Depth Inversion in the Surf Zone with Inclusion of Wave Nonlinearity Using Video-Derived Celerity

A process is described for computation of bathymetry in and near the surf zone, from spatially varying celerity and breakpoint location data. The procedure involves the use of three submodels: (1) a wave shoaling model (outside of the surf zone); (2) a wave breaking model (defining the offshore boundary of the surf zone); and (3) a wave dissipation model (inside the surf zone). Influence of wave amplitude on the wave dispersion relation and celerity is included. Output includes wave height and water depth throughout the domain. In the application described here, oblique digital video served as the initial data source, although the model could be applied to data derived from other sources. Results are compared with data recorded by in situ sensors and beach profile survey data acquired by traditional means. Results suggest that water depths can be computed within 15% normalized error (equally, less than 0.1 m in biased depth error) for in and near the surf zone characterized by high wave nonlinearity.

[1]  I. A. Svendsen,et al.  WAVE CHARACTERISTICS IN THE SURF ZONE , 1978 .

[2]  A. Kimura,et al.  THE MEASURED PROPERTIES OF IRREGULAR WAVE BREAKING AND WAVE HEIGHT CHANGE AFTER BREAKING ON THE SLOPE , 1988 .

[3]  Todd K. Holland,et al.  Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery , 2001, IEEE Trans. Geosci. Remote. Sens..

[4]  Fionn Murtagh,et al.  Cluster Dissection and Analysis: Theory, Fortran Programs, Examples. , 1986 .

[5]  R. Holman,et al.  An optical technique for the measurement of longshore currents , 2003 .

[6]  Hermann M. Fritz,et al.  2004 Indian Ocean tsunami flow velocity measurements from survivor videos , 2006 .

[7]  J. A. Roelvink,et al.  Nearshore subtidal bathymetry from time-exposure video images , 2005 .

[8]  H. Demir.  A process-based model for beach profile evolution , 2007 .

[9]  C. C. Piotrowski,et al.  Water depth and surface current retrievals from airborne optical measurements of surface gravity wave dispersion , 2001 .

[10]  Edward B. Thornton,et al.  Energy saturation and phase speeds measured on a natural beach , 1982 .

[11]  Patricio A. Catalán,et al.  Remote sensing of breaking wave phase speeds with application to non-linear depth inversions , 2008 .

[12]  J. Kamphuis.  Incipient wave breaking , 1991 .

[13]  Yi-Yu Kuo,et al.  COASTAL BATHYMETRY FROM THE WAVE SPECTRUM OF SPOT IMAGES , 1999 .

[14]  G. Farquharson,et al.  Comparison of optical and radar measurements of surf and swash zone velocity fields , 2003 .

[15]  R. Bracewell.  Two-dimensional imaging , 1994 .

[16]  J. Hansen,et al.  Periodic waves in the surf zone: Analysis of experimental data , 1990 .

[17]  Bruce A. Ebersole,et al.  Modelling waves and currents at the LSTF and other laboratory facilities , 2003 .

[18]  Robert A. Dalrymple,et al.  An approximate model for nonlinear dispersion in monochromatic wave propagation models , 1986 .

[19]  Characteristics of abnormal large waves measured from coastal videos , 2010 .

[20]  Robert G. Dean,et al.  Wave height variation across beaches of arbitrary profile , 1985 .

[21]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Robert A. Holman,et al.  Phase Speed and Angle of Breaking Waves Measured with Video Techniques , 1991 .

[23]  A. Benetazzo.  Measurements of short water waves using stereo matched image sequences , 2006 .

[24]  Neal R. Pettigrew,et al.  Observations of wave height and wave celerity in the surf zone , 1977 .

[25]  Edward B. Thornton,et al.  Transformation of wave height distribution , 1983 .

[26]  R. Holman,et al.  Estimation of wave phase speed and nearshore bathymetry from video imagery , 2000 .

[27]  Robert A. Holman,et al.  Quantification of sand bar morphology: A video technique based on wave dissipation , 1989 .

[28]  W. Dally.  Random breaking waves: Field verification of a wave-by-wave algorithm for engineering application , 1992 .