Date of Award

Fall 12-2015

Degree Type


Degree Name


Degree Program

Engineering and Applied Science



Major Professor

David E. Wells; George E. Ioup

Second Advisor

Juliette W. Ioup

Third Advisor

Stanley A. Chin-Bing

Fourth Advisor

Clifford J. Mugnier

Fifth Advisor

Maria T. Kalcic


The ocean and acoustic modeling community has specifically asked for roughness from bathymetry. An effort has been undertaken to provide what can be thought of as the high frequency content of bathymetry. By contrast, the low frequency content of bathymetry is the set of contours. The two-dimensional amplitude spectrum calculated with the nonequispaced fast Fourier transform (Kunis, 2006) is exploited as the statistic to provide several parameters of roughness following the method of Fox (1996). When an area is uniformly rough, it is termed isotropically rough. When an area exhibits lineation effects (like in a trough or a ridge line in the bathymetry), the term anisotropically rough is used. A predominant spatial azimuth of lineation summarizes anisotropic roughness. The power law model fit produces a roll-off parameter that also provides insight into the roughness of the area. These four parameters give rise to several derived parameters.

Algorithmic accomplishments include reviving Fox’s method (1985, 1996) and improving the method with the possibly geophysically more appropriate nonequispaced fast Fourier transform. A new composite parameter, simply the overall integral length of the nonlinear parameterizing function, is used to make within-dataset comparisons.

A synthetic dataset and six multibeam datasets covering practically all depth regimes have been analyzed with the tools that have been developed.

Data specific contributions include possibly discovering an aspect ratio isotropic cutoff level (less than 1.2), showing a range of spectral fall-off values between about -0.5 for a sandy- bottomed Gulf of Mexico area, to about -1.8 for a coral reef area just outside of the Saipan harbor. We also rank the targeted type of dataset, the best resolution gridded datasets, from smoothest to roughest using a factor based on the kernel dimensions, a percentage from the windowing operation, all multiplied by the overall integration length.


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