climpred.metrics._crpss_es¶

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

Continuous Ranked Probability Skill Score Ensemble Spread.

If the ensemble variance is smaller than the observed mse, the ensemble is said to be under-dispersive (or overconfident). An ensemble with variance larger than the verification data indicates one that is over-dispersive (underconfident).

$CRPSS = 1 - \frac{CRPS(\sigma^2_f)}{CRPS(\sigma^2_o)}$

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) – see crps_ensemble()

:param and mse():

Details:

minimum	-∞
maximum	0.0
perfect	0.0
orientation	positive
under-dispersive	> 0.0
over-dispersive	< 0.0

Reference:

Kadow, Christopher, Sebastian Illing, Oliver Kunst, Henning W. Rust, Holger Pohlmann, Wolfgang A. Müller, and Ulrich Cubasch. “Evaluation of Forecasts by Accuracy and Spread in the MiKlip Decadal Climate Prediction System.” Meteorologische Zeitschrift, December 21, 2016, 631–43. https://doi.org/10/f9jrhw.

Example

>>> HindcastEnsemble.verify(metric='crpss_es', comparison='m2o',
...     alignment='same_verifs', dim='member')
<xarray.Dataset>
Dimensions:  (init: 52, lead: 10)
Coordinates:
  * init     (init) object 1964-01-01 00:00:00 ... 2015-01-01 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 -0.01121 -0.05575 ... -0.1263 -0.007483