WaveSim: A Wavelet-based Multi-scale Similarity Metric for Weather and Climate Fields

2025-12-16

AI Summary

Traditional pointwise metrics fail to attribute errors to their physical scales and distinct error patterns, hindering robust multiscale spatial field similarity assessment. This paper introduces WaveSim—a novel multiscale similarity metric grounded in continuous wavelet transform—that orthogonally decomposes field similarity into three physically interpretable components: Magnitude (intensity), Displacement (spatial shift), and Structure (pattern fidelity). It enables the first physically scale-attributable quantification of field similarity. By integrating energy normalization, centroid-based displacement estimation, and multiscale weighted fusion, WaveSim supports user-defined weighting schemes and model intercomparison. Implemented in PyTorch, it demonstrates high sensitivity and physical consistency in synthetic perturbation experiments. In evaluating key climate variability modes across state-of-the-art climate models, WaveSim significantly outperforms conventional pointwise metrics, offering improved diagnostic capability for spatial pattern fidelity across scales.

Technology Category

• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multimodal Learning

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The metric is built by multiplying three orthogonal components derived from these coefficients: Magnitude, which quantifies similarities in the energy distribution of the coefficients, i.e., the intensity of the field; Displacement, which captures spatial shift by comparing the centers of mass of normalized energy distributions; and Structure, which assesses pattern organization independent of location and amplitude. Each component yields a scale-specific similarity score ranging from 0 (no similarity) to 1 (perfect similarity), which are then combined across scales to produce an overall similarity measure. We first evaluate WaveSim using synthetic test cases, applying controlled spatial and temporal perturbations to systematically assess its sensitivity and expected behavior. We then demonstrate its applicability to physically relevant case studies of key modes of climate variability in Earth System Models. Traditional point-wise metrics lack a mechanism for attributing errors to physical scales or modes of dissimilarity. By operating in the wavelet domain and decomposing the signal along independent axes, WaveSim bypasses these limitations and provides an interpretable and diagnostically rich framework for assessing similarity in complex fields. Additionally, the WaveSim framework allows users to place emphasis on a specific scale or component, and lends itself to user-specific model intercomparison, model evaluation, and calibration and training of forecasting systems. We provide a PyTorch-ready implementation of WaveSim, along with all evaluation scripts, at: https://github.com/gabrieleaccarino/wavesim.

Problem

• Develops a wavelet-based metric to evaluate spatial field similarity
• Addresses limitations of traditional point-wise error metrics in climate models
• Provides interpretable multi-scale analysis for weather and climate applications

Innovation

• Wavelet transforms decompose fields into scale-specific coefficients
• Multi-scale metric combines magnitude, displacement, and structure components
• Interpretable framework for model evaluation and forecasting system calibration