climpred.metrics._pearson_r_eff_p_value¶

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

Probability that forecast and verification data are linearly 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 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

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

Details:

minimum	0.0
maximum	1.0
perfect	1.0
orientation	negative