climpred.metrics._pearson_r_eff_p_value#

climpred.metrics._pearson_r_eff_p_value(forecast: xarray.Dataset, verif: xarray.Dataset, dim: Optional[Union[str, List[str]]] = None, **metric_kwargs: Any) → xarray.Dataset[source]#

pearson_r_p_value accounting for autocorrelation.

Note

Weights are not included here due to the dependence on temporal autocorrelation.

Note

This metric can only be used for hindcast-type simulations.

The effective p value is computed by replacing the sample size N in the t-statistic with the effective sample size, N_{eff}. The same Pearson product-moment correlation coefficient r is used as when computing the standard p value.

t = r\sqrt{ \frac{N_{eff} - 2}{1 - r^{2}} },

where N_{eff} is computed via the autocorrelation in the forecast and verification data.

N_{eff} = N\left( \frac{1 - \rho_{f}\rho_{o}}{1 + \rho_{f}\rho_{o}} \right),

where \rho_{f} and \rho_{o} are the lag-1 autocorrelation coefficients for the forecast and verification data.

Parameters

Notes

minimum

0.0

maximum

1.0

perfect

1.0

orientation

negative

See also

Example

>>> HindcastEnsemble.verify(
...     metric="pearson_r_eff_p_value",
...     comparison="e2o",
...     alignment="same_verifs",
...     dim="init",
... )
<xarray.Dataset>
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead) float64 0.02333 0.08552 0.2679 ... 0.2369 0.2588 0.2703
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_eff_p_value
    comparison:                    e2o
    dim:                           init
    reference:                     []

References

Bretherton et al. [1999]