Statistical data characterization of in situ nitrate-level time series in the Mississippi watershed

摘要

Data characterization of an eight-site nitrate-level time-series array using a suite of intra- and inter-site dimensional reduction and analysis algorithms was performed as the preliminary stage of a full Bayesian state-estimation approach for understanding the Illinois section of the Mississippi watershed. Preliminary analysis shows high mean nitrate levels in the northern, western, and southern parts of the Illinois watershed with significant correlations of nitrate levels appearing not only in the southern region, but also across a north-south transect. Intra-site dimensional reduction of the eight-site array, based on empirical orthogonal function analysis and nonnegative matrix factorization, demonstrates that specific time series, lower in number than the eight-site dimension, are responsible for both global and local variability. Inter-site dimensional reduction based on Gaussian mixture modeling applied to sets of dual-site time series in the north and south shows multimodal clusters characterized by mean and covariance information. Competitive-leaky-learning-based inter-site data group modeling depicts nonlinearly generated data clusters possessing labels also based on distinct mean and covariance structure. Hidden Markov model parameter estimation applied to dual time-series sets across northern and southern regions, and over two different seasonal time scales, provides emission matrix tables with maximum probability trends consistent with the results from Gaussian mixture modeling. All facets of the machine-learning results offer a means for quantitatively describing the Illinois watershed's nitrate-level dynamics over a fall-winter seasonal time scale.