climpred.metrics._uacc

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climpred.metrics._uacc#

climpred.metrics._uacc(forecast: Dataset, verif: Dataset, dim: str | List[str] | None = None, **metric_kwargs: Any) → Dataset | DataArray[source]#

Bushuk’s unbiased Anomaly Correlation Coefficient (uACC).

This is typically used in perfect model studies. Because the perfect model Anomaly Correlation Coefficient (ACC) is strongly state dependent, a standard ACC (e.g. one computed using _pearson_r()) will be highly sensitive to the set of start dates chosen for the perfect model study. The Mean Square Skill Score (MESSS) can be related directly to the ACC as MESSS = ACC^(2) (see Murphy [1988] and Bushuk et al. [2018]), so the unbiased ACC can be derived as uACC = sqrt(MESSS).

\[uACC = \sqrt{MSESS} = \sqrt{1 - \frac{\overline{(f - o)^{2}}}{\sigma^2_{ref} \cdot fac}},\]

where \(fac\) 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

Because of the square root involved, any negative MSESS values are automatically converted to NaNs.

Parameters:

  • forecast – Forecast.

  • verif – Verification data.

  • dim – Dimension(s) to perform metric over.

  • comparison – Name comparison needed for normalization factor fac, see _get_norm_factor() (Handled internally by the compute functions)

  • metric_kwargs – see xskillscore.mse()

Notes

minimum

0.0

maximum

1.0

perfect

1.0

orientation

positive

better than climatology

> 0.0

equal to climatology

0.0

References

Example

>>> HindcastEnsemble.verify(
...     metric="uacc", comparison="e2o", alignment="same_verifs", dim="init"
... )
<xarray.Dataset> Size: 164B
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 40B 1 2 3 4 5 6 7 8 9 10
    skill    <U11 44B 'initialized'
Data variables:
    SST      (lead) float64 80B 0.9093 0.9041 0.8849 ... 0.6894 0.5702 0.4763
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_initializations:     64
    number_of_members:             10
    alignment:                     same_verifs
    metric:                        uacc
    comparison:                    e2o
    dim:                           init
    reference:                     []
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