Uncertainty quantification and calibration of physical models

An ecosystem model is a representation of a real complex ecological system, and is usually described by sophisticated mathematical models. Terrestrial Ecosystem Model (TEM) is one of the ecosystem models, that describes the dynamics of car- bon, nitrogen, water and other vegetation related variables. There are uncertainties in the TEM which are attributed to inaccurate input data, insufficient knowledge of the parameters, inherent randomness and simplification of the physical model. Quantification of uncertainty of such an ecosystem model is computationally very heavy. Bayesian calibration method has been used as an efficient way to calibrate and quantify uncertainties of the computer models. In this work, I develop a new approach to emulate the TEM, and to estimate the parameters along with associated uncertainties. TEM has been implemented as a deterministic computer code model. In this computer model, the inputs are envi- ronmental variables and underlying parameters, and the outputs are gross primary production (GPP), net ecosystem production (NEP) and other variables. To make predictions of future outputs from the computer model, I also estimate the under- lying parameters. With an efficient Bayesian approximation, statistical models are developed to obtain inference for the parameters and then make predictions at future time point. Chapter 1 is an introduction to the research problems. In Chapter 2, I discuss the uncertainty arose from temporal scales. In Chapter 3, I discuss the Bayesian uncertainty quantification method and further developed Bayesian calibration of pa- rameters with application to TEM in Chapter 4