Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

A series of spatial wave images recorded by a conventional marine radar is analyzed to determine the three-dimensional E(kx, ky, ω) spectrum. In the absence of a surface current the spectral energy in this three-dimensional wave number frequency space will lie on a shell defined by the dispersion relationship. Any deviation from the expected dispersion relationship can be interpreted as being due to a current induced Doppler shift of the wave frequency. A least squares curve fitting technique is used to determine the surface current required to account for the observed Doppler shift. A comparison of the radar determined spectra and surface currents with ground truth data indicates that the radar system and analysis technique produces results consistent with conventional instrumentation.

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A three-dimensional analysis of marine radar images for the determination of ocean wave directionality and surface currents

The median Doppler shift of radar echoes is analyzed in measurements by ENVISAT's Advanced Synthetic Aperture Radar (ASAR) over the ocean. This Doppler centroid differs from a predicted signal based on the predicted motion of the satellite and Earth. This anomaly, converted to a surface Doppler velocity U D , appears to be of geophysical origin. Two wide-swath images over the Gulf Stream around Cape Hatteras suggest that U D contains high-resolution information on surface currents, while on a global scale, U D is found to vary with the wind speed in the range direction. A simple quantitative forward model is proposed, based on a practical two-scale decomposition of the surface geometry and kinematics. The model represents the effect of the wind through the wave spectrum, and gives U D ≈ γU 10 ∥ + U c ∥ , with U 10 ∥ and U c ∥ as the 10 m wind speed and quasi-Eulerian current in the line of sight of the radar projected on the sea surface, respectively, and γ as a coefficient function of the wind speed, wave development, and radar geometry. It is found that for an incidence angle of 23°, γ ≈ 0.3 for moderate winds and fully developed seas. This model is validated with a global data set of ASAR Wave Mode observations, with colocated model winds, acquired over the global ocean during the years 2003 and 2004. The Doppler signal therefore provides the signed parameter U D that can be used to reduce the wind direction ambiguity in the inversion of high-resolution wind fields from SAR imagery. A qualitative validation of current effects is shown for the English Channel where tidal currents dominate. Thus it should be possible to combine this previously ignored geophysical Doppler signal with traditional information on sea surface roughness, in order to provide very high resolution wind and current fields.

/pdf/direct-measurements-of-ocean-surface-velocity-from-space-3bb03mvyya.pdf

Direct measurements of ocean surface velocity from space: Interpretation and validation

The surface current response to winds is analyzed in a 2-yr time series of a 12-MHz (HF) Wellen Radar (WERA) off the west coast of France. Consistent with previous observations, the measured currents, after filtering tides, are on the order of 1.0%–1.8% of the wind speed, in a direction 10°–40° to the right of the wind, and with systematic trends as a function of wind speed. This Lagrangian current can be decomposed as the vector sum of a quasi-Eulerian current UE, representative of the top 1 m of the water column and part of the wave-induced Stokes drift Uss at the sea surface. Here, Uss is estimated with an accurate numerical wave model using a novel parameterization of wave dissipation processes. Using both observed and modeled wave spectra, Uss is found to be very well approximated by a simple function of the wind speed and significant wave height, generally increasing quadratically with the wind speed. Focusing on a site located 100 km from the mainland, the wave-induced contribution of Uss ...

https://hal.archives-ouvertes.fr/hal-00452616/document

Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface

Least-squares methods are demonstrated that extract surface current radial velocities from first-order Coastal Ocean Dynamics Applications Radar (CODAR) sea-echo Doppler spectra for the compact crossed-loop/monopole antenna system. Based on the known physics of first-order sea scatter at HF, these techniques, implemented as software, are objective and automatic in that they: a) determine from the sea-echo phase and amplitude correction factors for the antenna elements; b) separate the first-order spectrum from the surrounding continuum for arbitrarily varying current conditions; c) using statistical hypothesis testing, select and use either a single or dual-angle model for radial current patterns, whichever best fits the data; d) calculate angles associated with given radial velocities; e) combine the data into a polar-coordinate map of radial velocity versus position; and f) calculate radial velocity uncertainties at each point on the map. In addition, as interpretive aids, two methods are evaluated and compared that provide total current vectors from single-site CODAR data, along with their uncertainties: model fitting and the application of the equation of continuity. It is shown how these methods can be applied to the older, CODAR 4-element antenna system, however, the following advantages of the crossed-loop/monopole system are discussed: it is physically more compact; analysis procedures are more efficient; resulting current velocities are more accurate, because there are no side-lobe problems; and finally, it also gives the ocean wave-height directional spectrum. These methods are tested and optimized against data taken during the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE) storm (October 23-27, 1980), when surface currents varied in speed between 0-50 cm/s and over nearly 300° in angle. Current velocities were measured to a range of 36 km from the radar. Standard deviations in angle are typically 1°-3°; these translate to 2-3 cm/s rms radial velocity uncertainties over most of the coverage area, with decreased accuracy in angular sectors nearest the coast. Total current velocity vectors in strips parallel to shore obtained from model fitting have typical speed and angle uncertainties of 4 cm/s and 12°, respectively. Of the several formulations for the equation of continuity evaluated here, the best gave uncertainties of 5 cm/s, 12° at the closest range cells; these values increase rapidly with range to exceed 20 cm/s, 30° for distances greater than 20 km. The surface currents were observed to follow the wind throughout most of the storm at ARSLOE, but the current was almost always more closely parallel to the shore than the wind. An interesting exception occurred when the onshore storm wind that had prevailed for two days ceased; there was a rush of surface current directly offshore as the storm-surge sea level dropped. The surface current speed measured by CODAR in the upper meter of the ocean was, on the average, 2.1 percent of the windspeed.

http://www.codar.com/images/about/1983LipaBarr_LS.pdf

Least-squares methods for the extraction of surface currents from CODAR crossed-loop data: Application at ARSLOE

HF radio measurements of surface currents

HF radio waves backscattered from the ocean surface can be used to measure ocean surface currents. Measurements of the range-Doppler spectrum of these signals yields the wavelength and frequency of the scattering ocean waves, and thus their phase velocity. This velocity is subtracted from the velocity the wave would have in still water, and the difference is a measure of the average (over depth) of the surface current. To test these ideas, we measured currents using a conventional and the IiF technique, and found reasonable agreement between the two measurements.

Joseph W. Joy

Papers

HF radio measurements of surface currents

Hf radio measurements of ocean currents