climpred.metrics._nrmse¶
- climpred.metrics._nrmse(forecast, verif, dim=None, **metric_kwargs)[source]¶
Normalized Root Mean Square Error (NRMSE).
Root Mean Square Error (
rmse
) normalized by the standard deviation 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 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 (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:
Bushuk, Mitchell, Rym Msadek, Michael Winton, Gabriel Vecchi, Xiaosong Yang, Anthony Rosati, and Rich Gudgel. “Regional Arctic Sea–Ice Prediction: Potential versus Operational Seasonal Forecast Skill.” Climate Dynamics, June 9, 2018. https://doi.org/10/gd7hfq.
Hawkins, Ed, Steffen Tietsche, Jonathan J. Day, Nathanael Melia, Keith Haines, and Sarah Keeley. “Aspects of Designing and Evaluating Seasonal-to-Interannual Arctic Sea-Ice Prediction Systems.” Quarterly Journal of the Royal Meteorological Society 142, no. 695 (January 1, 2016): 672–83. https://doi.org/10/gfb3pn.
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='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