Physics-Guided Deep Learning-Based Emulation of Subgrid-Scale Turbulence Parameterization for Atmospheric Large Eddy Simulations

Accurate representation of turbulent processes remains a critical challenge in atmospheric modelling. Large Eddy Simulations (LES) serve as valuable tools for understanding atmospheric turbulence by explicitly resolving energy-containing eddies while parameterizing smaller-scale motions through subgrid-scale (SGS) models. In their most complex forms, these SGS parameterizations can significantly influence LES performance and computational efficiency, making their improvement useful for advancing atmospheric modelling capabilities. Neural Network based emulation of such parametrizations have proven effective in reducing the computational cost, while maintaining accuracy and stability.

Building upon recent advances in physics-informed neural networks (NN) for atmospheric modelling and emulation of physics-based processes, we present a physics-guided NN architecture for emulation of the SGS turbulence parameterizations that introduces several key innovations. Our approach uniquely combines scale-specific normalization with multi-scale feature extraction through parallel convolutional paths, distinguishing it from existing physics-guided machine learning frameworks. The deep learning-based (DL) model also incorporates physically-motivated constraints across different spatial scales while simultaneously ensuring conservation of momentum and energy.

Unlike earlier studies that focus on single aspects of physical conservation, our architecture implements a comprehensive physics-informed framework that combines Richardson number gradient handling for stability constraints, with explicit treatment of diffusion and viscosity coefficients, and scale-specific normalization for different atmospheric variables. The model was trained on limited high-resolution Radiative-Convective Equilibrium (RCE) simulations from the Met Office-Natural Environment Research Council (NERC) Cloud model (MONC), employing physics-based loss functions that enforce both conservation laws and stability constraints.

The training dataset consisted of 3-D diagnostics data from the RCE simulations, with a 64x64 km² domain and 1 km grid spacing in the horizontal. While the original simulations had 99 vertical levels with varying vertical resolution, the DL model was trained on random slices (vertical levels) chosen from the original data volume. The inputs consisted of the resolved state variables like velocity components (u, v, w) from the previous time step, the perturbations to potential temperature, mixing ratios and Richardson number, whereas the targets for the DL model were the SGS tendencies of the model prognostic fields resulting from the Smagorisnky parameterization and the coefficients of viscosity and diffusion.

The DL model's cross-regime applicability was evaluated through multiple independent test cases: (200-second sampling frequency) and different atmospheric conditions from the Atmospheric Radiation Measurement (ARM) program. The simulations from ARM atmospheric settings were mainly targeted at simulating shallow convection, with different grid/domain configurations. Results from the off-line tests demonstrate promising performance in predicting SGS and transport coefficients (viscosity and diffusion) across these varied conditions, particularly in maintaining physical consistency during regime transitions.

Our preliminary findings indicate that this enhanced multi-scale, physics-informed architecture can effectively learn SGS parameterizations from limited training data while maintaining physical fidelity across different atmospheric conditions and spatio-temporal resolutions. This approach demonstrates the potential for the development of high-fidelity, generalizable parameterizations for weather and climate models, suggesting a route forward for reducing the greater computational costs associated with more complex SGS parameterization schemes.