Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates

TL;DR

This paper introduces a neural operator framework that improves Earth system model predictions by applying bias corrections online during model integration, enhancing accuracy and stability in long-term simulations.

Contribution

It develops novel operator architectures based on U-Net that effectively learn bias correction tendencies, outperforming standard models and enabling scalable, stable hybrid Earth system simulations.

Findings

Operators generalize across height levels and seasons.

M extbackslash M architecture provides the most consistent bias reduction.

Framework maintains stability and feasibility in multi-year simulations.

Abstract

Coarse resolution, imperfect parameterizations, and uncertain initial states and forcings limit Earth-system model (ESM) predictions. Traditional bias correction via data assimilation improves constrained simulations but offers limited benefit once models run freely. We introduce an operator-learning framework that maps instantaneous model states to bias-correction tendencies and applies them online during integration. Building on a U-Net backbone, we develop two operator architectures Inception U-Net (IUNet) and a multi-scale network (M\&M) that combine diverse upsampling and receptive fields to capture multiscale nonlinear features under Energy Exascale Earth System Model (E3SM) runtime constraints. Trained on two years E3SM simulations nudged toward ERA5 reanalysis, the operators generalize across height levels and seasons. Both architectures outperform standard U-Net baselines in offline tests, indicating that functional richness rather than parameter count drives performance. In online hybrid E3SM runs, M\&M delivers the most consistent bias reductions across variables and vertical levels. The ML-augmented configurations remain stable and computationally feasible in multi-year simulations, providing a practical pathway for scalable hybrid modeling. Our framework emphasizes long-term stability, portability, and cadence-limited updates, demonstrating the utility of expressive ML operators for learning structured, cross-scale relationships and retrofitting legacy ESMs.