Belinda Lipa

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

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.

Chapter 3 Analysis and Interpretation of Altimeter Sea Echo

Publisher Summary This chapter focuses on analysis and interpretation of altimeter sea echo. It discusses the physics behind the use of Barricks model in information extraction and data interpretation. The convolutional form of Barricks model is presented, demonstrating a simpler but efficient method for its inversion. The model is based on deconvolution by straightforward fast Fourier transform (FFT) algorithms. The important and interesting phenomenon called electromagnetic bias is discussed. In this phenomenon, the altimeter reckons the mean sea surface position to be, compared with its actual position, with all other errors/biases removed. The study of altimetric biases using models is presented. Models are developed and employed to study various factors, both instrumental and near-surface effects, that bias or distort the altimeter echo. Seasat is used to demonstrate their application. A double-deconvolutional-based algorithm is discussed for altimeter echo analysis that can handle various antenna error and rain biases, is computationally efficient, and outputs parameter uncertainties along with the parameters themselves. Concepts related to antenna pointing-error effects and rain effects on altimeter echo are also discussed in detail.

SeaSonde Radial Velocities: Derivation and Internal Consistency

This paper describes the methods presently used to produce unaveraged radial velocity maps from radar voltage cross spectra measured by a SeaSonde, including a discussion of the multiple signal classification (MUSIC) algorithm as it is applied to SeaSonde data and methods employed to alleviate difficulties associated with the use of measured antenna patterns. We also describe internal consistency checks including visual observation of the radial velocity map, consideration of the computed uncertainties and quantitative tests of radial velocities measured by two radars along the baseline between the systems. Baseline analysis is illustrated by application to two SeaSonde networks, with contrasting results that lead to a better understanding of SeaSonde output

Statistical and computational uncertainties in atmospheric profiles from radio occultation - Mariner 10 at Venus

Abstract Radio occultation studies of planetary atmospheres and ionospheres are based on measurements of the frequency and amplitude of the received radio signal. These measurements have random errors due to noise in the receiving system and linearly mapped into atmospheric profiles to give uncertainties can be estimated from the data and linearly mapped into atmospheric profiles to give uncertainties in temperature, T , pressure, p , and absorption profiles. For Mariner 10 occultation immersion at Venus, the standard deviations of T and p due to receiver noise are less than 2° K and 2 mbar over the range of radii from 6087 to 6140 km, based on our reduction from analog, “ open-loop” data. The temperature has a systematic error due to boundary uncertainty, estimated to be 50°K at 6140 km, that decays rapidly with depth; below 6117 km, it is less than 0.5°K. For the attenuation profile, systematic errors incurred during our calculations are more important than statistical errors. We estimate an upper bound to the uncertainty which is 32% at the peak value of absorption, which is about 0.01 db/km and occurs at a radius of 6096 km. A calculation of the 95% confidence limits for T profiles indicates that the local deviations are statistically significant to about 1°K or less. We have also analyzed “closed-loop” data to give temperature profiles which deviate from the open-loop results by less than 0.2°K below 6110 km but by as much as 2°K in the upper atmosphere. For the same occultation and the same boundary conditions, our closed-loop T - p profile is within 2°K of that of P. D. Nicholson and D. O. Muhleman but differs from those derived by A. J. Kliore by as much as 10°K. We cannot account for deviations as large as the latter by minor differences in trajectory information or computational methods.

Directional wave information from the SeaSonde

This paper describes methods used for the derivation of wave information from SeaSonde data, and gives examples of their application to measured data. The SeaSonde is a compact high-frequency (HF) radar system operated from the coast or offshore platform to produce current velocity maps and local estimates of the directional wave spectrum. Two methods are described to obtain wave information from the second-order radar spectrum: integral inversion and fitting with a model of the ocean wave spectrum. We describe results from both standard- and long-range systems and include comparisons with simultaneous measurements from an S4 current meter. Due to general properties of the radar spectrum common to all HF radar systems, existing interpretation methods fail when the waveheight exceeds a limiting value defined by the radar frequency. As a result, standard- and long-range SeaSondes provide wave information for different wave height conditions because of their differing radar frequencies. Standard-range SeaSondes are useful for low and moderate waveheights, whereas long-range systems with lower transmit frequencies provide information when the waves are high. We propose a low-cost low-power system, to be used exclusively for local wave measurements, which would be capable of switching transmit frequency when the waveheight exceeds the critical limit, thereby allowing observation of waves throughout the waveheight range.

Correcting for distorted antenna patterns in CODAR ocean surface measurements

CODAR systems employ compact antenna elements such as electrically small loops and monopoles to extract bearing information in ocean surface observations. Past analysis methods have assumed that these element patterns are perfect, i.e., cosine and omnidirectional. Operations from metallic offshore platforms usually distort these patterns because of unavoidable objects in their near field. When such distortions are ignored, previous methods are shown to produce \sim35\deg rms bearing errors. Therefore least-squares methods are presented and demonstrated that deal with differential element pattern distortions. It is shown how the required relative patterns are easily measured by a boat circling the antenna, and these patterns are then stored as look-up tables in the least-squares inversion methods. Relative patterns (i.e., one element pattern divided by the other), rather than absolute, are all that are required for extraction of surface current, wave-height directional spectra, wind direction, and drifting transponder information with CODAR.

CODAR wave measurements from a North Sea semisubmersible

CODAR, a high-frequency (HF) compact radar system, was operated continuously over several weeks aboard the semisubmersible oil platform Treasure Saga for the purpose of wave-height directional measurement and comparison. During North Sea winter storm conditions, the system operated at two different frequencies, depending on the sea state. Wave data are extracted from the second-order backscatter Doppler spectrum produced by nonlinearities in the hydrodynamic wave/wave and electromagnetic wave/scatter interactions. Because the floating oil rig itself moves in response to long waves, a technique has been developed and successfully demonstrated to eliminate to second order the resulting phase-modulation contamination of the echo, using separate accelerometer measurement of the platforms lateral motions. CODAR wave height, mean direction, and period are compared with data from a Norwegian directional wave buoy; in storm seas with wave heights that exceeded 9 m, the two height measurements agreed to within 20 cm RMS, and the mean direction to better than 15 degrees RMS. >

Japan Tsunami Current Flows Observed by HF Radars on Two Continents

Quantitative real-time observations of a tsunami have been limited to deep-water, pressure-sensor observations of changes in the sea surface elevation and observations of sea level fluctuations at the coast, which are essentially point measurements. Constrained by these data, models have been used for predictions and warning of the arrival of a tsunami, but to date no detailed verification of flow patterns nor area measurements have been possible. Here we present unique HF-radar area observations of the tsunami signal seen in current velocities as the wave train approaches the coast. Networks of coastal HF-radars are now routinely observing surface currents in many countries and we report clear results from five HF radar sites spanning a distance of 8,200 km on two continents following the magnitude 9.0 earthquake off Sendai, Japan, on 11 March 2011. We confirm the tsunami signal with three different methodologies and compare the currents observed with coastal sea level fluctuations at tide gauges. The distance offshore at which the tsunami can be detected, and hence the warning time provided, depends on the bathymetry: the wider the shallow continental shelf, the greater this time. Data from these and other radars around the Pacific rim can be used to further develop radar as an important tool to aid in tsunami observation and warning as well as post-processing comparisons between observation and model predictions.

A Compact Transportable HF Radar System for Directional Coastal Wave Field Measurements

A low-powered transportable coastal radar system which can measure the first five angular Fourier coefficients of the wave height directional spectrum as a function of wave number is proposed and described. Operating at a single frequency in the upper HF region, the surface-wave radar employs a novel, stationary three-element receiving antenna to obtain angular information. The received signals from two crossed Zoop antennas and a monopole, all aligned along the same vertical axis and standing ~2 m high, are combined digitally to form and scan a broad cardioid beam. The second-order portion of the sea-echo Doppler spectrum is used to extract wave spectral information. This echo portion is described mathematically by a nonlinear integral equation. Trigonometric basis functions are used to represent the radar system output (both first and second order) as well as the wave height spectrum’s angular dependence.

Tsunami Arrival Detection with High Frequency (HF) Radar

Quantitative real-time observations of a tsunami have been limited to deep-water, pressure-sensor observations of changes in the sea surface elevation and observations of sea level fluctuations at the coast, which are essentially point measurements. Constrained by these data, models have been used for predictions and warning of the arrival of a tsunami, but to date no system exists for local detection of an actual incoming wave with a significant warning capability. Networks of coastal high frequency (HF)-radars are now routinely observing surface currents in many countries. We report here on an empirical method for the detection of the initial arrival of a tsunami, and demonstrate its use with results from data measured by fourteen HF radar sites in Japan and USA following the magnitude 9.0 earthquake off Sendai, Japan, on 11 March 2011. The distance offshore at which the tsunami can be detected, and hence the warning time provided, depends on the bathymetry: the wider the shallow continental shelf, the greater this time. We compare arrival times at the radars with those measured by neighboring tide gauges. Arrival times measured by the radars preceded those at neighboring tide gauges by an average of 19 min (Japan) and 15 min (USA) The initial water-height increase due to the tsunami as measured by the tide gauges was moderate, ranging from 0.3 to 2 m. Thus it appears possible to detect even moderate tsunamis using this method. Larger tsunamis could obviously be detected further from the coast. We find that tsunami arrival within the radar coverage area can be announced 8 min (i.e., twice the radar spectral time resolution) after its first appearance. This can provide advance warning of the tsunami approach to the coastline locations.