Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Analysis of spring break-up and its effects on a biomass feedstock supply chain in northern Michigan

Demand for bio-fuels is expected to increase, due to rising prices of fossil fuels and concerns over greenhouse gas emissions and energy security. The overall cost of biomass energy generation is primarily related to biomass harvesting activity, transportation, and storage. With a commercial-scale cellulosic ethanol processing facility in Kinross Township of Chippewa County, Michigan about to be built, models including a simulation model and an optimization model have been developed to provide decision support for the facility. Both models track cost, emissions and energy consumption. While the optimization model provides guidance for a long-term strategic plan, the simulation model aims to present detailed output for specified operational scenarios over an annual period. Most importantly, the simulation model considers the uncertainty of spring break-up timing, i.e., seasonal road restrictions. Spring break-up timing is important because it will impact the feasibility of harvesting activity and the time duration of transportation restrictions, which significantly changes the availability of feedstock for the processing facility. This thesis focuses on the statistical model of spring break-up used in the simulation model. Spring break-up timing depends on various factors, including temperature, road conditions and soil type, as well as individual decision making processes at the county level. The spring break-up model, based on the historical spring break-up data from 27 counties over the period of 2002-2010, starts by specifying the probability distribution of a particular county’s spring break-up start day and end day, and then relates the spring break-up timing of the other counties in the harvesting zone to the first county. In order to estimate the dependence relationship between counties, regression analyses, including standard linear regression and reduced major axis regression, are conducted. Using realizations (scenarios) of spring break-up generated by the statistical spring breakup model, the simulation model is able to probabilistically evaluate different harvesting and transportation plans to help the bio-fuel facility select the most effective strategy. For early spring break-up, which usually indicates a longer than average break-up period, more log storage is required, total cost increases, and the probability of plant closure increases. The risk of plant closure may be partially offset through increased use of rail transportation, which is not subject to spring break-up restrictions. However, rail availability and rail yard storage may then become limiting factors in the supply chain. Rail use will impact total cost, energy consumption, system-wide CO2 emissions, and the reliability of providing feedstock to the bio-fuel processing facility.