Arnoldi Singular Vector perturbations for machine learning weather prediction

TL;DR

This paper introduces Arnoldi-SV, a novel method for analyzing error growth in machine learning weather prediction models, which does not require linear or adjoint models and effectively identifies unstable error directions.

Contribution

The paper presents Arnoldi-SV, a new approach that approximates local error growth in weather prediction models using Krylov subspaces, applicable to both ML and traditional NWP.

Findings

A-SV finds meaningful error growth directions in the 24h Pangu Weather model.

A-SV transforms random noise into conditioned perturbations.

Method is applicable without linear or adjoint models.

Abstract

Since weather forecasts are fundamentally uncertain, reliable decision making requires information on the likelihoods of future weather scenarios. We explore the sensitivity of machine learning weather prediction (MLWP) using the 24h Pangu Weather ML model of Huawei to errors in the initial conditions with a specific kind of Singular Vector (SV) perturbations. Our Arnoldi-SV (A-SV) method does not need linear nor adjoint model versions and is applicable to numerical weather prediction (NWP) as well as MLWP. It observes error growth within a given optimization time window by iteratively applying a forecast model to perturbed model states. This creates a Krylov subspace, implicitly based on a matrix operator, which approximates the local error growth. Each iteration adds new dimensions to the Krylov space and its leading right SVs are expected to turn into directions of growing errors. We show that A-SV indeed finds dynamically meaningful perturbation patterns for the 24h Pangu Weather model, which grow right from the beginning of the forecast rollout. These perturbations describe local unstable modes and could be a basis to initialize MLWP ensembles. Since we start A-SV from random noise perturbations, the algorithm transforms noise into perturbations conditioned on a given reference state - a process that is akin to the denoising process of the generic diffusion based ML model of GenCast, therefor we briefly discuss similarities and differences.