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

Abstract

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.