climpred.metrics._msess_murphy¶

climpred.metrics._msess_murphy(forecast: xarray.Dataset, verif: xarray.Dataset, dim: Optional[Union[str, List[str]]] = None, **metric_kwargs: Any) → xarray.Dataset[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 – Forecast.
verif – Verification data.
dim – Dimension(s) to perform metric over.
metric_kwargs – see xskillscore.pearson_r(), mean() and std()

Notes

minimum	-∞
maximum	1.0
perfect	1.0
orientation	positive

See also

References

https://www-miklip.dkrz.de/about/murcss/
Murphy [1988]

Example

>>> HindcastEnsemble = HindcastEnsemble.remove_bias(alignment="same_verifs")
>>> HindcastEnsemble.verify(
...     metric="msess_murphy",
...     comparison="e2o",
...     dim="init",
...     alignment="same_verifs",
... )
<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
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_initializations:     64
    number_of_members:             10
    alignment:                     same_verifs
    metric:                        msess_murphy
    comparison:                    e2o
    dim:                           init
    reference:                     []

climpred documentation

climpred.metrics._msess_murphy¶