A Wavelet-Embedded AI Framework for Unified Representation of Sub-Grid Physics in NWP

The atmosphere is a complex, multiscale deterministic system in which processes across a wide range of spatial and temporal scales interact. Numerical weather prediction (NWP) models are designed to forecast the future state of the atmosphere. Processes operating at scales larger than a model’s grid spacing are explicitly represented through finite-difference approximations of the governing physical laws. In contrast, processes occurring at scales finer than the model’s numerical resolution cannot be explicitly resolved; their effects on the resolved scales are instead represented as a bulk forcing conditioned on the resolved state.

Traditionally, forcing from sub-grid scales is partitioned into several categories, such as convection, microphysics, and planetary boundary layer. The limitations of the physical parameterization schemes used for this purpose are well known. Although these schemes are physically motivated, they generally lack closed formulations, and their parameters must ultimately be tuned. Moreover, interactions among sub-grid physical processes, which are artificially separated into categories, remain largely unresolved. The development of such schemes is also labor-intensive. As a result, physical parameterizations have long been regarded as a major source of uncertainty in NWP models.

This study is motivated by the recognition that the influence of unresolved scales on the resolved flow is fundamentally a statistical problem. From this perspective, we seek a simple and efficient statistical framework to estimate sub-grid-scale forcing. We propose a novel approach that employs artificial intelligence (AI) to statistically emulate the combined effects of all sub-grid physical processes, rather than treating them separately as in traditional parameterization schemes. A key innovation of the proposed framework is the use of localized wavelet embedding to condition the statistical estimation of forcing on the relevant spatial scales influencing each model grid column. This wavelet-based representation captures both slowly evolving large-scale features and rapidly varying small-scale features.

In addition, a neural network (NN) model is trained to predict the difference between a dynamics-only model forecast and the corresponding verifying reanalysis. This trained NN can be interpreted as an AI-based all-physics model, as it effectively represents the stochastic effects of fine-scale processes unresolved by the NWP model on the resolved scales. By integrating information across scales and processes, this AI-based all-physics framework may enable even coarse-resolution global models to accurately simulate large-scale tropical waves arising from cross-scale interactions. This task remains challenging even for high-resolution global models. The proposed approach therefore offers a promising pathway toward more accurate and computationally efficient extended-range weather prediction.