On the enigma of day-to-day variability in equatorial spread F



[1] We show that large-scale wave structure (LSWS), in plasma density in the bottomside F layer, is a hitherto unheralded contributor to the long-standing enigma of day-to-day variability in equatorial spread F (ESF). Little is known about LSWS; it seems to appear in altitude near a vertical shear in zonal plasma drift, during the post-sunset rise of the F layer, and its growth via an interchange instability appears to predispose quasi-periodically spaced regions to development of plasma bubbles. First indications are that LSWS development is necessary and sufficient for ESF occurrence. We suggest that variability in LSWS development, perhaps together with the shear in zonal drift, may contribute to day-to-day ESF variability. A need revealed by this study is that a cluster of distributed sensors, not isolated ones, is necessary to pursue the problem of day-to-day variability.

1. Introduction

[2] The day-to-day variability problem is a befuddling inability to predict post-sunset development of irregularities (ΔN) in plasma density (N), referred to as equatorial spread F (ESF). The problem is perplexing because, climatologically, ESF is closely related to the appearance of an eastward electric field (equation image) during post-sunset rise (PSSR) of the F layer [Fejer et al., 1999; Hysell and Burcham, 2002]; yet, on a given evening, the two phenomena can appear unrelated. A popular approach to this problem has been to evaluate parameters in the linear growth rate of the interchange instability [e.g., Sultan, 1996]. On the other hand, there is mounting evidence that large-scale wave structure (LSWS) in bottomside F layer actually dictates ESF occurrence [Lyon et al., 1961; Röttger, 1973; Abdu et al., 1981; Tsunoda and White, 1981; Singh et al., 1997]. In this paper, we use information available about LSWS to consider how it might affect bubble development. Our findings were derived from a re-analysis of data from Tsunoda and White [1981] (hereinafter referred to as TW81), and other published evidence.

2. LSWS Before ESF Onset

[3] Very little is known about LSWS prior to ESF onset. A few such occurrences were first inferred by Röttger [1979], using data from transequatorial propagation (TEP) experiments. Two reports place initial LSWS appearance as early as just before E-region sunset: (1) TW81 found occurrence at 1911 LST, when shadow height of solar terminator was 45 km; and (2) Singh et al. [1997] found LSWS in ion density (AE-E measurements at 275 km altitude) to occur as early as 1820 LST. Most of our understanding comes from the only published, two-dimensional description of LSWS (from TW81), which is reproduced in Figure 1. The F-layer N distribution, obtained with ALTAIR, a steerable incoherent-scatter radar, during a PSSR period, is represented by isodensity contours plotted as a function of altitude and magnetic-east distance from ALTAIR. Contours are shown from log10N = 4.5 (N ≈ 3.2 × 104 el/cm3), at log10N = 0.25 intervals. The third contour from the bottom represents N = 105 el/cm3. (Smaller-scale variations in contours are statistical fluctuations and should be ignored.) The 20 min east-to-west scan, made with the radar beam orthogonal to equation image, is devoid of coherent ESF backscatter.

Figure 1.

Plasma-density distribution measured during an east-to-west scan with the ALTAIR incoherent-scatter radar, on 24 July 1979 between 0742:57 and 0803:20 UT [from Tsunoda and White, 1981].

[4] The interesting feature in this data set is a quasi-periodic modulation in altitude of isodensity contours in bottomside F layer, which is superimposed on a mean slope that increases in altitude from west to east. The slope is consistent with a post-sunset bulk rise of F layer. Modulation consists of three crests (local altitude maxima in isodensity contours) separated by two troughs (local minima). The zonal wavelength of 400 km agrees with those measured in situ [Singh et al., 1997] and those determined from TEP experiments [Röttger, 1973].

[5] TW81 noted that two features in Figure 1 are indicative of LSWS growth via interchange instability: (1) a modulation depth that is larger in east crest than in west crest, and (2) a gradient in N (i.e., ∇N) that is steeper in crests than troughs. The first is consistent with convective wave growth, if initial perturbations were equal. The second is not expected from bulk transport because F-region plasma is virtually incompressible in plane transverse to equation image. Local steepening, however, is consistent with existence of an eastward polarization equation image in crest region and magnetic-flux-tube interchange along dipolar-like streamlines [e.g., Ossakow et al., 1979].

3. LSWS Growth, ESF Onset, and Bubbles

3.1. Upwelling of Crests

[6] The only description of the temporal evolution of LSWS is by TW81. Their results are presented in stacked plots of radar backscatter (both coherent and incoherent) in Figure 2. Figure 2a is essentially Figure 1, but only the 105 el/cm3 isodensity (dashed) contour is shown. In Figure 2b, coherent backscatter, shown by solid-line contours of constant echo intensity, accompanies the 105 el/cm3 isodensity (dashed) contour. Similar features are shown connected by line segments to illustrate zonal displacements at different altitudes with time, as discussed by Tsunoda et al. [1981].

Figure 2.

Sequence of east-west scans that show growth in amplitude of bottomside modulation and development of plasma bubbles [from Tsunoda et al., 1981].

[7] Wave growth in Figure 2 was referred to as an upwelling by TW81, because crest isodensity contours are only displaced upward with time. Similar behavior is seen in computer simulations of bubble growth by interchange instability [e.g., Ossakow et al., 1979]. The best example of upwelling development is the west crest; where upward displacement of the isodensity contour with time is evident in Figures 2a, 2b, and 2c. Presence of more structure along the west wall than the east wall (Figure 2d) was interpreted in terms of interchange instability driven by an eastward neutral wind [Tsunoda, 1981, 1983]. If we assume that the tilted coherent-echo region delineates the west wall, the upwelling resembles an inverted-V.

[8] Of particular interest in Figure 2 are substantial tilts in isodensity contours, one approaching 45° (Figure 2d). Existence of substantial tilts is consistent with Röttger [1979], who concluded that discrete echoes from off-great-circle TEP paths prior to ESF onset were likely supported by steep horizontal ∇N during PSSR; a tilt of 30° in elevation appeared necessary to support off-great-circle paths. Tilts are also consistent with appearances of one or more quasi-replicas of the F trace that appear at displaced virtual heights in ionograms taken prior to ESF onset [e.g., Lyon et al., 1961; Abdu et al., 1981]. These “satellite” traces are likely produced by oblique reflections from upwelling walls.

3.2. Near-Stationary Growth

[9] A key discovery of this study is the manner in which upwellings form. It is apparent from Figure 2 that crests develop upward, perhaps to 500 km in altitude, without much horizontal transport. For example, if zonal drift speed was 110 m/s [Röttger, 1973], identifiable features should be displaced 400 km in an hour, the elapsed time between Figures 2a and 2d. Instead, displacements were much smaller, with all low-altitude features being virtually stationary. Eastward transport was substantial only above 500 km (e.g., see locations of east crest in Figures 2c, 2d, and 2e), which is consistent with behavior of the west crest. This finding is consistent with Lyon et al. [1961], who stated that satellite “echoes sometimes persist for several hours even after spread F is fully developed…”

[10] This behavior is consistent with development of a vertical shear in zonal drift during PSSR [e.g., Tsunoda et al., 1981]. The location of the shear node can be estimated from Figure 2. We see that a horizontally stratified backscatter region (Figures 2d and 2e), located below the east wall of the west upwelling, was stationary, while the west wall of the same upwelling appears to have moved eastward. Because other low-altitude features were also quasi-stationary, we would place the shear node below 400 km. This altitude compares favorably with three other estimates of shear-node location from Jicamarca radar measurements: (1) 420 km at 1950 LT [Kudeki et al., 1981], (2) 360 km at 1926 LT [Fejer et al., 1985], and (3) 250 km at 1930 LT [Kudeki and Bhattacharyya, 1999]. We also know that eastward drift becomes substantial only well above the shear node during this period [Fejer et al., 1985].

3.3. ESF Onset and Bubble Development

[11] Final stage of ESF development is the appearance of plasma bubbles from tops of upwellings. Bubbles in Figure 2 take the form of backscatter plumes, which are collocated with bubbles [Tsunoda, 1980]. Altitude-extended plumes are seen to have developed from east and west crests. In contrast, bubbles did not develop from troughs, a result that underscores the importance of LSWS in bubble development. The appearance of bubbles in upwelling regions specified by LSWS was also reported by Singh et al. [1997].

[12] Besides specifying bubble-development location, conditions associated with LSWS appear to be both necessary and sufficient for bubble development. Three pieces of supporting evidence exist. First, Singh et al. [1997] found 11 sets of data, from Atmospheric Explorer E (AE-E) satellite, in which (1) measurements in the same longitude sector were made on consecutive orbits, and (2) LSWS but not plasma bubbles were observed during first orbits. Plasma bubbles were found to develop in the following orbits, in all but one of those cases. Second, Lyon et al. [1961] obtained ionograms with high time resolution for about a month. Satellite traces were observed in ionograms prior to ESF development in all 23 cases in which ESF occurred. And third, Abdu et al. [1981], using ionograms from a full year, found that satellite traces preceded ESF occurrences on all but two nights. On the other hand, Eccles [2004], from San Marco satellite measurements, found that wavelike equation image perturbations (Δequation image) were often observed prior to E-region sunset, on both ESF and non-ESF nights. We conclude from his finding that while Δequation image may be necessary to produce LSWS, LSWS is not produced by all Δequation image.

3.4. Possible Role of LSWS

[13] We suggest that, while Δequation image appears to be a seed perturbation, LSWS development involves a separate process in which upwellings modify background conditions to favor growth of smaller-scale bubbles by interchange instability. Three local background features are modified by presence of LSWS: (1) curvature is introduced into isodensity contours, which acts to produce a polarization equation image (associated with LSWS) that is additive to the background equation image; (2) ∇N steepens in a crest region; and (3) a crest in an upwelling reaches a higher altitude, where ion-neutral collision frequency (νin) is smaller, than a stratified bottomside F layer. The larger total equation image and smaller νin drive a stronger eastward Pedersen current, and a steeper ∇N produces a larger change in Pedersen conductivity, for a given displacement in altitude; all act to enhance interchange instability. Once an upwelling forms, its west wall is susceptible to a wind-driven interchange instability [Tsunoda, 1981, 1983].

4. Source of LSWS

[14] Given that a vital role is likely played by LSWS in ESF development, the next step is to consider how LSWS is generated. To begin, observations indicate that LSWS amplitude can already be large by E-region sunset. From a data set by Singh et al. [1997], we found ΔN/N ≈ 0.5 at 275 km altitude, where N ≈ 3 × 105 el/cm3. We also found an example of the presence of Δequation image without ΔN in Singh et al. [1997], which occurred 40 min prior to E-region sunset. While conceivable that the more ubiquitous Δequation image are associated with atmospheric gravity waves [Singh et al., 1997; Eccles, 2004], the finding that LSWS are not equally ubiquitous suggests that the observed spatial Δequation image likely do not always persist long enough in time to produce LSWS. Another process seems necessary to produce LSWS before F-region polarization becomes effective.

[15] In this regard, it is interesting to note from Figure 2 that LSWS appeared at an altitude not far from the velocity-shear node. This observation is intriguing because there are theories involving velocity shear that predict maximum growth rates at a preferred wavelength that is comparable to those observed. Early results, however, have shown that velocity shear damps shorter-wavelength modes of interchange instability to produce a growth-rate maximum at kL ≈ 0.7, where k is the wave number and L is gradient scale length of N [e.g., Guzdar et al., 1982, 1983; Satyanarayana et al., 1984]. A difficulty is that the growth rate at the preferred scale size is less than an already modest growth rate of interchange instability in absence of velocity shear.

[16] Recently, Hysell and Kudeki [2004] found a growing mode for a collisional shear-instability that exists in absence of drivers for interchange instability. Moreover, the fastest growing mode satisfied the condition, kLV ≈ 0.5, where LV is gradient scale length associated with velocity shear. Although e-folding time for the case examined was only 50 min (less than that for interchange instability), they noted that the shear instability could become more active in presence of a steep ∇N. (Its growth rate is negligible in a homogeneous plasma.) Their finding leaves us to ponder whether velocity shear and ∇N could act to impose parameter control over ESF development via this instability.

5. A Practical Consequence

[17] Given that zonal equation image can vary substantially with longitude in presence of LSWS, we are led to conclude that measurement ambiguities are part of the day-to-day variability problem. First, LSWS is not detectable with a local measurement, because temporal oscillations cannot occur without horizontal transport. If undetectable, we cannot presume presence of LSWS or an associated polarization equation image. And, second, a local measurement of equation image × equation image motion cannot uniquely characterize either PSSR or the LSWS. For example, the isodensity contour in the west crest (Figure 2) rose from 350 to 550 km in altitude in an hour, a rise velocity of 56 m/s. During that time, the contour in the west trough rose from 300 to 350 km, a rise velocity of only 14 m/s. Clearly, either one of these estimates does not unambiguously describe the PSSR.

[18] The measurement problem is sketched in Figure 3. LSWS in the bottomside F layer at time, t1, is represented by a dotted isodensity contour (labeled constant N). At later times (t2 and t3), growth in LSWS amplitude is represented by dashed and solid isodensity contours, respectively. For an ionosonde, displacements in virtual height of signals reflected from an isodensity contour would be used to estimate rise velocity. At location a (under east trough), black dots indicate virtual heights for the three times. A small rise velocity is indicated by the small displacements. At location b (under east wall of center upwelling), dot separations indicate a larger rise velocity than measured at location a. The largest rise velocity would be measured at location c (under center upwelling). The largest velocity difference would occur between estimates from locations a and c, separated by one half the LSWS wavelength (e.g., 200 km for a wavelength of 400 km). Evidence consistent with the above scenario can be found in simultaneous ionosonde and radar measurements made at Huancayo and Jicamarca, locations that are separated zonally by only 160 km. Both Argo and Kelley [1986] and Fejer et al. [1996] found considerable day-to-day variability in the ratio of altitudes of the bottomside F layer in the evening. Argo and Kelley [1986] further noted that after 2100 LT, there was very little difference in altitude between them.

Figure 3.

Sketch showing amplification of wave structure and overhead measurements from four locations, labeled a, b, c, and d.

[19] A third measurement ambiguity arises because of rapid horizontal transport at high altitudes. Crests develop upward, up to about 500 km without significant horizontal displacement; eastward drift, however, is substantial above this altitude, as indicated by arrows sketched in the upper left corner of Figure 3. Bubbles, on the other hand, develop where eastward drift is substantial. A bubble, therefore, would be detected soon after t3 from location c, and perhaps later at locations b and a. For a horizontal wavelength of 400 km and eastward drift of 100 m/s, the bubble would arrive over location a, 33 min later. In other words, with local measurements, we could easily be comparing a local rise velocity, colored by presence of a polarization equation image, with ESF features associated with an upwelling to the west of the observing station.

6. Summary

[20] We have shown that LSWS is likely playing a vital role in ESF development, and that the yet-to-be-identified physics of LSWS development could contain a significant contribution to day-to-day variability in ESF occurrence. Its role could be to precondition the bottomside F layer in a manner that facilitates rapid bubble development in specified locations. The large amplitude of LSWS observed around E-region sunset suggests that another amplification source besides the F-region interchange instability may be needed. We suggest that a candidate mechanism could be velocity shear providing free energy via a collisional-shear instability [Hysell and Kudeki, 2004]. A key question might now be, under what conditions do LSWS develop, in presence of a seed Δequation image? Experimentally, we are now faced with the task of detecting LSWS, and uncovering the conditions for its development. It now appears that measurements with a cluster of distributed sensors are needed instead of isolated, local measurements.


[21] Research was supported under National Science Foundation grant ATM-0318674.