Marine X-band Radar Based Near-surface Current Profiling

Marine X-band radar (MR) returns arise primarily due to Bragg scattering of the microwaves by ocean waves of half the radar wavelength (~3cm). In order to retrieve near-surface currents from standard (i.e. non-coherent) MR backscatter data, one must exploit the ocean wave signatures within the radar images. MRs image ocean waves through three mechanisms: tilt modulation (the waves' influence on the local incidence angle), hydrodynamic modulation (the waves' orbital motion modulating the radar scattering elements), and shadowing (wave crests blocking the radar energy in the areas behind). After transforming a sequence of MR images to Fourier space, the near-surface current can be retrieved from the 3D image spectrum by measuring the current-induced Doppler shift (i.e. the wave signal's deviation from the still water linear dispersion relationship). For high-frequency (HF) radar, it has been shown that the current measurement is a weighted average (over depth) of the near-surface current. To be precise, assuming a current that is small compared with the wave speed, the current-induced Doppler shift can be expressed in form of the Laplace transform

where u(z) is the component of the horizontal current in the radar look direction as a function of depth z, and k is the ocean wavenumber that is in Bragg-resonance with the given radar frequency. For the special case of a linear current profile, they show that the radar senses the current at an “effective” depth of (2k)^-1, or about 7.8% of the ocean wavelength. If the current profile is logarithmic, then the radar probes the current at a depth of approximately 4.4% of the ocean wavelength. In principle, multi-frequency HF radars can therefore be used to determine near-surface current shear. For example, a radar that operates on frequencies of 5.0 and 15.0MHz probes ocean wavelengths of 30 and 10m. The corresponding “effective” depths are 234 and 78cm for a linear profile, or 132 and 44cm if the profile is logarithmic. However, typical multi-frequency HF radars operate at a limited number of frequencies only, which makes the filtering of the current shear signal from the noise challenging. In contrast to HF radar near-surface currents, which are derived from the radar signal's phase-information, MR-based currents are obtained from the ocean wave signatures through, essentially, image analysis techniques, as explained above. In spite of these differences, MR currents are, just like HF radar, derived from the difference in velocity between a wave in a current field and its still water counterpart. They are therefore following the same physical laws, and have one important advantage: MRs scan the sea surface at high temporal (~1.5s) and spatial (~7.5m) resolution up to a maximum range of ~4km. As a result, MR image sequences provide a much greater wealth of information about waves (and, hence, currents), covering waves with lengths ranging from 15m to 300m or longer. The disadvantage of the existing MR near-surface current retrieval method is, however, that it treats the wave signal within the 3D spectrum in bulk, i.e. a single near-surface current value is determined from all spectral locations with energy above a given threshold. This makes determining the “effective” depth of the MR near-surface current estimate impossible, which partly explains why a comprehensive validation of MR currents is still lacking in the scientific literature. Here, a new MR-based technique that determines the near-surface current as a function of ocean wavenumber is introduced. Assuming a linear or logarithmic current profile, this technique directly yields the “effective” depths of the near-surface current estimates. We will present first MR-based estimates of near-surface current shear and place them in context with measurements of waves and wind as well as other data in order to determine the dominant current forcing mechanism. For a general current profile, the “effective” depth of the radar measurement depends on both the current profile and the radar wavelength. Determining the general near-surface current profile therefore requires the inverse solution of the above Laplace transform. We will also discuss the feasibility of solving the inverse Laplace transform numerically under the given MR data constraints.