climpred.metrics._spearman_r_eff_p_value¶

climpred.metrics._spearman_r_eff_p_value(forecast, verif, dim=None, **metric_kwargs)[source]¶

Probability that forecast and verification data are monotonically uncorrelated, 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 Spearman’s rank 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

forecast (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
metric_kwargs (dict) – see spearman_r_eff_p_value()

Details:

minimum	0.0
maximum	1.0
perfect	1.0
orientation	negative

See also

Reference:

Bretherton, Christopher S., et al. “The effective number of spatial degrees of freedom of a time-varying field.” Journal of climate 12.7 (1999): 1990-2009.

Example

>>> HindcastEnsemble.verify(metric='spearman_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 0.02034 0.0689 0.2408 ... 0.2092 0.2315 0.2347