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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.
This report attempts to show that, by fitting particular nonlinear auto-covariance and cross-covariance functions to space-time covariance values calculated from satellite data, convective complex characteristics such as size, ellipticity, motion, growth, and decay of a storm can be determined. These modeled features then can be related to convective storm characteristics found by Scofield and Oliver. In turn, these characteristics are related to actual rainfall amounts. The results of this study are a first step in removing the subjectivity from current rainfall estimation techniques. Results from the 20 May 1977 storm over Texas and Oklahoma are presented. (Author).
A summary of past work and a description of new approaches to thinking about kriging, commonly used in the prediction of a random field based on observations at some set of locations in mining, hydrology, atmospheric sciences, and geography.
Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Features Gives readers the ability to actually solve significant real-world problems Addresses many types of nonstationary time series and cutting-edge methodologies Promotes understanding of the data and associated models rather than viewing it as the output of a "black box" Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website. Over 150 exercises and extensive support for instructors The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).