climpred.metrics._nmae¶

climpred.metrics._nmae(forecast, verif, dim=None, **metric_kwargs)[source]¶

Normalized Mean Absolute Error (NMAE).

Mean Absolute Error (mae) normalized by the standard deviation of the verification data.

$NMAE = \frac{MAE}{\sigma_{o} \cdot fac} = \frac{\overline{|f - o|}}{\sigma_{o} \cdot fac},$

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 NMAE, in the terminology of Murphy 1988. I.e., we use a single climatological standard deviation of the verification data within the experimental window for normalizing MAE.

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 mae()

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='nmae', 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 0.3426 0.3532 0.3914 0.3898 ... 0.6303 0.7194 0.7726