19 June 2001
VALIDATION OF THE LINEAR
DISPERSION EQUATION
USING FIELD OBSERVATION
K. T. Holland
Naval Research Laboratory
Stennis Space Center, MS 39529-5004
Abstract
The Naval Research Laboratory working with representatives from the Naval Meterology and Oceanography Command, the Naval Oceanographic Office, the Office of Naval Research, MEDEA, and MITRE, was tasked to investigate and validate two existing satellite remote sensing methods for determining bathymetry. Both of these methods utilize the linear, finite depth, dispersion equation for surface gravity waves to determine water depth from measurements of wavenumber magnitude as a function of frequency. Although the main objective of the team's efforts was to quantify the accuracy and efficiency of each method, a secondary task was to identify possible error sources resulting from the use of the dispersion relation under field conditions. This publication describes the results of the dispersion relation validation effort.
Several hundred observations of wavenumber magnitude for frequencies less than 0.3 Hz were obtained over a wide variety of conditions at the Duck, NC field site. These data were computed using sophisticated signal processing algorithms that yield precise estimates of wavenumber that were used to predict water depths assuming the linear dispersion relation. For water depths outside the surf zone region, the results indicate that the linear dispersion relation was highly accurate, with average depth estimation errors on the order of 6% of the observed depth. In shallower regions where wave breaking is evident and nonlinear effects are more pronounced, nominally 4 m and less for Duck, discrepancies between measured and predicted depths of well over 50% were observed.
Correlations between the magnitude of the depth error and measured wave amplitudes suggest the importance of wave amplitude in the calculation of shallow water phase speeds, and correspondingly in the use of the dispersion relation in the surf zone region.
Sponsored by the Office of Naval Research.
Published as
a Naval Research Laboratory report.
Naval Research Laboratory Contribution Number NRL/MR/7442 98-8084, March 2,
1998.
NRL Memorandum Report