Remote sensing of breaking wave phase speeds with application to non-linear depth inversions

Abstract A number of existing models for surface wave phase speeds (linear and non-linear, breaking and non-breaking waves) are reviewed and tested against phase speed data from a large-scale laboratory experiment. The results of these tests are utilized in the context of assessing the potential improvement gained by incorporating wave non-linearity in phase speed based depth inversions. The analysis is focused on the surf zone, where depth inversion accuracies are known to degrade significantly. The collected data includes very high-resolution remote sensing video and surface elevation records from fixed, in-situ wave gages. Wave phase speeds are extracted from the remote sensing data using a feature tracking technique, and local wave amplitudes are determined from the wave gage records and used for comparisons to non-linear phase speed models and for non-linear depth inversions. A series of five different regular wave conditions with a range of non-linearity and dispersion characteristics are analyzed and results show that a composite dispersion relation, which includes both non-linearity and dispersion effects, best matches the observed phase speeds across the domain and hence, improves surf zone depth estimation via depth inversions. Incorporating non-linearity into the phase speed model reduces errors to O (10%), which is a level previously found for depth inversions with small amplitude waves in intermediate water depths using linear dispersion. Considering the controlled conditions and extensive ground truth, this appears to be a practical limit for phase speed-based depth inversions. Finally, a phase speed sensitivity analysis is performed that indicates that typical nearshore sand bars should be resolvable using phase speed depth inversions. However, increasing wave steepness degrades the sensitivity of this inversion method.

[1]  Per A. Madsen,et al.  Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves , 1997 .

[2]  Robert T. Guza,et al.  Elevation and velocity measurements of laboratory shoaling waves , 1981 .

[3]  Paul S. Bell,et al.  Nested Radar Systems for Remote Coastal Observations , 2006 .

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

[5]  James R. Walker REFRACTION OF FINITE-HEIGHT AND BREAKING WAVES , 1976 .

[6]  Paul D. Komar,et al.  Beach Processes and Sedimentation , 1976 .

[7]  John P. Dugan,et al.  Accuracy of bathymetry and current retrievals from airborne optical time-series imaging of shoaling waves , 2002, IEEE Trans. Geosci. Remote. Sens..

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

[9]  J. Buhr Hansen,et al.  EXPERIMENTAL INVESTIGATION OF THE WAVE AND CURRENT MOTION OVER A LONGSHORE BAR , 1986 .

[10]  D. Peregrine Long waves on a beach , 1967, Journal of Fluid Mechanics.

[11]  Rolf Deigaard,et al.  A Boussinesq model for waves breaking in shallow water , 1993 .

[12]  M. Nicholas,et al.  Coastal engineering. , 1969, Science.

[13]  C. Guedes Soares,et al.  Comparison of Wave Spectra from Nautical Radar Images and Scalar Buoy Data , 2005 .

[14]  David R. Basco,et al.  A Qualitative Description of Wave Breaking , 1985 .

[15]  M. W. Dingemans,et al.  Water Wave Propagation Over Uneven Bottoms , 1997 .

[16]  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..

[17]  Terry Hedges,et al.  An empirical modification to linear wave theory , 1977 .

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

[19]  Ts Hedges TECHNICAL NOTE. AN EMPIRICAL MODIFICATION TO LINEAR WAVE THEORY. , 1976 .

[20]  M. Stive Energy dissipation in waves breaking on gentle slopes , 1984 .

[21]  W. Rosenthal,et al.  Ocean surface determination from X‐band radar‐image sequences , 2004 .

[22]  B. Gerben Ruessink,et al.  Video observations and model predictions of depth-induced wave dissipation , 2004, IEEE Transactions on Geoscience and Remote Sensing.

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

[24]  Per A. Madsen,et al.  Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves , 1997 .

[25]  J. Kirby,et al.  An approximate model for nonlinear dispersion in monochromatic wave propagation models, by J.T. Kirby and R.A. Dalrymple: Reply , 1987 .

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

[27]  T. Hedges An approximate model for nonlinear dispersion in monochromatic wave propagation models, by J.T. Kirby and R.A. Dalrymple: Discussion , 1987 .

[28]  P. Catalán,et al.  Nonlinear Phase Speeds and Depth Inversions , 2006 .

[29]  Philippe Bonneton WAVE CELERITY IN THE INNER SURF ZONE , 2005 .

[30]  W. W. Williams The Determination of Gradients on Enemy-Held Beaches , 1947 .

[31]  Robert A. Dalrymple,et al.  DETERMINING DEPTH FROM REMOTELY-SENSED IMAGES , 1999 .

[32]  Peter Howd,et al.  Beach Processes and Sedimentation, Second Edition , 1998 .

[33]  M. Stive VELOCITY AND PRESSURE FIELD OF SPILLING BREAKERS , 1980 .

[34]  I. A. Svendsen,et al.  Wave Breaking in Wave Groups , 2001 .

[35]  Ib A. Svendsen,et al.  Introduction to nearshore hydrodynamics , 2005 .

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

[37]  Paul S. Bell,et al.  Shallow water bathymetry derived from an analysis of X-band marine radar images of waves , 1999 .

[38]  Douglas L. Inman,et al.  Mixing in the surf zone , 1971 .

[39]  Michael B. Abbott,et al.  Computational Hydraulics , 1998 .

[40]  P. Stansby,et al.  Kinematics and depth-integrated terms in surf zone waves from laboratory measurement , 2005, Journal of Fluid Mechanics.

[41]  Colin MacFarlane,et al.  Experimental Investigation of Wave Breaking Criteria Based on Wave Phase Speeds , 2002 .

[42]  N. Booij,et al.  Gravity waves on water with non-uniform depth and current , 1981 .

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

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

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

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

[47]  I. Tseng,et al.  A New Shape Function for Bar-Type Beach Profiles , 2006 .

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

[49]  J. Buhr Hansen,et al.  DEFORMATION UP TO BREAKING OF PERIODIC WAVES ON A BEACH , 1976 .

[50]  C. P. Scott,et al.  Large-scale laboratory observations of turbulence on a fixed barred beach , 2005 .