Second-order Echo Research Articles

Wave-Height Map Extraction From Compact HF Surface-Wave Radar Network

The ocean-wave-height-measurement accuracy and coverage of high-frequency (HF) radars are affected by the echo intensity. Due to the effects of propagation attenuation and the wind-direction spreading function, the same sea area will generate different echo intensities for radars at different locations. Based on this characteristic, a new wave-height-measurement method combining multiple HF radars is proposed in this letter. First, the advantages of the radar network in enhancing the coverage and antiinterference performance of wave-height measurement are analyzed quantitatively. Furthermore, it is found that the signal-to-noise ratio of the second-order echo can be used as weights to fuse the wave heights measured by different radars. A field experiment over 23 days shows that the proposed fusion algorithm effectively improves the radar coverage and the wave-height-measurement accuracy.

Analysis of fetch-limited wave growth using high-frequency radars in the Gulf of Tehuantepec

Fetch-limited wave growth was analyzed using high spatial and temporal resolution measurements obtained with high-frequency (HF) radars. To calculate the wave spectrum, the second-order echo (S2N) was extracted from the Doppler spectrum and mapped to the wave frequency domain. The conversion of S2N to the wave frequency spectrum was carried out using a linear parametric model dependent on wind speed. Wave growth, represented by the dimensionless energy and peak frequency as a function of dimensionless fetch, was determined from the spectra calculated for 25 cells (~400 km2) in the vicinity of a moored Air–Sea Interaction Spar buoy. The buoy data were used as reference and to provide the wind information required for the wave growth analysis. The simultaneous data from the buoy and HF radars showed a suitable agreement with the wave growth curves. The analysis of the 25 cells showed an adequate agreement and certain dispersion around the growth curves. Possible causes of this dispersion are related to errors in the estimation of the frequency spectrum and fetch, and the assumption of homogeneous wind conditions. From the limited data set used, it was not possible to prove any impact of swell on wave growth; however, it is possible that analysis over a wider range of swell heights may provide this evidence. Nevertheless, the results suggest that the linear parametric model is able to reproduce fetch-limited wave growth. This work represents the first effort focused on fetch-limited wave growth using HF radars.

The Effect of the Bistatic Scattering Angle on the High-Frequency Radar Cross Sections of the Ocean Surface

High-frequency (HF) bistatic Doppler cross sections of the ocean surface are examined with respect to their dependency on the bistatic angle. Previously derived results which incorporate a pulsed dipole source and two orders of scatter are considered. It is trivially seen that the first-order result has a linear dependence on the cosine of the bistatic angle. The second-order echo accounts for a double scatter of incident radiation from first-order surface waves - the so-called electromagnetic term - and a single scatter from a second-order ocean wave. The latter, generally referred to as the second-order hydrodynamic term because it originates from coupling between first-order ocean waves, predominates the Doppler continuum in most regions of interest. The analysis presented here verifies that in addition to a cosine-dependent reduction in cross section magnitude with increasing bistatic angle, both components of the second-order scatter tend to zero under the condition of near-forward scatter for bistatic HF radar operation. Of course, this imposes practical limitations on the region over which a bistatically configured HF radar system may be used to remotely sense ocean surface parameters.

Second-Order Echo Signals in Two-Pulse Delayed Nutation

Nonstationary magnetic nutation signals of the second-order echo that occur during the effect of a resonance radiofrequency pulse of length t2 on a two-level inhomogeneously broadened spin system preliminarily excited by a pulse of length t1 < t2 have been studied theoretically. It has been found that in contrast to the delayed nutation echo whose formation is attributed to the restoration of the longitudinal magnetization that arose by the end of the first pulse, these signals result from the “reversal” in time of three effective signals of free precession generated after the termination of the first pulse. The theoretical results are in good agreement with the experimental data obtained in NMR of protons in glycerin. A conclusion on the validity of the theorem of coherent transient processes occurring in two-level systems in the presence of an exciting field is drawn.

Observations of the broadening and coherence of MF/lower HF surface-radar ocean echoes

Known broadening mechanisms for the first-order Bragg peaks in high-frequency (HF: 3-30 MHz) and very-high-frequency (VHF: 30-300 MHz) Doppler spectra of radar echoes from the sea surface are summarized. Observations of medium-frequency (MF: 0.3-3 MHz)/lower HF sea echoes were made with a surface-wave phased-antenna array transmitting Gaussian pulses of width /spl ap/40 and 70 /spl mu/s at frequencies 1.98, 3.84, and 5.80 MHz (sensitive to sea waves of length 76, 39, and 26 m, respectively). Some of the broadening of first order Bragg peaks in Doppler spectra was consistent with the effects of nonuniform surface-current fields across radar footprints. At these MF frequencies, however, the dominant cause of first-order broadening was the spread in Doppler shifts caused by the phase speeds of first-order gravity sea waves being modified by the comparatively shallow radar footprints. Second-order sea echoes were usually not observed with good signal-to-noise ratio because the sea wave heights were not a sufficient fraction of the radio wavelengths. However, data were obtained in which bathymetrically amplified, higher order sea echoes also contributed to the broadening. Examples of this confused data are presented to illustrate that the interpretation of data from a coastal surface-wave radar at MF is difficult, hence limiting the quality of wave heights estimated by inverting second-order sea echoes. Furthermore, the phase shifts of gravity sea waves caused by propagation through nonuniform surface-current and bathymetry fields helps to explain the considerable incoherence of sea echoes in coastal regimes. To this end, hundreds of Doppler spectra were analyzed from records taken during 2-3 day periods and across a range of frequencies and sea states. The results show that the coherence of Bragg peaks decreases with frequency and with water depth and confirm that they integrate less coherently than a stationary tone. There is also a suggestion that coherence depends on wave age. Consequently, on practical time scales (/spl sim/1000 s) incoherent spectral averaging is more effective at revealing spectral information otherwise buried in noise (e.g., second-order echoes containing sea-state information).

The role of the gravity-wave dispersion relation in HF radar measurements of the sea surface

Recent experimental and theoretical findings raise interesting questions about the applicability of the normal gravity-wave dispersion relation at wave frequencies that exceed the spectral peak frequency. The use of the dispersion relation in analysis of HF radar Doppler sea echo is examined in this paper. Drawing on the results of perturbation theory for wave-wave nonlinear interactions, we show that this relation, so essential to echo interpretation in terms of current and wave information, can be employed with no degradation in accuracy for current measurement when the dominant wave frequency is considerably less (by as much as 10) than the radar Bragg resonance frequency. This finding is supported by comparisons of currents measured by HF radar with surface truth; the first-order echo must only be identifiable in order to be used accurately. Wave-height directional spectral information can be extracted from the second-order echo at a given radar frequency up to the point (in wave height) where the perturbation solution employed in the inversion process fails; then a lower radar frequency must be used. On the other hand, most conventional wave measuring instruments should not use the dispersion relation for interpretation of data well beyond the spectral peak, because they do not observe wave height as a function of both space and time independently, as does HF radar.

Comparison of third-order plasma wave echoes with ballistic second-order plasma wave echoes

The apparent dispersion of third-order plasma wave echoes observed in a high frequency plasma is compared with that of simultaneously observed ballistic second-order echoes. Amplitude and wavelength of third-order echoes are found to be always smaller than those of second-order echoes; however, the dispersion curves of both types of echoes are very similar. These observations are in qualitative agreement with calculations of special ballistic third-order echoes. The ballistic nature of the observed third-order echoes may, therefore, be concluded from the authors' measurements.

Estimating wind speed from HF skywave radar sea backscatter

Linear expressions relating ocean surface wind speed to a theoretical estimate of the - 10 dB width of the high frequency (HF) sea echo Doppler spectrum (0.078 Hz Doppler shift frequency resolution) are derived for different radar frequencies. The -10 dB width, determined from theoretical model estimates of the Doppler spectrum as a function of radar frequency for a wide range of ocean wave conditions, changes in a complex way with the continuum of second-order echoes surrounding the stronger first-order echo. Because the amplitude of the second-order echoes is directly related to changes in the directional ocean wave spectrum, the wind speed estimates derived from these expressions are highly dependent on the wave field (both the total energy and its distribution with direction); significant differences in these expressions are also found, for example, between fetch-limited and fully developed seas, and for wind seas and swell. These expressions are extremely difficult to use experimentally to obtain reliable estimates of wind speed because a priori knowledge of the wave field is required to apply the correct expression, and yet this knowledge cannot be determined from the unresolved second-order structure at this spectral resolution. Several Doppler spectra recorded under known ocean wind and wave conditions illustrate the difficulty in applying these theoretical expressions to estimate wind speed. We conclude that the -10 dB width is not a good estimator of wind speed. Wind speed estimates are better obtained from HF radar spectra by first estimating the directional wind-wave spectrum from the second-order echoes (0.01 Hz Doppler shift frequency resolution) and then computing wind speed from a wind-wave prediction model.

Observation of gravity waves in the high-latitude F-layer by using fixed frequency sounding

Fixed frequency soundings at 4.2 MHz frequency were carried out at Sodankylä (67°22′N, 26°38′E) using aerials with a northward tilted antenna pattern. The second-order echo in virtual height versus time recording occasionally shows a peculiar sawtooth behaviour. Model calculations indicate that the phenomenon can be explained by medium-scale gravity waves in the F-layer. The period of the gravity wave can be reduced most accurately from the second-order trace, and it is possible to make a distinction between the poleward and the equatorward propagation of the disturbance. The measured periods vary from 15 to 65 min. In the daytime, when the measurement is possible, the propagation is invariably equatorwards. The phenomenon is only observable during the winter months. It does not seem to have any correlation with magnetic activity.

Second-Order Scattering from the Sea: Ten-Meter Radar Observations of the Doppler Continuum

Ten-meter radar observations of the sea have been used to study second-order interactions between waves in electromagnetic scattering from the sea. Techniques of coherent, pulsed radar provide echo frequency spectra from several range intervals. The echo spectra are resolved with an analysis window of a few millihertz. These spectra show a clear second-order echo continuum which appears as sidebands about the first-order Bragg scattering lines. Up to one-half of the total echo power has been observed in these sidebands. The principal characteristics of these sidebands vary with time, apparently in response to the sea state. The form of the echo spectra is consistent with the results of perturbation theory computations based on Rice's method.

Temporal Plasma Echoes

Results are given from a computer experiment conducted on a 9000-particle plasma to test the theoretical prediction of temporal echoes. The second-order echo is found at the time and wavenumber as predicted by the theory.

Spatial Ion-Wave Echoes

Theory and experiments of spatial ion-wave echoes are reported. In the collisionless approximation, the calculated line shape of the second-order echo is found to be a universal function of Δx/δ, the distance from the expected position of the echo divided by the Landau damping length of the ion-wave constituting the echo. Higher-order echoes predicted by Gould are observed up to the fourth order with respect to the external fields at the predicted positions with the predicted dependence of their amplitude on the amplitude of the primary waves. In addition, new types of higher-order echoes which result from the electric fields of other echoes are predicted and observed. Measurements of the peak amplitude of the second-order echo as a function of the separation l between the two exciters indicates that the memory of the past excitation retained in the distribution function damps exponentially with the attenuation length proportional to the wavelength of the excited wave. The effect of ion-neutral collisions on the peak amplitude is studied and explained fairly well by a simple relaxation time model, but the predicted effect of ion-ion collisions based on a Fokker-Planck-type equation is not observed within the separation length l of 20 cm and the plasma density of 1010/cm3.

Some comparative directional measurements on short radio waves over different transmission paths

Observations on first-and second-order F-layer echoes from a pulsed transmitter at frequencies of 5–8 Mc/s have been made at two direction-finders separated by 213 km. From a comparison of first-order bearings over the two paths it has been found that negligible correlation exists between similar components of the random ionospheric tilts at points separated by 106 km. However, relatively small average tilts over a period of an hour have been found to occur, and these are correlated over wide areas; they show a regular diurnal variation.The mid-points of the two transmission paths lay on land and on sea respectively, and a comparison of the directional variations exhibited by the second-order echo showed that the land behaved as a rougher reflector than the sea. The resulting difference in the total variance of bearings on this echo for the two paths was, however, small, as the deviations were mainly caused by ionospheric tilts.