A statistical measure of regularity for the study of wind-generated wave field images
The study of water waves has generated a wealth of sophisticated modeling developments in applied mathematics. Empirical observation capabilities have created a need for novel data analysis tools. This article is motivated by consideration of wind-generated wave field image data from a wave tank facility. A quantitative measure of wave field regularity is developed. The methodology is based on decomposition of the wave field into simple plane waves (an adaptation of projection pursuit). The percent variance explained as a function of the number of terms in the plane wave representation is used to define a variogram, and regularity of the wave field is assessed in terms of the weighted difference between the observed variogram and the expected variogram for a completely random field. The proposed regularity measure is illustrated by application to image data from wind-generated waves. The results suggest that the regularity measure is a function of parameters describing the generation of the wave field (wind speed and evolution). An analysis of the statistical behavior of the regularity measure as a function of sample size (image resolution) is carried out. Even though the regularity measure is based on the nonparametric estimation of functions, provided that this estimation is carried out in a consistent fashion, the error in estimation of regularity has a parametric dependence on image resolution. © 2006 American Statistical Association.
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Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1603 Demography
- 1403 Econometrics
- 0104 Statistics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1603 Demography
- 1403 Econometrics
- 0104 Statistics