climpred.metrics._less#

climpred.metrics._less(forecast: Dataset, verif: Dataset, dim: Optional[Union[str, List[str]]] = None, **metric_kwargs: Any) → Dataset[source]#

Logarithmic Ensemble Spread Score.

LESS = ln(\frac{variance}{MSE})= ln(\frac{\sigma^2_f}{\sigma^2_o})

Parameters:

  • forecast – Forecasts.

  • verif – Verification.

  • dim – The dimension(s) over which to aggregate. Defaults to None, meaning aggregation over all dims other than lead.

Returns:

less – reduced by dimensions dim

Notes

maximum

∞

positive

overdisperive / underconfident

perfect

0

negative

underdisperive / overconfident

minimum

-∞

orientation

None

Example

>>> # better detrend before
>>> from climpred.stats import rm_poly
>>> HindcastEnsemble.map(rm_poly, dim="init_or_time", deg=2).verify(
...     metric="less",
...     comparison="m2o",
...     dim=["member", "init"],
...     alignment="same_verifs",
... ).SST
<xarray.DataArray 'SST' (lead: 10)>
array([ 0.12633664, -0.12707636, -0.26143181, -0.25096537, -0.29267366,
       -0.2905725 , -0.43579508, -0.33774947, -0.46008438, -0.61010386])
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Attributes:
    units:    None

References

Kadow et al. [2016]