A Comparison of Data-Driven Reduced Order Models for the Simulation of Mesoscale Atmospheric Flow

TL;DR

This paper compares three reduced order models—DMD, HDMD, and PODI—for simulating mesoscale atmospheric flow, highlighting their accuracy and computational efficiency in weather forecasting benchmarks.

Contribution

It provides a comparative analysis of reduced order models for mesoscale atmospheric flow simulation, emphasizing the effectiveness of PODI with interpolation over DMD and HDMD.

Findings

PODI maintains accuracy over the entire forecast interval.

DMD and HDMD accuracy declines with longer forecast windows.

PODI effectively handles physical parameter variations.

Abstract

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order models that have successfully reduced the computational time for different applications in computational fluid dynamics while preserving accuracy: Dynamic Mode Decomposition (DMD), Hankel Dynamic Mode Decomposition (HDMD), and Proper Orthogonal Decomposition with Interpolation (PODI). The three methods are compared in terms of computational time and accuracy in the simulation of two well-known benchmarks for mesoscale flow. The accuracy of the DMD and HDMD solutions deteriorates rather quickly as the forecast time window expands, although these methods are designed to predict the dynamics of a system. The reason is likely the strong nonlinearity in the benchmark flows. The PODI solution is accurate for the entire duration of the time interval of interest thanks to the use of interpolation with radial basis functions. This holds true also when the model features a physical parameter expected to vary in a given range, as is typically the case in weather prediction.