climpred.metrics._pearson_r¶

climpred.metrics._pearson_r(forecast, verif, dim=None, **metric_kwargs)[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 (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
metric_kwargs (dict) – see pearson_r()

Details:

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>
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 0.9272 0.9145 0.9127 0.9319 ... 0.9315 0.9185 0.9112