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Improving regional weather forecasts with neural interpolation

James Jackaman, Oliver Sutton

TL;DR

The paper addresses the challenge of coupling coarse global models with high-resolution regional models by introducing a neural interpolation operator to improve boundary data in blending regions. It couples a U-Net–based CNN with a LearnFlow block that incorporates a fine-scale flow map, evaluated on a simplified 1D shallow water system discretized with compatible finite elements, and enforces energy-like stability through a weak regularization term. The approach demonstrates learnability of inter-scale dynamics but reports sizable errors compared to the finite element solution, with energy-regularization showing a trade-off between stability and accuracy. The work lays groundwork for extending to 2D dynamics and higher-order discretizations, with future directions including graph-based architectures to handle more complex geometries and dynamics in regional weather cores.

Abstract

In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we expose a methodology for approaching the problem through the study of a simplified model, with a view to generalise the results in this work to the dynamical core of regional weather models. Our approach will exploit a combination of techniques from image super-resolution with convolutional neural networks (CNNs) and residual networks, in addition to building the flow of atmospheric dynamics into the neural network

Improving regional weather forecasts with neural interpolation

TL;DR

The paper addresses the challenge of coupling coarse global models with high-resolution regional models by introducing a neural interpolation operator to improve boundary data in blending regions. It couples a U-Net–based CNN with a LearnFlow block that incorporates a fine-scale flow map, evaluated on a simplified 1D shallow water system discretized with compatible finite elements, and enforces energy-like stability through a weak regularization term. The approach demonstrates learnability of inter-scale dynamics but reports sizable errors compared to the finite element solution, with energy-regularization showing a trade-off between stability and accuracy. The work lays groundwork for extending to 2D dynamics and higher-order discretizations, with future directions including graph-based architectures to handle more complex geometries and dynamics in regional weather cores.

Abstract

In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we expose a methodology for approaching the problem through the study of a simplified model, with a view to generalise the results in this work to the dynamical core of regional weather models. Our approach will exploit a combination of techniques from image super-resolution with convolutional neural networks (CNNs) and residual networks, in addition to building the flow of atmospheric dynamics into the neural network
Paper Structure (5 sections, 8 equations, 3 figures, 1 table)

This paper contains 5 sections, 8 equations, 3 figures, 1 table.

Table of Contents

  1. Motivation
  2. Methodology
  3. Implementation
  4. Conclusion
  5. Discrete dynamical core

Figures (3)

  • Figure 1: A visualisation of the coarse global model, LAM (regional model) and interface region.
  • Figure 2: A coarse visualisation of the 1D mesh partitioned into three nodes with two elements. We represent a function in the velocity space in blue, marking the DOF with crosses, and a function in the pressure space in red, again marking the DOF with crosses. Note that, as the domain is periodic, $u(0)=u(3)$.
  • Figure 3: The square of the $L_2$ error for the neural interpolator applied to the validation dataset with various regularisation parameters $\sigma$.