A single digisonde, used as a receiver for ionospheric high frequency signals from broadcast stations, was able to determine the wave characteristics of traveling ionospheric disturbances (TIDs) using frequency shift and arrival angle measurements. During a measurement campaign, aimed at recovering large-scale wave-like processes in the upper atmosphere, in March 2001 at the MIT Haystack Observatory (Millstone Hill, MA), a Digisonde Portable Sounder (DPS) made simultaneous observations with the incoherent scatter radar (ISR). The DPS was upgraded to include the frequency and angular sounding (FAS) technique previously developed at the Institute of Radio Astronomy in Kharkov, Ukraine, for TID diagnostics. The DPS with four spaced receive antennas received the radio signals at 3.33 MHz and 7.335 MHz from Radio CHU of the Canadian Time Service (Ottawa, Ontario). The FAS technique recovered the basic parameters of TIDs, i.e., amplitude, speed, and the direction of the propagation vector by modeling the ionosphere as a perfectly reflecting surface. For three days during the campaign the Millstone Hill ISR monitored the ionospheric midpoint using a triangulation mode to identify the direction of motion and speed of the wave-like ionospheric disturbances. Comparison of the results from the two diagnostic techniques showed good agreement. The wave directions were within 10 to 15 degrees, and speed and wavelength were within 10 to 12%.
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 Atmospheric gravity waves (AGWs) are an important agent for transferring energy from the Earth's surface and lower atmosphere to ionospheric and higher altitudes and vice versa. They also play an important role in the energy exchange and coupling between various regions of the upper atmosphere. Because of the dispersion properties of the atmosphere and the presence of inverse temperature layers in the troposphere, AGWs are able to propagate over large distances with relatively small attenuation, thus carrying information about their sources of excitation as well as dispersion properties of the medium. At ionospheric heights these wave-like disturbances produce quasi-periodic fluctuations of the charged particle density known as traveling ionospheric disturbances (TIDs), which in turn cause modulation of the parameters of radio signals propagating through the Earth's ionized atmosphere. Such modulations affect ground-based and satellite radio links, but they also make it possible to use remote radio probing for the investigation of this kind of ionospheric disturbance.
 Since the mid 1980s the Institute of Radio Astronomy of the National Academy of Sciences of Ukraine (RINAN) has been conducting extensive research on TID diagnostics applying “frequency and angular sounding” (FAS) techniques. The characteristic feature of these experiments was the use of the transmissions from so-called transmitters of opportunities (e.g., high frequency (HF) broadcast stations) as probing signals. The variations of the received signal parameters such as arrival angles and Doppler frequency shifts were used to determine the characteristics of the TIDs present along the propagation path of the radio signal. Under geometro-optical assumption it was possible to solve the direct and inverse problems of the reflection of radio waves from wave-like ionospheric disturbances modeled as a perfectly reflecting surface [Beley et al., 1995]. This approach proved to be very fruitful for determining dynamical and statistical parameters of TIDs, and for the development of algorithms for the detection and visualization of the ionospheric disturbances. It also made it possible to reconstruct the spatial spectrum of these inhomogeneities, and determine the wave speed and direction. Using the phased antenna array of the world's largest decametric radio telescope, the UTR-2 [Braude et al., 1978], a dedicated data acquisition system had been developed based on the FAS technique. Long-term TID FAS observations covering different seasons found that the moving solar terminator is the main source of the disturbances in the middle-latitude F-region under quiet geomagnetic conditions. During periods of magnetic storms the source was normally located at high latitudes, and the TIDs were propagating equatorward [Kovalevskaya et al., 1987]. To validate these findings, the Millstone Hill incoherent scatter radar (ISR) conducted multipositional measurements of the wave-like disturbances using the steerable antenna [Galushko et al., 1998]. During a dedicated measuring campaign at the Millstone Hill Observatory in 1995, the ISR observations confirmed the previously reported FAS results that the solar terminator is the main source for TIDs.
 Despite the consistent interpretation of the large volume of experimental results, a question remains about the legitimacy of representing the TID by an effective reflecting surface at ionospheric heights. Naturally, a more realistic model would be a plasma density wave propagating in the ionosphere. The mathematical treatment for such a model, however, is difficult. Although the comparison of numerical simulation results for the equivalent surface and wave models shows good agreement, direct experimental proof is still required that the representation of the TID by a perfectly reflecting surface is able to derive the correct TID parameters. Finally in 2001, as part of a Ukraine - USA cooperative project (STCU Project 827), the Digisonde Portable Sounder, the DPS-4 with its small antenna array, conducted FAS measurements at Millstone Hill while the ISR monitored the ionospheric reflection region of the selected broadcast signals.
2. Frequency and Angular Sounding Technique
 The FAS TID diagnostics is based on the following premises. Firstly, for over the horizon propagation, an HF radio wave emitted from the Earth's surface experiences at least one reflection from the ionosphere. Viewing the ionosphere simply as a reflecting “mirror,” the propagation of the radio wave can be described in the frame of geometro-optical approximations. Secondly, the main contributions to the signal parameter variations come from the fluctuations of the plasma medium at or near the highest point of the propagation path, i.e., the vicinity of the reflection point. Finally, it is assumed that in the radio-illuminated region far from the space caustic, small and smooth variations caused by the TIDs result in small variations of the signal trajectory. The latter assumption stipulates a linear relationship between the parameters of the disturbance itself and the trajectory parameters of the reflected radio wave. Hence, it is convenient to select the angles of arrival (AA), namely, azimuth φ(t) and elevation angle ε(t), and the Doppler frequency shift (DFS) Fd(t) of the probing signal as input parameters for the inverse problem. As was shown in Beley et al.  for a single hop propagation mode and geometro-optical approximations, the variations of these parameters are related to the shape of the effective reflecting surface H. We set
where H0 is the mean height of the reflection, and h(x, y, t) represents the relative height variations. Using this model, Beley et al.  described the inverse problem of restoring the dynamical and statistical parameters of the effective reflecting surface from the characteristics of the radio waves. In this paper we merely summarize the algorithms for the reconstruction of the spatial-temporal spectral and statistical parameters of the disturbance. Assuming the height variations h, and the slopes γx = and γy = to be small and smooth
and restricting the analysis to linear approximations, it is possible to relate the surface parameter variations to the variations of the arrival angles and Doppler frequency shifts of the signal:
where Δε = ε − ε0, ε0 = tan−1(2H0/D), D is the distance between transmitter and receiver, and λ is the received signal wavelength.
 It was shown in Beley et al.  that the restoration of the surface parameters can be performed either in a statistical or dynamical approach. Assuming the surface height variations h(x, y, t) to be statistically homogeneous and stationary, we introduce the spatial-temporal correlation function of the surface
Here (Ω, χ, θ) is the spatial spectrum of the surface variations, is the position vector with the components ρx and ρy, χ = is the wave number, and θ = tan−1. Now the spatial-temporal auto-correlation and cross-correlation functions of the trajectory parameters, Kεε(,τ), Kφφ(,τ), KFF(,τ), KεF(,τ), Kεφ(,τ), KφF(,τ), can be expressed through (4) and one can set up the system of equations for the restoration of the spatial spectrum of the surface and the dispersion law of the traveling disturbances. For certain physically realistic models of the surface spectrum (Ω,χ,θ), it is possible to restore even the shape of the surface in the dynamical approach
 Thus, given the measurements of the arrival angles and Doppler frequency shift variations of the received signal on a single hop radio path, the TID model of a perfectly reflecting surface can restore the main parameters of the wave-like disturbances and construct the effective reflecting surface itself. By changing the sounding frequency on a fixed path, it would in principle be possible to reconstruct the ionospheric disturbances at different ionospheric heights, and construct a three-dimensional TID wave.
3. Numerical Simulation of the TID Reconstructions
 The initial justification of using a perfectly reflecting surface to represent the TID was provided by numerical simulations. The variations of the HF radio signal trajectory parameter on the oblique radio path were calculated with the ionospheric disturbances modeled as electron density waves
Here N0(z) is the undisturbed vertical electron density profile; νi is the relative fluctuation of the electron density of the ith spectral component; Ωi and Ψi are circular frequency and initial phase; and θi is the direction of motion of the disturbance with the wave number χi in respect to the radio path. Numerical integration of the eikonal equations determined the AA and DFS variations of the reflected signal. The two-point problem of determining the arrival angles in the horizontal and vertical planes was solved using the gradient method. The error in the ray-tracing procedure was set to be no larger than 100 m. A parabolic model for the undisturbed profile N0(z) was used in the simulation. The calculated signal parameters were then used to construct the effective reflecting surface with the FAS method. Table 1 shows the initial and restored spatial-temporal characteristics: wavelength Λi = 2π/χi, velocity Vi = Ωi/χi, direction of motion θi, and time period Ti = 2π/Ωi. The modeled disturbance consisted of two spatial spectral components. The disturbance parameters were chosen such that only a single solution existed for the two-point problem (single-mode propagation). One can see that the errors in reconstructing these parameters are not larger than 6%. Some difficulties were expected in the reconstruction of the relative amplitudes of the electron density fluctuations, ν = δNe/N0, and the height variations of the reflecting surface, h = δH/H0. The results show, however, that for sufficiently small amplitudes (smaller than 10%) the difference in assumed and reconstructed values of ν and h was smaller than 15–20%. These results were confirmed with the following computer experiment. For the same spatial-temporal characteristics and relative amplitudes of fluctuations, the direct problem of trajectory parameters calculation was solved, with the disturbance modeled as a perfectly reflecting surface and as density waves. Figure 1 shows some of the results of this numerical experiment for a short single hop radio path (about 150 km) similar to the one used in the real measurements. The fluctuations of the trajectory parameters calculated using both models are in good agreement with each other, not only qualitatively but also quantitatively, since the differences between the values are not larger than 15%. Similar comparisons performed for different radio paths under different ionospheric conditions demonstrated that both models produce similar results. Thus the numerical modeling indicates that a perfectly reflecting surface is a good representation of a three-dimensional large-scale ionospheric disturbance for the purpose of the TID analysis.
Table 1. Modeled and Reconstructed Spatial-Temporal Parameters of a Two-Component Disturbance
Spectral Component 1
Spectral Component 2
4. Measuring Technique and Data Acquisition Systems
 As mentioned, the FAS method uses mainly the angles of arrival and Doppler frequency shift measurements of HF broadcasting signals propagating along oblique radio paths. The frequency range 5–25 MHz is widely used in long-distance radio communication. According to the International Telecommunication Union about 6000 radio stations are operating throughout the world. Application of the FAS method is based on the following conditions: (1) the absence of modulation frequencies within a 50 Hz band around the carrier frequency; (2) high frequency stability of the broadcast station transmitters (δf0/f0 ≈ 10−9 to 10−10).
 Typical emission spectra of broadcasting signals are generally free of modulations within ∼50 Hz around the carrier fulfilling the first condition, but they are random-like outside the central 50 Hz band and, therefore, cannot directly be used for coherent ionospheric sounding without first applying narrow-band filtering. Such filtering removes the signal modulation components and any measured frequency variation is of purely ionospheric origin. In practice, using the suggested quasi-monochromatic reception scheme, Doppler frequency shift variations caused by the passage of TIDs can be measured with the accuracy of ∼0.03 Hz [Yampolski et al., 1997]. The main challenge for the experimental implementation of the FAS method is the precise measurement of the arrival angles with an accuracy of better than 0.5 degree. Large phased-antenna arrays having antenna beams narrower than 0.5 degree would be the most efficient solution, however, they require a kilometer size antenna aperture. Obviously, such instruments are rare and extremely expensive to build and operate. An example of such a system is the world's largest HF phased antenna array, the UTR-2 radio telescope [Braude et al., 1978], built in the 1970s, consisting of more than 2000 dipoles. The first FAS measurements were conducted with this system in the early 1980s [Kovalevskaya et al., 1987]. About one thousand hours of observations were carried out, but it is not realistic to expect such observations to be carried out on a global base. We therefore designed a new compact data acquisition system that can use Doppler interferometry for signal trajectory measurements. Bibl and Reinisch  had introduced Doppler interferometry into ionospheric sounding by developing the digisonde. Since multimode propagation is a frequent occurrence in ionospheric wave propagation, the resulting field at the receiver location is generally the sum of magneto-ionic components of the high and low angle rays reflected from the ionospheric layer [Gething, 1978; Reinisch, 2000; Galushko and Yampolski, 1996]. Such fields make it impossible to use standard interferometer techniques for finding the wave vectors of the received signals (unless huge-aperture antenna arrays are used). Doppler-filtered interferometry selects the spatial signal components in the spectral domain making use of the differences in the Doppler frequency shifts between signals propagating along different trajectories. With sufficiently high signal-to-noise ratios (of the order of 40 dB) and integration times of the order of 20–40 s this method provides an arrival angle resolution of ∼0.5°. This digisonde technique uses a small-baseline antenna array shown in Figure 2. The standard DPS receive system has a bandwidth of 34 kHz, designed for receiving the pulsed signals emitted by the DPS transmitter [Reinisch, 1996]. Therefore, in order to be able to receive and correctly process the broadcasting signals, some modification of the DPS software was required. The received signal, digitized at the 225 kHz intermediate frequency, was digitally filtered with a 30 Hz bandwidth, which is sufficiently narrow to remove the modulation components from the broadcast signal spectrum. The DPS-4 based FAS system at the Millstone Hill Observatory (42.6°N, 71.5°W) provides an opportunity to run TID diagnostics simultaneously with the Millstone Hill ISR measurements.
5. FAS Measurements at Millstone Hill
 A measurement campaign dedicated to the comprehensive diagnostics of traveling ionospheric disturbances was carried out at the Millstone Hill Observatory during 10 days around the spring equinox March 13–22, 2001. Simultaneous ISR and digisonde measurements were made during three of these days, March 14–16. For these experiments the Canadian time-service broadcast station CHU, located near Ottawa (45.3°N, 75.8°W), was used as the source of the probing signals. This station operates continuously at the carrier frequencies 3.333, 7.335 and 14.67 MHz. The distance from Ottawa to Millstone Hill is 450 km, and the transmitter's azimuth is 312.5° (counted clockwise from geographic north). For typical ionospheric conditions the highest CHU operating frequency of 14.67 MHz is substantially higher than the maximal usable frequency (MUF) for this radio path, and the DPS system was therefore set to receive the CHU transmissions at 3.333 and 7.335 MHz. The approximate signal reflection heights were between 150 and 250 km depending on the operating frequency and the time of day. In order to provide vector measurements in the near vicinity of the HF signal reflection point, the ISR steerable antenna was cycled through a tightly spaced three-position experiment with (elevation/azimuth) pointing directions (54/312), (39/322), and (39/302). The horizontal ISR antenna beam separation at 250 km altitude was ∼70 km. This three-position experiment made it possible to use a triangulation technique to determine the direction and speed of the observed wave-like ionospheric disturbances. The complete data-taking cycle for four orientations of the ISR antennas (one zenith and three oblique ones) was about 5 min, limiting spectral analysis to periods larger than 10 min. Calibration of the ISR measurement was provided by the ionograms recorded every 5 min by a second collocated DPS system operating in the standard vertical ionogram sounding mode.
 For the purpose of TID restoration, data from two magnetically quiet (Kp < 2.3) days, March 15 and 16, were selected for the analysis. Another reason for not including March 14 data into TID reconstruction was contamination of the DPS received signal by some interferer of unknown origin. Since we expected the moving solar terminator to be the main source of the disturbances, we centered the analysis on the time intervals from 0700 to 1100 mean local time (1200–1600 UT). The CHU carrier frequency of 7.335 kHz provided the best TID diagnostics. The reception at this frequency became possible immediately after the time of passage of the solar terminator through the reflection point (around 1130 UT). The 3.333 MHz signal spectra were frequently contaminated by the strong spectral components produced by signals reflected from the regular and sporadic ionospheric layers E, F1, and Es that complicated the analysis. Figure 3 shows a fragment of the measured DFS and AA variations of the 7.335 MHz signal. The quasiperiodic variations with characteristic periods of 20–30 min are present in all three data series. Simultaneous data from the vertical DPS sounding (Figure 4) also show the presence of wave-like disturbances of similar periods in the height interval of 190–210 km. This height range corresponds to the expected height of the CHU signal reflection (plasma frequencies of 5.6 to 6 MHz). ISR data collected with the steerable antenna illuminating the reflecting ionospheric region also show the presence of the quasiperiodic variations with similar periods in the electron density records (Figure 5).
 Spectral analysis of the signal variations ε(t), φ(t), Fd(t), and Ne(t) reveals the most energetic components of the wave-like disturbances. The strongest spectral component had a period of 32 min (see, for example, Doppler frequency shift spectrum shown in Figure 6), typical for TIDs generated by the solar terminator at the middle latitude F-region [Galushko et al., 1998].
 The data for this two-day period were processed with the FAS method determining the amplitude of the disturbances, their wavelengths, speeds and directions of motion. The results are presented in Table 2. The time-evolving reflecting surface was constructed in the dynamical approach [Beley et al., 1995]. Figure 7 shows a fragment of the restored surface at 1225 UT on March 15, 2001. Seven strongest spectral components (see the spectrum in Figure 6) were included in the surface reconstruction. Solving the inverse problem with the dynamical approach made it possible to determine the relative amplitudes δH/H0 and δNe/N0, i.e., the relative surface height and electron density variations for the strongest spectral component. It turns out that δH/H0 was in the range of 0.8 to 1.5%, while δNe/N0 was between 1 and 2.5% depending on the time of the day and the height:
Table 2. Spatial Characteristics of the 32-min Period TID Obtained With the FAS and ISR Methods
DPS FAS Results
 The accuracy of making an individual electron density measurement by the ISR method depends on the radar system calibration (here direct calibration with the local Digisonde was provided) and the statistical uncertainty of combining discrete samples within the sampling volume. The statistical accuracy of the measurement is directly proportional to the overall level of signal to noise ratio (i.e., the absolute electron density) and improves as the square root of the number of samples (pulses) integrated. A statistical accuracy of ∼10% is characteristic of the raw ISR density data taken in these experiments. Therefore, by taking a Fourier spectrum of the raw ISR density data over a 2-hour time window with 5-min data samples, the noise reduction becomes ≈ 5 for a single spectral component of the electron density spectrum. The next spectrum was calculated over the time window shifted by one data point. δNe/N0 values were determined as the ratio between the amplitude of the spectral component of interest to the electron density averaged over the corresponding time interval. This type of postprocessing results in the accuracy of electron density variation measurements of about 2%. The accuracy of the DPS electron density measurements was similar.
 TID parameters were also calculated from the ISR measurements using triangulation techniques. First, to identify the height range where the wave-like disturbances were propagating, the correlation coefficients at the adjacent heights were calculated. The data collected by the ISR zenith antenna with the height resolution of 21 km were used. Only the electron density fluctuations δNe(t) calculated as a difference between the raw data and the daily trend (see equation (7)) were analyzed. The daily trend was calculated using 2-hour wide running average windows.
 The results of the correlation analysis showed that wave-like disturbances with periods ∼30 min were present practically throughout the whole F-region of the ionosphere at the altitudes of 200–400 km. Next, we calculated the cross spectra of electron density variations between four different space points at the height range where TIDs were observed. The phase differences Ψi between the corresponding spectral components at the different space points were used to reconstruct the disturbance wave vector. It was assumed that each frequency component corresponds to the spatial component with its own wave number (Ω). Then, knowing the separations between the points of measurements i and corresponding phase differences Ψi, it was possible to determine the wave number , and therefore, the spatial wavelength, velocity and speed of motion of the TID.
Table 2 presents the measured characteristics of the strongest 32 min period TID, reconstructed for 4-hour time samples on two days of observations with both the digisonde FAS method and the ISR measurements. It is worth noting that the ISR measurements made it possible to reconstruct the full three-dimensional vector of the TID motion, while the perfectly reflecting surface model can only determine the horizontal component. However, the ISR results indicated that the observed TID propagated almost horizontally. That is why only the absolute values of velocity vector and the direction of motion in the horizontal plane are shown in the table. The spatial TID characteristics obtained with the two different techniques are in good agreement. For example, the relative differences for the TID wavelength and speed of motion obtained with the two techniques is no greater than 10–12%, and the directions of motion differ by no more than 15°.
 1. A dedicated instrument for frequency and angular sounding (FAS) diagnostics of TIDs has been developed using a Digisonde Portable Sounder, DPS-4. The characteristic feature of the FAS TID restoration is the use of transmitters of opportunity as sources for the probing signals.
 2. A measurement campaign was carried out at Millstone Hill in March 2001 with simultaneous operation of the FAS-adapted DPS and the ISR. Both instruments were able to detect the presence of the solar terminator generated ionospheric disturbances in the F-region of the ionosphere. The main periods of the observed TIDs were shown to be in the order of 30 min. The wavelengths of the observed disturbances were in the range of 260–620 km, and the velocities were in the range of 130–340 m/s.
 3. The height variations of the effective reflecting surface, modeling the TID, were shown to be in good agreement with the actual variations of the electron density fluctuations measured by the ISR and the digisonde ionograms.
 4. Comparisons of the observed TID parameters measured with the HF FAS technique and the ISR observations show that for the strongest spectral TID components, the difference between TID wavelength and velocity determined with the two methods is not greater than 10–12%.
 These experiments served as a validation of the FAS technique using the representation of TID by an effective reflecting surface. Thus, we have demonstrated a feasible system for global monitoring and diagnostics of wave-like ionospheric disturbances that can be established by implementing the FAS adaptation in the large global network of DPS stations. Each modified DPS could receive selected signals from HF transmitters of opportunities (broadcast stations) as the sources for the probing signals.
 The authors wish to thank Drs. V. G. Bezrodny, S. B. Kascheev, and V. G. Sinitsyn for their attention to the work and useful critical comments. This work was partially supported by the Science and Technology Center in Ukraine (STCU project agreement 827 and 827c). B.W.R. was in part supported by AF contract 19628-96-C-0159, and V.V.P. was supported by a CFCI research assistantship of the University of Massachusetts, Lowell. Millstone Hill Observatory operations and analysis are supported through a National Science Foundation cooperative agreement with the Massachusetts Institute of Technology.