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Improving mechanistic understanding and prediction capabilities of long-term organic soil system dynamics is a high priority for biogeochemists, soil scientists, and climate policy researchers who aim to reduce uncertainty regarding changes in the global trajectory of soil carbon sequestration and emissions. While popular "black box" machine learning and classical statistics approaches including XGBoost, LSTM, and ARIMA have been demonstrated to be effective and efficient for time series forecasting, they are not designed to inform on the physical processes underlying a data generating process. Instead, we can turn to soil biogeochemical models, also known as soil carbon models, to jointly predict and falsify soil dynamics. Soil biogeochemical models are formulated to simulate the microbe-driven movement of organic elements between terrestrial pools of soil organic matter. As dynamical systems, they provide an avenue to mathematically translate and formalize hypotheses about soil system mechanics into parameterized differential equations.If we assume that soil biogeochemical models superior at describing empirical soil measurements more closely represent the actual data generating processes, we can surmise that models better at fitting data under biologically realistic parameter regimes are more useful for forecasting purposes; mismatch to data can suggest a need to reparameterize or restructure a model. However, the determination of statistical frameworks that can rigorously assess the capability of models to assimilate observations under compute time and resource limitations remains an open and unsettled issue. On this note, we will first expound on soil biogeochemical models in greater detail and motivate the use of Bayesian statistical methods as a means of model fitting and parameter inference while incorporating expert uncertainty and beliefs across the first two chapters of this interdisciplinary dissertation. Subsequently, we will demonstrate the use of a contemporary inference algorithm to assimilate two models with the same data set and then compare their goodness-of-fit quantified with Bayesian information criteria and cross-validation metrics. Finally, in the remaining chapters, we will trial the ability of two novel Bayesian soil biogeochemical model inference schemes offering improved computational efficiency to recover observations and parameter values of known synthetic data generating processes and evidence algorithm functionality worthy of future exploration.

Abstract: Project risks and uncertainties cause unpredictable project performance. This research intended to demonstrate that project control can be improved with the proceeding of a project, by exploiting new, available project information, and reducing uncertainties. The purpose of this study was to investigate effective tools and methods for dynamic project control. The main research work refers to the creation of a project monitoring system, tunnel construction simulation, adaptive modeling, project forecasting and planning, and cost contingency forecasting. A project monitoring system was developed to capture progress data. It also provides project progress data for updating a tunnel construction simulation model, which is built on the High Level Architecture. A Bayesian updating simulation component was developed to automatically integrate progress inputs to update key simulation model inputs. Thus, the simulation model is able to revise the inputs in light of the actual progress, to reflect the latest performance, and to ensure the validity of model inputs. The simulation results are then used to forecast future performance, and plan future work. Systematic project schedules and plans were provided, identifying the production, labour hours, equipment hours, and time to completion, as well as the resource and constraints of each main task. Additionally, this research introduced and applied Value at Risk to forecast project contingency, by utilizing actual daily cost as inputs. The forecasted cost contingency, together with labour hours and equipment hours from the simulation model, provides the basis for project budget planning and allocation. The web-based project progress monitoring system can reduce the time and effort needed for project control. The simulation model provides dynamic project planning and helps the project management team to gain insight into ongoing projects. The cost contingency forecast method provides opportunities to update contingencies, and allocate appropriate contingencies at project milestones, which allows companies to improve capital fund utilization. This research lays a solid foundation for future endeavours in how to make use of newly available project information to improve project control and planning as the project progresses.

With the advent of the tremendous development in multifrequency, polarimetric and interferometric techniques in synthetic aperture radar (SAR) imaging systems, the need for developing efficient and robust computerized automatic information extraction algorithms is becoming increasingly important for the utilization of SAR imagery. Due to the multi-resolution nature and time-frequency localization property of wavelet representations, image processing in the wavelet domain becomes more efficient and effective. In this dissertation, we develop multi-resolution algorithms for SAR image processing problems, speckle reduction and image registration in particular. Speckle is generally modeled as multiplicative random noise. New techniques based on wavelet multi-resolution analysis have been recently applied in the area of SAR image processing. In some specific cases, these techniques call for a signal model with additive white Gaussian noise and a logarithmic transform is traditionally used to adapt the SAR signal to this requirement. In the first part of this dissertation, the statistical properties of the log-transformed speckle noise are studied. The characterization of the transformed speckle given in this part is meant to call attention to the potential problems of such an approach, and to help in formulating the proper and quantitative justification for this passage. Speckle reduction is a vital first step for most SAR image processing tasks. In the second part of this dissertation, two wavelet despeckling algorithms are developed. The first one fuses the wavelet Bayesian estimation technique and Markov random field modeling to achieve spatially adaptive filtering. In contrast with the first method, the second is designed to work directly on the original SAR image without performing a logarithmic transformation. It accomplishes speckle reduction via the minimum mean square error estimation technique in the wavelet domain. Experiments indicate that both of the two proposed algorithms provide considerable improvement over the other relevant algorithms. In the last part of this dissertation, the potential of mutual information as a similarity criterion for automated SAR image registration is investigated. In order for mutual information to be applicable for SAR images, a couple of remedies are proposed, consisting of speckle reduction prior to registration and a cautious selection of the number of bins for histogram construction. In addition, a multiresolution framework is devised for SAR image elastic registration. An example of registering a pair of real SAR images demonstrates the use of mutual information as a registration quality measure along with the proposed remedies.