sea-echo Doppler spectra

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. Cll, PAGES 25,227-25,236, NOVEMBER 15, 1997 Ocean surface currents obtained from microwave sea-echo Doppler spectra John A. McGregor, E. Murray Poulter, nd Murray J. Smith National Institute of Water and Atmospheric Research, Wellington, New Zealand Abstract. Ocean currents may be determined from the positions of Bragg peaks in Doppler spectra of radar echoes from the sea surface. In this paper the applicability of this technique at microwave frequencies is investigated. Advantages of high range resolution and sensitivity to currents within centimeters of the ocean surface ensue from the short Bragg wavelength at microwave frequencies. A disadvantage is that the technique is restricted to low wind speed, fetch-limited sea conditions for which individual Bragg peaks are resolvable in the Doppler spectra. Experiments at low grazing angles with an $ band (3 GHz) Frequency-modulated interrupted continuous wave radar show that in these conditions surface drift currents can be measured to better than 4-2 cm s -1 accuracy over a large range of azimuth angles with respect to the wind direction. In conditions under which the Bragg peaks are not resolvable, currents may be measured by using local wind direction measurements to correct the mean Doppler velocity for the relative contributions of the advancing and receding Bragg peaks. Experiments revealed that the accuracy of current measurements obtained in this manner was better than ß 5 cm s -1. The technique was applied to the mapping of tidal currents in an inlet, demonstrating the significant potential of the radar measurements for nearshore and coastal dynamics studies. 1. Introduction Ocean currents may be measured by radar by using ocean wave components as tracers of the current motion. Past work has predominantly used long gravity waves, with wavelengths of tens to hundreds of meters, as tracers. These waves can be sensed either directly by HF Bragg scattering [Stewart and Joy, 1974; Barrick et al., 1977], or indirectly by dual frequency microwave radar [Schuler, 1978] or via the wavenumber- frequency spectrum calculated from radar data [Young et al., 1985]. Some work has considered the use of much shorter ocean waves as current tracers, these being sensed by Bragg scattering of electromagnetic energy in the microwave region of the spectrum. Keller et al. [1982] and Plant and Keller [1990] have shown that Doppler velocities of microwave sea backscatter are consistent with sea surface current velocities measured by alternative means. Poulteret al. [1994] and Smith et al. [1996] have provided evidence confirming this finding. In addition, microwave Bragg scattering is the basis for the interferometric synthetic aperture radar (INSAR) technique for mapping surface currents from aircraft [Goldstein et al., 1989]. This work further examines and applies current measurements obtained by using Bragg scattering waves in Copyright 1997 by the American Geophysical Union. Paper number 97JC /97/97JC ,227 the microwave region of the spectrum as tracers. Significant motivations for this are that first, the ocean currents are sensed over a depth which is a fraction of the wavelength of the Bragg scattering ocean wave component [Stewart and Joy, 1974; Teague, 1986;Alpers et al., 1981]. At microwave frequencies this depth is of the order of centimeters and provides the possibility of a remote sensing technique for measuring surface drift currents. Second, owing to the shorter wavelengths of microwave Bragg scattering components, this technique has the potential to achieve significantly higher spatial resolution than is available from existing HF or dual frequency microwave (Ak) radars. While HF radars have enjoyed considerable success in offshore, open water, and coastal applications, there are many nearshore situations for which much higher spatial resolution is desirable, and the extended range coverage available at HF is not warranted. With currents obtained from mi- crowave Bragg scattering components, range resolutions down to a few meters are possible, opening up possibilities for high spatial resolution studies of current flows in situations such as inlets, estuaries, rivers, and river mouths and in the vicinity of headlands. A further motivation for this work is that the dif- ference between the scales of Bragg scattering waves at HF and microwave frequencies has implications for the physics of the scattering processes. The second order perturbation theory which describes ocean surface backscatter at HF relies on the assumption of a slightly rough surface. This assumption rarely holds

2 25,228 MCGREGOR ET AL.: OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR at microwave frequencies, thus microwave backscatter is best described by composite surface theory [Wright, 1968; Plant, 1990]. Further, there is evidence that alternative, non- Bragg scattering mechanisms come into play at microwave frequencies, particularly at shallow grazing angles. For these reasons the techniques used to measure currents at HF cannot simply be applied at microwave frequencies without caution, and further verification is desirable. Data demonstrating the application of this technique to the measurement of surface drift currents in condi- tions where both Bragg peaks can be resolved in the microwave backscatter Doppler spectra are presented. These data are used to assess the accuracy of the current measurement technique and to test for the presence of systematic errors due to non-bragg scattering mechanisms. In conditions where the advancing and receding Bragg peaks cannot be resolved in the Doppler spectra, it is proposed that currents may be obtained by using a knowledge of the local wind direction and an assumed directional spreading function for the Bragg waves to estimate the relative contributions of the ad- vancing and receding Bragg waves to the Doppler spectra. The assumptions inherent in this method are tested by comparison with the previous, resolved Bragg peak data and by means of an intercomparison with an S4 current meter. Data are then presented which demonstrate the application of these techniques to the measurement of tidal currents in an inlet. Finally, we investigate the use of a method suggested by Lipa and Barrick [1983] for calculating full vector currents from the radial components produced by the radar. 2. Radar Description The radar used for this work is a ground based $ band (3 GHz) (Frequency modulated continuous wave) radar which is operated with a single antenna by using an interrupted transmission sequence. The operating principles of FMCW radars have been documented by Barrick [1973] and their operation with a single antenna by using frequency modulated interrupted continuous wave (FMICW) schemes has been discussed by Shearman and Unsal [1980] at HF and McGregor et al. [1994] at microwave frequencies. Relevant parameters of the radar system used here are given in Table I of McGregor et al. [1994]. The radar antenna is mounted in an elevated position (typically m above sea level) and transmits a beam which intercepts the ocean surface at a shallow grazing angle (typically between 5 ø and 20ø). Echoes received from the sea surface are analyzed by a digital signal processor which computes their power spectra for display in real time. Output from the radar is a series of Doppler spectra of backscattered sea echo, one from each of a number of contiguous range cells on the sea surface. These range cells have a range dependent width (typically of the order of 50 m) given by the beam width of the antenna and a typical range extent of m, determined by the bandwidth of the FM sweep. The Doppler spectra are obtained at time intervals of s, this being the coherent integration time required to achieve the desired Doppler velocity resolution. Data are stored on optical disk for subsequent processing. 3. Current Measurements With Bragg Peaks Resolved 3.1. Theory The basic data produced by the radar are a time series of Doppler spectra of backscattered sea echo. In order to use Bragg scattering waves as tracers of ocean surface currents, the velocities of the Bragg waves must be determined from these Doppler spectra. At microwave frequencies and for moderate grazing angles the Doppler spectrum of radar energy backscattered from the sea surface is adequately described by composite surface theory [Wright, 1968; Plant, 1990; Plant and Keller, 1990]. In this theory the sea surface is divided into patches with small dimensions compared to the wavelengths of the long gravity waves so that Bragg scatter theory holds on each patch. Then, provided that the dimensions of the patches are large compared to the decorrelation length of the Bragg scale waves, the Doppler spectrum of the total returned echo may be calculated by incoherently adding the powers backscattered by each of the patches. The Doppler velocity v(t) and the corresponding Doppler shift fd (t) of the echo from a single patch are v(t)- fz)(t)a0 2 = u(t)cos(a)+ w(t)sin(a) (1) where X0 is the radar wavelength, a is the grazing angle and u(t) and w(t) are the horizontal and vertical components of the scatterer velocity, respectively. The scatterer will be advected by the surface current that we wish to measure and by the orbital motion of longer gravity waves. Considering a monochromatic gravity wave with frequency w wavenumber k, and amplitude A, in water of depth d, the components of the scatterer velocity will then be [Plant et al., 1978] = v0 cos(t) + + w(t) -- Uotanh(kd)sin(wt) C ))(2) where vs is the intrinsic velocity of the scatterer (i.e., the velocity it would have in the absence of advection by currents and waves), v is the component of the total current vector along the projection of the radar line of sight direction on the mean sea surface, and C is the long gravity wave phase velocity, and the orbital velocity U0 is given by U0 = J coth(kd) (3)

3 MCGREGOR ET AL.' OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR 25,229 The Doppler shifting of the gravity wave frequency by the current was not considered by Plant et al. [1978]; however, this is immaterial in the present analysis as we wish to remove all time dependent terms involving v in order to estimate the constant current term vt. This horizontal radial component of current may be estimated by averaging the time series of velocities v(t) over a time long compared to the period of any gravity waves, in order to remove the terms associated with the orbital velocities vc = vs (4) The uncertainty in the average in (4) sets a lower bound on the uncertainty of the current measurement. The standard deviation cr of the time series v(t) will be the rms sum of the uncertainty in the estimation of the line of sight Doppler velocity from the Doppler spectrum [Barrick, 1980] and the rms value of the orbital velocity contributions to (2). The orbital velocities of resolved ocean waves will introduce correlations be- tween the Doppler velocity samples which will reduce the effectiveness of the averaging in reducing the uncertainty. At this point the estimation of the current velocity from the Doppler spectra of the echo from a single patch on the ocean surface has been considered. The actual sea echo Doppler spectra will consist of contributions from all of the scattering patches within the radar resolution cell. Spatial variations in the velocities of the patches and temporal variations during the time required to calculate a spectrum will both act to broaden the Bragg lines. As pointed out by Plant and Keller [1990], spatial velocity variations will be caused by gravity waves shorter than the resolution cell, while spatially resolved gravity waves will cause temporal variations. Broadening will restrict the sea conditions under which the two Bragg peaks will be resolvable. The criterion for resolving the peaks has been presented by Plant and Keller [1990]. Further, the power backscattered from a patch will be modulated by its position on the longer gravity wave. This is described by a modulation transfer function (MTF). Peak backscattered power is obtained from a position near to, but nevertheless somewhat shifted from, the wave crest. In the extreme case the wave crests may shadow the troughs from the radar beam, resulting in selective removal of the trough velocities from the Doppler spectra and velocity time series. For spatially unresolved wave components the modulation and shadowing will introduce an asymmetry into the broadening of the Bragg peaks. This may bias estimates of the Doppler velocity. When all wave components are resolved, modulation will have no effect on the Doppler velocity time series provided that the individual Doppler spectra are not preaveraged to improve statistical reliability before the velocities are estimated. These situations are discussed, with reference to experimental data, in sections 3.2, 4.1 and Experimental Results In order to assess current measurements obtained from resolved Bragg peak positions, an experiment was performed at Petone Wharf on Wellington Harbor, New Zealand. Details of this experiment have been provided by Poulteret al. [1994]. The radar beam was scanned in azimuth over the sea surface in conditions for which the only current present was a wind- induced surface drift. The magnitude and direction of this drift current may be predicted with reasonable accuracy from wind measurements taken in conjunction with the radar data [ Wu, 1975; Lange and Hiihnerfuss, 1978]. Wind speeds were measured at 5.3 m above sea level and converted to 10 m height by assuming that the variation of wind speed with height was logarithmic [e.g., Smith, 1988]. A significant drop in wind speed occurred for a short period during the experiment. The mean 10 m wind speed outside of this period was 6.0 m s - with a standard deviation of 0.8 m s - while the corresponding values during this period were 4.4 ms - and 0.3 ms -, respectively. The fetch varied from approximately 110 m to 390 m over the area covered by the radar. If the surface drift vector is assumed to be uniform over the radar coverage area, then the radial component of the current velocity will vary as the cosine of the azimuth angle. The accuracy of the radar current measurements may therefore be assessed by a least squares fit of the measurements to a cosine curve. The magnitude and direction of the surface drift vector may be obtained from the parameters of the least squares fit. The radar beam was scanned over the sea surface in 20 ø increments. At each, azimuth data were recorded for 5 min with 1.28 s of data being required to calculate each Doppler spectrum. This gave a time series of 234 individual Doppler spectra at each of 20 range cells, of 5 m radial extent, between 40 m and 140 m on the sea surface. Doppler spectra from some representative azimuths are presented by Poulteret al. [1994]. These are averages of 200 individual spectra from the range cell at 60 m and clearly show broadening due to the orbital velocities of ocean waves and asymmetry due to modulation and shadowing effects. Given the fetch and wind speed appropriate to this data, the predominant ocean wave components will not be resolvable. The asymmetry is thus a feature of individual Doppler spectra, rather than a result of modulation induced power variations from one spectrum to the next and must be accounted for when velocities are estimated from the Doppler spec- tra. The usual practice at HF has been to estimate Doppler spectrum peak positions from the centroid of a restricted portion of the Doppler spectrum [Leise, 1984]. However, this estimate will be biased by the asymmetry in the peak. In order to minimize this bias, the peak po-

4 25,230 MCGREGOR ET AL' OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR sitions here are determined by parabolic interpolation about the maximum value in the Doppler spectrum. The least squares fit of a cosine curve to the radar derived radial currents is shown in Figure 1. Radar data obtained during the period of lower wind speed are represented by open circles in Figure I and have not been included in the least squares fit in order to preserve the assumption of a uniform current. The rms scatter of the radar data about the fitted curve is q ms -. This scatter will be partly due to the uncertainty in the current measurement and partly due to genuine spatial and temporal variations in current velocity. It was not possible to estimate the magnitude of these variations in this situation. Consequently, the figure of m s - is adopted as an upper bound on the uncertainty of each of the radial current measurements. The time series of individual velocity estimates have standard deviations of approximately 0.08 m s -. This is of the order of the velocity resolution of the radar ( m s - ) and is consistent with the absence of resolved waves. Assuming that the 234 points in the time series are independent, this gives a lower bound on the random uncertainty of the current measurements of ms -. Having used the least squares fit in this manner to estimate bounds on the uncertainty of the data, it is lent agreement with the average wind direction (181 ø with a standard deviation of 5ø), as is expected for a no longer meaningful to perform a X 2 test for goodness sheltered of fit. However, the deviation of the data points from site with shallow water. the fitted curve is of a random nature and shows no evidence of obvious systematic trends. The presence or absence of systematic biases due to MTF or shadowing effects may be assessed by comparison of the parameters of the fit with the surface drift vector predicted for the conditions of the experiment.., o ß o.2 The magnitude and direction of the surface drift vector estimated from the least squares fit were q m s - and 180 ø q- 1.7 ø, respectively. The uncertainties in these parameters were estimated by using the 0.02 m s - upper bound uncertainty in the data points and the covariance matrix for the fit [Berington, 1969]. The radar derived surface drift is thus 3.54% of the 10 m wind speed. Lange and Hiihnerfuss [1978] have reported values of the ratio of surface drift to wind speed ranging between 2.6% and 5.5%, the lower values corresponding to laboratory measurements and the higher values corresponding to measurements made in the field. The difference between field and laboratory was attributed to the Stokes drift of long gravity waves. Weber [1983] gives values of 3.1% to 3.4% for this ratio in open water with equilibrium wind waves present. Wu's [1983] expression for the variation of total surface drift with fetch gives 3.2% to 3.4% for the range of fetches in the exper- iment discussed here. The fact that this variation with fetch is small supports the previous assumption that the surface drift vector is uniform over the radar coverage area. The radar result is thus in good agreement with reported values of the magnitude of the surface drift. Similarly, the direction of the surface drift is in excel- Shadowing and MTF effects may bias the individual current measurements away from zero and thus increase the estimated magnitude of the current vector. To within the uncertainty of the reported values of surface drift, there is little evidence of such a bias in the data. An upwind/downwind asymmetry in either shadowing or the MTF will give rise to a constant offset in the azimuth scan data. The constant term in the least squares fit was q m s - which is insignificant. In Figure I a significant systematic deviation between the open circles, corresponding to the low wind values, and the fitted curve is evident. Using the value of 3.54% for the ratio of surface drift to wind speed obtained previously, a value of ms - is predicted for the surface drift during this low wind period. This is consistent with the values represented by the open circles and shows that the surface drift current has responded to this wind fluctuation on a timescale less than that needed to collect the data for one azimuth, that is 5 min O Radar azimuth (degrees) Figure 1. Azimuth scan from the Petone Wharf, Wellington Harbor. Radial components of current velocity are deduced from the positions of Bragg peaks in the Doppler spectra of sea surface echoes. The curve represents a uniform current vector that has been fitted to the data by least squares. The open circles are data corresponding to a drop in wind speed and have not been included in the fit. 4. Current Measurements With Bragg Peaks Unresolved 4.1. Theory As sea state increases, a point will be reached where the orbital velocities of the unresolved gravity waves will broaden the Bragg peaks to the extent that they can no longer be resolved [Plant and Keller, 1990]. In this case the Doppler spectrum will consist of a single peak, composed of unresolved power contributions from both

5 MCGREGOR ET AL.' OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR 25,231 Bragg scattering waves. The current velocity may be determined in this situation from the time series of the centroid (first moment) velocity of this peak by using (4) with an effective scatterer velocity (5) where Pa and Pr are the powers backscattered from the advancing and receding Bragg components, respectively, and vb is the Bragg velocity (0.295 ms -1 for the radar frequency and grazing angle used here). Shemet et al. [1993] have obtained airborne measurements of surface currents by analyzing interferometric synthetic aperture radar (INSAR) data in this manner. These authors determined the relative contribution of the Bragg peaks, Pa/Pr, experimentally by examining reflections from nearby bodies of still water. For ground based systems this ratio may be determined from a knowledge of the local wind direction and the directional distribu- tion of the Bragg waves. The problem is essentially the inverse of the technique used at HF to estimate wind direction from the ratio of the powers of the Bragg peaks [Long and Trizna, 1973]. A directional distribution suggested by Longuet-Higgins al. [1963] and applied to HF radar data by Heron and Rose [1986] has been shown by Poulteret al. [1994] to be applicable to 3 GHz Doppler spectra. This function has the form cos2s(or-ow) 2 Where 0R is the radar beam azimuth and Ow is the azimuth of the wind velocity vector. Poulteret al. [1994] found that a suitable value of s under these conditions was 2.5. The Bragg peak power ratio is thus P = cos2s(0 - w/2) (6) where 0 - [(0R-0w)/2[. The expression for the current velocity then becomes < v(t)> (cos2s(0) + -- sin2s (0)) = (7) where < v(t) > is the time series of centroid velocities of the individual Doppler spectra. Strict application of (7) requires a knowledge of the wind direction at the sea surface for every radar resolution cell and at every time for which a Doppler spectrum is measured. For practical reasons it would be preferable to be able to use a single value of mean wind direction measured on land at the radar site. In this case, (7) may be approximated by < cos(a) v(t) > ( cøs2 cos 2s ( ) + - sin 2s ( ))(8) Vc -- VB Owing to the nonlinear dependence of the effective scatterer velocity on wind direction, the averages in (7) and (8) are not equivalent, and a bias may be introduced as a result. Further, the uncertainty in the measurement of wind direction will increase the uncertainty in the current measurements. These effects may be illustrated by reference to Figure 2, which is a plot of the effective scatterer velocity normalized to vb, for various values of the spreading parameter s. For s greater than or equal to 2, three separate situations are apparent. First, for radar azimuths within 45 ø of upwind/downwind the effective scatterer velocity approximates to 4-1 and very little bias or increased scatter in the current measure- ments due to uncertainty in the wind direction is expected. Second, for radar azimuths within 20 ø of crosswind the effective scatterer velocity is approximately linear. In this situation any uncertainty in the wind direction will increase the uncertainty in the current measurement, but there will be little bias in these measurements. Finally, for radar azimuths near 60 ø and 120 ø from upwind/downwind the effective scatterer velocity has considerable curvature. In this situation, uncertainty in the wind direction will introduce both bias and increased scatter into the current measurements. Additional uncertainties will result from uncertainty in the knowledge of the spreading parameter and the precise form of the spreading function. However, Figure 2 shows that for values of s > 2 the effective scatterer velocity is not particularly sensitive to the value of s. Further biases will be caused by any systematic differences between wind directions over land and sea caused by, for example, local topography Experimental Results The importance of these effects was assessed experimentally, by using (8) to calculate current velocities from the data from the Petone Wharf experiment described in the section 3.2. The current velocities were 1.0 ' 0.4 > 0.2-0o , 'x\, ]... s = 1.0 ", \\ ', [ ---- s = 2.0 ", \, I - - s--3.0 '-,, \\,, I Azimuth from downwind (degrees) Figure 2. The effective scatterer velocity, normalized to v, plotted as a function of azimuth angle with respect to the wind.

6 25,232 MCGREGOR ET AL.' OCEAN CURRENT MEASUREMENT BY.MICROWAVE RADAR then compared with those obtained previously by using (4). This comparison was made for various values of the spreading parameter s. The optimum value of this parameter was found to be s - 3, and good results were obtained for values of s between 2 and 4. This reflects the insensitivity of the method to the precise form of the spreading function. The rms scatter of the data points about the fitted curve has increased from the value of 0.02 m s -1, obtained previously, to m s -1. The magnitude of the fitted current vector is ß m s -1 and its direction is 183 ø + 7 ø. As previously, the uncertainties have been estimated using the rms scatter as a measure of the uncertainty in the data points. These values are in good agreement with the surface drift current expected from the wind conditions. The magnitude of the radar derived surface drift current is 3.6% of the average wind speed at 10 m. The correlation between the radial current velocities obtained by the two methods is shown in Figure 3. The low wind values eliminated from the least squares fits have been included here as it is no longer necessary to assume a constant wind. As expected, the scatter in the data points is noticeably reduced for azimuths near upwind or downwind where the effective scatterer velocity approximates to 4-VB. The regression line has a slope of 1.06 and an intercept of m s -1. The three azimuth regimes discussed previously are evident in Figure 3. Near upwind/downwind (+ 0.2 ms -1) the data points are tightly clustered within 0.02 ms-1 of the regression line, showing that the wind direction uncertainty has introduced little additional scatter. These points are systematically biased by about 0.01 m s-1 from the ideal regression line because of the fact that the centroid velocities are more susceptible to bias- ing by the MTF and shadowing-induced asymmetries in the Doppler spectra than are the peak positions determined by parabolic interpolation. The asymmetries in the Doppler spectra are greatest for upwind and downwind azimuths and are such that the direction of the bias will be away from 0 m s -1 [Poulteret al., 1994]. Near crosswind (0 m s -1) the scatter in the data points has increased, but there is little evidence of systematic bias. For azimuths near 60 ø and 120 ø from downwind (+ 0.1 m s -1) both an increase scatter and a bias of m s -1 are noticeable. 5. Tidal Current Measurements 5.1. S4 Current Meter Intercomparison The current at depth within the ocean differs from that at the surface when wind-induced surface drift currents are present. This complicates the task of comparing radar measurements, which are sensitive to surface current, with conventional sensors which measure cur m Tauranga Harbour 0.3, 0.2 e % ,. o 0.0 e e ee ß e ee o $.kati Entrance ! Current from Bragg peak position (m s -l) Figure 3. Correlation between currents obtained from Bragg peak positions (Figure 1) and from the wind direction-corrected centroid method. Figure 4. Geometry and estimated sea surface illumination patterns for the Katikati entrance experiment. The depth contours are at 5, 10, and 20 m. The points labeled A, B, C, and D are the S4 current meter positions. Points E and F are the positions of the tidal cycles in Figure 5.

7 ß, MCGREGOR ET AL' OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR 25,233 rent at greater depths. Tidal flows through inlets are a good situation in which this difficulty may be minimized as tidally induced bulk flows, which can be of the order of 1 m s -1 or more, and will dominate the surface drift current, which is typically of the order of 0.1 ms -1. In addition, long wave activity is reduced in this situation because of attenuation by the inlet and wave breaking over any associated offshore bars. An intercomparison between the radar and an S4 current meter was performed at the Katikati Entrance to Tauranga Harbor, New Zealand. The location and experiment geometry are illustrated in Figure 4. The S4 was deployed at a depth of approximately 0.5 m at four positions within the entrance at a time near the time of maximum flood flow. The four positions are the points labeled A, B, C, and D in Figure 4. The radar was positioned 50 m above sea level on a hill overlooking the entrance. At each S4 position, radar data were taken for a period of approximately 5 min, with the radar beam directed toward the S4. Sea surface velocity was estimated from the S4 data by vector addition of a surface drift estimated from wind measurements made at the radar site. As the bulk current velocity ( 1.6 cms -1) is significant with respect to the wind velocity ( 5 ms-l), the wind velocity relative to the bulk flow was used to estimate the surface drift. A surface drift to relative wind speed ratio of 3.5% was adopted, this being appropriate to the short fetch, low sea conditions at the site. The estimated surface drifts will be uncertain, because of the uncertainty in this ratio and because of unknown differences in wind velocity between the radar site and the sea surface. However, this uncertainty is expected to be a small percentage of the total surface current velocity. Results of the comparisons from the four S4 positions are given in Table 1. Agreement between the radar and the S4 varies from 3 cm s -1 to 9 cm s -1, which is similar to the magnitudes of the uncertainty in the radar current measurements obtained previously Tidal Cycle lumination pattern produced by the intersection of the 10 ø wide conical antenna beam with the plane of the sea surface at each azimuth position is shown in Figure 4. Data are obtained from contiguous 10 m range resolution cells within these ellipses. The corresponding range of grazing angles is 14.4 ø to 5.1 ø. Radial components of current velocity from two representative azimuths are plotted as functions of time in Figure 5. At each azimuth, data from 10 consecutive range cells near the center of the inlet are plotted. The centers of these regions are indicated by the points labeled E and F in Figure 4. The tidal cycle variation is evident in this data, as is the fact that this variation is nonsinusoidal. Nonlinear distortion of tidal flow is a common feature of the tidal dynamics of inlet/bay systems and has been discussed by Aubrey and $peer [1985]. The distortion may result from preferential amplification of higher harmonics (overtides) of the open ocean forcing tide or from nonlinearities in the flow re-.,. E O.d 1.5 c> -0.5 In a separate experiment the ability of the radar 1.0. to obtain spatially resolved measurements was used to 0.5 map the tidal flow through the entrance. The radar 0.0' beam was scanned over the entrance in 10 ø azimuth increments with 30 s of data being recorded at each az imuth. This process was repeated every half hour for ; -.0 almostwo full tidal cycles. The elliptical sea surface il i ß '"1 ' ß i i Tide gauge,' I, I, I, I ' I - ' I Point E, I, '1 ', ' I, ' I,,, ' ß I Point F I,,I, I, I, I,,, Table 1. Comparison of Radial Components of Surface Current (m s -1) From the Radar and the S4 Position A B C D Radar current S4 current Time (hours) Figure 5. Tidal cycles of radar derived radial components of current velocity from representative regions within the inlet. Tide gauge data and fitted curve are shown in the top graph. The middle and bottom graphs show radar data and fitted curves from regions centered on the points labeled E and F, respectively, in Figure 4.

8 25,234 MCGREGOR ET AL.' OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR sponse of the inlet that occur when the tidal elevation is an appreciable fraction of the water depth. The latter mechanism can generate overtides even when none exist in the forcing tide. Tidal flow distortion is often manifested as an asymmetry in the flow between flood and ebb, which can have important consequences for the transport of sediment into and out of the inlet [Aubrey and Friedrichs, 1988]. In Figure 5 a function consisting of the sum of three Up to this point only radial components of current have been presented. It is interesting to consider under what conditions full vector currents may be obtained from the radar data. Lipa and Barrick [1983] discuss three methods by which current vectors may be ob- tained from radial components. First, two radars may be used to view the same area of the ocean surface. Sec- ond, if the current vector can be assumed to be constant within some area of the ocean surface, then its magnitude and direction may be estimated by least squares fitting a cosine curve to the azimuthal variation of the radial components over this area. Finally, current vec- Table 2. Ratios (%) of the Amplitudes of the Harmonics to the Fundamentals for Fits to the Radar and Tide Gauge Data Second Harmonic, Third Harmonic, Tide gauge Radar, point E Radar, point F tors may be estimated by applying the continuity equation to radial component maps. The second of these methods was used to calculate current vector maps from the Katikati data. Figures 6 and 7 show the results for the peak flood and peak ebb tides, respectively. Radial current data were subdivided into blocks of five ranges by six azimuths, with corresponding dimensions of 50 m in range by 300 m in the azimuthal direction. This provided a sufficient number of points for the least squares fits while still giving reasonable spatial resolution. The assumption of a uniform current within each block was evaluated by using cosines with periods corresponding to the principal semidiurnal tide (M2, period hours) and'its second and third harmonics has been fitted to the data by using least squares techniques. The rms deviation of the points from the fitted curve is 0.12 m s -1 at point E and 0.14 m s -1 at point F. Data were available from a tide gauge at Moturiki, an exposed coastal site approxithe reduced chi-square statistic for the fit X2 [Bevington, 1969]. The optimum value of this statistic is 1.0, and fits with values greater than 2.0 are indicated by dashed vectors in Figures 6 and 7). The current vector mately 25 km from the radar site. Tides at the Katikati uncertainties calculated from the covariance matrices of Entrance are known to have a 10 rain time delay when compared with tides at Moturiki (T. Dolphin, private communication, 1993). Accepting that the amplitude of the tide at Katikati may differ slightly from that at Moturiki, the tide gauge data, when time shifted by this delay, may be taken as a reasonable representation of the open ocean forcing tide at the Katikati Entrance. The tide gauge data were fitted by the same functional the fits are typically m s -1 for the magnitude and 4 ø - 6 ø for the direction. On this occasion, no detailed ground truth for these measurements was possible; however, the peak currents in the center of the inlet (1.6 m s -1, ebb and 1.3 m s -1, flood) are in excellent agreement with charted values (1.62 m s -1, ebb and 1.35 ms -1, flood). The radar measured current velocities will be the vecform that was used to fit the radar data, and the results tor sum of the tidal current and a wind-induced surface are shown in Figure 5. Table 2 presents the ratios of drift current. For the flood tide (Figure 6) the wind the second and third harmonics to the fundamental for speed was 4.6 m s -1 from 100øN, and for'the ebb tide these three fits. It is evident that the tidal elevation is (Figure 7) the wind speed was 5.8 m s - from 64øN. approximately sinusoidal. This suggests that the tidal flow harmonics are generated by nonlinear mechanisms rather than their being an amplification of preexisting harmonics in the open ocean tide. In both cases the wind direction was approximately through the entrance into the inlet. The surface drift current, estimated as 3.5% of the wind speed, was 0.16 m s-1 for the flood tide and 0.2 m s -1 for the ebb tide. These surface drifts are of the order of 10% of the peak 5.3. Vector Measurements tidal current, justifying the previous assertion that the surface drift is a small component of the peak total current in the inlet. Tauranga Harbour... :..., 100 m /..' ßlms..'.:' N "'-. ""... /... :.NN.. ::"':11':::':. ::i;i... Radar site Kate... nt an Figure 6. Vector map of current flow within the Katikati inlet at peak flood tide.

9 ß. MCGREGOR ET AL.- OCEAN CURRENT MEASUREMENT BY MICROWAVE RADAR 25,235. I I..."....' '."..'...'...i '"'.....:.... K fikati Entrance Figure 7. Vector map of current flow within the inlet at peak ebb tide. Dashed vectors have reduced X 9' values greater than 2. Other noteworthy features of these vector maps are the significant difference between the flood and ebb flow patterns. There are current shears in the vector fields that suggest the presence of eddies, and these eddies are in different positions in the flood and ebb flow patterns. The presence of an eddy in the flood flow to the southeast of the radar site was observed visually. The eddy in the ebb flow on the opposite side of the inlet to the radar appears to be associated with the sheltering of a region of the inlet from the current flow by a headland. in the knowledge of the wind direction at the sea surface caused a degradation of the current measurement uncertainty to approximately 5 cm s -. An intercomparison between the radar and an S4 current meter in a tidal inlet showed that uncertainties of this magnitude are maintained even in this situation where the local to- pography could potentially cause significant variations in wind direction on the sea surface. The success of the technique in this situation stems from the fact that neither the wind direction at the sea surface nor the form of the spreading function need to be known precisely. We investigated one of the techniques suggested by,p,,,,, [ uool u obtaining vector currents from the radial components provided by a single radar. Good results were obtained for the tidal flow vector at the center of an inlet. However, the technique relies on the validity of the assumption of a uniform current within the small cell over which the analysis is performed. Therefore, the technique may fail in regions of strong current shear or where there is significant curvature or vorticity in the flow. Further discussion of this point has been provided by Barrick [1990]. An example of such a situation is current flow around a headland. The X test for goodness of fit was effective in giving some indication of where this assumption of uniformity was being violated. We envisage the principal application of this technique being the measurement of currents in channels where the flow is confined parallel to the channel and topography permits only a single radar to view the flow at right angles. Examples of these situations include inlets, rivers, and tidal channels in estuaries. In more general situations it would be preferable to use two radars to measure vector currents. 6. Summary and Conclusions In this work we have investigated the potential of Bragg scattering in the microwave region of the spectrum to provide high spatial resolution, remotely sensed measurements of ocean surface currents. When an absence of long wave activity allows individual Bragg peaks to be resolved in the backscatter Doppler spectra, we find that currents may be obtained with a random scatter of less than 2 cm s -1 over a wide range of azimuths with respect to the wind direction and grazing angles ranging from 2.2 ø to 7.5 ø. The radar measured current was entirely consistent with the surface drift current expected from the measured wind speed thus demonstrating the sensitivity of microwave Bragg scattering to currents in the top few centimeters of the ocean. When long wave activity prevents individual Bragg peaks from being resolved in the Doppler spectra, we propose that independent measurements of local wind direction may be used to estimate the relative contribution of each Bragg peak to the broadened Doppler spectrum thereby enabling estimates of the current to be obtained. Investigations showed that the uncertainty Acknowledgments. The authors wish to acknowledge Tony Dolphin, Terry Hume, and Rob Bell for their assistance and for providing the tide gauge data and Richard Barr for helpful comments on the manuscript. This work was supported by the New Zealand Foundation for Research, Science and Technology under contract CO1303. References Alpers, W. R., J. SchrSter, F. Schlude, H. Mfiller and K. P. Koltermann, Ocean surface current measurements by an L band two-frequency microwave scatterometer, Radio Sci., 16, , Aubrey, D. G., and C. T. Friedrichs, Seasonal climatology of tidal non-linearities in a shallow estuary, in Lecture Notes on Coastal and Estuarine Studies, edited by D. G. Aubrey and L. Weishar, pp , Springer-Verlag, New York, Aubrey, D. G., and P. E. Speer, A study of non-linear tidal propagation in shallow inlet/estuarine systems, I, Observations, East Coast Shelf Sci., 21, , Barrick, D. E., FM-CW radar signals and digital processing, Tech. Rep. ERL 283 WPL-26, Nat. Oceanic and Atmos. Admin., Silver Spring, M., Barrick, D. E., Accuracy of parameter extraction from sample-averaged sea-echo Doppler spectra, IEEE Trans. Antennas Propag., AP-28, 1-10, 1980.

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