climpred.metrics._msess_murphy¶

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

Murphy’s Mean Square Error Skill Score (MSESS).

$MSESS_{Murphy} = r_{fo}^2 - [\text{conditional bias}]^2 - [\frac{\text{(unconditional) bias}}{\sigma_o}]^2,$

where $r_{fo}^{2}$ represents the Pearson product-moment correlation coefficient between the forecast and verification data and $\sigma_{o}$ represents the standard deviation of the verification data over the experimental period. See conditional_bias and unconditional_bias for their respective formulations.

Parameters

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

:param mean() and std():

Details:

minimum	-∞
maximum	1.0
perfect	1.0
orientation	positive

See also

Reference:

https://www-miklip.dkrz.de/about/murcss/
Murphy, Allan H. “Skill Scores Based on the Mean Square Error and Their Relationships to the Correlation Coefficient.” Monthly Weather Review 116, no. 12 (December 1, 1988): 2417–24. https://doi.org/10/fc7mxd.

Example

>>> HindcastEnsemble = HindcastEnsemble.remove_bias(alignment='same_verifs')
>>> HindcastEnsemble.verify(metric='msess_murphy', 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 0.8306 0.8351 0.8295 0.8532 ... 0.8471 0.813 0.8097