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.

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

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 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)
metric_kwargs (dict) – see mse()

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.