PROCEEDINGS OF THE IEEE, VOL. 62, NO. 6, JUNE 1974 673
Sea Backscatter at HF: Interpretation and Utilization of the Echo
DONALD E. BARRICK, MEMBER, IEEE, JAMES M. HEADRICK, SENIOR MEMBER, IEEE, ROBERT W. BOGLE, DOUGLASS D. CROMBIE
AND
Abstract-Theories and concepts for utilization of HF sea echo are compared and tested against surface-wave measurements made from San Clemente Island in the Pacific in a joint NRL/ITS/NOAA Although the heights of ocean waves are generally small experiment. The use of first-order sea echo as a reference target for in terms of these radar wavelengths, the scattered echo is calibration of HF over-the-horizon radars is established. Features of the higher order Doppler spectrum can be employed to deduce the nonetheless surprisingly large and readily interpretable in principal parameters of the wave-height directional. spectrum (i.e., terms of its Doppler features. The fact that these heights are sea state); and it is shown that significant wave height can be read small facilitates the analysis of scatter using the perturbation from the spectral records. Finally, it is shown that surface currents approximation. This theory [2] produces an equation which and current (depth) gradients can be inferred from the same Doppler 1) agrees with the scattering mechanism deduced by Crombie sea-echo records. from experimental data; 2) properly predicts the positions of I. INTRODUCTION the dominant Doppler peaks; 3) shows how the dominant echo magnitude is related to the sea wave height; and 4) per mits an explanation of some of the less dominant, more com T WENTY YEARS ago Crombie [1] observed sea echo plex features of the sea echo through retention and use of the with an HF radar, and he correctly deduced the scatter higher order terms in the perturbation analysis. Hence the ing mechanism which accounted for the peculiar and dominant spectral features explained by the simple, lowest unique dominant peaks in the observed Doppler spectrum. order terms of the perturbation analysis are referred to as This gave rise to further research and suggested the exciting "first-order" sea echo, while the remaining, less dominant fea possibility of measuring sea state at great distances with HF tures are termed "higher order" because they arise from the sky-wave radars. A current joint program involving NOAA, smaller (i.e., second-order, third-order, etc.) terms. NRL, and ITS on San Clemente Island has provided data for By way of introduction to the basic type of HF echo testing three possible applications of HF sea echo: 1) as a records upon which the discussion in this paper is based, we standard or reference target for calibrating the sensitivity show a typical received Doppler spectrum in Fig. 1. This plot of sky-wave radars; 2) as a means of deducing sea state (viz., represents the received signal power versus normalized Dop the dominant features of the wave-height directional spec pler shift± from the carrier (the carrier being located at zero, trum); and 3) as a method for measuring surface-current and the predicted positions of the dominant peaks at posi features. HF, as considered here, extends from the broadcast tions 1). Details of the conditions and system behind this band to VHF, including radar wavelengths between 10 and spectral record will be discussed later, but for now we refer 200 m. to it to illustrate how the three previously+1) claimed applica tions will be subsequently developed from data such as these. Manuscript received September 12, 1973; revised January 21, 1974. D. E. Barrick is with the Wave Propagation Laboratory, National 1) The dominant, first-order peak (near will be tested for Oceanic and Atmospheric Administration, Boulder, Colo.80302. use as a standard or reference echo. 2) The higher order J. M. Headrick and R. W. Bogle are with the Naval Research Lab oratory, Washington, D. C. 20375. Doppler features (i.e., their shapes, peak positions, and am D. D. Crombie is with the Institute for Telecommunication Sciences, plitudes) will be used to deduce sea state. 3) The overall shift Boulder, Colo.80302. of the first-order echo peaks from ± 1 will be used to deduce 614 PROCEEDINGS OF THE IEEE, JUNE 1974
:p--qqFirst-order sea echo 4
Fig. 2. Buoy-measured nondirectional wave-height spectra for morning (dashed) and afternoon (solid)of December 4, 1972. Triangle is model used in theoryto approximate afternoon spectrum.
tional to the heightof this wave component squared. Hence it 0-21 -I 0 I 2 is evident that measurement of the first-order radar cross Normalized Doppler Frequency section of the seaversus radar operating frequencywill deter- . Example of an averaged radar sea-echo Doppler epectrum at 9.4 mine thewater-wave spectrum along theradar azimuthal MHz. Carrierwould appear at center,with *1 corresponding to bearing. By looking along several bearings, one can thereby Doppler shifts k0.313 Hz from the carrier. Resolution is 4.01 Hz. construct the “wave-height directional spectrum,”a quantity which has heretofore defied simple measurement by oceanog- (radial) currents. Since the radar echo is produced by scatter raphers. However, the radar frequency region corresponding from ocean waves, the approach taken in this paper is to re- to the importantlong-wave portion of the gravity-wave spec- late the echo features to surface features. Ocean waves and trum responsible for “sea state” spans the region from about currents are largely produced by winds, and thus one should 300 kHzto 5 MHz.Constructing and calibrating an azi- be able to ultimately deducewind features from these echoes; muthal scanning radar which sweeps over this region would this is the approach taken in parallel analyses of HF sea echo be a formidable task, in addition to the difficulty that this by Ahearn et al. [3] and Long and Trizna [4]. frequency region is already heavily occupied by users (broad- cast band, marine band, etc.). Furthermore, propagation at 11. BACKGROUNDAND INTERPRETATION these lower frequencies is restricted to ground wave (limiting Let us explain the simple interpretation of the first-order the radar range to <200 km), since ionospheric modes will Dopplerspikes of Fig. 1 as firstdeduced byCrombie [l]. be severely attenuated most of the time. Though the sea to a casualobserver generally looks like a Incontrast, sea scatterin the upper HF region (6-30 random, moving, scattering surface, the dominant, crisp, and MHz), at which ionospheric propagation to great distances equally displaced Doppler peaks lead one to believe that the (-4000 km) is favored, is of a somewhat different character. radar is actually observing twotargets moving radially at The first-order resonant peaks are still evident and usually discrete readily identifiable velocities. Thefact that these dominant, as shown in Fig. 1. However, other features in the Doppler displacements are observed to vary with the square Doppler spectrum are also present, and these features appear root of the carrier frequency suggests something unique aboutto vary more significantly with sea state than do the first- HF sea echo in contrast to echoes from other moving targets. order echopeaks. These additional features are referred to Since it is well known that gravitywaves in deep water travel as “higher order,” of which “second-order” effects are felt to at a phase velocity proportional to the square root of their be the dominant contributors. On the other hand, the larger lengths L (Le., Y= dgL/2*, where g is the gravitational con- fimt-order echo is for the most part constant andinsensitive to stant), then the length of the waves producing scatter can be sea state. The reasonfor this is that the wavesproducing uniquelydeduced from the radar-derived “target” velocity. scatter, being half the radar wavelength, vary in length be- This length (for backscatter near grazing incidence) is pre- tween 25 and 5 m. Waves of this length on the open-oceans cisely one-half the radar wavelength, and explains theob- are nearly always present and are developed to their maxi- served square-rootrelationship between the Doppler and mum allowableheight, as limited by breaking. This region carrier frequencies. Thus the Ocean wave trains are behaving of thewave-height spectrum in which saturation occursis like a series of diffraction gratings, only one of which has the called the equilibrium region; Phillips [6] has shown that the orientation and spacing to scatter back toward the radar (to nondirectional temporal wave-height spectrum should follow first order). This is the double set of sea wave trains with an f5 law (jequals wave frequency in hertz) in this region. L=X/2 (or K= 2k0, where X is the radar wavelength, with Fig. 2 isa buoy measurement of this spectrumat two different K = 2*/L and ko = 2*/x being the scatteringOcean wavenumber times for 20- and 25-knot wind-driven seas in the scattering and radar wavenumber, respectively) moving radially toward area off San Clemente Island. The r5saturation region is and away from the radar.Hence the double Dopplerecho pair. clearly evident in these records; a scale at the bottom shows Theory[2], [SI alsoshows that the backscattered echo that the radar frequencies at which first-order scatter would energy from this identifiable “resonant” water waveis propor- be observed clearly fall in this saturated equilibrium region BAKRICK el a!. : SEA BACKSCATTER AT HF 675 for all operating frequencies above about 2-3 MHz. The fact be optimal, and hence most sea-echo data were recorded at that the first-order echoes at favorable ionospheric propaga- these ranges. At these ranges, the water depthexceeds 1000 ft, tion frequencies originate from wavesof known height charac- so that bottom effects on the wave characteristics are neg- teristics suggests that these echoes can be used as a standard ligible. target for radarsystem sensitivity calibration. Theory [2] The transmitter provided an outputpower of 75-kW peak. shows that the first-order scattering coefficient' uoshould,be a The transmitting antenna was a twin+bay log-periodic rnono- constant, approximately -17 dB, independent of frequency pole array producing vertical.polarization; with a gain of 14 (above some lower - HF limit) and sea state:In a large num- dB,it provideda one-way beamwidth of 60" centered on ber of ground-wave operations on the Chesapeake Bay,uo was 255' T. The receiving antenna was an 850-ft-long broadside indeedfound to increaseto an upper limiting value corre- monopole array.Elements were switchedin and out auto2 sponding to -17dB. Sky-wave radar operations by many maticallyversus frequency so that the beamwidthdid not groups have also confirmed the constancy and absolute value vary too drastically over the decade frequency range; as a (- 17 dB) of first-order uo. result, the one-way beamwidth was about 15' at 3 MHz and As mentioned previously, the higher order sea-echo Dop- 7" at 24 MHz. Data were processed and recorded digitally on pler spectrum does appear to vary appreciably withsea state. magnetictape, both in raw IF form and as 200-s coherent Thefeatures of this echo takeseveral forms: 1) secondary spectra. peaks appear around the first-order spikes, whose positions In order to check the radar data, a Datawell Waverider and amplitudes vary with sea state: 2) a continuum or floor buoy was moored in the scattering area. This device provided around the first-order spikes appears which rises and spreads both the sea-significant wave-height and noadirectional wave- withincreasing sea state;and 3) thedistribution of these height spectra. The buoy output was confirmed and supple- higher order peaks and continuum about the first-order lines mented by wave hindcast tables prepared by OSI, Inc.; these varies with wave direction. A theory for the second-ordercon- data indicatedwave direction and also listed theheight, tributionto these higher order echoeswas advanced by period, and directionof any swell present. Barrick [7], and the agreement thus.far withexperimental data is quite encouraging. A significant advantage .of using IV. FIRST-ORDERSEA ECHOFOR RADAR second-order echo to deduce sea state at upper BF is that one SENSITIVITYCALIBRATION is comparingthis portion of the signal spectrum with the Boththeory [2] andsurface-wave/sky-wave measure- saturatedfirst-order peaks, which serve asthe reference. ments have shown that the first-order sea-echo energy in the Hence unknown ionospheric path losses and Doppler transla- upper HF region approaches a constant value for the open tions do not hamper interpretation of the higher order echo ocean, independent of sea state. As discussed previously, this in terms of sea state. saturation occurs because the shorter ocean waves being ob- Oceancurrents can also be extractedfrom the sea-echo served at these frequencies are developed to their maximum Doppler spectrum. The first-order resonant Doppler peaks are possible heights. Referring again to the buoy-measured wave- oftenobserved to beshifted equally from their predicted height spectra of Fig. 2, it is evident that for seas fully de- positions (see Fig. 1) by a small amount. Thisimplies that the veloped by 20-knot winds, frequencies above about 2 MHz wavescausing first-order scatteringare superimposed on a are observing waves in the saturated or equilibrium range of sea surface which isphysically moving due to surfacecur- the spectrum; for 10-knot winds,frequencies above 8 MHz rents. The radial component ofthis surface-current vector canwill likewise fall in this region of the spectrum. For vertical thus be calculated in terms of,the Doppler translation of the polarization, the average radar cross section per unit area,uo, first-order lines to beu =Adgc/(4?rfo), where g is the accelera- turns out tobe about - 17 dB, independentof frequency;and tion of gravity, c is the velocity of light, fo is the carrier fre- nearlyindependent of incidenceangle in the region within quency,and A is the normalizedDoppler translation,as about 30" of grazing.' This suggests using the first-order sea measured in Fig. 1. Further interpretation of this concept will echo as a referenceor standard target-for calibration of be undertaken later in this paper. sky-waveradars operating ever the oceans (wherewinds nearly always exceed 10 knots). Such calibration is desirable 111. EXPERIMENTALFACILITY and necessa-ry because, unlike microwave radars where trans- A series of HF surface-wavemeasurements of seaecho mission loss is generally dose to thepredicted free-space value, were undertaken in a joint experiment between NRL, ITS, ionospheric absorption is highly variable and unpredictable. and NOAA/U'PL on San Clemente Island off California. Be- Hencesome sort of calibrathn (ofteninvolving the use of tween November l, 1972, and April 30, 1973, approximately beacons or repeaters of known reradiation levels) is required 25 h of sea-echo Doppler spectra were gathered. The facility in order to help select the optimal operating frequency and is located on the northwest side of the island and looks west- determine expected signakto-noise ratio and/or probabiiityof ward into the Pacific. It is capable of transmitting any num- detection against a given class of radar targets. ber of frequencies (up to 100)simultaneously from 2 to 25 One .way of testing the concept of using first-order sea MHz in a pulse-to-pulse progression, and processing the re- echo as a reference target over the HF band is to show that turns on each frequency coherently. Pulsewidths available are the measuredvalue of someparameter in theradar range 20, 50, and 100 ps with a 200-pulse-per-second (pps) repetition equation follows predictions when one uses a constant value rate. The sea echo from several range gates can be processed simultaneously: to provide adequate signal-to-noise ratio, the * Horizontally polarized sea echo is quite sensitive to incidence angle; echoes at 22.5, 30, and 37.5 km from the radar were found to near grazing, however, it is at least 20 dB lower than the vertical corn- ponent. Hence it would never be used in surface-wave propagation, and would not be seen with sky-wave propagation due to the presence of the 1 The average radar backscatteringmoas section per unit surface area. much stronger vertical return. 676 PROCEEDINGS OF TEE IEEE, JUNE 1974
t I 1
- 10 fo, MHz p, 1 I I 1 5 10 I5 20 fo, MHz
Fig. 4. Predicted (solid line) andmeasured (via firet-order sea scatter) antenna gain product.
fo, MHz 2;4 to 20 MHz. The ddline represents the gain product at Fig. 3. Surface-wave loas and bandwidth loas the center of the two receiving beam positions as measured factors vemus radar operating frequency. via a standard target in a small boat versus frequency; the discontinuities in the ptedicted gain curve arise from the fact that different receiving array elements were switched in orout for uo.For this demonstration, the radar equation is rewritten at certain frequencies so as to reduce the pattern variation in terms of the antennagain product: over the decade frequency operating range. The comparisonis favorable, and shows that the first- order echo can indeed serve as a reliable reference target.The spread in points at the lower frequencies miry be due to inac- curateassumptions in the sea description. However, the where R is the range to the scattering areaA, PT and PR are spread of points near 13.4 MHzis a true indexof the variation the transmitted and received power (in the dominant first- in the results, and all points lie within +2 dB of the mean. order Doppler echo), andh, LBW are ‘loss factors” account- This spread is most likely due to the fact that the 1/2 h of ing for two-way surface-wave propagation over the sea and incoherent spectral averaging representedin obtaining each of Doppler line broadening, respectively.All of the factorson the the points was not long enough to permit observation of a right side of (1) are assumed known. The sea area A, within large ensemble of independent, random sea surfaces within the resolution cell, is of course related to the antenna beam- theradar resolution area; hence thepoints were nottrue widths (and hence gains), but in a known, calculable manner. means.This k2-dB spread, however,compares favorably Thus the antenna-gain product can be ‘measured” and com- with the accuracies of other types of sky-wave radar sensitiv- paredwith predictions. The excess two-waysurface-wave ity calibrators which have been used,such as beaconsand propagation loss Lgw over the sea out to 30 km versus fre- repeaters (where the output power level can fluctuate due to quency and sea state is shown in Fig. 3(a), prepared from electronic instabilities and aging) or islands/mountains whose Barrick [8]. The bandwidth lossa LBW was calculated by apparent cross sections can change due to surface moisture forming the ratioof the observed width of the dominant first- content and Faraday polarization rotation. order Doppler echo with the width at the lowest operating frequency; this is shown in Fig. 3(b). Data from December 4 V. SECOND-ORDERSEA ECHO FOR and December 7,1972, were selected for this comparison, since SEA-STATE DETERMINATION the seas for both were driven by 2Q-knot (or greater) winds, Theoretical explanations for second-order sea echo, present predominantly from the west, and hence could be expected to onnearly all recordsabove 4 MHz, have been offeredby produce a saturated positive first-order Doppler echo at all Barrick [7] and Hasselman [g]; the readeris referred to these operating frequencies. Therefore, a uo was used in (1) corre- referencesfor details of themathematical derivation. The spondingto -17 dB(but normalized tothe ground-wave basic interpretation of this process is illuminating and worth definition of antenna gains). some discussion. The theory shows that the radar waves in- The comparison between calculated and ‘measured” values teract with ocean wave trains as though the latter were dif- of GTGR versus frequency is shown in Fig. 4. Data plotted as fraction gratings. Hence Bragg scatter and/or Feynman in- points were obtained on the two different days, for the two teractiondiagrams are well suited to explain the various antenna beam positions (at270’ and 2M0)at frequencies from “orders” of scatter. To first order the scattering and Doppler relationships are described in termsof Bragg scatter follows: a This “lod merely allows one to read the amplitude of the *ed as fht-order Doppler peak, since the actual desired quantity PR is the area under this peak. BARRICK et al.:SEA BACKSCATTER AT HF 677
o* = 0' * n. (2b) where the variable of integration K may be either xlru2, or any linearcombination of thetwo. The quantity I' is the Here k' and k are the two-dimensionalcomponents of the coupling or interaction coefficient between thetwo sets of three-dimensional incident and scattered wavenumber vector water waves. Two contributions to r have been identified as lying in the mean sea-surface plane, and d,d are the radian [7]: 1) ahydrodynamic term arising from retention of the temporal frequencies of the incident and scattered fields. The second-order (perturbational) terms in the nonlinear bound- vector K is the spatial wavenumber of'the water wave re- ary conditions at the free water-air interface; and 2) an elec- sponsible for scatter (i.e., K= IKI = 2r/L, where L is the water tromagnetic term arising frominclusion of second-order terms wavelength), and n, the temporal wavenumber, is related to K from the boundary perturbational expansion for the scattered through the first-order gravity-wave dispersion tquation fields at the water surface. The latter contribution is merely multiple scatter of the radar wavefrom one setof ocean waves n = dg.. to a second set and then back to the radar. The former con- tributionrepresents the nonlinear interaction of twowater Thus, as an example, for backscatter at grazing incidence we waves to form a small water-surface component with wave- can choose our coordinate system so that the (-x) axis co- number x1 first-order radar scatter then takes place from incideswith the propagationdirection. Thus k= KO? and +KZ; this second-order water wave. Oceanographers refer to this - KO? (KO= 2r/x), so that the scalar first-order resonance k'= second-order water wave as 'trapped" or evanescent because condition stated previously is established from (2a): 2ko=~or it can neither carry energy away from the first-order wave L=X/2. Then the radian Doppler shifts of the energy-de- spectra nor can it exist without or propagate independently of fined as the differencebetween theincident (carrier) fre- each of the first-order waveswhich produce it. quencyand the actual scattered frequency-are wa-d With the help of this theory, one can test various methods = f d/gw = & 4%. Thus through simultaneous satisfaction for inferring wave properties (such as significant wave height, of (2) we have established the length and direction of water dominant wave period, and dominant wave direction) from waves responsible for first-order scatter, and also the unique the second-order echo characteristics. An example of the suc- square-root relationship for the discrete first-order Doppler cess realized thus far in inferring significant wave height6 from echoes which had been established experimentally by Crombie the records will be discussed here; further details on dominant two decades ago. The average spectral strengthof the grazing wave period and directionality will be presented elsewhere. first-order backscatter cross section per unit area (for vertical polarization) per radian/second bandwidth is found to be Radar records for December 4, 1972, were selected for ex- amination herebecause: 1) buoywave-height spectra are uo(o) = 27rk04s(Kz, K,,)~(~- J+ n) available on thatday; 2) hindcastshave determined that winds and waves were predominantly from the west, nearly = 27~Ro'S(2ko,O)~(W. - ~i f 4-0) (4) along the 270' radar beam; and 3) the measured wave-height where S(K=,K,,) is the spatial wave-height directional spectrum spectra have the shape characteristicof fully developed wind- for the sea. wave conditions (i.e., a saturated f6 equilibrium region and a. Understanding of the extension of this interaction mecha- fairly sharp lower end cutoff). Thus the shape of the wave nism to second order is now straightforward; in place of (2) spectra can be modeled by triangles, one of which is shown in we have' Fig. 2 representing the 1630 (afternoon) wave conditions; the spectral energy omitted by this type of modeling is not sig- nificant in these two cases. In solving the integral (6)for these wave spectra models,it is assumed that the dominant wavedirection is coincident Now two water waves-with spatial wavenumbers xl,uq, and with theradar propagation direction. Furthermore, two temporal frequencies = d& and 8=dF-enter into the models of azimuthal wave patternswere tested in the integra- process. For backscatter at grazing incidence, (Sa) shows that tion of the directional spectra S(K=,K,,): a cosine-squared pat- there are a whole double set of interacting water wave trains tern and a semi-isotropic pattern. This directional pattern has which, if they are present, can produce second-order scatter. been a very difficult oceanographic quantity to measure, but These water wavenumber combinations, x1 and KP, form two the sparse data available indicate that most wind-wave pat- sides of a vector triad whose resultantthird side is k- 6' terns lie somewhere between cosine squared andsemi-isotropic. = 2K02; hence they need not be collinear with the radar propa- When calculating theoretical values for the integral (6), gation direction. Imposition of the scalar Doppler condition it is found that when the sea is fully developeda set of Doppkr (Sb) furtherconstrains the relationship between K] and KZ, curvescan be preparedas a function of asingle universal reducing the number of independent degrees of freedom from parameter 8: thisparameter is proportionalto the carrier two to one. Thus, in place of (4), theory shows that the second- frequencytimes therms wave height @--8Chfo h/c). Thus order spectral contribution takes the form Doppler spectra calculated for a given wave height but for severalradar frequenciescan be interpreted in terms of a single radarfrequency but different wave heights. This is JJ illustrated in Table I, where in the first set of columns the actual frequencies used on December 4 are shown. Fig. S(a)- (c) showscalculated versus measured Doppler spectra for
4 It is interesting to note that multiplication of (2) or (5) by Planck's constant gives the familiar conservation of momentum and energy equa- Significant wave height is an oceanographic term referring to the tions in quantum mechanics for angle and double wave-particle inter- average peak-tetrough height of the highest one-third of the waves. It is actions. related to rms wave height (for a Gaussian 8ea surface) h by El/~=4h. 678 PROCEEDINGS OF THE IEEE, JUNE 1974
TABLE I -4 1 I I I ,,,,,/,,, 0 PARAXETERINTERDEPENDENCE BETWEEN CARRIER k x 4 Dec 1972. 1030 FREQUENCYAND SIGNIFICANT WAVE HEIGHT
Pararter 4 ActualConditions at Scaled Conditions 1630, 4 kc. 1972
foWz) H1/3 (ft) foWz) $3 (Et)
1.7 2.41 7.8 18 1.0 5.2 4.54 7.8 18 2.0 4.9 6.92 7.8 18 3.0 6.6 9.40 7.8 18 4.1 9.5 13.40 7.8 18 5.8 2- 2- I 4 5 6 IISD 15 20 12.37.6 17.4018 7.8 PL\RAMETER j3 14.2 20.15 7.8 18 8.7 Fig. 6. Measured (points)and predicted amplitude of eemd-order peak P+s Upper and lower solid lines represent theoretical cosine- squared and -mi-isotropic direaional models, respectively. Dashed line is mean fit to measured data. Frequency = 4.54 MHz rg 4 Dec. 1972, 1625 LT I wind) sides of the spectra were calculated, with the dotted curve representing the cosine-squared and the dashed curve the semi-isotropic directionalmodels. Both the measured and calculated spectra are normalized in frequency (with unity being the first-order Doppler position, i.e., fB= f t/2gko/2r), smoothed' by a Gaussiansmoothing function of width 0.087 XfB, normalized in amplitude to the topof the dominant first-order echo, and finally, the measured spectra are reposi- tioned so that the current offset is removed. Thus Fig. 5(b) actually represents Fig. 1 after the smoothing process and re- moval of the current offset. Frequency = 9 40 MHz Several characteristics of the second-order echo vary with 4 Dec. 1972, 1625 LT -l0--25 knot wind from 290' theparameter B (i.e., withfrequency or wave height); as evident from Fig. 5. The amplitude and.positions of the two second-order peaks designated P+t and P-cwith respect to the first-order peak-change with increasing 8. We examine - here only the amplitude of P+t, and show in Fig. 6 the calcu- W -30 2 lated and measured values of P+, in decibels below the first- !z order peak. The upper line is the cosine-squared theoretical i W model, the lower is the semi-isotropic theoreticalmodel, while a the points comprise all of the measurements taken at 22.5-km -2 -I 0 I 2 and 30-km range at the seven frequencies and for the morning 0 I I I I 1 I and afternoon sea conditions represented by the wave spectra Frequency = 17.40 MHz of Fig. 2. Besides illustratingthe good agreement between % 4 Dec. 1972, 1625 LT -lo- 25 knot wind from 290" theory and measurement, this plot demonstrates a more im- portant point. A relationship can be established between the relative height of P+t and the parameter 8; thus at a known radar operating frequency, the smoothed spectracould be re- normalized (using the dashed calibration curve of Fig. 6) so that significant wave height can be read out directly as the height of P+*.This is demonstrated in Fig. 7(a) and.(b), which - I 3'. i -40 I/ are the smoothed spectra for 9.4 MHz at 22.5-km range for L -t the morning and afternoon of December 4, respectively. The -501 I I I 1; I I I J significant wave heights read from the two radar records are -2 -I 0 I 2 about 5.5 and 8.5 ft, while buoy measurements and hindcasts NORhMLlZED DOPPLER FREOUENCY indicated actual wave heights of 5 and 8 ft for morning and Fig. 5. Comparison of smoothed and normalized aea-edho spectra at afternoon. Similar displays on the other frequencies yielded different frequencies. Solid curve8 are measured (December 4, 1972), these wave heightsalso, with an error commensurate with the while dotted (cosine squared)and dashed (semi-isotropic) are pre- dicted spectra for wave ditionaahown in Fig. 2. point spread in Fig. 6, caused primarily by insufficient inco- herent averaging time.
three frequencies in the afternoon of December 4; the mea- 'Smoothing waa used for two reanom: 1) so that the widths of the sured spectra represent the sum of nine separate 200-sco- 6mt-order echm would be braadened by a known amount bey& any herent power spectra, for a total of 1/2-h incoherent averag- system resolution and/or higher order aea dispersion efiects, permitting their amplitudeto be a true measure of their total energy conkat; and 2) ing. The theoretical spectra include both the first-order and becam ionmphaic motions are exe&dtn intrduct broadening d the second-order contributions; only the dominant, positive (up spectm by approximately the amount used here BARRICK et al. : SEA BACKSCATTER AT BF 679
8/22/13 0 240" + 270" -.E -20
-20
Normallzed Doppler Frequency Normallzed Doppler Frequency (4 (b) -10 Fig. 7. Upper portions of smoothedsea-echo spectra at 9.4 MHz, calibrated to showsignificant sea waveheight (in feet) as height 0 20 40 60 8C 0 20 40 60 80 of P+r. Sea Wavelength, L Sea Wavelength, L
Fig. 8. Radar-inferred currents (radial to the radar) versus water wave- VI. CURRENT MEASUREMENT length being observed by radar. Relatively high sea states. As mentionedin theIntroduction and demonstrated in Fig. 1, currents are evident ih therecords as anoverall offset of the radar datawith simultaneous observations of the driftof a the first-order Doppler peaks from their expected (normalized) submerged drogue. This effect is much like the decrease in positions at fl. Data obtained on several days at the San velocity of surface waves in shallow water, and one could ex- Clemente Island facility have been examined from the stand- pect here also that surface waves should be influenced sig- point of deducing currents. Using the relationship u =Adgc/(4do) nificantly by currents to a depth comparable to their wave- mentioned in the Introduction, surface currents radial to the length. If the current changes with depth, as is usually the radar were deduced and plotted in Fig. 8. These plots show case, the short waves will have a different velocity than the the radial current componentin centimeters per second along longer waves. This has been shown by Plate and Trawle [ll], 240' (circles) and 270" (crosses) as a function of the first-order followingBiesel [12], who showed that the observedwave sea wavelength L corresponding to the seven operating fre- phasevelocity u oninfinitely deep water,having a linear quencies. Error bars give an estimateof the current magnitude vertical gradient of current velocity du/dz with depth z, could precision. The precision is limitedby the resolution of the be related to the surface-current velocity u., and the theoreti- spectral analysis at the longer wavelengths, while (1/200 Hz) cal wave phase velocity inthe absence of current YO, by at the short wavelengths the limit is imposed by the natural broadeningof the firstaorderlines due to higher ordersea 1 effects. (0 - U,)Z + - du/dz(v - U,) = Yo2 (7) The data in Fig. 8 are for relatively high sea conditions, K with the windblowing roughlyin the direction of.the two K being the wavenumber.Note that when 1/~=L/2r= 0, antenna beams. Incomparing the data inFig. 8, several u=oo+u,. Thus we canestimate the surface current from points are worthy of discussion. Note firstof all that there is a Fig. 8 by inspection, as wavelength approaches zero. considerable variability in the observed current velocities. In Likewise, the vertical current gradient du/dz can be in- general, the apparent current magnitudes observedon the two bearings are different, which can be explained on the basis ferred from the records by a perturbation on (7). We employ that the currentflow is more nearly parallel to one radar beam the fact that u.