earthkit.meteo.score.xarray.crps_from_cdf¶

earthkit.meteo.score.xarray.crps_from_cdf(fcst, obs, over, weight=None, return_components=False)¶

Calculates the continuous ranked probability score (CRPS) for forecasts provided as CDFs.

Warning

Experimental API. This function may change or be removed without notice.

The CRPS score for a CDF forecast is defined as:

\begin{align*} o(x) &= 0 ~\text{if}~ x < \text{obs and}~ 1 ~\text{if}~ x \ge \text{obs}, \\ \operatorname{CRPS}\left[f, o\right] &= \int_{-\infty}^{\infty}{w(x)\,(f(x) - o(x))^2\,\text{d}x} \end{align*}

where:

\(f\) is the forecast CDF,
\(o\) is the observation converted to CDF form,
\(w(x)\) is an optional non-negative threshold weight function.

With return_components=True, this function returns the decomposition defined below. The output is an xarray.Dataset with no new dimension added; instead it contains data variables named crps, underforecast_penalty, and overforecast_penalty at the same non-threshold coordinates. The overall CRPS is given by underforecast_penalty + overforecast_penalty.

\[\operatorname{CRPS}[f, o] = O(f, o) + U(f, o)\]

\begin{align*} O(f, o) &= \int_{\text{obs}}^{\infty}{w(x)\,(f(x) - 1)^2\, \text{d}x} \quad& \text{(overforecast penalty)} \\ U(f, o) &= \int_{-\infty}^{\text{obs}}{w(x)\,f(x)^2\,\text{d}x} \quad& \text{(underforecast penalty)} \end{align*}

Note that there are several ways to decompose the CRPS and this decomposition differs from the one used in crps_from_ensemble().