Parameterization and uncertainty analysis in modeling: An application to soil greenhouse gas emission models

The aims of the dissertation were to understand and simulate soil greenhouse gas (GHG) emissions as a decision-support tool using both the systematic- and process-based models and to develop uncertainty and identifiability analysis method for model parameterization and evaluation. The proposed systematic method, a two-parameter gamma-distribution-based unit response curve (UR) model, has potential to be used to estimate the extra GHG emissions from manure and fertilizer applications. The Bayesian inference and the Markov Chain Monte Carlo (MCMC) method were combined to evaluate uncertainties in model parameters and structure and tested on a process-based model (SoilGHG) developed in this study. Results showed that nearly all the posterior parameter ranges from the multivariate normal proposal distribution (MND) of the Metropolis-Hastings algorithm were reduced to be within an order of magnitude. In addition, the covariance matrix of parameters for MND can be estimated from the parameter samples using a univariate distribution; and it is more effective to generate a Markov Chain by updating a single parameter rather than to update the entire parameter vector each time. The uncertainty analysis also generates a small posterior parameter space, which can contribute to the identification of model parameters. The covariance-inverse (CI) was adapted to derive the Hessian matrix via the inverse of the covariance matrix where the condition number of the Hessian is used for the diagnosis of model identifiability (i.e., adequate model performance determined by unique parameter values). Compared with the widely-used difference quotients (DQ) and quasi-analytical (QA) methods, CI is more effective and reliable. The identifiability diagnosis on the SoilGHG model using the CI method implied that the full model was poorly identified, but a reduced model with fewer parameters was "conditionally identifiable". Parameter optimization using the Shuffled Complex Evolution at University of Arizona (SCE-UA) algorithm implied the existence of equifinality (i.e., adequate model performance corresponds to different parameter values) in the model and proved to be effective in reducing the equifinality by attaining most of the parameters with low variations. In conclusion, the proposed uncertainty analysis and identifiability diagnosis methods can provide guidance to model development, parameterization, and evaluation.