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.

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Aircraft and satellite‐borne multispectral sensors such as ocean color scanners, spectrometers, and scanning Lidar's have proved to be effective in detecting submarine shallow‐water bottom topography in clear coastal waters. For such studies the blue‐green band of the visible electromagnetic spectrum (wavelength between 400 and 580 nm) is used, because natural light in this range has the deepest penetration into the water column. However, if the water becomes turbid, the reflection from the submarine sea bed disappears. In this case the only possible mechanism available in the optical range of the electromagnetic spectrum for detecting surface signatures of shallow water bottom topography is through the observation of direct sunlight specularly reflected from a roughened sea surface, known as sun glitter radiance. As the tidal flow over irregularities on the submarine sea bed creates surface roughness variations, sun glitter imagery can be used to detect such features. In this paper a first‐order theory of the sun glitter imaging mechanism of submerged sand waves is presented. The results of sun glitter radiance modulations are compared with simulations of P band radar cross‐section modulations and with experimental data. Calculations of both the constant background sun glitter radiance and the sun glitter radiance modulation show that these parameters are very sensitive to wind speed, to view angle with respect to acquisition time, and to observation geometry as a whole.

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The simple theoretical model of Alpers and Hennings describing the radar imaging of submarine bottom topography in coastal waters with strong unidirectional tidal currents is analytically extended to show the influence of advection. The theory applies for L band radar, where second‐order terms in the hydrodynamic interaction can be neglected as a first approximation. If future imaging radars from satellites and space platforms as the ERS‐I (First European Remote Sensing Satellite), the JERS‐I (First Japanese Earth Remote Sensing Satellite), and the EOS (Earth Observing System) are to be used for cartographic applications, it is necessary to include the effect of advection to improve accuracy. This extension of the model simulates the position of the radar cross‐section modulation relative to coastal geomorphological bedforms. By application of that theory it is possible to map features such as the crests of sandbanks and sand waves.