Although the source that controls day-to-day variability in the occurrence of equatorial plasma structure (i.e., equatorial spread F, or ESF) remains to be identified, progress is being made. There is evidence that the appearance of large-scale wave structure (LSWS) in the bottomside F layer, around the time of its post-sunset rise (PSSR), is a more-direct precursor of ESF than the PSSR itself. The bulk of the evidence, however, is in the form of “satellite” F traces in ionograms, which may be viewed as less than convincing, because these signatures have not been shown to be causally related to LSWS. In this paper, incoherent-scatter radar and ionosonde data, both collected on 24 July 1979 from the Kwajalein atoll, Marshall Islands, are used to show that this is indeed the case.
 Recently, we have investigated the possibility that large-scale wave structure (LSWS) is a more direct precursor for equatorial plasma structure (i.e., equatorial spread F, or ESF) than simply the vigor of the post-sunset rise (PSSR) of the equatorial F layer [Tsunoda, 2005, 2006; Tsunoda and Ecklund, 2007]. That is, while PSSR and ESF are correlated climatologically [e.g., Fejer et al., 1999; Hysell and Burcham, 2002], they can appear unrelated on a day-to-day basis [e.g., Hysell and Burcham, 2002]. On the other hand, LSWS and ESF seem to have nearly a one-to-one relationship [Tsunoda, 2005]. Whether ESF is more directly related to LSWS than PSSR is crucial, because the avenues that must be taken to be able to forecast ESF, on any given evening, will differ substantially.
 At present, LSWS has yet to be embraced by the research community as a central player in ESF physics. This should not be the case, given that the excitation of LSWS now has a theoretical basis [Hysell and Kudeki, 2004]. A reason for this lag in acceptance may be that LSWS is not easily detectable, at least not during its early growth phase, with instruments currently being used for ESF research [Tsunoda, 2005]. The difficulty appears to be that LSWS grow in amplitude, initially, without significant zonal drift [e.g., Tsunoda and White, 1981]. This means LSWS cannot be detected as time-varying oscillations by upward-looking sensors, such as a fixed-beam radar. Thus far, LSWS has been detected only by using ALTAIR, an incoherent-scatter radar with a steerable beam [e.g., Tsunoda and White, 1981], a coherent-scatter radar with multiple beams [Tsunoda and Ecklund, 2007], in situ probes on satellites in a low altitude, low-inclination orbit [Singh et al., 1997], and by measuring the satellite-to-ground total electron content, also using satellites in low-inclination orbits [Tsunoda and Towle, 1979].
 A reason for this apparent lag in acceptance could also be that the evidence for LSWS, presented to date, is less than convincing. The most direct evidence, from ALTAIR, amounts to only a few cases. The in situ data, from the Atmospheric Explorer E (AE-E) satellite, include 11 sets in which measurements were made on consecutive orbits in the same longitude sector. LSWS but no plasma bubbles were detected during first orbits. Plasma bubbles were found to have developed by the following orbit, in all but one of those cases. That is, bubbles developed in 10 out of 11 cases (i.e., 91 percent), when LSWS was detected during the previous orbit. The only other evidence cited by Tsunoda  has to do with “satellite” traces in equatorial ionograms. These traces appear as replicas of the usual F traces, which are produced by one or more reflections from the bottomside of the F layer. Although the database is substantial, satellite traces have not yet been shown, at least convincingly, to be associated with LSWS.
 Without other means for obtaining descriptions of LSWS prior to ESF onset, it is also possible that experimenters have been unable, to date, to respond to this need. For example, two ionosondes, with an appropriate separation in longitude, should be capable of detecting LSWS [Tsunoda, 2005]. In this regard, Saito and Maruyama  have shown that that the virtual height of the bottomside F layer at 2.5 MHz, h′(2.5), at two locations separated by 6.3° in longitude, can differ substantially when ESF develops, but are usually similar when ESF does not develop.
 The objective of this paper is to show that satellite traces are indeed a direct consequence of LSWS. We do so with a case study of ionograms, which were obtained on 24 July 1979 with a Vertichirp sounder on Kwajalein, when ALTAIR measurements revealed the presence of LSWS [Tsunoda and White, 1981; Tsunoda, 2005]. With this demonstration, satellite traces can now be considered as ionogram signatures of LSWS, and both as direct precursors of ESF. With these results, ionosondes can also be added to the list of sensors capable of detecting and perhaps describing LSWS.
2. Satellite Traces and ESF
 We first summarize the evidence that relates satellite traces to ESF. (Surprisingly, only a few of the papers that describe the onset of ESF do so by presenting actual ionograms [e.g., Wright, 1959; Lyon et al., 1961; Rastogi, 1977, 1984; Abdu et al., 1981].) Although satellite traces can be seen in ionograms presented by Wright , Lyon et al.  were the first to conclude that satellite traces appear to be a precursor for ESF. They obtained ionograms at Ibadan (3°S dip latitude) from 24 April to 1 June 1958. Ionograms were collected continuously, without pause, throughout this interval. Satellite traces were found in ionograms prior to ESF development in all 23 of the cases in which ESF occurred.
 They found that satellite traces occurred between 1836 and 2045 LT, with a mean time of 1915 LT, or 80 min after local ground sunset. The time between the first appearances of a satellite trace and range spreading of the F trace varied from zero to 45 min, with a mean time of 15 min. In other words, the mean onset time of ESF, for this data set, was 1930 LT. The virtual-height difference between main and satellite traces varied between 25 and 160 km with an average of 80 km. The satellite trace was, almost always, higher than the main trace, although, occasionally, a satellite trace appeared about 60 km below the main trace. In many cases, the satellite trace was nearly stationary. Up to three or four (but rarely more) satellite traces are seen simultaneously. Remnants of these satellite traces sometimes persist for several hours, even after ESF is fully developed. Lyon et al.  also found that doubling occurred with about the same frequency at other equatorial stations. For example, for Huancayo, out of 10 days when ionograms taken at 5 min intervals were available, satellite traces prior to full development of ESF were noted in all but one case. They concluded that doubling is a characteristic precursor of ESF over the entire equatorial belt. Among other possible source mechanisms for ESF, they mentioned that oblique echoes from a highly irregular lower surface of the F layer could be possible.
Abdu et al.  examined ionograms, taken at 15 min intervals from Fortaleza (1.7°S dip latitude), from August 1978 to July1979. They found that satellite traces preceded occurrences of ESF on all but two nights. Satellite traces observed at night, well after the PSSR, were also found to precede ESF development. They concluded, as did Lyon et al. , that satellite traces are a necessary precursor to the development of range type ESF.
3. Results From 24 July 1979
3.1. Overview and Satellite Trace
 The PSSR and ESF that occurred on this night are presented in Figure 1, where the minimum virtual height of the F trace (h′F) is plotted as a function of universal time (UT). At Kwajalein (9.4°N, 167.5°E, geographic; 4.3° dip latitude), local time (LT) leads UT by 11 hr 10 min. Black dots indicate presence of a normal F trace without any significant spreading. Asterisks indicate presence of ESF. The PSSR can be estimated from displacements of h′F values with time, above altitudes of about 300 km, where recombination loss effects are insignificant [Bittencourt and Abdu, 1981; Tsunoda and White, 1981]. From displacements in h′F, we estimate that the PSSR was about 33 m/s at 0800 UT (1910 LT).
 The ionograms of interest are presented in Figure 2a, a reference ionogram taken prior to the PSSR, at 0711 UT (1821 LT), and in Figure 2b, the first ionogram to display a satellite trace in the second-hop (2F) F trace, taken at 0744 UT (1854 LT). In Figure 2a, h′F was less than 300 km and foF2 was 9 MHz. Presence of the 2F and third-hop (3F) F traces indicates that F layer was still horizontally stratified and unstructured. There is no evidence of ESF at this time. Some spread sporadic E is present, but is of no consequence for this study. In Figure 2b, h′F has increased to 320 km, there is a second-hop but not a third-hop F trace, and foF2 has decreased to about 7 MHz.
 The feature of interest here is the presence of two 2F traces, where we expect only one. We refer to this pair of traces as a 2F doublet. Another ionogram (not shown), taken 10 min later at 1904 LT, also contained the same features. This phenomenon, referred to as “doubling,” was first described by Lyon et al. . The ionogram in their example was taken at 1900 LT on 1 May 1958. The local times of our ionograms are within minutes of their doublet occurrence. It is also interesting to note that doubling, in their example, also occurred in the 2F trace and not in the first hop (1F) F trace. They further showed that doubling occurred in the 1F trace, together with a tripling of the 2F trace, as shown in an ionogram taken 15 min later. Diffuse range spread ESF appeared in their ionogram taken at 1945 LT, 30 min later. In our ionograms, doubling of the 1F trace was observed at 1921 LT. In this ionogram, a somewhat diffuse, 2F trace appeared in place of the doublet. Range spreading at lower frequencies appeared in the ionogram taken at 1926 LT.
3.2. LSWS in ALTAIR Scan
 A clear description of LSWS, obtained with ALTAIR by scanning its antenna in an east-west direction, while keeping the beam directed orthogonally to geomagnetic field () lines is presented in Figure 3 [from Tsunoda and White, 1981]. The spatial distribution of N, made during a scan, from 0743 to 0803 UT, contains a bottomside F layer, which has a mean tilt, which is consistent with the PSSR, and a sinusoidal oscillation in isodensity contours, which is the LSWS. The rise velocity of 33 m/s, estimated from h′F displacements, is consistent with the mean tilt. This is an example of clear presence of an LSWS in the bottomside of the F layer, which appeared prior to the development of coherent backscatter (i.e., ESF). The three upwellings in the LSWS are labeled west, center, and east crests. We note, for our purposes here, that the center crest is situated more or less over Kwajalein (ALTAIR) at this time.
 Given that the ionosonde was located under the center crest of the LSWS, where isodensity contours are concave, the source of the 2F doublet seems to have a simple explanation, as shown by the sketch in Figure 2c. For reference, we have drawn a circular arc (gray line) with a radius r0, which is equal to the virtual height of the F-layer reflection (at the ionosonde frequency of interest). If the circular arc is centered over the ionosonde, we could obtain the 1F and 2F reflections for an overhead transmission, as shown by the arrow labeled VI. If we assume that the isodensity contours have a radius of curvature that is larger than r0, it should be evident that transmissions with a non-zero zenith angle (χ) would not return to the ionosonde directly after a VI 1F reflection. Instead, the 1F signal proceeds downward and is reflected by the ground at point G. From Figure 2c, we see that the G-reflected signal then faces a 2F reflection. Clearly, the off-vertical 2F-reflected signal could return to the ionosonde together with the VI 2F signal to produce the 2F doublet (e.g., Figure 2b).
 The geometry required to produce a 2F doublet also places constraints on the horizontal wavelength of the LSWS and its depth of modulation. If we assume r0 = 300 km and the modulation depth is 10 km, the horizontal chord for that arc would be about 150 km. In order to support the 2F doublet, the radius of curvature of the isodensity contours would have to be larger than 150 km, which implies that the wavelength of the LSWS must be greater than 300 km. And, in fact, the wavelength of the LSWS in Figure 3 is about 400 km. We, therefore, conclude that the propagation path that supported occurrence of the satellite trace, in the form of a 2F doublet, was likely a direct consequence of the LSWS.
 Intuitively, concave isodensity contours are expected to support obliquely-incident paths that could produce not only a 2F doublet, as we have shown, but also a 1F doublet, and even a multiplicity of satellite traces. The exact form of the ionogram signature that appears, therefore, will depend on the actual structure in the isodensity contours and its location relative to the ionosonde. For the case in which the ionosonde is centered under a crest, there is the possibility that there could be a large number of 1F reflections, which could appear as diffuse range spreading, if the reflections cannot be resolved. This is, in fact, what is referred to as range ESF.
 Even if there is only a single 1F reflection, its signal strength could be enhanced by the focusing effect of concave isodensity contours. Rastogi  noted the occurrence of echoes that appeared to have undergone a high number of reflections; that is, an nF reflection, where n is a large number. He suggested that this feature could be produced by the curvature produced in isodensity contours by the rapid rise and fall of the F layer (especially during solar maximum conditions) around sunset. That is, an nF reflection becomes detectable because of the increase in reflected signal strength. We suggest that a crest of an LSWS is a more likely source of this enhancement than the PSSR, because the radius of curvature associated with a PSSR is much larger than that associated with an LSWS.
 If the ionosonde is not centered beneath a crest, the usual overhead echoes would not occur, but a tilt is likely to support at least one direct reflection. We, therefore, surmise that the disappearance of multi-hop reflections may be an early indicator that an LSWS is developing. The virtual absence of the 3F trace in Figure 2b, for example, could be a consequence of the fact that the crest was not exactly centered over the ionosonde. If nF reflections are observed, their intervals in altitude may be unequal in the presence of an LSWS.
 Having demonstrated that satellite traces are likely produced by reflections from isodensity contours within a crest of an LSWS, we can now claim that satellite traces in equatorial ionograms are, indeed, direct signatures of LSWS. We can further conclude that the evidence is now convincing for the hypothesis that LSWS is a more direct precursor of ESF than the PSSR. We have already given reasons why this should be so [Tsunoda, 2005]. First, the PSSR, measured by usual means, will contain contributions to eastward electric field from both the true PSSR and polarization effects associated with the LSWS [Tsunoda, 2005]. Hence, day-to-day variability will be introduced into the measurements simply from the presence or absence of LSWS. And, second, the steepness of the gradient in N differs from crest to trough in an LSWS, which is a natural consequence of two-dimensional polarization processes, such as the collisional-shear and Rayleigh-Taylor instabilities. Hence, the presence or absence of an LSWS can be crucial to the development of plasma bubbles. The near one-to-one relationship that exists between LSWS and ESF is evidence that two-dimensional effects are crucial to ESF development.
 In closing, we further note that LSWS does not appear to be a simple seeding by atmospheric gravity waves [Tsunoda, 2005]. That is, random seeds appear to be ubiquitous [Eccles, 2004], whereas LSWS and ESF have a day-to-day variability. Much remains to be done, but it seems clear that progress in understanding LSWS would be a step in the right direction.
 This research was supported by the National Science Foundation under grant ATM-0318674.