climpred.metrics._mse¶

climpred.metrics._mse(forecast, verif, dim=None, **metric_kwargs)[source]¶

Mean Sqaure Error (MSE).

$MSE = \overline{(f - o)^{2}}$

The average of the squared difference between forecasts and verification data. This incorporates both the variance and bias of the estimator. Because the error is squared, it is more sensitive to large forecast errors than mae, and thus a more conservative metric. For example, a single error of 2°C counts the same as two 1°C errors when using mae. On the other hand, the 2°C error counts double for mse. See Jolliffe and Stephenson, 2011.

Parameters

forecast (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
metric_kwargs (dict) – see mse()

Details:

minimum	0.0
maximum	∞
perfect	0.0
orientation	negative

See also

mse()

Reference:

Ian T. Jolliffe and David B. Stephenson. Forecast Verification: A Practitioner’s Guide in Atmospheric Science. John Wiley & Sons, Ltd, Chichester, UK, December 2011. ISBN 978-1-119-96000-3 978-0-470-66071-3. URL: http://doi.wiley.com/10.1002/9781119960003.

Example

>>> HindcastEnsemble.verify(metric='mse', comparison='e2o', alignment='same_verifs',
...     dim='init')
<xarray.Dataset>
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead) float64 0.006202 0.006536 0.007771 ... 0.02417 0.02769