Printable version

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

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The following definitions should be used
Mean error Image Removed error 

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M = \frac{1}{S_w} \sum_{i=1}^n w_i (x_f - x_v)_i

where the sum of the weights

Mathdisplay
S_w = \sum_{i=1}^n w_i

Root mean square (rms) error Image Removed

Mathdisplay
rmse = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (x_f - x_v)_i^2 }

Correlation coefficient between forecast and analysis anomalies
Image Removed
rms vector wind error Image Removed
Mean absolute error Image Removed
rms anomaly Image Removed
standard deviation of field Image Removed where Image Removed
S1 score Image Removed
Where:
Image Removed

Mathdisplay
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

Mathdisplay
rmse = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (\vec{V}_f - \vec{V}_v)_i^2 }

Mean absolute error

Mathdisplay
MAE = \frac{1}{S_w} \sum_{i=1}^n w_i | x_f - x_v |_i

rms anomaly

Mathdisplay
rmsa = \sqrt {\frac{1}{S_w} \sum_{i=1}^n w_i (x - x_c)_i^2 }

standard deviation of field 

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

where

Mathdisplay
M_x = \frac{1}{S_w} \sum_{i=1}^n w_i x_i

S1 score

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

Where:

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x_f

= the forecast value of the parameter in question;

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x_v

Image Removed = the corresponding verifying value;

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x_c

Image Removed = the climatological value of the parameter
Image Removed ; n = the number of grid points or observations in the verification area;

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M_{f,c}

Image Removed = the mean value over the verification area of the forecast
anomalies from climate
Image Removed ;

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M_{v,c}

= the mean value over the verification area of the analysed
anomalies from climate
Image Removed ;

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\vec{V}_f

= the forecast wind vector;

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\vec{V}_v

= the corresponding verifying value;

The
Image Removed = Image Removed
Image Removed = Image Removed
where the differentiation is approximated by differences computed on the verification grid.
The weights Image Removed :

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e_g = \left ( \left | \frac{\partial}{\partial x}(x_f-x_v)\right | + \left | \frac{\partial}{\partial y}(x_f-x_v)\right | \right )

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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:

...

• Mathinline
  w_i = \cos \theta_i

  , cosine of latitude at the the grid point i

• Verification against observations:

...

• Mathinline
  w_i = 1/n

  , all observations have equal weight