TY - JOUR

T1 - On the distribution of wave height in shallow water

AU - Wu, Y.

AU - Randell, D.

AU - Christou, M.

AU - Ewans, K.

AU - Jonathan, P.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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. © 2016 Elsevier B.V.

AB - 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. © 2016 Elsevier B.V.

KW - Generalised Pareto

KW - Miche

KW - Shallow water

KW - Wave height

KW - Weibull

KW - Distribution functions

KW - Ocean currents

KW - Parameterization

KW - Probability density function

KW - Probability distributions

KW - Water waves

KW - Shallow waters

KW - Wave heights

KW - Weibull distribution

KW - breaking wave

KW - ocean wave

KW - shallow water

KW - water depth

KW - wave breaking

KW - wave height

KW - Weibull theory

U2 - 10.1016/j.coastaleng.2016.01.015

DO - 10.1016/j.coastaleng.2016.01.015

M3 - Journal article

VL - 111

SP - 39

EP - 49

JO - Coastal Engineering

JF - Coastal Engineering

SN - 0378-3839

ER -