climpred.metrics._nmse¶
- climpred.metrics._nmse(forecast, verif, dim=None, **metric_kwargs)[source]¶
Normalized MSE (NMSE), also known as Normalized Ensemble Variance (NEV).
Mean Square Error (
mse
) normalized by the variance of the verification data.where 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 NMSE, 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 (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
comparison (str) – Name comparison needed for normalization factor fac, see
_get_norm_factor()
(Handled internally by the compute functions)
- Details:
minimum
0.0
maximum
∞
perfect
0.0
orientation
negative
better than climatology
0.0 - 1.0
worse than climatology
> 1.0
- Reference:
Griffies, S. M., and K. Bryan. “A Predictability Study of Simulated North Atlantic Multidecadal Variability.” Climate Dynamics 13, no. 7–8 (August 1, 1997): 459–87. https://doi.org/10/ch4kc4.
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.verify(metric='nmse', 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 0.1732 0.1825 0.217 0.2309 ... 0.5247 0.6749 0.7732