What's in the latent space? Exploring coupled tropical Pacific variability within a Multi-branch $\beta$-Variational Autoencoder

Abstract

What is encoded in the latent space of a multi-branch $\beta$-variational autoencoder ($\beta$-VAE) trained on coupled tropical Pacific climate fields? To answer this question, we assess the reconstruction skill and physical interpretability of the latent space of a multi-branch $\beta$-VAE trained on sea surface temperature, ocean heat content, and outgoing longwave radiation across the tropical Pacific from a 500-year preindustrial control simulation. The model generalizes well, with only modest degradation from training to test performance, and preserves the dominant basin-scale structure of all three fields. Latent-space diagnostics show that variability is organized unevenly across dimensions: sea surface temperature is concentrated in a smaller subset of latent dimensions, whereas ocean heat content and outgoing longwave radiation are more broadly distributed across multiple dimensions. Comparisons with conventional tropical Pacific diagnostics further show that several latent dimensions align with known El Ni\~no and La Ni\~na variability, while others capture related coupled ocean-atmosphere variability on decadal or longer timescales. Sensitivity experiments and latent traversals identify dimensions associated with eastern-Pacific-like, central-Pacific-like, coastal, subsurface-dominant, and atmosphere-dominant variability. Together, these results show that the multi-branch $\beta$-variational autoencoder yields a skillful and physically informative reduced representation of coupled tropical Pacific variability.