climpred.metrics._crpss_es

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climpred.metrics._crpss_es#

climpred.metrics._crpss_es(forecast: Dataset, verif: Dataset, dim: str | List[str] | None = None, **metric_kwargs: Any) → Dataset | DataArray[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 – Forecast with member dim.

  • verif – Verification data without member dim.

  • dim – Dimension to apply metric over. Expects at least member. Other dimensions are passed to xskillscore and averaged.

  • metric_kwargs – see xskillscore.crps_ensemble() and xskillscore.mse()

Notes

minimum

-∞

maximum

0.0

perfect

0.0

orientation

positive

under-dispersive

> 0.0

over-dispersive

< 0.0

References

  • Kadow et al. [2016]

Example

>>> HindcastEnsemble.verify(
...     metric="crpss_es",
...     comparison="m2o",
...     alignment="same_verifs",
...     dim="member",
... )
<xarray.Dataset> Size: 5kB
Dimensions:     (lead: 10, init: 52)
Coordinates:
  * init        (init) object 416B 1964-01-01 00:00:00 ... 2015-01-01 00:00:00
  * lead        (lead) int32 40B 1 2 3 4 5 6 7 8 9 10
    valid_time  (init) object 416B 1964-01-01 00:00:00 ... 2015-01-01 00:00:00
    skill       <U11 44B 'initialized'
Data variables:
    SST         (lead, init) float64 4kB -0.01121 -0.05575 ... -0.1263 -0.007483
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_members:             10
    alignment:                     same_verifs
    metric:                        crpss_es
    comparison:                    m2o
    dim:                           member
    reference:                     []
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