Spectral representations for regional AI-based weather prediction

Both dynamical and AI-based NWP have seen success in using spectral transformations to represent atmospheric variables efficiently. In particular, Fourier-based representations are widely adopted due to fast computational methods and compact encoding of large-scale structure. However, as the NWP community targets higher-resolution models, Fourier-bases may inadequately represent the sharp gradients and multi-scale features that often characterise extreme weather events. Furthermore, for limited-area domains, Fourier representations can impose artificial periodicity, making them less physically appropriate.

In this work, we investigate whether alternative spectral transformations better support AI-based NWP in regional, extreme-weather settings. We systematically compare neural forecasting models trained using Fourier, wavelet, and Legendre spectral representations, assessing their ability to predict multiple atmospheric variables over the Aotearoa New Zealand domain.  Wavelet and polynomial bases are explicitly designed for bounded domains and provide multi-scale, non-periodic representations, making these transformations more suitable for the regional forecasting task.

Aotearoa New Zealand provides an ideal test-bed for these methods, as a region with complex coastlines, steep orography, and frequent exposure to high-impact weather systems. Models are trained and evaluated on reanalysis datasets (ERA5 and BARRA-2), using standard verification metrics and case studies of major Aotearoa New Zealand storms such as Cyclones Gabrielle and Bola. Our results demonstrate that spectral choice has a measurable impact on forecast skill, particularly for extremes and fine-scale structure.

By analysing how different spectral representations influence AI-NWP performance in a regional context, this work provides guidance on the appropriate use of spectral methods for limited-area forecasting, and contributes to the development of more accurate and physically consistent AI-driven weather prediction systems for localised and extreme events.