climpred.metrics._uacc¶

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

Bushuk’s unbiased Anomaly Correlation Coefficient (uACC).

This is typically used in perfect model studies. Because the perfect model Anomaly Correlation Coefficient (ACC) is strongly state dependent, a standard ACC (e.g. one computed using pearson_r) will be highly sensitive to the set of start dates chosen for the perfect model study. The Mean Square Skill Score (MESSS) can be related directly to the ACC as MESSS = ACC^(2) (see Murphy 1988 and Bushuk et al. 2019), so the unbiased ACC can be derived as uACC = sqrt(MESSS).

$uACC = \sqrt{MSESS} = \sqrt{1 - \frac{\overline{(f - o)^{2}}}{\sigma^2_{ref} \cdot fac}},$

where $fac$ is 1 when using comparisons involving the ensemble mean (m2e, e2c, e2o) and 2 when using comparisons involving individual ensemble members (m2c, m2m, m2o). See _get_norm_factor().

Note

Because of the square root involved, any negative MSESS values are automatically converted to NaNs.

Parameters

forecast (xarray object) – Forecast.
verif (xarray object) – Verification data.
dim (str) – Dimension(s) to perform metric over.
comparison (str) – Name comparison needed for normalization factor fac, see _get_norm_factor() (Handled internally by the compute functions)
metric_kwargs (dict) – see mse()

Details:

minimum	0.0
maximum	1.0
perfect	1.0
orientation	positive
better than climatology	> 0.0
equal to climatology	0.0

Reference:

Bushuk, Mitchell, Rym Msadek, Michael Winton, Gabriel Vecchi, Xiaosong Yang, Anthony Rosati, and Rich Gudgel. “Regional Arctic Sea–Ice Prediction: Potential versus Operational Seasonal Forecast Skill.” Climate Dynamics, June 9, 2018. https://doi.org/10/gd7hfq.
Allan H. Murphy. Skill Scores Based on the Mean Square Error and Their Relationships to the Correlation Coefficient. Monthly Weather Review, 116(12):2417–2424, December 1988. https://doi.org/10/fc7mxd.

Example

>>> HindcastEnsemble.verify(metric='uacc', 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 0.9093 0.9041 0.8849 0.877 ... 0.6894 0.5702 0.4763