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climpred.metrics._nrmse

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climpred.metrics._nrmse#

climpred.metrics._nrmse(forecast: Dataset, verif: Dataset, dim: str | List[str] | None = None, **metric_kwargs: Any) → Dataset[source]#

Compute Normalized Root Mean Square Error (NRMSE).

Root Mean Square Error (rmse) normalized by the standard deviation of the verification data.

NRMSE = \frac{RMSE}{\sigma_{o}\cdot\sqrt{fac}} = \sqrt{\frac{MSE}{\sigma^{2}_{o}\cdot fac}} = \sqrt{ \frac{\overline{(f - o)^{2}}}{ \sigma^2_{o}\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().

Note

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

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.rmse()

Notes

minimum

0.0

maximum

∞

perfect

0.0

orientation

negative

better than climatology

0.0 - 1.0

worse than climatology

> 1.0

References

Example

>>> HindcastEnsemble.verify(
...     metric="nrmse", 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 0.4161 0.4272 0.4658 0.4806 ... 0.7244 0.8215 0.8793
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:                        nrmse
    comparison:                    e2o
    dim:                           init
    reference:                     []
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