deeplearning/modulus/modulus-core-v040/_modules/modulus/metrics/climate/efi.html

Core v0.4.0

Source code for modulus.metrics.climate.efi

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#     http://www.apache.org/licenses/LICENSE-2.0
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# TODO(Dallas) Introduce Distributed Class for computation.

import torch

from modulus.metrics.general.entropy import entropy_from_counts
from modulus.metrics.general.histogram import normal_cdf

Tensor = torch.Tensor


[docs]def efi_gaussian( pred_cdf: Tensor, bin_edges: Tensor, climatology_mean: Tensor, climatology_std: Tensor, ) -> Tensor: """Calculates the Extreme Forecast Index (EFI) for an ensemble forecast against a climatological distribution. Parameters ---------- pred_cdf : Tensor Cumulative distribution function of predictions of shape [N, ...] where N is the number of bins. This cdf must be defined over the passed bin_edges. bin_edges : Tensor Tensor of bin edges with shape [N+1, ...] where N is the number of bins. climatology_mean : Tensor Tensor of climatological mean with shape [...] climatology_std : Tensor Tensor of climatological std with shape [...] Returns ------- Tensor EFI values of each of the batched dimensions. Note ---- Reference: https://www.atmos.albany.edu/daes/atmclasses/atm401/spring_2016/ppts_pdfs/ECMWF_EFI.pdf """ clim_cdf = normal_cdf(climatology_mean, climatology_std, bin_edges, grid="right") return ( 2.0 / torch.pi * torch.trapz( (clim_cdf - pred_cdf) / torch.sqrt(1e-8 + clim_cdf * (1.0 - clim_cdf)), clim_cdf, dim=0, ) )
[docs]def efi(bin_edges: Tensor, counts: Tensor, quantiles: Tensor) -> Tensor: """Compute the Extreme Forecast Index for the given histogram. The histogram is assumed to correspond with the given quantiles. That is, the bin midpoints must align with the quantiles. Parameters ---------- bin_edges : Tensor The bin edges of the histogram over which the data distribution is defined. Assumed to be monotonically increasing but not evenly spaced. counts : Tensor The counts of the histogram over which the data distributed is defined. Not assumed to be normalized. quantiles : Tensor The quantiles of the climatological or reference distribution. The quantiles must match the midpoints of the histogram bins. See modulus/metrics/climate/efi for more details. """ bin_widths = bin_edges[1:] - bin_edges[:-1] pred_cdf = torch.cumsum(counts * bin_widths, dim=0) / torch.sum( counts * bin_widths, dim=0 ) return ( 2.0 / torch.pi * torch.trapz( (quantiles - pred_cdf) / torch.sqrt(1e-8 + quantiles * (1.0 - quantiles)), quantiles, dim=0, ) )
[docs]def normalized_entropy( pred_pdf: Tensor, bin_edges: Tensor, climatology_pdf: Tensor, ) -> Tensor: """Calculates the relative entropy, or surprise, of using the prediction distribution with respect to the climatology distribution. Parameters ---------- pred_cdf : Tensor Cumulative distribution function of predictions of shape [N, ...] where N is the number of bins. This cdf must be defined over the passed bin_edges. bin_edges : Tensor Tensor of bin edges with shape [N+1, ...] where N is the number of bins. climatology_pdf : Tensor Tensor of climatological probability function shape [N, ...] Returns ------- Tensor Relative Entropy values of each of the batched dimensions. """ if pred_pdf.shape != climatology_pdf.shape: raise ValueError( "Prediction PDF and Climatological PDF must have the same shapes" + f"but recieved {pred_pdf.shape} and {climatology_pdf.shape}." ) return 1.0 - entropy_from_counts(pred_pdf, bin_edges) / entropy_from_counts( climatology_pdf, bin_edges )
© Copyright 2023, NVIDIA Modulus Team. Last updated on Jan 25, 2024.