ( \left | \frac{\partial x_f}{\partial y}\right | , \left | \frac{\partial x_v}{\partial y}\right | \right) \]The weights *w* _{i} applied at each grid point or observation location are defined as

Verification against analyses: \( w_i = \cos \theta_i \) , cosine of latitude at the the grid point

*i*Verification against observations: \( w_i = 1/n \) , all observations have equal weight