# Source code for modulus.metrics.climate.acc

# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

# TODO(Dallas) Introduce Distributed Class for computation.

import torch
from modulus.metrics.climate.reduction import _compute_lat_weights

Tensor = torch.Tensor

[docs]def acc(pred: Tensor, target: Tensor, climatology: Tensor, lat: Tensor) -> Tensor:
"""Calculates the Anomaly Correlation Coefficient

Parameters
----------
pred : Tensor
[..., H, W] Predicted tensor on a lat/long grid
target : Tensor
[..., H, W] Target tensor on a lat/long grid
climatology : Tensor
[..., H, W] climatology tensor
lat : Tensor
[H] latitude tensor

Returns
-------
Tensor
ACC values for each field

Note
----
Reference: https://www.atmos.albany.edu/daes/atmclasses/atm401/spring_2016/ppts_pdfs/ECMWF_ACC_definition.pdf
"""
assert (
pred.ndim > 2
), "Expected predictions to have at least two dimensions (lat, lon)"
assert (
target.ndim > 2
), "Expected targets to have at least two dimensions (lat, lon)"
assert (
climatology.ndim > 2
), "Expected climatology to have at least two dimensions (lat, lon)"

# subtract climate means
pred_hat = pred - climatology
target_hat = target - climatology

# Get aggregator
lat_weight = _compute_lat_weights(lat)
# Weighted mean
pred_bar = torch.sum(
lat_weight[:, None] * pred_hat, dim=(-2, -1), keepdim=True
) / torch.sum(
lat_weight[:, None] * torch.ones_like(pred_hat), dim=(-2, -1), keepdim=True
)

target_bar = torch.sum(
lat_weight[:, None] * target_hat, dim=(-2, -1), keepdim=True
) / torch.sum(
lat_weight[:, None] * torch.ones_like(target_hat), dim=(-2, -1), keepdim=True
)
pred_diff = pred_hat - pred_bar
target_diff = target_hat - target_bar

p1 = torch.sum(lat_weight[:, None] * pred_diff * target_diff, dim=(-2, -1))
p2 = torch.sum(lat_weight[:, None] * pred_diff * pred_diff, dim=(-2, -1))
p3 = torch.sum(lat_weight[:, None] * target_diff * target_diff, dim=(-2, -1))
m = p1 / torch.sqrt(p2 * p3)
return m

© Copyright 2023, NVIDIA Modulus Team. Last updated on Aug 8, 2023.