|dc.description.abstract||This dissertation consists of three parts, two of which examine methods for estimating spatial soil moisture patterns while the third investigates the reconstruction of a fluvially-eroded paleotopography. Part I of the dissertation evaluates unsupervised machine-learning techniques' effectiveness for estimating soil moisture patterns and compares them with linear regression. Physical processes that impact soil moisture are typically expressed as nonlinear functions, but most previous research on the estimation of soil moisture has relied on linear techniques. In the present work, two machine learning techniques, a spatial artificial neural network (SANN) and a mixture model (MM), that can infer nonlinear relationships are compared with multiple linear regression (MLR) for estimating soil moisture patterns using topographic attributes as predictor variables. The methods are applied to time-domain reflectometry (TDR) soil moisture data collected at three catchments with varying characteristics (Tarrawarra, Satellite Station, and Cache la Poudre) under different wetness conditions. The methods' performances with respect to the number of predictor attributes, the quantity of training data, and the attributes employed are compared using the Nash-Sutcliffe Coefficient of Efficiency (NSCE) as the performance measure. The performances of the methods are dependent on the site studied, the average soil moisture and the quantity of training data provided. Although the methods often perform similarly, the best performing method overall is the SANN, which incorporates additional predictor variables more effectively than the other methods. Next, Part II of the dissertation presents the development and testing of a new conceptually-based model for estimating soil moisture patterns and describes the investigation of the climatic, vegetation and soil characteristics that affect pattern organization and temporal stability with the model. Soil moisture is a key hydrologic state variable for the Earth's surface affecting both energy and precipitation partitioning. Additionally, the nonlinear dependence of hydrologic processes on soil moisture means that not only is the average moisture condition important for many applications, but the spatial patterns of soil moisture are also important. At the catchment scale, soil moisture patterns have been observed to exhibit different types of dependence on topography. Some catchments have their wettest locations in the valley bottoms, while others have their wettest locations on hillslopes that are oriented away from the sun. Additionally, some catchments have moisture patterns that maintain a similar organization at all times (time stability), while other catchments have soil moisture patterns that change through time (time instability). Although these tendencies are well known, the reasons for their occurrence at a particular catchment are not well understood. In this paper, we investigate the conditions under which the different types of topographic dependence and different degrees of time instability occur through the use of a new conceptual model. The type of topographic dependence and the degree of instability are quantified by two metrics that are also introduced in the paper, and the effects of soil, vegetation, and climatic parameters on these metrics are then evaluated. The evaluations indicate that saturated horizontal hydraulic conductivity, pore disconnectedness, vegetation evapotranspiration efficiency, and an exponent relating the horizontal hydraulic gradient to the topographic slope have the strongest effects on the organization and instability of the soil moisture patterns. In contrast, annual potential evapotranspiration alone does not strongly impact the organization or its stability. Finally, Part III of the dissertation describes the modification of a previously-developed interpolation scheme for fluvial topography and the reconstruction of a paleotopography that may be potentially important to groundwater movement by the modified method. Many applications in geology require estimation of the depth and thickness of lithologic layers based on limited observations. The boundaries of such layers are typically estimated using Kriging or other estimation methods that produce smooth surfaces. In some cases, however, smooth surfaces may be inappropriate. A boundary that is formed by a preserved hillslope and valley paleotopography, in particular, is expected to exhibit drainage characteristics and inherent roughness that are not consistent with standard estimation methods. This paper discusses the generalization of a technique originally designed to interpolate fluvially-eroded topography. The method incorporates a simple river basin evolution model to generate realistic topography and adjusts an erodability parameter in space to match observed elevations. The method is generalized to allow flow to enter from outside the interpolation region, which is a likely scenario when reconstructing paleotopography. The method is then applied to the lower boundary of the Tshirege Member of the Bandelier Tuff, which underlies Los Alamos National Laboratory and Bandelier National Monument in north-central New Mexico. The method produces surfaces with major valleys that are consistent with previous observations. The method is also applied in a framework that estimates the likelihood that any particular point within the interpolation region drains through a specified boundary. Although the surfaces vary between simulations, most portions of the interpolation domain drain through consistent boundaries.