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Project Completion Report / OWRT Project No. A-027-ARIZ / Development of a mathematical model of infiltration which includes the effects of raindrop impact / Agreement No. 14-31-0001-3503 / Project Dates: July 1971-December 1972. / The purpose of this investigation was to use an existing mathematical model of infiltration to assist in determining which factors, including raindrop impaction, were responsible for infiltration characteristics of a bare semiarid watershed. The infiltration model developed by Roger Smith was selected as best suited for this investigation. Several laboratory and field rainfall simulator runs were modeled. Good correlation was found between the modeled and experimental results for both the infiltration data and the saturation profiles, for both bare and grass covered plots. For the lab and field experiments a realistic rotating disk rainfall simulator was used. In the field tests bare and grass covered plots were tested. In the lab specially constructed soil boxes were used that permitted measurement of infiltration and saturation profiles with time. Gross changes in saturated hydraulic conductivities due to crusting effects were also measured. Gamma ray attenuation techniques were used to obtain density and soil moisture profiles for the laboratory experiments. It was found that the Smith model can be used to simulate infiltration from different surface conditions as long as there is some method to calibrate the model. Carefully obtained saturated and unsaturated hydraulic properties for the soil types present in the watershed are needed in addition to infiltration data from a realistic rainfall simulator or through hydrograph analysis from unit subwatersheds.

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Spatial competition, in the context of industry-wide changes in retailing formats and strategies, is addressed in this dissertation from a theoretical modelling perspective. Chapter2 develops a normative individual choice model to explore how "power retailers" affect grocery shopping behaviour, and, consequently, market share. Power retailers are very large retail outlets that compete primarily on price, and are known variously as warehouse clubs, category killers, and superstores. The model shows that consideration of consumer stockpiling can lead to an "increasing returns" nonlinear response of market share to price reductions, and that the effect is not noticeable when competitors have small price differences. The model also differentiates between perishable and nonperishable goods, and shows that this may drive planned multistore shopping. Chapter 3 starts with the observation that competent management in many sectors of retailing, including grocery retailing, requires an ability to respond quickly and effectively to unexpected adversity. This dynamic is included in an oligopolistic spatial interaction model, and the system is shown to evolve to a novel and robust stochastic steady state known as self-organized criticality (SOC). One characteristic of the SOC state is that it allows small exogenous shocks to produce large responses at a rate greater than would be expected if the law of large numbers applied. This work represents the first known investigation of SOC in a marketing setting.

The main topic of this thesis is how to combine model outputs from deterministic models with measurements from monitoring stations for air pollutants or other meteorological variables. We consider two different approaches to address this particular problem. The first approach is by using the Bayesian Melding (BM) model proposed by Fuentes and Raftery (2005). We successfully implement this model and conduct several simulation studies to examine the performance of this model in different scenarios. We also apply the melding model to the ozone data to show the importance of using the Bayesian melding model to calibrate the model outputs. That is, to adjust the model outputs for the prediction of measurements. Due to the Bayesian framework of the melding model, we can extend it to incorporate other components such as ensemble models, reversible jump MCMC for variable selection. However, the BM model is purely a spatial model and we generally have to deal with space-time dataset in practice. The deficiency of the BM approach leads us to a second approach, an alternative to the BM model, which is a linear mixed model (different from most linear mixed models, the random effects being spatially correlated) with temporally and spatially correlated residuals. We assume the spatial and temporal correlation are separable and use an AR process to model the temporal correlation. We also develop a multivariate version of this model. Both the melding model and linear mixed model are Bayesian hierarchical models, which can better estimate the uncertainties of the estimates and predictions.

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