Scalable diagnostics, forecasting and reduced-order model discovery for global atmospheric chemistry data*

We introduce a new set of algorithmic tools capable of producing scalable decompositions for the diagnostics, forecasting, and model reduction of global atmospheric chemistry data.  By exploiting emerging randomized linear algebra algorithms, a suite of decompositions are proposed that extract low-rank features from atmospheric data with improved interpretability.  Importantly, our proposed algorithms scale with the intrinsic rank rather than the ever increasing spatio-temporal measurement space.  In addition to scalability, three additional innovations are proposed for improved interpretability:  (i) a non-negative decomposition of the data is demonstrated, improving interpretability by constraining the chemical space to have only positive expression values, and (ii) sparse matrix decompositions, which thresholds low-correlations to zero, thus highlighting dominant spatial activity, and (iii) a model discovery technique for building reduced order models of global chemistry.   Our methods are demonstrated on global chemistry data, showing improvements in computational speed and interpretability.  Such technologies are critically enabling for real-time global monitoring.