Sensitivity Analysis for Climate Science with Generative Flow Models

Abstract: Sensitivity analysis is a cornerstone of climate science, essential for understanding phenomena ranging from storm intensity to long-term climate feedbacks. However, computing these sensitivities using traditional physical models is often prohibitively expensive in terms of both computation and development time. While modern AI-based generative models are orders of magnitude faster to evaluate, computing sensitivities with them remains a significant bottleneck. This work addresses this challenge by applying the adjoint state method for calculating gradients in generative flow models, with diffusion models as a special case. We apply this method to the cBottle generative model, an emulator of ERA5 data, to perform sensitivity analysis with respect to sea surface temperatures. Furthermore, we propose a novel gradient self-consistency check to quantitatively validate the computed sensitivities against the model's own outputs. Our results provide initial evidence that this approach can produce reliable gradients, reducing the computational cost of sensitivity analysis from weeks on a supercomputer with a physical model to hours on a GPU, thereby simplifying a critical workflow in climate science.