climpred.metrics._crps¶

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

Continuous Ranked Probability Score (CRPS).

The CRPS can also be considered as the probabilistic Mean Absolute Error (mae). It compares the empirical distribution of an ensemble forecast to a scalar observation. Smaller scores indicate better skill.

$CRPS = \int_{-\infty}^{\infty} (F(f) - H(f - o))^{2} df,$

where $F(f)$ is the cumulative distribution function (CDF) of the forecast (since the verification data are not assigned a probability), and H() is the Heaviside step function where the value is 1 if the argument is positive (i.e., the forecast overestimates verification data) or zero (i.e., the forecast equals verification data) and is 0 otherwise (i.e., the forecast is less than verification data).

Note

The CRPS is expressed in the same unit as the observed variable. It generalizes the Mean Absolute Error (MAE), and reduces to the MAE if the forecast is determinstic.

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, see crps_ensemble()

Details:

minimum	0.0
maximum	∞
perfect	0.0
orientation	negative

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.
https://www.lokad.com/continuous-ranked-probability-score

See also

crps_ensemble()
crps_ensemble()

Example

>>> HindcastEnsemble.verify(metric='crps', comparison='m2o', dim='member',
...     alignment='same_inits')
<xarray.Dataset>
Dimensions:  (lead: 10, init: 52)
Coordinates:
  * init     (init) object 1954-01-01 00:00:00 ... 2005-01-01 00:00:00
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead, init) float64 0.1722 0.1202 0.01764 ... 0.05428 0.1638