On the distribution of wave height in shallow water
File(s)WuEA15_SWW_submitted_revision1_20151215_for_spiral.pdf (3 MB)
Accepted version
Author(s)
Wu, Y
Randell, D
Christou, M
Ewans, K
Jonathan, P
Type
Journal Article
Abstract
The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet-Higgins, 1952) and Weibull distributions (Forristall, 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth requires new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull–Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche, 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is effectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.
Date Issued
2016-05-01
Date Acceptance
2016-01-30
Citation
Coastal Engineering, 2016, 111 (1), pp.39-49
ISSN
0378-3839
Publisher
Elsevier
Start Page
39
End Page
49
Journal / Book Title
Coastal Engineering
Volume
111
Issue
1
Copyright Statement
© 2016 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
https://www.sciencedirect.com/science/article/pii/S0378383916300060
Subjects
Science & Technology
Technology
Engineering, Civil
Engineering, Ocean
Engineering
Wave height
Shallow water
Weibull
Generalised Pareto
Miche
INTERMEDIATE
0403 Geology
0405 Oceanography
0905 Civil Engineering
Oceanography
Publication Status
Published
Date Publish Online
2016-02-23