Multipulse and double-pulse velocities of Scandinavian Twin Auroral Radar Experiment (STARE) echoes

Authors


Abstract

[1] The Scandinavian Twin Auroral Radar Experiment (STARE) coherent radars are a powerful instrument for studying auroral zone plasma convection. In recent years the STARE radars have been collecting both double-pulse (DP) and multipulse (MP) data to measure the Doppler velocity of auroral echoes. We assess here DP-MP measurements for eight events covering 28 hours of operation. More often, there is a reasonable agreement between the DP and MP velocities. Exceptions are afternoon-evening observations for which the Finland radar DP velocity is nearly half the MP velocity obtained through fitting of the autocorrelation function of a received signal (ACF-FIT), although the DP and MP1 (first lag) velocities are in reasonable agreement. We demonstrate that for periods with strong differences between the DP and MP ACF-FIT velocities the spectra are strongly asymmetric, and the phase angle–lag number dependence is nonlinear with a slower rate of angle increase at small-number lags (<3) and a faster rate of angle increase at larger-number lags. Contrary to the DP velocity, the MP ACF-FIT velocity (obtained in some cases without one or two first-lag data) is fairly close to the spectral power peak and power-weighted (over spectrum) velocity. In an attempt to understand the DP-MP velocity differences, we consider the role of the asymmetry of observed spectra and show that it can explain the discrepancies but only partially. As another potentially important effect, we consider the possibility of weak, but not negligible, cross-range correlation between the signals coming from the target and aliasing volumes that are closely spaced for the current STARE mode of operation.

1. Introduction

[2] The Scandinavian Twin Auroral Radar Experiment (STARE) (VHF) and Super Dual Auroral Radar Network (SuperDARN) (HF) systems of coherent radars are widely used for convection studies [Greenwald et al., 1995]. In the original design, each radar of the system measures the Doppler velocity of auroral coherent echoes, and then two line-of-sight (LOS) velocities at radar beam crossings are merged into plasma convection vectors by assuming that the LOS velocity is the cosine component of the plasma flow.

[3] Although the capabilities of STARE and SuperDARN are quite different, both systems use the same principle of velocity determination from a soft target. A SuperDARN radar transmits a multipulse (MP) sequence so that the correlation between pulses of various time separations (at every range bin) can be analyzed. The Doppler velocity is then determined through the least squares fit of the phase angle for the autocorrelation function (ACF) of a received signal [Hanuise et al., 1993; Greenwald et al., 1995]. The STARE radars, being the predecessors of SuperDARN, have been operating for a long time in a mode with transmission of single-pulse and double-pulse (DP) sequences. The Doppler velocity for STARE echoes is determined from the phase delay between two received pulses of the DP train [Greenwald et al., 1978; Nielsen, 1989, 2004]. In late 1997, the STARE radars were upgraded to allow additional MP transmissions (after the nominal single pulse and DP transmissions), similar to the SuperDARN sequences. The ranges for such transmissions were limited to the central portion of the STARE viewing zone including an area where European Incoherent Scatter (EISCAT) measurements of the plasma convection are often performed. Since then, a substantial body of STARE MP data has been accumulated, but the assessment of these data in terms of the relationship to the DP data and to the convection (or the electron drift in the E region) in the ionosphere has just begun [Nielsen and Rietveld, 2003; Uspensky et al., 2004]. In the past, Schlegel et al. [1986] compared DP and MP (the so-called matched-filter) velocities for the Wick (Scotland) SABRE VHF radar and found that the MP velocities were quite often different from the DP velocities. A concern was expressed on the quality of DP velocity data [Schlegel et al., 1986; Whitehead, 1988, 1990]. Schlegel et al. [1986] attributed the DP-MP velocity discrepancies to the asymmetric nature of the auroral backscatter spectra, a persistent feature of the STARE echoes [Nielsen et al., 1984].

[4] More recent STARE data [Uspensky et al., 2004] show that the DP velocities are consistently smaller than the MP ones in the evening sector of observations at large flow angles. This finding is puzzling, especially in view of the fact that for the morning sector of observations the DP and MP velocities do not differ significantly [Uspensky et al., 2003, 2004].

[5] These inconsistencies instigated a closer look at the STARE DP and MP velocity data. Additional interest in the comparison originates from the fact that the new STARE MP-DP data (http://www.geo.fmi.fi/PLASMA/RADAR/STARE/index.html) can be used for various studies of the high-latitude ionosphere, including convection mapping and the physics of electrojet irregularities. For these projects, it is fundamentally important to understand the reasons for differences between the DP and MP velocities.

[6] In this study we broaden the STARE velocity study of Uspensky et al. [2004] by considering more extensive data sets and focusing specifically on the differences between the DP and MP velocities. We also attempt to understand the reason for these differences.

2. STARE Modes of Operation

[7] We consider here STARE data in beams 3–5 (for both radars) because these beams cross each other in the area of EISCAT observations so that information on the electron drift (plasma convection) can, in principle, be added from concurrent EISCAT measurements (Figure 1). In Figure 1 we also show the aspect angles (at a height of 110 km) for the Norway (N) and Finland (F) radars, the thick dashed and thick solid oval-shaped lines, respectively. The flow angles with respect to the L shells over the EISCAT area are ∼45° and ∼76° for the N and F radars, respectively.

Figure 1.

Field of view of the STARE radars (outlined with thick square) with the Hankasalmi Finland radar and the Midtsandan Norway radar (with beams 3–5 inside) assuming the 110-km height of scatter. Shading shows range limits where the multipulse (MP) data were collected. The three-beam azimuth limit was chosen arbitrarily to keep aspect angles roughly as in the EISCAT flux tube (open circle). Thick dashed and thick solid lines are 110-km aspect angles for the Norway and Finland radars, respectively. The arrow illustrates a typical ratio between the Finland DP and MP ACF-FIT LOS velocities in the afternoon-evening. The solid lines represent the Polar Anglo-American Conjugate Experiment (PACE) magnetic latitudes.

[8] The radar pulse sequence consists of a single pulse, then a double pulse ∼10 ms later and, finally, a multipulse transmission ∼9 ms later. This pulse train is repeated with a frequency of ∼11 Hz. The pulse length is ∼80 (100) μs, and the base pulse separation τ (lag) is 200 μs for both DP and MP schemes. The MP transmission consists of six pulses radiated in a time position 0, 1, 4, 10, 12 and 17 of τ (intervals between pulses are 1:3:6:2:5 of τ). The radar's receiver provides the single-pulse (SP) power, the DP first lag correlation coefficient and the 13-lag MP autocorrelation function (ACF) for 8 antenna beams and 50 (14) 15-km range gates for the DP (MP) data. The DP data are collected at ranges 495–1245 km while the MP data are available between 825 and 1035 km for the Finland radar and between 675 and 885 km for the Norway radar. Both the original DP and MP data have a standard integration time of 20 s. In handling the MP data, we ignored measurements for all lags more than 13 (note that lag 14 data have range ambiguity). In this study we consider the DP and MP data obtained after 100 s averaging of measured parameters (five original 20-s intervals); for example, for the MP data we averaged the ACF real and imaginary parts over 100 s.

[9] Introduction of the MP sequences for STARE was motivated by the desire to collect more information on auroral backscatter, first of all with respect to the spectral width and the shape of the spectra. It was anticipated that the MP velocities would be comparable to the DP velocities; however, rather unexpectedly, it turned out that the velocities could be significantly different. This is in contrast to the expectation of Nielsen [1989], who predicted a minor decrease of the DP velocity (∼15%) with respect to the power-weighted velocity of a spectrum that can be derived from the MP measurements. We think that this kind of event needs to be studied in greater detail as it might provide additional information on the processes of signal collection and electrojet irregularity formation.

3. STARE Velocities With DP and MP Transmissions

[10] Figure 2 shows four examples of afternoon measurements of DP (solid line) and MP velocities (open gray diamonds) by the Finland and Norway radars (bottom and top insets, respectively). For the MP data handling, we adopted the velocity obtained through fitting of the autocorrelation function of a received signal (ACF-FIT) method similar to the one used in the SuperDARN radar operation [Villain et al., 1987; Hanuise et al., 1993]. To increase statistics, we considered only those measurements for which lags 0 to 7 data were all good in a sense that there were no strong and chaotic departures of individual lag phases from an expected mean phase angle line (after quadrant correction).

Figure 2.

Norway (N) and Finland (F) STARE radar velocity data (100-s running average of the original data) for four afternoon-evening events. The DP and MP measurements are shown by solid lines and open gray diamonds, respectively. The numbers in each plot are the mean point-to-point MP/DP velocity ratio for the corresponding time interval.

[11] In Figure 2 the MP velocity magnitudes are generally larger than the DP velocity magnitudes. To assess these differences quantitatively, we indicate the mean MP/DP velocity ratio (over the event duration) by numbers on each plot. The mean MP/DP velocity ratio was around 1.1 for the Norway radar and much larger, around 1.7, for the Finland radar. One might relate the observed MP-DP velocity differences to some software/hardware problems. However, on the same day, the DP velocities in the westward electrojet (earlier in the morning) were roughly the same as the MP velocities. This indicates that the instrumental effects were not the dominant factor in the discovered differences; more thoughts on possible equipment artifacts are given in Appendix C.

[12] Figure 3 shows morning sector data, again for both STARE radars. In contrast to the afternoon-evening observations, the MP/DP velocity ratios are close to one (even for the same calendar days, 12 February and 16 September, considered in Figure 2), between 1 and 1.1.

Figure 3.

Same as in Figure 2 but for four morning events.

[13] To find out clues as to why there were significant differences between the MP and DP velocities for the evening sector of observations, we consider the Fourier spectra for certain radar cells. In Figure 4 we give examples of spectra observed by the Finland radar for signals with relatively high signal-to-noise (and signal-to-clutter) ratios (which is not typical). The spectra are based on data in 13 lags; the measured points of the spectra were interpolated to simplify the quantitative description of the parameters of the spectra. For each spectrum in Figure 4, on the left of each plot, we show values of the peak velocity (Peak), the power-weighted velocity (PW, indicated by inverse triangle on the spectra), the matched-filter velocity (MF, triangle), the ACF-FIT velocity (ACF), the MP1 velocity determined from the ACF lags 0 and 1 (MP1, cross), the measured DP velocity (DP, open circle) and the half-power spectral width (W0.5). The matched-filter velocity was computed similarly to the techniques of Rino [1972] and Schlegel et al. [1986]. To remove the noise in determining the power-weighted velocity, only spectral components with power more than 0.1 of the peak (−10 dB, dashed line) for the evening data and more than 0.12 (−9.2 dB) of the peak for the morning data were considered. The insets in Figure 4 show the real (black) and imaginary (gray) parts of the ACFs for a corresponding spectrum and the phase angle–lag dependence (black line with diamonds). The gray open circles are the linear regression lines to the experimental data. For the evening spectra (right), the gray dotted and black dash-dotted lines in the insets represent the DP and MP1 phase angle variations. For the morning spectra (left) these lines run through the gray open circles and are nonvisible. To simplify the comparison, we inverted the signs of the imaginary parts for both morning spectra.

Figure 4.

Four ACF-FIT spectra observed by the Finland STARE radar. For each spectrum the inverse triangle shows the power-weighted (PW) velocity, and the triangle shows the matched filter (MF) velocity; the open circle and cross show the DP and MP1 velocities, respectively. The numeric values for these velocities as well as for the peak and ACF-FIT velocity are given in each plot. The dashed line shows the level of noise components with power less than −10 dB (−9.2 dB for the morning spectra), which were ignored. The insets show the ACF real and imaginary parts and the phase angle–lag dependence (black diamonds and solid line) and its linear regression line (open gray circles). The gray dotted and black dash-dotted lines seen in the two right-hand plots are the phase angle dependence for the DP and MP1 data, respectively.

[14] We note that all four spectra in Figure 4 are slightly asymmetric. It was a surprise to discover that the DP and MP1 velocity (open circle and cross, respectively) in the evening were about the same but much smaller than the ACF-FIT velocity, the power peak velocity and the power-weighted velocity of the spectra. (The ratios were 1.5–1.8 for the evening spectra of Figure 4, which is consistent with the data presented in Figure 2). In contrast to the evening cases, the morning spectra had velocities (except MFs) that are reasonably close to each other despite the fact that both spectra are asymmetric. The MF velocity magnitudes are the smallest (comparing to the peak velocity) for both evening and morning cases, probably because of a significant influence of the clutter and noise.

[15] We believe that the ACF-FIT velocity estimates obtained by the phase angle regression are the most accurate irregularity velocity estimates. These velocities are reasonably close to (slightly above) the power-weighted velocities and reasonably close to the peak velocities obtained after interpolation of the spectra, although the spectra themselves have a rather poor velocity resolution (see small open circles along the solid line for every ∼200 m/s).

[16] One may wonder why the DP and MP1 velocities were so small. As discussed in Appendix C, it is very unlikely that there were some hardware/software deficiencies. We also rule out the effects of a noise correlation due to interpulse separation [Farley, 1969; Sahr et al., 1989] by an experimental check. An indirect support to the above conclusions is the fact that the morning observations do not show significant differences for the velocities. To gain more understanding on the issue, we explore in detail the shape of the phase angle curve for the observed ACFs.

4. Shape of the ACF Phase Angle Curve

[17] We start by presenting a typical afternoon-evening ACF phase angle curve for echoes with large MP/DP velocity ratios (Figure 5a, solid line with open circles). One can recognize a nonlinear shape of the curve for several first lags. The dotted line in Figure 5a is the linear least squares fit to the experimental data. The slope of this line defines the ACF-FIT velocity. The dashed line passing through the open circle at lag 1 shows the phase angle line for the DP velocity. The difference in slopes of the dotted and dashed lines reflects the difference between the ACF-FIT and DP velocities. The slope of the dashed line is about the same as the slope of the MP1 line (the line connecting two heavy points for lags 0 and 1). Both the DP and MP1 values were obtained for the same lag time of 200 μs.

Figure 5.

(a) Typical ACF phase angle curve for an echo with large MP/DP velocity ratio (solid line with open circles). The dotted line is the linear least squares fit of the experimental data, and the dashed line and the open circle at lag 1 show the phase angle line for the DP velocity measured. (b) Family of afternoon-evening MP and DP velocities; the vertical dotted line shows the moment under consideration (Figure 5a). The ACF-FIT velocity is the top thick gray line, the DP velocity is the bottom thick gray line, and the five MP1,.5 velocities in between those two extremes are represented by the thin lines.

[18] Figure 5b shows a family of MP and DP velocities (averaged with a 15-min running window) measured on 12 February 1999 in the afternoon-evening sector. The vertical dotted line indicates the moment considered in Figure 5a. Figure 5b includes the ACF-FIT velocity (top thick gray line), standard DP velocity (bottom thick gray line) and five MP1,.5 velocities in between those two extremes (thin lines). The five MP1,2,.,5 velocities are the DP velocities obtained for pulse pairs with separations τn(1,2,.,5) = 200, 400,., 1000 μs.

[19] One can see that the DP and MP1 velocities have only minor differences and both velocities are significantly smaller than the ACF-FIT velocity. The MP2…,5 velocities are larger in magnitude; they are progressively larger for a larger pulse separation so that the MP5 velocity is the closest one to the ACF-FIT velocity. We note that the largest velocity measured in this example, ∼500 m/s, is slightly smaller than the 1000-μs aliasing velocity of ∼520 m/s.

5. Velocities for an Asymmetric Spectrum

[20] The observed features in the phase angle variation of the ACFs in Figure 5a can be related to the fact that the spectra are asymmetric. To investigate this possibility, we model an observed echo by a superposition of two Gaussian spectra and consider the relationship between the DP velocity and other velocities that can be assigned to the spectrum. Figure 6a shows an experimental Fourier spectrum (solid line with small open circles), based on 13 lag ACF data for the real and imaginary parts that are presented in Figure 6b (solid lines with the open circles and crosses, respectively). One can clearly see that the spectrum is asymmetric with a longer tail toward positive velocities.

Figure 6.

(a) Measured (12 February 1999, Fin STARE b4, bin 36/14, 1215:40 UT) spectra (solid line with small circles) and model spectra (thick gray line). (b) Measured (real, solid line with small circles; and imaginary, solid line with crosses) and model (thick gray line) ACFs matched to Figure 6a. (c) Velocity-lag plots with the measured (solid line with small circles) and the model (thick gray line) velocities. Horizontal dotted and dash-dotted lines are experimentally determined velocities; horizontal gray dashed lines are velocities determined from the model; and diamonds at the right-hand vertical axis are peaks of two components in the model spectrum. (d) Phase angle–lag plots matched to Figures 6a–6c. The open circle at lag 1 is the DP phase angle.

[21] The two Gaussian components, approximating the observed spectrum, are presented in Figure 6a by thick gray lines together with the resultant spectrum of these two components, the thick gray line which runs mainly below the solid line. One can see that the model spectrum reasonably matches the observed spectrum. The real and imaginary parts of the resultant model spectrum are given in Figure 6b (solid gray lines). There are some minor differences between the measured and model imaginary ACF parts for lags 1 and 2 and for both real and imaginary parts for lags larger than 6.

[22] The measured DP and MP1 velocities (−155 m/s, open circle, and −161 m/s, cross, respectively) are indicated on the spectrum itself in Figure 6a. Both velocities are ∼2 times smaller in their magnitudes than the peak velocity (−364 m/s) and the power-weighted velocity (−294 m/s). The ACF-FIT velocity magnitude (−327 m/s) is slightly less than the rough estimate of the peak velocity. The matched-filter velocity magnitude (−254 m/s, triangle, 13 lag estimate) is not as low as the one in Figure 4.

[23] We show various experimentally (model) determined velocity magnitudes by horizontal dotted and dash-dotted (gray dashed) lines in Figure 6c. We also present the experimental MP(1,.,13) velocities by small open circles that are connected by a solid line for future comparison with the model dependence. The experimental curve shows a somewhat faster increase of the velocity between lags 1–3 and fairly constant velocity values for lags 3–13. We also present here the theoretical velocity-lag number variation (thick gray line) for the model spectrum. This curve was obtained from the ACF coefficients (see Appendix A, equation (A4b)). From this theoretical curve one can determine the DP velocities corresponding to various pulse separations within the model. We note that the experimental and theoretical velocity-lag number dependencies demonstrate similar trends, but for small lag numbers the velocity values are quite different.

[24] Now, let us compare the parameters of the experimental and model spectra. The peak and ACF-FIT velocities are close to each other. The same is true for the power-weighted velocities. In contrast to the above similarities, the experimental DP and MP1 velocities and their model analogs (thick gray line, lags 1 and 2) are significantly different. Figure 6d illustrates the above conclusions in terms of the ACF phase angle–lag number dependence. All dotted and dash-dotted lines run through zero, although the lines are not shown as such in order to leave open space for the comparison of the experimental and model phase angle dependencies. One can see that the two dependencies are quite different for lags 1–2 and the phase angle slope difference is less pronounced for larger lags. We should say that according to our analysis, all the conclusions described above are correct for both afternoon spectra shown in Figure 4.

[25] From the above analysis one can conclude that in a case of an asymmetric spectrum the DP velocity can be decreased up to the value of the power-weighted velocity. It can happen if the pulse separation is small, for example, τ < τt (Appendix A). In the model with two Gaussian components consistent with the measured spectrum, the low-lag power-weighted velocity is ∼1.25 times smaller than the high-lag peak velocity (thick gray line in Figure 6c). The experiment shows much stronger difference of ∼2 between the measured DP (MP1) and measured MP power-weighted velocity. In spite of the velocity difference in lags 1 and 2, the ACF-FIT velocity based on all measured lag data (−327 m/s) is reasonably close to the matched model ACF-FIT velocity (−340 m/s). (See the horizontal gray dashed and black dotted lines in Figure 6c and the light gray line with open circles in Figure 6d.) If in the measured phase angle dependence shown in Figure 6d (small circles with solid line) one excludes the point at zero lag (since the zero-first lag slope is too small) and applies the linear least squares fit to the remaining points, then the new measured and model ACF-FIT velocities are the same within a few m/s. This conclusion can be seen directly if all measured points in Figure 6d (except the zero lag) are shifted upward by the value of the phase angle difference in the 1st model-to-measured lag.

[26] Using the formalism given in Appendix A we found a spectrum (not shown here), which reasonably represents the measured velocity-lag and phase angle–lag dependences given in Figures 6c and 6d. This spectrum has width larger than the observed one and the spectrum itself is of a different shape. This happens because the weaker Gaussian spectral component has to have an opposite Doppler velocity as compared to that seen in Figure 6a (roughly +250 m/s versus −50 m/s). We cannot offer a reasonable explanation for the above discrepancies.

[27] The phase angle curve given in Figure 5a has been adapted from this joint study to a separate theoretical work by Nielsen [2004]. He used another approach to describe the relationship between the spectral shape of an echo and the expected velocity [see Nielsen, 1989, equation (42)]. Nielsen [2004] found that the phase angle curve in Figure 5a can be reasonably reproduced; the nonlinear character of the phase angle curve was attributed to the fact that the spectrum is nonsymmetric. A similar conclusion can be made from our consideration in Appendix A (and in Figure 6) using the Gaussian approximation for the spectral components of a nonsymmetric spectrum. Both approaches show that there is a tendency for the measured phase angle dependence to be slower than the theoretical phase angle dependence at small lags. Below we discuss possible reasons for this discrepancy.

[28] Since we experimentally found a rather strong dependence of the MP velocity pairs on the lag separation (especially for lags 1–2, Figure 6c), the old STARE DP velocities (1977–1992) obtained with the pulse separation of 300 μs should show generally larger velocities than the new data (after 1997) for the same observational conditions. It is not a surprise then that the ratio of the EISCAT E × B velocity to the STARE velocity component was ∼1.4 for the old STARE data [Kustov and Haldoupis, 1992] and it is ∼1.8 for the new STARE data (our data and that of Uspensky et al. [2004]).

6. Discussion

[29] The above-presented information on the STARE velocities appears to be complicated. In short, we showed the following.

[30] 1. The ACF-FIT velocity agrees reasonably well with the velocity of the echo power maximum even for an asymmetric spectrum.

[31] 2. The DP and MP1 velocities (observed at the large flow angles in the afternoon-evening sector) are close to each other, but both are much smaller than the velocity of the peak as well as the mean power-weighted velocity.

[32] 3. The DP velocity determined from lag pairs of MP data is progressively closer to the ACF-FIT velocity with increase of the lag separation.

6.1. Are the MP/DP Velocity Ratios Found Consistent With Previous Observations?

[33] Schlegel et al. [1986] considered a unique set of 77,000 MP-DP data for 153.2-MHz SABRE radar in Wick. The geometry of this radar with respect to the L shells was similar to the STARE Norway radar. The base pulse separation was 300 μs, the integration time was 60 s, and the velocity estimates were based on 230 echo samples which is comparable to the STARE averaging of 220 samples.

[34] Schlegel et al. [1986] presented a plot of the DP velocity versus the MF (matched-filter) multipulse velocity (their Figure 8). Several features from this diagram should be mentioned. For moderate to small MF velocity magnitudes, <350 m/s, the limited data are grouped along the line of nearly ideal agreement between the DP and MF velocities (the slope close to 1). However, for the MF velocities around zero, the DP velocities are mostly negative, and not zero as expected. (We think that this inconsistency can partially be explained by the structuring of the scattering volume so that in some domains the plasma drift departs from the average flow [e.g., Uspensky et al., 1989]). More important for the present study is that for the MF velocities larger than 350 m/s (up to ∼800 m/s) the DP velocity is progressively smaller than the MF velocity. In our analysis, the statistics is not as large as those used by Schlegel et al. [1986], but the data exhibit similar features.

[35] Whitehead [1988] expanded the study by Schlegel et al. [1986] by applying a slightly different approach for a limited data set. He showed that negative SABRE DP and MF velocities were comparable in the morning while positive DP velocities were somewhat (∼10%) less than the MF velocities in the afternoon-evening, which is about the same trend as in our data, though not as strong. Whitehead [1988] also noted that STARE data (perhaps, for the Norway radar) exhibited similar features.

[36] Schlegel and Thomas [1988] presented a huge original SABRE data set as a scatterplot of the DP and MF velocities derived simultaneously. The scatterplot indicated that both DP underestimation and overestimation of the MF velocity are possible but underestimation seems to be more typical. These data indicate significant spread (our MF velocities were also more spread than other MP velocities); the DP and MF velocities can be of opposite signs and the MF velocity can be 4–5 times larger than the DP velocity (see the isolated cloud of points in their Figure 1 for the MP velocity of 1000–1200 m/s). With respect to the observed MF-DP differences, Schlegel and Thomas [1988] stated that they “should be regarded as a warning that geophysical results based solely on the double-pulse velocity should be considered with some caution”. The present study fully supports this warning.

[37] Whitehead [1990] was the first who found that the large-lag MP velocities (he called them the velocities of long-lived irregularities) of the Finland STARE radar were considerably larger than the DP velocities measured simultaneously. His data were collected 18 years earlier than ours (in 1981) using 1.5 times larger basic pulse separation of 300 μs. Similarly to our study, Whitehead [1990] did not find large MP-DP velocity differences for the Norway STARE and, in addition, for the Wick SABRE radars. He suggested that since the Finland radar collected echoes at large flow angles, it can see both higher velocity primary irregularities (long-lived ones) and low-velocity secondary irregularities. Then the DP scheme with smallest pulse separation would estimate the power-weighted velocity of the spectrum but the large-lag MP velocity is closer to the spectral peak velocity. This conclusion is very close to what we found here in our Gaussian model of an asymmetric spectrum (Appendix A) as well as in the model by Nielsen [2004]. Whitehead [1990] did not show the measured spectra and did not compare spectral parameters with his model predictions. He believed that his DP velocities were in reality the power-weighted velocities of the spectra. However, we showed above that the measured DP velocity and measured MP power-weighted velocity of a spectrum can be different.

[38] Haldoupis and Schlegel [1990] and more recently Nielsen et al. [2002] and Nielsen [2004] mentioned that the DP method could underestimate the “true” drift velocity for specific conditions. As the cause for the velocity differences, Schlegel et al. [1986] referred to the fact that the DP technique determines the power-weighted velocity, which can be away from the echo spectrum maximum because of asymmetry of the spectra. Our experimental data as well as the modeling support this idea. Indeed, according to our modeling, the power-weighted velocity is smaller than the peak velocity for asymmetric spectra. However, the velocity difference is expected to be rather moderate, much smaller than the difference between the measured DP velocity and the measured MP power-weighted or peak velocity. Thus the previous studies are in agreement with our experimental findings. One significant fact of our observations is that the DP and MP data agree well in the morning sector. The other potentially important circumstance is that Schlegel et al. [1986] observed echoes from the subauroral ionosphere while STARE observations were performed in the auroral zone where the electrojet is more structured.

6.2. Clutter-Target Cross-Correlation?

[39] The double-pulse (as well as multipulse) coding anticipates the existence of range ambiguity or range aliasing because, together with the wanted echo, one inevitably receives unwanted echoes [Farley, 1972]. The widely accepted assumption is that the signals from the target volume and the aliasing volume(s) are uncorrelated, in other words their phase difference is completely random [e.g., Woodman and Hagfors, 1969; Farley, 1969]. Under this assumption, one expects that the unwanted signal contribution to the received echo is effectively cancelled after data are averaged over a number of independent samples.

[40] In this section we consider what would happen if, in fact, the above cancellation is not complete; that is, the main signal and clutters partially correlate. A similar question was discussed by Karashtin [1996]. We do not have support for this suggestion, although it seems to us an interesting opportunity. In our case one may think about large-scale processes which can control irregularity motion over the main and aliasing volumes. The common motion may result from large-scale (30–200 km) electrostatic and electromagnetic waves, variations of the neutral atmosphere (gravity waves) and particle precipitation. The electron density can control the phases because the radar wave velocity might depend on it. We assume that the typical timescale of the above motions is larger than the STARE pulse group interpulse interval (∼90 ms) and comparable to or smaller than the 20-s integration time. A common low-frequency motion of auroral echoes can be seen in the data by Providakes et al. [1985, Figures 6a–6c]] and by Sahr et al. [1992, Figures 6 and 7], as similar spectra with similar temporal variations at different ranges. These features are particularly important if the target and clutter echoes have spectral components with a close to zero Doppler velocity.

[41] In Appendix B we consider what would happen with the measured DP velocity determined from the phase angle data if a weak cross-range correlation (of the order of ≤0.3) between the signals from the target and aliasing volumes is assumed. To simplify consideration we assumed that the echo spectrum is symmetric. The primary expected effect is a noticeable velocity decrease as compared to the power-weighted velocity or velocity of the spectral peak. The velocity decrease is independent on the sign of the velocity but lag time–dependent; the correlation, very likely, disappears as the separation between the target and aliasing volume increases. We found also that the low-lag velocity can be decreased, while the middle- to high-lag velocity should be close to the velocity of the peak.

[42] We would like to make a comment that in order for the correlation to affect the velocity determination, the frequency of the signals from the target and aliasing volumes should be close to each other. One can estimate the required frequency difference as the RMS uncertainty in the velocity determination Δv [Woodman and Hagfors, 1969, equations (13)–(16)]. The cited authors found that velocity uncertainty is an inverse function of the signal autocorrelation coefficient rρs (r < 1 is a constant that takes into account the DP range ambiguity) and the number of the sample pairs N1/2. For ρs ∼ 0.5, r = 1 (0.7), and N = 220 one gets Δv ∼ 70 (160) m/s. Recall that the afternoon-evening echoes have the largest spectral widths [Nielsen et al., 1984] and thus the smallest ρs (largest Δv).

[43] If a weak signal-clutter cross-range correlation exists, one would expect enhanced total ACF power at low ACF lags. To test this expectation, we analyzed the power-lag dependence for some periods of observations. Figure 7 gives two examples for each of the STARE radars. The ACFs were obtained roughly for 1 hour of operation in the morning and evening. In the morning, both radars show a smooth decrease of power with lag increase. In the evening, the Finland radar sometimes detects an anomaly: the DP power PDP = (Reequation image + Imequation image)1/2 and the MP power for the 1st and 2nd lags PMP1 = (Reequation image + Imequation image)1/2 and PMP2 = (Reequation image + Imequation image)1/2, were all close to or slightly larger than 1, that is, larger than the normalized single-pulse power PSP. We found that such evening ACF features can only be seen for the backscatter with relatively narrow spectra; in this case, it confirms the assumption about the cross-range correlation. Because narrow Finland spectra are not frequently observed in the afternoon-evening, we cannot relate each large MP/DP velocity ratio and the anomaly in the power-lag variation. In the case of a wider spectrum one can consider that the 1–2 lag phase angle underestimates are due to a moderate ReMP1, ReMP2 overestimates. We stress that Finland morning observations and Norway observations in both sectors show a decaying power-lag dependence.

Figure 7.

Examples of the averaged total ACF magnitude of auroral backscatter measured by the Finland and Norway STARE radars in the morning and evening; the diamonds are the total autocorrelation coefficient derived by the DP scheme.

6.3. Why is the DP Velocity Decreased Only in the Afternoon-Evening?

[44] If one relates the low evening DP velocities to the effect of signal correlation from the target and aliasing volumes, a reasonable question is why this happens only in that sector.

[45] We note that for all considered afternoon-evening observations, the backscatter was seen in a latitudinally extended band of the eastward electrojet. The echo regions were homogeneous, and all their spatial and temporal variations were smooth. One might then expect that signals from the target and aliasing volumes had nearly the same as well as close to zero Doppler velocities (over the integration time).

[46] During other periods, for example, in the morning sector, the echoes are less spatially and temporally uniform, their spectra are narrower and the signals from the target and aliasing volumes can have larger and quite different Doppler velocities. If the velocity difference is more than ∣Δv∣ (this value in the morning is less than in the evening), one may not expect significant cross-signal correlation from the target and aliasing volumes. In support of this argument we note that the spectral width of echoes is smaller for the Norway STARE radar [Haldoupis et al., 1984]. This is well matched with better observed agreement of DP and MP data.

6.4. Improving the STARE Convection Estimates

[47] The reported discrepancies between the DP and MP velocities pose a question: how to obtain reasonable convection estimates from the DP STARE data? With respect to the data collected from 1997, a reasonable solution would be an introduction of the mean correction factors for the LOS velocities. This factor for the Finland radar should be ∼1.7 for the afternoon-evening velocities (eastward electrojet) and ∼1.1 for all other periods. The correction factor for the Norway radar should be 1.1 for all time sectors. The corrected LOS velocities then can be merged to obtain the full vector of the plasma convection by the standard method. This procedure has actually been applied to some periods of STARE/EISCAT observations [Uspensky et al., 2004], and it showed a reasonable performance.

[48] We should note that the above velocity correction factors were derived for the area around the EISCAT flux tube. In this area, both STARE radars collect nearly orthogonal backscatter from ∼100-km altitude [Koustov et al., 2002]. For other parts of the STARE system field of view the radars can see echoes from higher (lower) heights, and the correction factors should be slightly modified. The latter is in our future plans.

[49] As for the future VHF radar experimentation with STARE-like radars, one should think about improving the coding scheme. Although the MP transmission has advantages in comparison to the DP transmission [Farley, 1972], we feel that there is a danger of having a low signal-clutter ratio between the echoes coming from the main and aliasing volumes because they are not far apart as compared to the SuperDARN radars. For the SuperDARN case, the minimum (maximum) pulse separation is τSD = 2.4 ms (27 τSD). Then the smallest (largest) spatial separation of aliasing/target volumes is cτSD/2 = 360 km (9720 km). Thus the SuperDARN range ambiguity matrix covers ±9720 km with a range grid being a multiple of 360 km. For the STARE case, the minimum and maximum pulse separation is τ = 200 μs (17τ), and the smallest (largest) separation of the volumes is 30 (510) km. The STARE range ambiguity matrix is thus much finer. Now, the backscatter typically covers 500–1000 km at HF and 500–700 km at VHF. This means that at HF (SuperDARN case) the scatter from the target volume can be contaminated by scatter from 1–2 aliasing volumes, and one can even easily reject these 1–2 lags if the contamination is too strong. For the STARE case, the scatter from the target volume for each range gate can be contaminated by a similar or stronger scatter from up to 5 aliasing volumes. This would lead to very noisy ACFs, which is certainly the case for some STARE observations.

[50] In earlier STARE studies the above deficiency of the MP scheme was greatly diminished by implementation of the so-called multiple double pulse pattern [Nielsen et al., 1984; Schlegel et al., 1986]. The radar radiated one single pulse and then a series of double pulses with increasing interpulse separation (each double pulse can be radiated 9–10 ms after the previous one). For this scheme, there is no range ambiguity for neighboring double pulses. The shortcomings of this pattern are a limited number of lags and an increased transmitter duty cycle. For more efficient MP scheme in a new generation of VHF auroral radars one can, perhaps, use experience of the incoherent scatter measurements, where the range-ambiguity noise of MP schemes is effectively decreased by a more sophisticated pulse coding [Lehtinen and Haggstrom, 1987; Nygren, 1996].

7. Conclusions

[51] The main conclusions of the present study can be summarized as follows:

[52] 1. We confirmed the previously published results by Schlegel et al. [1986], Schlegel and Thomas [1988] and Whitehead [1990] that the DP velocity of STARE echoes can be significantly different from the velocity inferred from the MP data. Similarly to findings of Schlegel et al. [1986] and Whitehead [1990], we found that the DP scheme typically underestimated the MP velocity in the afternoon-evening sector when the spectra were broad, the Finland radar observed at the large flow angles and the backscatter was homogeneous and stable. The DP velocity underestimation effect was weak or not observed in the morning sector.

[53] 2. Using the model of asymmetric spectrum (combination of two Gaussian components) we confirmed earlier suggestions by Nielsen [1989, 2004] that the DP scheme at low lags should estimate the power-weighted center or the first moment of an asymmetric spectrum. We showed that the spectral asymmetry can explain the observed MP-DP velocity discrepancies but only partially.

[54] 3. We also showed experimentally that the DP velocities were close to the MP1 velocities inferred from lag pair 0 and 1 of MP data and both velocities can be ∼2 times smaller than the ACF-FIT velocities in the afternoon-evening sector. The mean ACF-FIT/DP velocity ratio was ∼1.7.

[55] 4. The least squares fit procedure applied to the STARE ACF phase angle dependence (similar to the SuperDARN FITACF scheme) either to all lags or ignoring the first 1–2 lags (when the phase dependence is nonlinear) gives a reasonable estimate of the peak power velocity and the power-weighted velocity of a spectrum.

[56] 5. We suggested that the DP-MP velocity differences occur because of weak (but not negligible) correlation between the signals from the main and aliasing volumes, for example, due to close to zero Doppler velocities, a large-scale common motion of backscatter irregularities or some others factors. The effect favors the afternoon-evening sector for which the auroral backscatter at the large flow angles is homogeneous in time and space and the spectra are broad. Another sign of a weak correlation is the afternoon-evening anomaly in the small number lag ratio of the averaged multipulse/single pulse power(≥1).

Appendix: Appendix A: ACF Velocity of an Asymmetric Spectrum

[57] To estimate the potential effect of the spectrum asymmetry on various velocities that can be assigned to the spectrum of a coherent echo [Nielsen, 1989, 2004] we consider a signal consisting of two normalized Gaussian components (assuming no extra noise)

equation image

where p1 and p2 are the relative weight of each component and

equation image

[58] Here ω12) is the frequency of the power maximum for the component 1 (2), and ∼2.35 σ1 (∼2.35 σ2) is the half-power width for the component 1 (2). The autocorrelation function of signal (A1)

equation image

is (after integration)

equation image

where

equation image

are the powers of each spectral component.

[59] From the imaginary and real parts of (A2a)

equation image

one obtains the phase shift as a function of the lag value τ,

equation image

and the Doppler velocity

equation image

where k is the irregularity wave number.

[60] For a case of spectral components with similar widths σ1 = σ2

equation image

Under the condition ∣ω1,2τ∣ ≪ 1, equation (A4c) reduces to

equation image

which is the same as the power-weighted center of an asymmetric spectrum,

equation image

that can be obtained by integration

equation image

Thus for the case of σ1 = σ2 and any p1,2equation (A4c) gives a velocity estimate close to the power-weighted velocity of an asymmetric spectrum.

[61] In a more realistic case, the higher Doppler-shifted and stronger spectral component ω1 is more narrow (σ1 < σ2). An increase of τ in equation (A2b) above a “threshold” τtequation image2 gives P1P2 (despite the fact that p1 is not significantly larger than p2). Thus for τ ≥ τt, equation (A4b) reduces to V ≅ ω1/k; that is, the measured velocity is close to the spectral peak velocity. For STARE echoes with the moderate (large) spectral width of ∼400 (1000) Hz (we assume that the resultant spectral width is determined by the wider spectral component), one can find σ2 ≈ 2πequation image ≈ 103 (2.5 103) rad s−1 and the threshold lag time of τt ≈ 1.4(0.5) ms [Haldoupis et al., 1984]. The latter means that for the spectral widths of ∼1000 Hz, the MP1 and MP2 velocities (for lags 1 and 2) should be close to the power-weighted velocity but starting from lag 3 the velocities MP3,4,. increase gradually to the peak velocity.

[62] In summary, for an asymmetrical spectrum measured through the ACF formalism, the measured velocity can be between two extremes. The smallest measured velocity would be the power-weighted velocity at low lags τω1,2 ≪ 1 and for σ1 ∼ σ2. The largest measured velocity would be the velocity of the peak for moderate (high) τω1,2 and for σ1 < σ2.

Appendix B:: Target-Clutter Echo Correlation and DP Velocity

[63] Figure B1 illustrates the principle of the DP measurements by the range-time diagram (range-ambiguity matrix). The DP pulse train includes two pulses that are transmitted at two moments t0 and t0 + τ, τ = 200 μs. The echo from the target volume at distance d0 consists of two signals received at two moments t1 and t1 + τ (black areas). Simultaneously with the target volume signals, the radar receives two clutter signals from two aliasing volumes, d+ and d (gray areas) that are 30 km farther and closer to the target volume, respectively. The total size of the STARE DP range-ambiguity matrix is 60 km.

Figure B1.

STARE DP range ambiguity matrix with two wanted echoes at the distance d0 for the time delay τ (black areas) and the two clutter echoes from the distances d and d+, originated from the second and first radiated pulses (gray areas). The spatial (time) separation between the main and clutter volumes (echoes) is 30 km (τ = 200 μs).

[64] Because of the small separation between the target and aliasing volumes, the power and Doppler velocity of signals from them can be of about the same magnitude. In every gate the received echo E consists of a wanted signal and a contamination, E1 = A1 + C2 and E2 = A2 + C1. The correlation coefficient equation image at the time lag τ is

equation image

[65] In equation (B1) and equations to follow, the angle brackets denote the ensemble averaging, which is equivalent to averaging over infinitely long time interval, provided the process is ergodic and stationary. As hereafter in measurements, averaging over a finite time is used to obtain a sample correlation coefficient. The correlation coefficient equation (B1) includes the wanted echo part ρ = 〈A1A*2〉 and the contamination part 〈A1C*1 + C2A*2 + C2C*1〉. In the case of no correlation between the signals from the target and aliasing volumes, the averaging leads to vanishing of the contamination terms. This is a widely accepted assumption in radar measurements [e.g., Farley, 1969; Woodman and Hagfors, 1969]. We would like to explore what happens if (for some specific conditions) the signals from the target and aliasing volumes are weakly correlated, for example, due to close to zero components of the echo spectra and large-scale common velocity variations within the integration period.

[66] One can present equation (B1) in a complex form

equation image

where ϕ1, ϕ2, ψ1, ψ2 are the phases of the target and clutter contributions of the 1st and 2nd pulses, respectively. The parameters a1,2, ϕ1,2 and ψ1,2 are functions of time.

[67] Let us assume that the phase term pairs in (B2a) include variations of two kinds: correlated and uncorrelated (random) phase components. The correlated components can be due to any common motions in the three volumes under the influence of an external, large-scale source. We can write for the first term ϕ = ϕ1 − ϕ2 = ϕ0 + equation image, where ϕ0 is the correlated component, ϕ0 = τ〈dϕ/dt〉 = ωτ, and equation image is the random component. For the three clutter-related terms in (B2a) we assume that the common phase parts are of the form Φ1 − Ψ1, −Φ2 + Ψ2, −Ψ1 + Ψ2 (where −Φ2 + Ψ2 = ωτ − (Φ1 − Ψ2)) and the random phase parts are equation image1,2,3. We assign to each clutter-related term the magnitude, m1,2,3. One can rewrite equation (B2a) in the normalized form

equation image

where 〈a2〉 is the wanted echo power.

[68] For the simplicity of the subsequent analysis, we assume that the common phase differences in (B2b) are all equal to zero. Now, if the random phases are all normally distributed, equation image1,2N(0, σϕ), ϕ1,2,3N(0, σϕ), and if the integration time is large, then equation (B2b) can be rewritten in a compact form

equation image

where ρs = equation image and ρcj = equation image (j = 1, 2, 3) stand for the autocorrelation coefficients corresponding to the target and various clutter-related signals.

[69] The measured Doppler velocity V = equation image tan−1equation image is

equation image

[70] We can now evaluate the effect of the signal correlation. Let us assume that the integration time is large enough (so that the errors in the definition of ρs are negligible) and the autocorrelation coefficient for the wanted (target) echo is ρs = 0.5. This value is consistent with the broad HF backscatter spectra obeying the exponential decorrelation [Hanuise et al., 1993] or the VHF signals with half power width of 1000–1200 m/s observed in the eastward electrojet at large flow angles [Nielsen et al., 1984]. Let us assume a moderate values of ρc1,2 ∼ 0.3 and ρc3 = ρc1/2 (30 and 60 km separation between the clutter volumes, respectively) and small ωτ so that cos ωτ ∼ 1. Then the term in the brackets of equation (B4) is 0.64 · sin ωτ. In absence of clutter, this term is 1 · sin ωτ, meaning that the velocity decrease is by a factor of 1/0.64∼1.56. This factor is the same for positive and negative Doppler velocities. If the width of the spectrum is ∼200 m/s [Nielsen et al., 1984] so that ρs ∼ 0.9, then the phase angle (velocity) decrease is 1/0.73∼1.37. We see that the spectral width influences the amount of the velocity decrease.

[71] If there is no correlation between the signals from the main and aliasing volumes ρc1,2,3 = 0, equation (B4) reduces to V = equation image tan−1 (sin ωτ/cos ωτ) = ω/k, implying no velocity decrease. We believe such conditions are satisfied for the morning sector of STARE observations when the echoes are strongly structured.

Appendix C:: Can the MP/DP Velocity Difference Be an Equipment Artifact?

[72] One of the potential sources affecting the low-lag data can be combined hardware and software effects leading to some “noise coherence”. On the hardware side, the short pulse separation in the radiation pattern can lead to a remnant impulse response as the filter output is brought to the neighboring range gate [Farley, 1969; Sahr et al., 1989]. Besides the effect of a short pulse separation, the noise coherence can be introduced by several other hardware features.

[73] We use here an indirect way of illustrating the combined effect of the pulse radiation pattern and the radar hardware design by considering the autocorrelation function of the receiver (RX) noise for an interval without auroral echoes (Figure C1). In producing this diagram, the RX noise was integrated over ∼6000 s. In a case of the hardware/software problems, one would expect in Figure C1: (1) not large difference between the RX noise power (which equals to 1 here) and the ACF products for “pure” noise (after ∼70,000 pulse sampling) and (2) a power enhancement (reduction) in several low-lag ACFs as compared to the large-lag ones. We see that all lags show power values around 0.02 (−17 dB) which is reasonably weak to affect the measured velocities. The measured ACF products are ∼5 times larger than the expected value of (70,000)−1/2. The enhanced noise level is a combined effect of industrial noise, meteor echoes and hardware features (for the sampling of ≤3000, the measured and expected values of ACF products are close to each other). When we varied slightly the interval of data integration (data not shown) we noticed that the 1st ACF coefficient can be smaller than others, perhaps because of some noise coherence. The distribution of the ACF phases for the lags 1–13 does not reveal a lingering noise; the phase occurrence rate distribution for all lags is slightly nonuniform inside ±π limit because of the 20-s raw data integration over ∼220 samples (data not shown).

Figure C1.

Mean total autocorrelation function of the RX noise over a 1.7-hour interval with no auroral backscatter; the diamond is the DP autocorrelation coefficient.

[74] Another possible instrumental effect is the difference in the hardware response to the RX noise and to much stronger auroral echoes. We believe that this effect is not significant because the receiver runs under gain control. As a result the remnants-to-signal ratio is close to the remnants-to-noise ratio. One can also suspect that the transmitter is not shut off completely after the pulse transmission and the TX pulse remnants disturb the DP velocity measurements by creating a false signal component with zero Doppler shift. However, this suggestion is not supported by the experimental data shown in Figure C1 and/or this effect should occur both in the evening and in the morning. The transmitter frequency chirp can also modify the velocity measurements. This effect acts oppositely for positive and negative velocities; for example, it would decrease (increase) the evening (morning) velocities. We found that the data do not support this idea; noticeable spectral peaks at close to zero Doppler velocity were seen equally frequently in both evening and morning data sets.

[75] We confirmed our conclusions regarding hardware by using a stable frequency synthesizer which produced an external CW signal for the Finland radar. We found that the measured Doppler frequencies of the radar linearly followed the external signal frequencies with reasonable accuracy.

[76] A specific feature of the STARE radar design is the RX antenna Butler matrix which has a limited sidelobe isolation. Although the sidelobe effect can be detected during strongly structured backscatter events in the form of similar range-power profiles for neighboring beams, it cannot be responsible for velocity contamination because the auroral backscatter is mostly spatially homogeneous (almost nonstructured) in the afternoon-evening sector.

[77] The discussion above allows us to conclude that the instrumental effects cannot be a factor responsible for the low DP velocities seen by the Finland STARE radar in the evening sector.

Acknowledgments

[78] STARE is operated by the Max-Planck-Institut für Aeronomie, Germany, and by the Finnish Meteorological Institute, Finland, in cooperation with the Technical University of Norway, Trondheim. We acknowledge Pekka Janhunen for fruitful discussions and programming. The authors thank G. Leppelmeier for useful discussion and comments. Critical comments of both referees are appreciated. This research was supported by NSERC (Canada) grant to A.K. and an Academy of Finland grant to O.A. S.M. was supported by PPARC grant PPA/N/S/2000/00197.

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