Reduced Order Modeling for Global Atmospheric Chemistry Simulation Data

The GEOS-Chem global Chemical Transport Model (CTM) simulates atmospheric chemistry by solving 3-D coupled continuity equations for the interacting concentrations of chemical species. GEOS-Chem can also serve as an atmospheric chemistry module for the NASA GEOS-5 Earth System Model (ESM), where the ESM calculates the ensemble of processes affecting the Earth system. These models are used to study a wide range of environmental issues including air pollution and chemistry-climate interactions. Chemical compounds have order of magnitude differences in lifetimes resulting in numerically stiff evolution equations. Simulating the high-dimensional, stiff coupled system on a 3D global grid is thus computationally intensive and constitutes a major limitation of atmospheric chemistry models. We apply data-driven techniques to this global atmospheric chemistry simulation data with the goal of building an accurate and computationally tractable Reduced Order Model (ROM) for the evolution of chemical species in the atmosphere.

Computation of the Proper Orthogonal Decomposition (POD) of the preprocessed simulation data identifies the dimension of the low-order dynamics and produces chemical modes on which the global chemistry evolves. Our ROMs are capable of extracting the leading-order features of chemical concentrations for the purpose of diagnostics, reconstruction and future state prediction. Additionally, our data-driven diagnostics show a consistent pattern of low dimensional features across the global chemistry landscape, thus demonstrating that ROM architectures are capable of reconstructing low-rank models for future state estimation.

Indeed, the reconstruction and future state prediction of global chemistry can be achieved using the Dynamic Mode Decomposition (DMD), which is a regression technique that integrates Fourier transforms and singular value decomposition. The DMD method originated in the fluid dynamics community as an equation-free, data-driven method capable of providing an accurate decomposition of complex flows into a simple representation based on spatio-temporal coherent structures that may be used for short-time future state prediction and control. For global atmospheric chemistry, only the leading-order DMD modes are necessary to reconstruct the chemical concentration time series and predict future states of the high-dimensional dynamics. Thus, the complex chemical processes in the atmosphere can be well approximated by judicious selection of variables representing global chemistry.