Mana computer programs have been developed for solving slope stability problems. Since slope stability problems can be characterized as optimization problems, many optimization techniques can be used for searching for the lowest safety factor for a given problem and the corresponding critical slip surface. Most of the slope stability programs use the direct search method which requires only the function value (i.e., safety factor value). In this thesis, a new optimization technique, the Broyden (1970), Fletcher (1970), Goldfarb (1970), and Shanno (1970) (BFGS) quasi-Newton optimization method, is used in conjunction with the STABR program of Lefebvre (1971) to solve slope stability problems. This method of optimization requires the function value and the first derivative value, which can be found by the finite difference method. A new program CSLIP3, incorporating the BFGS technique, is used to solve a variety of realistic slope stability problems. It is determined that CSLIP3 is reliable and efficient.

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While the applications of Geographic Information Systems (GIS) have progressed from a descriptive tool to a decision making and modeling tool, the understanding of errors and variability of the components of a GIS has lagged behind. Slope is one of these components. This dissertation evaluates different methods for determining and characterizing slope values in polygons and how these methods affect natural resource models. Eight different previously used methods for determining cell slope values were compared using elevation data from the USGS Big Stone Gap, Virginia, Digital Elevation Model. The 28 pairwise comparisons were statistically different, but for practical applications six of the comparisons were similar with an average slope difference of less than one percent. In a decision model the effect of changing just the slope method used to determine cell slope values can influence the results of a model enough to cause almost a 10 fold difference. Since usually the smallest administered unit in natural resource management is the stand (polygon), nine ways of describing the slope of a polygon for 240 polygons using an aggregation of cell slope values were investigated. These polygon descriptors were mean, trim mean, median, mode, first quartile, third quartile, standard deviation, minimum and maximum cell slope value. Also, a new method of determining polygon slope was examined using trend surface techniques, which is not based on aggregation of single cell slope values. The distributions of cell slope values in a polygon cannot be assumed normal since few polygons had a normal distribution. The sensitivity of these polygon slope descriptors to polygon area and surface complexity, based on fractal dimension, was examined and found not to affect these polygon characteristics. The application and logical decisions required to choose an appropriate slope method and polygon slope descriptor(s) based on model objectives are shown in two examples, a harvesting and USLE model. Automating the process of choosing the appropriate polygon slope descriptor(s) and how to integrate these methods in an operational GIS using an Expert System is discussed. / Ph. D.