Refinements to an Optimized Model-Driven Bathymetry Deduction Algorithm

• Main Authors: Narayanan, Chandrasekher, Kaihatu, James M
• Format: Publication
• Language: English
• Published: 01.09.2001
• Subjects: ALGORITHMS; BATHYMETRIC PROFILE PARAMETERS; BATHYMETRY; CYBERNETICS; FREE SURFACE IMAGERY; KORTEWEG-DEVRIES EQUATION; LEVENBERG-MARQUARDT NUMERICAL OPTIMIZATION; MATHEMATICAL MODELS; NEARSHORE BATHYMETRY DEDUCTION; OCEAN BOTTOM; OCEAN WAVES; OPTICAL DETECTION AND DETECTORS; OPTICAL RADAR; PEN62435; PHYSICAL AND DYNAMIC OCEANOGRAPHY; REMOTE DETECTION; REMOTELY-SENSED WAVE CHARACTERISTICS BATHYMETRY; SAND BAR; SHALLOW WATER; SIGNAL PROCESSING; SYMPOSIA; TIME DOMAIN; TIME-DOMAIN NONLINEAR MODELS; WAVE KINEMATICS ALGORITHMS; WAVE MODELS

In this study we describe a numerical algorithm which deduces characteristics of the bottom bathymetry given free surface elevation records dense in space but sparse in time. The method makes use of the Levenberg-Marquardt numerical optimization scheme in conjunction with a time-domain nonlinear model. Iteration occurs until the mismatch between the free surfaces of the data and model are minimized; the bathymetry is adjusted in order to achieve this minimum. The sensitivity measure is a by-product of the calculation, and determines the invertibility of the system. Due to robustness concerns, we limit ourselves to deduction of bathymetric profile parameters. Tests of the system using monochromatic, irregular and groupy waves show favorable results; the latter is particularly notable give the difficulty standard inversion methods have had with groupy waves. A two-stage system is also outlined, in which a simple parameterization for a nearshore bar is developed and utilized. The first stage determines the mean profile, while the second stage determines the bar characteristics using the first stage results as the initial iterate. To extend the method's capabilities further, the use of phase speed records is discussed. Supported as part of 6.2 NRL Core program "Dynamically Constrained Nowcasting of Near Coastal Waves and Bathymetry." Prepared in collaboration with the Naval Research Lab (NRL), Stennis Space Center, MS. Presented at the International Symposium on Ocean Wave Measurement and Analysis (4th), WAVES2001, San Fransisco, CA, on 2-6 Sep 2001 and published in the proceedings, p924-933.