`crps`¶

Import path: earth2studio.statistics.crps

Documentation¶

Compute the Continuous Ranked Probability Score (CRPS).

Uses this formula # int [F(x) - 1(x-y)]^2 dx

where F is the emperical CDF and 1(x-y) = 1 if x > y.

This statistic reduces over a single dimension, where the presumed ensemble dimension does not appear in the truth/observation tensor.

Parameters:

ensemble_dimension (str) –

A name corresponding to a dimension to perform the ensemble reduction over. Example: 'ensemble'
reduction_dimensions (list[str] | None, default: None ) –

A list of dimensions over which to average the crps over. optional, by default none. If none, no additional reduction is done.
weights (Tensor, default: None ) –

A tensor containing weights to assign to the reduction dimensions. Note that these weights must have the same number of dimensions as passed in reduction_dimensions. Example: if reduction_dimensions = ['lat', 'lon'] then assert weights.ndim == 2. By default None.
fair (bool, default: False ) –

If true, the CRPS is calculated using the fair CRPS formula. By default False.

__call__(
    x: Tensor,
    x_coords: CoordSystem,
    y: Tensor,
    y_coords: CoordSystem,
) -> tuple[Tensor, CoordSystem]

Apply metric to data x and y, checking that their coordinates are broadcastable. While reducing over reduction_dims.

Parameters:

x (Tensor) –

Input tensor of ensemble forecast or prediction data. This is the tensor over which the CRPS/CDF is calculated with respect to.
x_coords (CoordSystem) –

Ordered dict representing coordinate system that describes the x tensor. reduction_dimensions must be in coords.
y (Tensor) –

Observation or validation tensor.
y_coords (CoordSystem) –

Ordered dict representing coordinate system that describes the y tensor. reduction_dimensions must be in coords.

Returns:

tuple[Tensor, CoordSystem] –

Returns CRPS tensor with appropriate reduced coordinates.