Geoid determination in the coastal areas of the Gulf of Mexico
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Coastal areas of the Gulf of Mexico are important for many reasons. This part of the United States provides vital coastal habitats for many marine species; the area has seen-ever increasing human settlement along the coast, ever increasing infrastructure for marine transportation of the nation's imports and exports through Gulf ports, and ever increasing recreational users of coastal resources. These important uses associated with the Gulf coast are subject to dynamic environmental and physical changes including: coastal erosion (Gulf-wide rates of 25 square miles per year), tropical storm surges, coastal subsidence, and global sea level rise. Coastal land subsidence is a major component of relative sea level rise along the coast of the Gulf of Mexico. These dynamic coastal changes should be evident in changes to the geoid along the coast. The geoid is the equipotential gravity surface of the earth, which the best fits the global mean sea level. The geoid is not only been seen as the most natural shape of the Earth, but also it serves as the reference surface for most of the height systems. By using satellites (GRACE mission) scientists have been able to measure the large scale geoid for the Earth. A small scale geoid model is required to monitor local events such as flooding, for example, flooding created by storm surges from hurricanes such as Katrina (2005), Rita (2005), and Ike (2008). The overall purpose of this study is to evaluate the accuracy of the local coastal geoid. The more precise geoid will enable to improve coastal flooding predictions, and will enable more cost effective and accurate measurement of coastal topography using global navigation satellite systems (GNSS). The main objective of this study is to devise mathematical models and computational methods to achieve the best possible precision for evaluation of the geoid in the coastal areas of the Gulf of Mexico. More specifically, the numerical objectives of this study are 1) to obtain a continuous map of gravity anomalies and a continuous map of gravity by using spatial interpolation methods and to evaluate errors; 2) to solve the Laplace boundary value problem and evaluate errors; 3) to evaluate precision of the local geoid by using geospatial statistical tools and numerical techniques. This dissertation investigates modeling of the geoid, especially the gravimetric equipotential surface that approximates mean sea level, in the coastal areas of the Gulf of Mexico as well as errors in the geoid determination. The document begins with Chapter 1 which introduces the study of this dissertation. Different models of kriging are used to determine the precision of the geoid based on the free-air gravity anomalies data supplied by United States Naval Research Laboratory and the airborne gravity data provided by the U.S. National Geodetic Survey, which can be found in Chapters 2 and 3. Research in Chapters 2 shows that more precise evaluation of errors in gravity anomalies can be achieved by using different models of kriging. Results from Chapters 2 and 3 show that ordinary kriging with the stable semivariogram model provide better predictions. Research results from Chapter 3 provide estimation of maximum possible errors in the calculation of the geoid undulation. The dissertation also investigates behavior of gravity equipotential surfaces around coastal lines and its impact on the geoid evaluation. Chapters 4 and 5 are about evaluation of errors in the Dirichlet problem for calculation of gravity potential with uncertain boundary and boundary values has been achieved by solving the Laplace equation by means of separation of variables. Research has provided a theoretical model in Chapter 4 to estimate very small changes in gravimetric potential relative to the coast. Maximum possible error in the solution of Direchlet problem is determined in Chapter 5. Maximum possible error depends on the errors of boundary values and the precision of the boundary itself. Chapter 6 describes a novel approach to sea level rise modeling. Factor analysis is used to analyze local and global sea level rise and relationships between changing sea levels, currents, and the shape of the Earth. Results of factor analysis from Chapter 6 show that the elevation of sea level relates to the geoid and ocean circulation. Chapter 7 describes the relationship between the geoid and wetlands modeling. Research in Chapter 7 shows that the predicted continuous elevation map obtained through the ordinary stable kriging was sufficiently precise and fairly reliable. Chapter 7 is an exploratory chapter, and the ideas of this chapter will help the future research.