Reduced Order Model for Global Atmospheric Chemistry Data

Abstract

Global atmospheric chemistry is an exceptionally high-dimensional problem as it involves hundreds of chemical species that are coupled with each other via a set of ordinary differential equations. Models of atmospheric chemistry that are used to simulate the spatio-temporal evolution of these chemical constituents need to keep track of each chemical species on a global scale (longitude, latitude, elevation) and at each point in time. This data can be exceptionally high-dimensional so as to be not computationally tractable. Thus computationally scalable methods are required for the analysis, reproduction and forecasting of atmospheric chemistry dynamics. First, we introduce a new set of algorithmic tools capable of producing scalable, low-rank decompositions of global spatio-temporal atmospheric chemistry data. By exploiting emerging {\em randomized linear algebra} algorithms, a suite of decompositions are proposed that extract the dominant features from {\em big data} sets with improved interpretability. Importantly, our proposed algorithms scale with the intrinsic rank of the global chemistry space rather than measurement space, thus allowing for efficient representation and compression of the data. Next, we introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model of global atmospheric chemistry dynamics. Forecasting is also achieved with a low-rank linear model that uses a linear superposition of the dominant spatio-temporal features. Bagging OPtimized DMD or BOP-DMD produces an ensemble of DMD models, thereby quantifying uncertainty, reducing model variance and suppressing over-fitting by design. We compute the temporal uncertainty metrics for the optDMD forecasts using the BOP-DMD architecture. Lastly, we explore a data-driven scalable sparse sensor placement architecture for monitoring and reproduction of global atmospheric chemistry dynamics. By combining 1) machine learning, i.e. the POD dimensionality reduction technique, which learns and extracts a set of tailored library of features in the training data to produce low-dimensional representations of the full state, and 2) sparse sampling, i.e. designing highly specialized optimal sensors using the tailored features and QR pivoting, we reconstruct the full signal in the POD basis from a small subset of sensor or point measurements instantaneously. We also discover correlation between different chemical species, indicating that the chemical space can also be compressed.