climpred.metrics._msess¶

climpred.metrics._msess(forecast: xarray.Dataset, verif: xarray.Dataset, dim: Optional[Union[str, List[str]]] = None, **metric_kwargs: Any) → xarray.Dataset[source]¶

Mean Squared Error Skill Score (MSESS).

$MSESS = 1 - \frac{MSE}{\sigma^2_{ref} \cdot fac} = 1 - \frac{\overline{(f - o)^{2}}}{\sigma^2_{ref} \cdot fac},$

where $fac$ is 1 when using comparisons involving the ensemble mean (m2e, e2c, e2o) and 2 when using comparisons involving individual ensemble members (m2c, m2m, m2o). See _get_norm_factor().

This skill score can be intepreted as a percentage improvement in accuracy. I.e., it can be multiplied by 100%.

Note

climpred uses a single-valued internal reference forecast for the MSSS, in the terminology of Murphy [1988]. I.e., we use a single climatological variance of the verification data within the experimental window for normalizing MSE.

Parameters

forecast – Forecast.
verif – Verification data.
dim – Dimension(s) to perform metric over.
comparison – Name comparison needed for normalization factor fac, see _get_norm_factor() (Handled internally by the compute functions)
metric_kwargs – see xskillscore.mse()

Notes

minimum	-∞
maximum	1.0
perfect	1.0
orientation	positive
better than climatology	> 0.0
equal to climatology	0.0
worse than climatology	< 0.0

References

Griffies and Bryan [1997]
Murphy [1988]
Pohlmann et al. [2004]
Bushuk et al. [2018]

Example

>>> HindcastEnsemble.verify(
...     metric="msess", 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 0.8268 0.8175 0.783 0.7691 ... 0.4753 0.3251 0.2268
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
    comparison:                    e2o
    dim:                           init
    reference:                     []

climpred documentation

climpred.metrics._msess¶