climpred.metrics._pearson_r

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climpred.metrics._pearson_r#

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

Pearson product-moment correlation coefficient.

A measure of the linear association between the forecast and verification data that is independent of the mean and variance of the individual distributions. This is also known as the Anomaly Correlation Coefficient (ACC) when correlating anomalies.

corr = \frac{cov(f, o)}{\sigma_{f}\cdot\sigma_{o}},

where \sigma_{f} and \sigma_{o} represent the standard deviation of the forecast and verification data over the experimental period, respectively.

Note

Use metric _pearson_r_p_value() or _pearson_r_eff_p_value() to get the corresponding p value.

Parameters:

  • forecast – Forecast.

  • verif – Verification data.

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

  • metric_kwargs – see xskillscore.pearson_r()

Notes

minimum

-1.0

maximum

1.0

perfect

1.0

orientation

positive

See also

Example

>>> HindcastEnsemble.verify(
...     metric="pearson_r",
...     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 0.9272 0.9145 0.9127 ... 0.9315 0.9185 0.9112
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:                        pearson_r
    comparison:                    e2o
    dim:                           init
    reference:                     []
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