Evaluating northern hardwood management using retrospective analysis and diameter distributions

Northern hardwood management was assessed throughout the state of Michigan using data collected on recently harvested stands in 2010 and 2011. Methods of forensic estimation of diameter at breast height were compared and an ideal, localized equation form was selected for use in reconstructing pre-harvest stand structures. Comparisons showed differences in predictive ability among available equation forms which led to substantial financial differences when used to estimate the value of removed timber. Management on all stands was then compared among state, private, and corporate landowners. Comparisons of harvest intensities against a liberal interpretation of a well-established management guideline showed that approximately one third of harvests were conducted in a manner which may imply that the guideline was followed. One third showed higher levels of removals than recommended, and one third of harvests were less intensive than recommended. Multiple management guidelines and postulated objectives were then synthesized into a novel system of harvest taxonomy, against which all harvests were compared. This further comparison showed approximately the same proportions of harvests, while distinguishing sanitation cuts and the future productive potential of harvests cut more intensely than suggested by guidelines. Stand structures are commonly represented using diameter distributions. Parametric and nonparametric techniques for describing diameter distributions were employed on pre-harvest and post-harvest data. A common polynomial regression procedure was found to be highly sensitive to the method of histogram construction which provides the data points for the regression. The discriminative ability of kernel density estimation was substantially different from that of the polynomial regression technique.

Development of a physically-based method for delineation of hydrologically homogeneous regions and flood quantile estimation in ungauged basins via the index flood method

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data is unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. It is generally accepted that hydrologic similarity results from similar physiographic characteristics, and thus these characteristics can be used to delineate regions and classify ungauged sites. However, as currently practiced, the delineation is highly subjective and dependent on the similarity measures and classification techniques employed. A standardized procedure for delineation of hydrologically homogeneous regions is presented herein. Key aspects are a new statistical metric to identify physically discordant sites, and the identification of an appropriate set of physically based measures of extreme hydrological similarity. A combination of multivariate statistical techniques applied to multiple flood statistics and basin characteristics for gauging stations in the Southeastern U.S. revealed that basin slope, elevation, and soil drainage largely determine the extreme hydrological behavior of a watershed. Use of these characteristics as similarity measures in the standardized approach for region delineation yields regions which are more homogeneous and more efficient for quantile estimation at ungauged sites than those delineated using alternative physically-based procedures typically employed in practice. The proposed methods and key physical characteristics are also shown to be efficient for region delineation and quantile development in alternative areas composed of watersheds with statistically different physical composition. In addition, the use of aggregated values of key watershed characteristics was found to be sufficient for the regionalization of flood data; the added time and computational effort required to derive spatially distributed watershed variables does not increase the accuracy of quantile estimators for ungauged sites. This dissertation also presents a methodology by which flood quantile estimates in Haiti can be derived using relationships developed for data rich regions of the U.S. As currently practiced, regional flood frequency techniques can only be applied within the predefined area used for model development. However, results presented herein demonstrate that the regional flood distribution can successfully be extrapolated to areas of similar physical composition located beyond the extent of that used for model development provided differences in precipitation are accounted for and the site in question can be appropriately classified within a delineated region.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.