Navigating the Noise: Bringing Clarity to ML Parameterization Design With O $\boldsymbol{\mathcal{O}}$ (100) Ensembles

Abstract

Machine-learning (ML) parameterizations of subgrid processes (here of turbulence, convection, and radiation) may one day replace conventional parameterizations by emulating high-resolution physics without the cost of explicit simulation. However, uncertainty about the relationship between offline and online performance (i.e., when integrated with a large-scale general circulation model) hinders their development. Much of this uncertainty stems from limited sampling of the noisy, emergent effects of upstream ML design decisions on downstream online hybrid simulation. Our work rectifies the sampling issue via the construction of a semi-automated, end-to-end pipeline for $O\left(100\right)$ size ensembles of hybrid simulations, revealing important nuances in how systematic reductions in offline error manifest in changes to online error and online stability. For example, removing dropout and switching from a Mean Squared Error to a Mean Absolute Error loss both reduce offline error, but they have opposite effects on online error and online stability. Other design decisions, like incorporating memory, converting moisture input from specific humidity to relative humidity, using batch normalization, and training on multiple climates do not come with any such compromises. Finally, we show that ensemble sizes of $O\left(100\right)$ may be necessary to reliably detect causally relevant differences online. By enabling rapid online experimentation at scale, we can empirically settle debates regarding subgrid ML parameterization design that would have otherwise remained unresolved in the noise.