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.