Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Landscape Patterns of Permafrost Disturbance and Degradation in the Canadian High Arctic

Intensification of permafrost disturbances such as active layer detachments (ALDs) and retrogressive thaw slumps (RTS) have been observed across the circumpolar Arctic. These features are indicators of unstable conditions stemming from recent climate warming and permafrost degradation. In order to understand the processes interacting to give rise to these features, a multidisciplinary approach is required; i.e., interactions between geomorphology, hydrology, vegetation and ground thermal conditions. The goal of this research is to detect and map permafrost disturbance, predict landscape controls over disturbance and determine approaches for monitoring disturbance, all with the goal of contributing to the mitigation of permafrost hazards. Permafrost disturbance inventories were created by applying semi-automatic change detection techniques to IKONOS satellite imagery collected at the Cape Bounty Arctic Watershed Observatory (CBAWO). These methods provide a means to estimate the spatial distribution of permafrost disturbances for a given area for use as an input in susceptibility modelling. Permafrost disturbance susceptibility models were then developed using generalized additive and generalized linear models (GAM, GLM) fitted to disturbed and undisturbed locations and relevant GIS-derived predictor variables (slope, potential solar radiation, elevation). These models successfully delineated areas across the landscape that were susceptible to disturbances locally and regionally when transferred to an independent validation location. Permafrost disturbance susceptibility models are a first-order assessment of landscape susceptibility and are promising for designing land management strategies for remote permafrost regions. Additionally, geomorphic patterns associated with higher susceptibility provide important knowledge about processes associated with the initiation of disturbances. Permafrost degradation was analyzed at the CBAWO using differential interferometric synthetic aperture radar (DInSAR). Active-layer dynamics were interpreted using inter-seasonal and intra-seasonal displacement measurements and highlight the importance of hydroclimatic factors on active layer change. Collectively, these research approaches contribute to permafrost monitoring and the assessment of landscape-scale vulnerability in order to develop permafrost disturbance mitigation strategies.