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Information about extreme precipitation is of great interest for a variety of purposes, which include dam design and its operation, public safety, engineering projects concerned with river management and drainage as well as rainfall-runoff relations. These require knowledge about the spatial and temporal variability of average rainfall over an area. Design rainfall values are generally expressed in the form of point rainfall intensity values which is the rainfall depth at a location. In order to obtain areal average values for an area, hydrologists and engineers require techniques whereby point rainfall amounts can be transformed to average rainfall amounts over a specified area. This problem of point-to-area rainfall conversion can be addressed using depth-area curves which require the use of areal reduction factors. The derivation of areal reduction factors is a focal issue and has been dealt with in diverse manners. Though the methods of derivation of the areal reduction factors vary, results shown by them are comparable. But all these methods have certain shortcomings in the procedures adopted by them. In this application the analysis is based on radar rainfall values obtained from NEXRAD for the study area of Texas as provided by West Gulf River Forecasting Centre (WGRFC). Using NEXRAD radar rainfall data, geographically fixed depth area relationships will be determined. Here the objectives are to develop areal reduction factors using radar data and to identify the potential obstacles that might hinder the use of such data. The values of the factors developed will be finally compared to other studies which have been carried out. This approach aims to mitigate the difficulties faced in the applications of various procedures and the shortcomings of the various techniques used to determine the values of areal reduction factors.
This dissertation includes two parts. Part 1 develops a geostatistical method to calibrate Texas NexRad rainfall estimates using rain gauge measurements. Part 2 explores the asymptotic joint distribution of sample space-time covariance estimators. The following two paragraphs briefly summarize these two parts, respectively. Rainfall is one of the most important hydrologic model inputs and is considered a random process in time and space. Rain gauges generally provide good quality data; however, they are usually too sparse to capture the spatial variability. Radar estimates provide a better spatial representation of rainfall patterns, but they are subject to substantial biases. Our calibration of radar estimates, using gauge data, takes season, rainfall type and rainfall amount into account, and is accomplished via a combination of threshold estimation, bias reduction, regression techniques and geostatistical procedures. We explore a varying-coefficient model to adapt to the temporal variability of rainfall. The methods are illustrated using Texas rainfall data in 2003, which includes WAR-88D radar-reflectivity data and the corresponding rain gauge measurements. Simulation experiments are carried out to evaluate the accuracy of our methodology. The superiority of the proposed method lies in estimating total rainfall as well as point rainfall amount. We study the asymptotic joint distribution of sample space-time covariance esti-mators of stationary random fields. We do this without any marginal or joint distri-butional assumptions other than mild moment and mixing conditions. We consider several situations depending on whether the observations are regularly or irregularly spaced, and whether one part or the whole domain of interest is fixed or increasing. A simulation experiment illustrates the asymptotic joint normality and the asymp- totic covariance matrix of sample space-time covariance estimators as derived. An extension of this part develops a nonparametric test for full symmetry, separability, Taylor's hypothesis and isotropy of space-time covariances.
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