Depth Inversion in the Surf Zone with Inclusion of Wave Nonlinearity Using Video-Derived Celerity Jeseon Yoo 1 ; Hermann M. Fritz, M.ASCE 2 ; Kevin A. Haas, M.ASCE 3 ; Paul A. Work, M.ASCE 4 ; and Christopher F. Barnes 5 Abstract: 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 applica- tion 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. DOI: 10.1061/(ASCE)WW.1943-5460.0000068. © 2011 American Society of Civil Engineers. CE Database subject headings: Breaking waves; Surf zones; Remote sensing; Water depth; Wave velocity; Wave equations; Data analysis. Author keywords: Water depth; Surf zone; Remote sensing; Wave velocity; Breaking waves; Wave equations. Introduction Remote sensing potentially provides several significant advantages over conventional measurement techniques for acquisition of bathymetric survey data in coastal environments. Spatial and tem- poral coverage can be more continuous, sensors can operate outside of the harsh surf zone environment, and multiple parameters can often be monitored simultaneously with one installation. Digital video imagery has already been used for the documentation of many different physical and geological parameters and processes in surf zone settings (Stockdon and Holman 2000; Puleo et al. 2003; Benetazzo 2006; Fritz et al. 2006; Yoo et al. 2010). Remote sensing of bathymetry, as opposed to the traditional approaches that usually involve marine vessels with acoustic sen- sors, is very desirable because it has the potential to eliminate the need for a human presence in the immediate vicinity of the area being surveyed. Video imagery is relatively easy and inexpensive to acquire, but signals in the visible light spectrum do not propagate well through the water at most sites of interest. Thus if video is to be used, a proxy for water depth must be used. Several previous stud- ies have described techniques for doing what is essentially inverse modeling, i.e., determining water depth from a signal describing the time-dependent shape of the sea surface. Some of the techniques previously applied for computation of bathymetry from video imagery are as follows: two- and/or three- dimensional Fourier Fast Transform (Leu et al. 1999; Dugan et al. 2001); cross-shore image timestack (Stockdon and Holman 2000); and time-exposure imaging (Aarninkhof et al. 2005). The first and second techniques estimate depth on the basis of a linear wave dispersion relation using local wave number and frequency analyzed from the remotely measured image pixel arrays. While the two methods provide accurate depth estimates seaward of the surf zone (errors of about 5% compared to the surveyed depth), their accuracy for the surf zone is highly degraded due to wave nonlinearity and the obscuring of image intensity signals between breaking and nonbreaking waves. The third technique uses the cross-shore intensity profile of a time-exposure (in minutes) image as the dissipation proxy for the roller energy to compute local seabed erosion and seabed accretion over the nearshore sub- tidal zone, thereby continuously monitoring bathymetric evolution, starting from the initially known beach profile over extended time scales (e.g., months to years). This work aims to invert water depth in and near the surf zone with inclusion of wave nonlinearity, using wave properties such as celerity obtained solely from remotely captured videos without any supplementary hybrid inputs of wave parameters. Direct applica- tion of the shallow-water, linear wave theory dispersion relation 1 Senior Research Scientist, Climate Change and Coastal Disaster Research Dept., Korea Ocean Research and Development Institute, 1270 Sa-2-dong, Ansan 427-744, Korea; formerly, School of Civil and Environ- mental Eng., Georgia Institute of Technology, 210 Technology Circle, Savannah, GA 31407. E-mail: jyoo@kordi.re.kr 2 Associate Professor, School of Civil and Environmental Eng., Georgia Institute of Technology, 210 Technology Circle, Savannah, GA 31407 (corresponding author). E-mail: fritz@gatech.edu 3 Associate Professor, School of Civil and Environmental Eng., Georgia Institute of Technology, 210 Technology Circle, Savannah, GA 31407. E-mail: khaas@gatech.edu 4 Associate Professor, School of Civil and Environmental Eng., Georgia Institute of Technology, 210 Technology Circle, Savannah, GA 31407. E-mail: paul.work@gtsav.gatech.edu 5 Associate Professor, School of Electrical and Computer Eng., Georgia Institute of Technology, 210 Technology Circle, Savannah, GA 31407. E-mail: chris.barnes@gatech.edu Note. This manuscript was submitted on August 26, 2009; approved on June 24, 2010; published online on July 5, 2010. Discussion period open until August 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 137, No. 2, March 1, 2011. ©ASCE, ISSN 0733-950X/2011/2-95–106/$25.00. JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING © ASCE / MARCH/APRIL 2011 / 95 Downloaded 10 Mar 2011 to 203.241.164.40. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org