climpred.metrics._crpss¶

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

Continuous Ranked Probability Skill Score.

This can be used to assess whether the ensemble spread is a useful measure for the forecast uncertainty by comparing the CRPS of the ensemble forecast to that of a reference forecast with the desired spread.

$CRPSS = 1 - \frac{CRPS_{initialized}}{CRPS_{clim}}$

Note

When assuming a Gaussian distribution of forecasts, use default gaussian=True. If not gaussian, you may specify the distribution type, xmin/xmax/tolerance for integration (see crps_quadrature()).

Parameters

forecast (xr.object) – Forecast with member dim.
verif (xr.object) – Verification data without member dim.
dim (list of str) – Dimension to apply metric over. Expects at least member. Other dimensions are passed to xskillscore and averaged.
metric_kwargs (dict) –
optional gaussian (bool, optional): If True, assume Gaussian distribution for

baseline skill. Defaults to True.

see crps_ensemble(), crps_gaussian() and crps_quadrature()

Details:

minimum	-∞
maximum	1.0
perfect	1.0
orientation	positive
better than climatology	> 0.0
worse than climatology	< 0.0

Reference:

Matheson, James E., and Robert L. Winkler. “Scoring Rules for Continuous Probability Distributions.” Management Science 22, no. 10 (June 1, 1976): 1087–96. https://doi.org/10/cwwt4g.
Gneiting, Tilmann, and Adrian E Raftery. “Strictly Proper Scoring Rules, Prediction, and Estimation.” Journal of the American Statistical Association 102, no. 477 (March 1, 2007): 359–78. https://doi.org/10/c6758w.

Example

>>> hindcast.verify(metric='crpss', comparison='m2o',
        alignment='same_verifs', dim='member')
>>> perfect_model.verify(metric='crpss', comparison='m2m', dim='member',
        gaussian=False, cdf_or_dist=scipy.stats.norm, xminimum=-10,
        xmaximum=10, tol=1e-6)