A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar

Abstract

A simple theoretical model of the imaging mechanism of underwater bottom topography in tidal channels by real and by synthetic aperture radar (SAR) is presented. The imaging is attributed to surface effects induced by current variations over bottom topography. The current modulates the short‐scale surface roughness, which in turn gives rise to changes in radar reflectivity. The bottom topography‐current interaction is described by the continuity equation, and the current‐short surface wave interaction is described by weak hydrodynamic interaction theory in the relaxation time approximation. This theory contains only one free parameter, which is the relaxation time. It is shown that in the case of tidal flow over large‐scale bottom topographic features, e.g., over sandbanks, the radar cross‐section modulation is proportional to the product of the relaxation time and the gradient of the surface current velocity, which is proportional to the slope of the water depth divided by the square of the depth. To first order, this modulation is independent of wind direction. In the case of SAR imaging, in addition to the above mentioned hydrodynamic modulation, phase modulation or velocity bunching also contributes to the imaging. However, in general, the phase modulation is small in comparison to the hydrodynamic modulation. The theory is confronted with experimental data which show that to first order our theory is capable of explaining basic features of the radar imaging mechanism of underwater bottom topography in tidal channels. In order to explain the large observed modulation of radar reflectivity we are compelled to assume a large relaxation time, which for Seasat SAR Bragg waves (wavelength 34 cm) is of the order of 30–40 s, corresponding to 60–80 wave periods.

Sun glitter imaging of submarine sand waves on the Taiwan Banks: Determination of the relaxation rate of short waves

“…[9] Weak hydrodynamic interaction theory has been used to describe the interaction of the surface short water waves with a variable current [Alpers and Hennings, 1984]. The first-order expression is deduced based on the Fourier transform as…”

“…According to Alpers and Hennings [1984], u(K) is expressed as [10] The term K(U 0 + c g ) in equation (1) is defined as the advection rate m a [Alpers and Hennings, 1984] and its reciprocal is the advection time t a…”

“…[5] The relaxation rate (or wave growth rate) m r is one of the most important parameters in imaging models of sea bottom topography for both space-borne radar [Alpers and Hennings, 1984;Zimmerman, 1985;Vogelzang et al, 1997] and Sun glitter [Hennings et al, 1994]. The magnitude of water depth variations retrieved from SAR or Sun glitter imagery depends critically on making a correct choice for m r .…”

“…A more recent study reveals that deep water (>500 m) oceanic bathymetric features are also observable in radar imageries in the Gulf Stream region, where strong currents (about 2 m s −1 ) and favorable stratification occur. The generally accepted model used to explain the imaging mechanism of submarine topography in a homogeneous ocean using Synthetic Aperture Radar (SAR) is associated with three processes [Alpers and Hennings, 1984;Shuchman et al, 1985;Romeiser and Alpers, 1997]: (1) interactions between sea bottom topography and current cause modulations in the surface current velocity; (2) modulations in surface current cause variations in the spectrum of surface short waves that determine the sea surface roughness; and (3) variations in the sea surface roughness show up in radar imageries as intensity modulations. The first process can be described by a flow model such as that based on the continuity equation in the simplest case; the second process by a wave model solving the action balance equation; and the third process by a radar backscatter model.…”

Bathymetric mapping of submarine sand waves using multiangle sun glitter imagery: a case of the Taiwan Banks with ASTER stereo imagery

“…3,4 Since then, numerous studies have found that under low-to-moderate wind and strong tidal current conditions, real aperture radar and synthetic aperture radar (SAR) can detect bottom topography features in both shallow 1,[5][6][7] and deep waters. 2 One-dimensional (1-D) SAR imaging of shallow water bottom topography was first proposed by Alpers and Hennings,8 and a theoretical model was provided. 8,9 Many researchers have subsequently studied ocean topography in SAR images worldwide.…”