climpred.metrics._threshold_brier_score¶

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

Brier score of an ensemble for exceeding given thresholds.

$CRPS = \int_f BS(F(f), H(f - o)) df$

where $F(o) = \int_{f \leq o} p(f) df$ is the cumulative distribution function (CDF) of the forecast distribution $F$ , $o$ is a point estimate of the true observation (observational error is neglected), $BS$ denotes the Brier score and $H(x)$ denotes the Heaviside step function, which we define here as equal to 1 for $x \geq 0$ and 0 otherwise.

Parameters

forecast (xr.object) – Forecast with member dim.
verif (xr.object) – Verification data without member dim.
dim (list of str) – Dimension to apply metric over. Expects at least member. Other dimensions are passed to xskillscore and averaged.
threshold (int, float, xr.object) – Threshold to check exceedance, see properscoring.threshold_brier_score.
metric_kwargs (dict) – optional, see threshold_brier_score()

Details:

minimum	0.0
maximum	1.0
perfect	0.0
orientation	negative

Reference:

Brier, Glenn W. Verification of forecasts expressed in terms of probability.” Monthly Weather Review 78, no. 1 (1950). https://doi.org/10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2.

See also

threshold_brier_score()
threshold_brier_score()

Example

>>> # get threshold brier score for each init
>>> HindcastEnsemble.verify(metric='threshold_brier_score', comparison='m2o',
...     dim='member', threshold=.2, alignment='same_inits')
<xarray.Dataset>
Dimensions:    (lead: 10, init: 52)
Coordinates:
  * init       (init) object 1954-01-01 00:00:00 ... 2005-01-01 00:00:00
  * lead       (lead) int32 1 2 3 4 5 6 7 8 9 10
    threshold  float64 0.2
    skill      <U11 'initialized'
Data variables:
    SST        (lead, init) float64 0.0 0.0 0.0 0.0 0.0 ... 0.25 0.36 0.09 0.01

>>> # multiple thresholds averaging over init dimension
>>> HindcastEnsemble.verify(metric='threshold_brier_score', comparison='m2o',
...     dim=['member', 'init'], threshold=[.2, .3], alignment='same_verifs')
<xarray.Dataset>
Dimensions:    (lead: 10, threshold: 2)
Coordinates:
  * lead       (lead) int32 1 2 3 4 5 6 7 8 9 10
  * threshold  (threshold) float64 0.2 0.3
    skill      <U11 'initialized'
Data variables:
    SST        (lead, threshold) float64 0.08712 0.005769 ... 0.1312 0.01923