Validation of the CUTLASS HF radar gravity wave observing capability using EISCAT CP-1 data

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Introduction
Since the seminal work of Hines (1960), gravity waves have been recognised as an important phenomenon in the upper atmosphere (see Hunsucker, 1982;Hocke and Schlegel, 1996, for reviews).They are able to transport energy and momentum from the middle atmosphere and from the auroral regions to mid-latitudes (Chimonas and Hines, 1970).Whilst periodic ¯uctuations in the auroral current can induce gravity waves (e.g.Millward, 1994), single pulse disturbances need to undergo dispersive re¯ection from the Earth's surface to exhibit wavelike properties (Francis, 1974).Periodic waves may also be generated by instability processes associated with convection electric ®elds in the auroral F-region (Robinson, 1994).
Much of our knowledge of thermospheric gravity waves comes indirectly from studying the induced response of the ionosphere (e.g.Munro, 1958;Georges, 1968).Often this work was carried out using vertical HF radio transmitter/receiver pairs such as ionosondes and Doppler sounders.However, the relationship between the waves and the ionosphere is not a simple one and quite sophisticated inversion techniques have been adopted to obtain wave parameters from ionospheric measurements (Kirchengast et al., 1995(Kirchengast et al., , 1996)).A useful test of the ionospheric disturbances' similarity to the underlying gravity wave ®eld comes from applying Hines ' (1960) dispersion relationship for the neutral waves.Reasonable agreement between the two indicated a broadly linear response (e.g.Tedd and Morgan, 1985).Samson et al. (1990) have demonstrated that travelling ionospheric disturbances (TIDs) associated with atmospheric gravity waves can be detected from the modulations in the power and Doppler shifts of the ground-backscatter returns from oblique HF radars.Whilst this has allowed a determination of the period of the waves and the direction of the sources, ¯uctuations in the signal strength have hampered attempts to obtain the amplitude of the disturbances using this technique.
We shall present results from the Collaborative United Kingdom Twin Located Auroral Sounding System (CUTLASS) radar facilities in Iceland and Finland which can provide information about the period, azimuth and amplitude of the travelling ionospheric disturbances related to atmospheric gravity waves.We employ a new technique which makes use of the `®rst skip' radar propagation path which is relatively insensitive to ¯uctuations in backscattered power.As part of the validation process, a comparison with the European Incoherent Scatter (EISCAT) UHF radar was made.The EISCAT facility has been in operation for around ®fteen years (see, e.g., Baron, 1984) and has been used successfully to study a number of gravity wave properties (Schlegel, 1986;Natorf et al., 1992;Lanchester et al., 1993;Shibata and Schlegel, 1993;Williams et al., 1993).Further re®nements of the ®rst skip technique will be discussed.

`First skip' theory
The problem of range determination using radars is an old one (see, e.g., Gething, 1991 for a review).If the radar waves propagated in straight lines and the ionosphere behaved like a smooth re¯ecting surface, then the true distance of a target on the ground could be obtained from simple trigonometry.Modern ray-tracing techniques have taken account of the continuous variations in the refractive index of the ionosphere to produce a more accurate estimate of the range, but temporal and spatial variations in the medium remain (Tedd et al., 1984).Gravity waves are able to distort the apparent position of a target by modifying the re¯ection angle of the ray path.A combination of ray-tracing and a detailed knowledge of the current state of the ionosphere would be needed to get a complete picture of the variation in the ®rst returns from the F-layer.
In simple `tilting mirror' theory, the apparent range of an object will change depending on the angle of the ionosphere presented to the rays.If the ray path is fairly oblique, then relatively small tilts will produce signi®cant variations in the range.Assume a perfect re¯ecting mirror and monochromatic waves such that e e 0 sinkx À xt / 1 where e 0 is the amplitude of the wave, k is the wave number, x is the angular velocity and / is the phase.Then the gradient is given by The range as a function of tilt angle can be given from the following equations: where h is the vertical distance to the re¯ecting layer, h 1 is the horizontal distance from the radar to the re¯ection point, h 2 is the horizontal distance from the re¯ection point to the ground scatter region and h tilt is the gradient of the re¯ecting layer with respect to the undisturbed ionosphere.D R and D T are the elevation angles of the transmitted/received wave and the ground-scatter angle respectively.See Fig. 1 for a schematic view of the geometrical arrangements.
The oblique angle of the CUTLASS radars ensures that relatively small variations in the eective vertical re¯ection height can result in signi®cant changes in the horizontal skip distance.It should be noted however that the response tends to be non-linear.The mean skip distance will tend to increase away from the radar and a monochromatic wave will generate higher frequency components in the skip which must not be confused with genuine non-linearity in the ionospheric response to the passage of a gravity wave (see, e.g., Arnold and Robinson, 1994). 3 The CUTLASS Iceland and Finland radars Located at sites in Hankasalmi in central Finland and Pykkvibaer in Iceland, the CUTLASS radars each comprise of a linear array of 16 antennas fed by a distributed system of transmitters/receivers.The design closely follows that of a number of other radars that form part of the SuperDARN observing network, deployed to observe the auroral region (Greenwald et al., 1995).The radars can operate over a range of HF frequencies varying from 8±20 MHz.The antenna area produces a beam with a main lobe 4°wide and side lobe power down by over a factor of 10.Electronic phase delays can be imposed on the dierent antennas to rotate the direction of the beam by up to 45°.
A coded pulse sequence is transmitted and autocorrelation functions of the received signal provide information about the power, Doppler velocity and spectral width.Range data can be inferred with a resolution of 45 km for 70 range gates out to approximately 3000 km.The integration time for the standard operational mode is seven seconds, allowing a complete scan of the 16 viewing positions every 2 min.This is suciently below the Nyquist limit to permit studying gravity waves with periods of 15 min or more.The signal-to-noise ratios are high enough for an integration period of one second, but this sampling rate would only become necessary when more than one complete scan at a range of frequencies was required.Samson et al. (1989Samson et al. ( , 1990) ) have interpreted wave-like modulations in the ground-scatter power returns as being due to the focusing and defocusing of the radio waves by the passage of atmospheric gravity waves.Bristow et al. (1994) and Bristow and Greenwald (1995)  have computed the atmospheric gravity wave spectra using 2-h samples of the power return data at each range-beam element.They relied on the power variation of the gravity wave modulated ground scatter data.However, this data is sensitive to changes in the ionospheric propagation conditions that aect the signal strength.In addition, there are a few days each year when the ionospheric conditions are such that strong ground-scatter returns over an extended number of radar ranges are quite rare.Our technique provides complementary evidence that is less sensitive to absolute power ¯uctuations and can be applied when good observations can be obtained for a limited number of range gates.Ground-scattered power has been identi®ed from the very low Doppler shifts present during the measurements (absolute values less than 50 ms A1 ).Similar patterns were obtained for the other beams, indicating that the disturbances were of a spatially extended nature, consistent with a propagating wave front.As the time of arrival of the phase front was delayed with respect to the nearer range gates, one can infer that the waves were travelling towards the radar.
Careful inspection of the phase fronts of the earliest radar returns from the F-region, starting around 05:00 UT and continuing up to 08:00 UT in Fig. 2, and the latest starting around 15:00 UT, indicate that these waves were travelling away from the radar.This apparent anomaly was resolved by Milan et al. (1997) who proposed that when the forward-directed beams are looking at the ionosphere when it is still in darkness, the backward-looking side lobes are able to receive signals propagating via the sunlit ionosphere at lower latitudes.The radar is suciently sensitive to detect these signals above the noise threshold.Any signi®cant forwardlooking data will overwhelm this signal during the daylight hours at higher latitudes due to gain bias towards that direction.The forward direction ®eld-ofview is over the SodankylaÈ region, whilst the backward view is between Moscow and Riga.As we could not obtain ionosonde data for Riga we had to settle for the station at Uppsala.This is to the west of the CUTLASS ®eld-of-view but is at a similar latitude.Interferometric information from the radars allows the elevation angle of the incoming signal path to be determined from which the look direction can be unambiguously deduced.
A method that is independent of the Finland radar for checking the look direction makes use of a combination of computational ray tracing and ionosonde data near the ®elds-of-view.The ionosondes provide information about the thickness and height of the electron density pro®le that are then input parameters to a model ionosphere.Radio wave ray paths are then computed for the Finland radar location and the range of the ®rst detectable signal return established every hour.Figure 3 presents the results for January 11th, 1997, at Soda-nkylaÈ , Uppsala and Moscow.SodankylaÈ produces a signi®cant ionospheric propagation for fewer hours, compared with the longer periods for the more southerly locations and also results in a greater ®rst skip distance that is not consistent with the CUTLASS observations for this month.The latter two exhibit a temporal displacement in line with their diering longitudinal positions.
The number of hours of daylight are closely related to the periods of signi®cant power returns.However, changes in the ionosphere will be superimposed upon this.The Moscow ionosonde observed the electron density levels fall o quite noticeably around 12:00 UT and this was re¯ected in the CUTLASS power returns.Intervals have to be selected carefully where such events will not be present to contaminate the results and this usually means geomagnetically quiet conditions.To obtain the ®rst ground-scatter returns from the F-region in the CUTLASS data set, it is necessary to discriminate against contamination from the E-region returns.This is often a simple task by visual inspection, but for routine data analysis, it is preferable to automate this activity.One means of accomplishing this is to compile a monthly climatology of ®rst returns from the radar.
For every day of CUTLASS common programme observations and for each beam, the frequency of occurrence of the ®rst power returns is noted as a function of range and time.The climatology for the Iceland data for January 1997 can be found in Fig. 4. Back-scatter returns have been ignored for the ®rst ten range gates where geometrical considerations make it unlikely that the response is coming from the F-region.These range gates have thus been omitted from the ®gure.During daylight hours, the data corresponds to a smeared-out version of the ray-traced plot.The variability is caused by the passage of gravity waves and variations in the propagation conditions over the period of study.There is a small time shift for each beam which will produce added variability of the ®rst returns, but this eect is small outside of the dawn/dusk periods where local time changes are far greater than TID displacements.E-region contamination is also quite noticeable in the near range gates.The ®rst return statistics have been improved considerably by assuming that the F-region cannot be detected within the ®rst 10 range gates.The only major dierence between the Iceland and the Finland climatologies is a local time shift of four hours, which is consistent with the geographic separation of the two radars.
The mean range and ®rst standard deviation at each time interval can then be computed.A ®ve-point temporal ®lter smoothes out the variations caused by the relatively small statistical samples.The separation between the ®rst standard deviations is of the order of 8 range gates.Any gravity wave disturbance from a typical day would be expected to generate F-region returns within this region.All observations more than Occasionally, the E-region ®rst return is part of an extended area and so this ®lter can fail, producing contamination.Therefore, any data that is obtained at the nearest allowable range gate to the radar is considered to be unsound and no information from that sampling interval takes part in any further processing.A second stage of processing is then carried out using the ®lter outlined above for individual days.This procedure can then be repeated for the other 15 beams.A band pass ®lter can be applied to identify oscillations with periods of between 15 and 120 min.An example from Iceland on January 8th, 1997, in Fig. 5 indicates that the waves are coherent across a number of beams, suggesting that the returns are likely to be from the same region of the ionosphere.

Comparison between CUTLASS and EISCAT TIDs on 1/3/95
The EISCAT facility comprises of a UHF system and a VHF radar.These wavelengths are ideal for measuring the scatter from acoustic waves inherent in the ionospheric plasma, rather than depending on coherent structures, as is the case for CUTLASS.However, the scattering cross section is very small and large power output is needed to compensate for this.Consequently, there are only a handful of such instruments in operation around the world and they do not run on a continuous basis.
We have selected a day when the EISCAT UHF instrument was running its Common Programme mode 1, namely with a high temporal resolution in a single look direction along the geomagnetic ®eld with good vertical resolution.Figure 6 shows the band-pass ®ltered electron density as a function of height and time on 1st March, 1995.The application of the ®lter makes these waves much more prominent.The disturbances tend to appear at a later time at lower altitudes, which is consistent with the downward propagating phase fronts and upward propagating energy of gravity waves.Previous studies have con®rmed that these structures are closely related to AGWs (e.g.Shibata and Schlegel, 1993).Figure 7 shows the band-pass ®ltered electron density perturbations at 250 km.The gravity waves change in amplitude and phase with height and so it is important to compare the correct EISCAT altitude with the eective re¯ection height of the observed CUTLASS data.Therefore, any technique that relies upon the re¯ection from the ionosphere would be height dependent.The peak in the EISCAT electron density pro®le on this day is 260 km.CUTLASS has the ability to transmit at a range of frequencies between 8±20 km that can result in re¯ecting o dierent parts of the ionosphere, both height and range in a complex way that requires a combination of ray tracing and a comparison with EISCAT to fully understand.
The CUTLASS ®rst hop climatology for March 1995 was constructed in the manner described in Sect. 4 and then the resulting E-region ®lter was applied to the ®rst day of the month.Attention was Fig. 5. Perturbations in the Iceland ®rst returns after removing the diurnal variation for 8 January, 1997 across all 16 radar beams focused on beam 5 that looks towards the EISCAT radar site.There were a number of disturbances present in the daily ®rst skip return that suggested strong gravity waves activity.
There appeared to be reasonable agreement between the CUTLASS and EISCAT time series.However, theoretical considerations indicate that for a maximum in electron density, the range should be at a minimum.This discrepancy may be accounted for by allowing a ®nite time for the wave that appears in the EISCAT radar ®eld of view to reach the CUTLASS ®rst return position.The range of the ®rst CUTLASS returns for 1st March, 1995, are presented with a time delay added to take account of a delay for any wave to propagate from Tromsù to the CUTLASS ®eld-of-view (Fig. 8).This time is proportional to the distance of the observations from Tromsù and assuming a constant line of sight phase speed of 250 m/s.
The correlation between the EISCAT and CUTLASS data for the interval 08:00 UT and 15:00 UT was computed to obtain the best agreement as a function of altitude and also of phase front speed.A correlation of A0.8 was obtained when EISCAT data at 235 km was used (Fig. 9) with a time delay of 108 s (Fig. 10).This is suciently below the peak electron density to assume   that any perturbations in the electron density ®eld would produce a linear change in the altitude of the re¯ection point.The level of agreement is very good considering that two completely dierent measuring techniques were employed.No attempt was made at this stage to correct for the non-linear distortion discussed in Sect. 2 and the gravity wave ®eld itself would have changed between the EISCAT and the CUTLASS ®rst return positions.By assuming re¯ection occurs from the same height for each of the other 15 beams, electron densities over a 45°arc may be derived.This would allow separation of purely temporal and spatial/temporal changes in the electron density ®eld.
This result indicates that the technique can reproduce the general features of the electron density pro®le.Also, there is sensitivity to the perturbations due to the passage of gravity.Figure 10 shows that the correlation improved by 0.08 when the delay of 108 s was included in the CUTLASS data to allow for the propagation of the waves from Tromsù.As the ionospheric range is half the distance of the ground range, then each range gate represents a displacement of 22.5 km in the ionosphere.At an eective height of 235 km, this produces a propagation speed of 210 m/s towards the radar, consistent with previously reported measurements of medium-scale TIDs.

Conclusions
The CUTLASS radars are able to observe an extended region of the ionosphere from the ground backscattered power returns.Wave-like perturbations in the distance to the ®rst F-region power returns are consistent with atmospheric gravity wave propagation.Variations in this distance give a good indication of the period of the waves and more uniquely, of their amplitude.The CUTLASS observations are consistent with a comparison with EISCAT data.We may therefore infer that we are seeing the signature of gravity waves in the CUTLASS radar skip distance signatures.
CUTLASS provides nearly continuous coverage of gravity waves over a wide area and a narrow height range, whilst the EISCAT radar gives very good height information at a single point (or three points in a dierent mode) on a few days every month.Therefore they can complement each other very well.In combination with the EISCAT Svalbard Radar, it will be possible to continue to monitor the evolution of waves from the polar cap ionosphere.
There are a number of ways to improve the experiment.The amplitudes of the atmospheric gravity waves can be inferred using a ray-tracing model that reproduces the expected range displacements.Information about the azimuthal orientation can be obtained from the details of the shape of the ®rst returns.Also, it is possible to operate the radar at multiple frequencies with a constant scan rate by reducing the integration time proportionately.In this mode, one can probe the ionosphere at several separated regions from the radar.Information about the phase front speed of the disturbances towards the radar can then be inferred directly without reference to an external instrument such as EISCAT.The observational ®eld of view improves considerably at the same time.
Iceland data became available from the middle of November, 1995, so further studies can make use of both CUTLASS radars after this date.Finally, increasing the horizontal resolution from 45 km to 15 km, which is a proven feature of the instruments, will enhance the range sensitivity by a factor of three.EISCAT is an international collaborative project funded by the UK, France, Norway, Japan, Sweden, Germany and Finland.
Topical Editor D. AlcaydeÂ thanks W. Bristow and K. Schlegel for their help in evaluating this paper.

Fig. 2 .
Fig. 2. Ground-scattered `backward-looking' power returns from the Finland radar on the 11 January, 1997 for the beam closest to Moscow

Fig. 3 .
Fig. 3. Ray-tracing calculations of the F-region skip distance at 9.97 MHz on 11/1/97 using ionospheric parameters obtained from the SodankylaÈ , Uppsala and Moscow ionosondes

Fig. 6 .
Fig. 6.Band-pass ®ltered electron density perturbations as a function of height and time from the EISCAT radar on 1 March 1995.The units are 10 10 m A3

Fig. 8 .
Fig. 8. Filtered ®rst return data from CUTLASS Finland on 1 March, 1995 with the timing adjusted to allow for propagation for the Tromsù site assuming a line-of-sight phase velocity of 250 ms A1 Acknowledgements.The authors wish to thank the sta at the Radio and Space Plasma Physics Group at Leicester for building and operating the CUTLASS radars.The Particle Physics and Astronomy Research Council of the United Kingdom funded this

Fig. 9 .
Fig. 9. Correlation coecient between CUTLASS ®rst range returns and the EISCAT electron density at a range of altitudes, assuming a delay of 108 s for the CUTLASS data

Fig. 10 .
Fig. 10.Correlation coecient between CUTLASS ®rst range returns and EISCAT electron density at 235 km, introducing a time delay in the CUTLASS data proportional to the distance from Tromsù