# Validating Climate Models with Spherical Convolutional Wasserstein Distance

arXiv: https://arxiv.org/abs/2401.14657 · HTML: https://mlsanity.com/paper/2401.14657/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 71 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Builds on (most cited first, 8 of 8)

- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Energy-Based Sliced Wasserstein Distance](https://mlsanity.com/paper/2304.13586/) (2023)
- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Evaluating proxy influence in assimilated paleoclimate reconstructions -- Testing the exchangeability of two ensembles of spatial processes](https://mlsanity.com/paper/1909.01273/) (2019)
- [Regularized Variational Data Assimilation for Bias Treatment using the Wasserstein Metric](https://mlsanity.com/paper/2003.02421/) (2020)
- [Permutation Tests for Equality of Distributions of Functional Data](https://mlsanity.com/paper/1803.00798/) (2018)

## Built on by (most cited first, 9 of 9)

- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [Lightspeed Geometric Dataset Distance via Sliced Optimal Transport](https://mlsanity.com/paper/2501.18901/) (2025)
- [Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions](https://mlsanity.com/paper/2404.15378/) (2024)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Linear Spherical Sliced Optimal Transport: A Fast Metric for Comparing Spherical Data](https://mlsanity.com/paper/2411.06055/) (2024)
- [Quantifying uncertainty in climate projections with conformal ensembles](https://mlsanity.com/paper/2408.06642/) (2024)
- [Amortized Optimal Transport from Sliced Potentials](https://mlsanity.com/paper/2604.15114/) (2026)
- [LLM-based Evaluation Policy Extraction for Ecological Modeling](https://mlsanity.com/paper/2505.13794/) (2025)
- [Every Fixed Metric Has a Blind Spot: A Learned Atmospheric Critic for Scoring Forecast Realism](https://mlsanity.com/paper/2609.18381/) (2026)

## Abstract (arXiv)

The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and reanalysis data. This new similarity measure accounts for spatial variability using convolutional projections and quantifies local differences in the distribution of climate variables. We apply this method to evaluate the historical model outputs of the Coupled Model Intercomparison Project (CMIP) members by comparing them to observational and reanalysis data products. Additionally, we investigate the progression from CMIP phase 5 to phase 6 and find modest improvements in the phase 6 models regarding their ability to produce realistic climatologies.