Date of Award:

5-2009

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

Juergen Symanzik

Abstract

The circular dataimage is defined by displaying direction as the color at the same direction in a color wheel composed of a sequence of two-color gradients with color continuity between gradients. The resulting image of circular-spatial data is continuous with high resolution. Examples include ocean wind direction, Earth's main magnetic field, and rocket nozzle internal combustion flow. The cosineogram is defined as the mean cosine of the angle between random components of direction as a function of distance between observation locations. It expresses the spatial correlation of circular-spatial data. A circular kriging solution is developed based on a model fitted to the cosineogram. A method for simulating circular random fields is given based on a transformation of a Gaussian random field. It is adaptable to any continuous probability distribution. Circular random fields were implemented for selected circular probability distributions. An R software package was created with functions and documentation.

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Mathematics Commons

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