Predictive Modeling of Environmental Systems: Applications of parameter estimation, data assimilation, sensitivity analysis, and model emulation

In 2013, the World Meteorological Organization (WMO) urged the global community for coordinated international action against accelerating and potentially devastating climate change. Preliminary data indicated that CO2 levels increased more between 2012 and 2013 than during any other year since 1984, and this was possibly related to reduced uptake by the Earth's biosphere in addition to the steadily increasing emissions from the Earth's surface. In the upcoming decades, it will be critical for scientists and policy makers to not only resolve the problem of carbon emissions by assessing human behavior, but also to understand as thoroughly as possible the underlying coupled processes of the Earth's atmosphere and biosphere in order to adequately measure and estimate the fluxes of carbon, water, and energy that are dictating the climatic trends we observe today. Fortunately, our ability to understand Earth's processes and predict climate change is improving. This thesis covers a suite of environmental models and numerical methods to disentangle information found both in observed data as well as model simulations. Various methods are applied such as parameter estimation with Markov Chain Monte Carlo (MCMC), state estimation with data assimilation using the Ensemble Kalman Filter (EnKF), and sensitivity analysis of model parameters using the Fourier Amplitude Sensitivity Test (FAST), which all in one way or another offer treatments to predictive uncertainty. Furthermore, applying these methods on more sophisticated and complex models can be impossible sometimes due to their high CPU costs; in this thesis model emulators are built using Polynomial Chaos Expansion (PCE) to reduce the computational burden for various environmental models. Overall, our goal in this dissertation is to present what tools are currently available for making predictions of environmental systems, with emphasis on maintaining accuracy of model simulations when compared to observed data, optimizing the efficiency of computationally heavy models to minimize their run time costs, and obtaining fidelity of model structures to properly represent the underlying hydrologic, biophysical, and biogeochemical processes occurring on our Earth