climpred.metrics._effective_sample_size#

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

Effective sample size for temporally correlated data.

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 sample size extracts the number of independent samples between two time series being correlated. This is derived by assessing the magnitude of the lag-1 autocorrelation coefficient in each of the time series being correlated. A higher autocorrelation induces a lower effective sample size which raises the correlation coefficient for a given p value.

The effective sample size is used in computing the effective p value. See _pearson_r_eff_p_value() and _spearman_r_eff_p_value().

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

∞

perfect

N/A

orientation

positive

References

Bretherton et al. [1999]

Example

>>> HindcastEnsemble.verify(
...     metric="effective_sample_size",
...     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 5.0 4.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
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:                        effective_sample_size
    comparison:                    e2o
    dim:                           init
    reference:                     []