climpred.metrics._msess_murphy¶

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

Murphy’s Mean Square Error Skill Score (MSESS).

$MSESS_{Murphy} = r_{fo}^2 - [\text{conditional bias}]^2 - [\frac{\text{(unconditional) bias}}{\sigma_o}]^2,$

where $r_{fo}^{2}$ represents the Pearson product-moment correlation coefficient between the forecast and verification data and $\sigma_{o}$ represents the standard deviation of the verification data over the experimental period. See conditional_bias and unconditional_bias for their respective formulations.

Parameters

forecast (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
metric_kwargs (dict) – see xskillscore.pearson_r, xarray.mean and xarray.std

Details:

minimum	-∞
maximum	1.0
perfect	1.0
orientation	positive