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.

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