Small Scales, Vast Ocean

Abstract

Ocean surface topography (OST), the hills and valleys of the ocean surface, provides information on several physical phenomena at different spatial and temporal scales. At scales between 100 km and 500 km, the mesoscales, the currents of the ocean flow between the topographic highs and lows. OST measurements from nadir radar altimeters have facilitated the study of the mean oceanic flow and substantially improved oceanographic knowledge. At the smaller submesoscales, 10 km to 100 km, variations of the OST are related to eddies and fronts. Additionally, tropical and extratropical cyclones produce strong disturbances of the surface topography. At the lower end of the submesoscales, with wavelengths of only a few kilometers, internal waves produced by the interaction of tidal currents and bottom topography leave perturbations on the height of the surface.

Synthetic-aperture radar (SAR) is a unique remote sensing instrument, particularly at C-band, capable of sensing the ocean surface at the submesoscales, with a wide swath, and in nearly all weather conditions. Harmony, the European Space Agency’s 10th Earth Explorer, features two SAR companion satellites. Two, out of a total of five, years of the mission’s life will be spent in a formation where the system will operate as a cross-track interferometer. Cross-track interferometry (XTI) is a technique that estimates the relative height of the surface from two SAR images of the same scene. Thus, Harmony could theoretically retrieve variations of the OST. In other words, the system could operate as a bistatic wide-swath ocean altimeter (WSOA). At the same time, Harmony will retrieve stress-equivalent wind fields, and instantaneous surface currents. Therefore, Harmony has the potential of providing an unprecedented wealth of co-located simultaneous data related to the ocean and the atmosphere. The aim of this thesis is to devise a method to estimate submesoscale ocean surface topography with a bistatic SAR interferometer, such as Harmony.

Assessing the design of a bistatic WSOA requires knowledge of the interferometric sensitivity, and temporal lag. The first obstacle that we encountered was that there is no model or analytical expression for these parameters that apply to a bistatic SAR with a squinted line of sight. The established relations found in the literature assume a zero-squint geometry. Hence, we use the Fourier Diffraction Slice Theorem to derive an analytical expression for the interferometric sensitivity, and the temporal lag. We show that forming an interferogram aligns the regions of support of the two images in the Fourier domain at each resolution cell, and that the temporal lag is the time offset that aligns the two regions. The sensitivity is equal to the vertical component of the aligned wave vectors projected on the elevation direction. We verify our results using simulations and confirm that our analytical expressions agree with the well-established relations for sensitivity and temporal lag for zero-squint systems.

We use the analytical expressions of sensitivity and temporal lag to build an interferometric performance model that computes the standard error of the height estimate for a formation-flying cross-track interferometer. The model considers the following random error sources: temporal decorrelation, thermal noise, spectral shift, volumetric decorrelation, and the effect of removing the phase due to motion of the surface using the individual phase centers of the instruments. Additionally, we derive a relation between the formation parameters that, when satisfied, minimizes the effective temporal lag, while maximizing the interferometric sensitivity. We then proceed to assess the performance over an orbit and along the 250 km-swath of an optimized formation.

Finally, we propose a data-driven algorithm to synchronize the signals of the independent SAR receivers. The algorithm achieves an unbiased root mean square error of 0.010◦ , reducing the phase synchronization error to within the error budget allocation.

Overall, the thesis presents how one can design, analyze, and retrieve relative ocean topography at the submesoscales with a bistatic SAR interferometer. It sets the foundations for an experimental OST product for the Harmony mission. Adding such a product to the mission would offer the first simultaneously acquired observations of wind field, current field, directional wave spectrum, and relative sea-surface height at high resolution and over a 250 km-wide swath.