ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-34-927-2016Observational evidence for new instabilities in the midlatitude E and F regionHysellDavid L.david.hysell@cornell.eduLarsenMiguelSulzerMichaelDepartment of Earth and Atmospheric Sciences, Cornell University,
Ithaca, New York, USADepartment of Physics and Astronomy, Clemson University,
Clemson, South Carolina, USAArecibo Observatory, Arecibo, Puerto RicoDavid L. Hysell (david.hysell@cornell.edu)3November2016341192794119May20168September201616October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/34/927/2016/angeo-34-927-2016.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/34/927/2016/angeo-34-927-2016.pdf
Radar observations of the E- and F-region ionosphere from the Arecibo
Observatory made during moderately disturbed conditions are presented. The
observations indicate the presence of patchy sporadic E (Es)
layers, medium-scale traveling ionospheric disturbances (MSTIDs), and
depletion plumes associated with spread F conditions. New analysis
techniques are applied to the dataset to infer the vector plasma drifts in
the F region as well as vector neutral wind and temperature profiles in the
E region. Instability mechanisms in both regions are evaluated. The
mesosphere–lower-thermosphere (MLT) region is found to meet the conditions
for neutral dynamic instability in the vicinity of the patchy Es
layers even though the wind shear was relatively modest. An inversion in the
MLT temperature profile contributed significantly to instability in the
vicinity of one patchy layer. Of particular interest is the evidence for the
conditions required for neutral convective instability in the
lower-thermosphere region (which is usually associated with highly stable
conditions) due to the rapid increase in temperature with altitude. A
localized F-region plasma density enhancement associated with a sudden
ascent up the magnetic field is shown to create the conditions necessary for
convective plasma instability leading to the depletion plume and spread F.
The growth time for the instability is short compared to the one described by
. This instability does not offer a simple analytic
solution but is clearly present in numerical simulations. The instability
mode has not been described previously but appears to be more viable than the
various mechanisms that have been suggested previously as an explanation for
the occurrence of midlatitude spread F.
Ionosphere (midlatitude ionosphere)Background
The relative importance of plasma and neutral drivers in the midlatitude
ionosphere is being debated in the contexts of sporadic E (Es)
layers, medium-scale traveling ionospheric disturbances (MSTIDs), and plasma
density irregularities associated with midlatitude spread F. This paper
informs the debates with observations from the Arecibo Radio Observatory.
Patchy Es layers, MSTIDs, and midlatitude spread F occurred
during the night of the 11 to the morning of 12 July 2015, over Arecibo during moderately
disturbed, low solar flux conditions. The midnight collapse occurred as well.
The event complements one reported on by recently
which also exhibited these phenomena, albeit with important differences.
These observations represent the most complete set of ground-based plasma and
neutral state parameters available and are crucial for ranking the different
mechanisms that could be responsible for the ionospheric irregularities,
particularly at night.
Midlatitude sporadic E (Es) ionization layers have been affecting
communications since the earliest days of radio (see reviews by
; ; ;
). The dense metallic layers reflect, refract,
diffract, and scatter radio signals, facilitating some radio applications and
inhibiting others. While the layers can occur on continental spatial scales,
the irregularities within that cause coherent radar scatter to extend down to
meter scales or less. Deployments of coherent scatter radars in the modern
era also highlighted important intermediate-scale structuring in the layers
. The coherent
echoes have been termed “quasiperiodic” or QP because of periodicities in
their range–time–intensity representations.
Rocket experiments have shown that QP echoes come from patchy sporadic E
layers accompanied by strong polarization electric fields and strong neutral
wind shear e.g.,and references
therein.
Studies using radar interferometry and imaging have shown that the echoes and
underlying patchiness tend to be organized along fronts
e.g.,. The fronts
propagate with periods of 5–10 min, wavelengths of a few tens of
kilometers, and directions preferentially toward the southwest in the
Northern Hemisphere, although directions can vary significantly within and
between events. The polarization electric fields spanning the fronts are
often large enough to excite Farley–Buneman instability
, but field-aligned irregularities (FAIs) exist throughout the patchy layers
even when the condition for Farley–Buneman instability is not met.
Irregularities often come in bursts lasting about 1 h.
Sporadic E layer structuring leading to QP echoes is sometimes attributed
to gravity waves
or an
Es-layer plasma instability forced by neutral wind shear
. The billowy appearance
of the layers in incoherent scatter radar observations like those presented
by and points to neutral
shear (dynamical) instability as the cause
.
This premise is consistent with results from
and , and others which suggest that the
mesosphere lower thermosphere region is frequently dynamically if not
convectively unstable.
combined coherent and incoherent scatter radar
measurements in a common volume to test the premise. They solved a boundary
value problem (the Miles and Howard problem: ) for neutral dynamic instability,
incorporating neutral wind profiles measured at Arecibo. The fastest-growing
eigenmodes were found to have wavelengths, frequencies, and propagation
directions comparable to the fronts in radar imagery from a coherent scatter
radar on St. Croix. The e-folding time for the most unstable mode was only
about 1 min, and the instability was seen to be robust. That neutral rolls
could be responsible for intermediate-scale Es-layer structuring is
furthermore consistent with green-line optical imagery from Arecibo, which
sometimes shows waves at least superficially similar to those seen in the
coherent scatter radar imagery see, e.g.,.
Subsequently, simulated plasma instability in patchy
Es layers produced by the aforementioned mechanism. The 3-D
simulation code was unique in that it did not assume equipotential magnetic
field lines, which is essential for studying ionospheric drift waves, for
example. A fast-growing class of collisional drift waves was found to emerge
from polarized, patchy layers. These waves, which had kilometer scales, were
similar to waves found in Es layers using a high-resolution
observing mode at Arecibo . These transitional-scale
waves were interpreted as being the primary plasma waves necessary to drive
the meter-scale FAIs detected by the coherent scatter radar. Field-aligned
currents played an essential role in the growth of the waves.
Arecibo data show that patchy Es layers sometimes occur in
conjunction with medium-scale traveling ionospheric disturbances (MSTIDs)
and, more rarely, with midlatitude spread F (see for
early Arecibo MSTID observations). MSTIDs are wavelike variations in the
F-region ionization that exhibit periods of the order of 1 h, wavelengths
of hundreds of kilometers, and propagation speeds of
∼ 100 m s-1. They propagate mainly southwestward in the Northern Hemisphere. They are electrically polarized and
represent the predominant ionospheric irregularities at middle latitudes.
have furthermore shown evidence that traveling ionospheric disturbances
(TIDs) propagating to low latitudes can instigate equatorial spread F, something
have been able to reproduce in simulations.
showed that small-scale FAIs are also embedded in
the phases of MSTIDs as if driven by the associated polarization electric
fields under gradient drift instability (see also
). Small-scale field-aligned
irregularities have indeed been detected at the phase nodes of MSTIDs
observed in GPS-TEC (total electron content) maps in one event and in the troughs of MSTIDs observed
in all-sky imagery in another. The irregularities give rise to spreading in
ionogram traces and consequently to midlatitude spread F by definition.
However, the term “midlatitude spread F” usually refers to the results of
plasma convective instability in the midlatitude F region which is
morphologically similar to equatorial spread F (ESF).
The plasma convective instability responsible for equatorial spread F grows
from perturbations to an equilibrium force balance between gravity and the
J×B force due to Pedersen currents at low latitudes. The
perturbation can be thought of as vertical displacements of slabs of plasma
in planes parallel to the magnetic meridian plane. Since quasi-neutrality
guarantees that the zonal Pedersen current be continuous in this case,
perturbations in the weights of the slabs cannot be balanced, and so denser
slabs descend, while less dense slabs ascend. Where the stratification is
unstable, descending slabs get heavier, ascending ones lighter, and instability
results. The instability is similar to the Rayleigh–Taylor instability in
neutral fluids except that inertia need not play an important role in the
ionospheric case.
found that depleted plasma slabs or “bubbles”
ascend under the aforementioned conditions until the magnetic
flux-tube-integrated ion mass density matches that of the background. In
their simulations, bubbles stopped rising at magnetic apex altitudes between
1200 and 1600 km where the stratification became stable. While this figure
depends on background conditions in nature, bubbles would have to rise
considerably higher to impinge on the ionosphere above Arecibo and higher
than they have been observed rising over Jicamarca, even during strongly
disturbed periods.
considered a generalization of the plasma convective
instability responsible for ESF that permits something like it to operate at
middle latitudes. The generalization is to consider field-aligned slabs of
plasma that are tilted, i.e., from the vertical at the dip equator. In this
case, quasi-neutrality guarantees that the current density is continuous in
the direction normal to the slabs, but since this is no longer the zonal
direction, the zonal current density giving rise to the component of
J×B that balances gravity can vary between slabs. The
tendency is for plasma on lower (higher) flux tubes with greater (lesser)
flux-tube-integrated Pedersen conductivities to support smaller (larger)
zonal Pedersen currents and to descend (ascend), leading to instability. The
treatment was generalized later by to include the effects
of background density gradients and neutral winds.
Perkins' instability is often cited as playing a role both in MSTIDs and
midlatitude spread F. Numerical simulations have been able to reproduce
realistic MSTIDs from random noise that conformed to the prescriptions of
Perkin's linear theory until saturating
. In the latter case, the
simulations were performed on complete flux tubes. Saturation occurred in
that case after about 30 min.
The long e-folding time of the Perkins instability, which is typically of the
order of 1 h according to linear theory, together with its tendency to
saturate at small amplitudes, suggests that other factors might be involved
in MSTIDs and spread F. and
argued that MSTIDs are induced merely by gravity waves rather than by Perkins
instability and that they propagate in the direction for which dissipation is
the weakest see also. This could be called the
“Perkins stability” effect, whereby the midlatitude ionosphere exerts a
damping force unless Perkin's criteria are met, in which case it is neutral.
A long time history of airglow observations from Indonesia presented by
supports the idea that MSTIDs are the result
of gravity waves generated primarily by deep tropospheric convection rather
than by plasma instability. Wind patterns in the troposphere were argued to
be sufficient to account for the propagation directions observed.
Some lines of inquiry hold that E- and F-region phenomena need to be
considered together. argued that the growth
rate of the Perkins instability and Es-layer instabilities acting
together is larger than that of either one acting alone see
also. The hypothesis has been tested in a
number of numerical investigations e.g.,.
and found a correlation
between MSTIDs and intense Es layers and Es-layer
irregularities, respectively. recently found
evidence that sporadic E layer irregularities and MSTIDs have related
occurrence phenomenology in TEC data derived from the Very Large Array (VLA).
also correlated MSTID and QP echo behavior over the
MU radar in Japan but
could not ascertain the causal relationship, i.e., which is the cause, which
is the response?
The mechanism behind midlatitude spread F (in the irregularity sense) and
its relationship to MSTIDs and Es layers are not well established.
Irregularities accompany MSTIDs during the summer during periods of low solar
activity but also emerge at other times when
conditions are geomagnetically disturbed .
Midlatitude spread F has also been associated with the steep bottom-side
gradients that can form around the midnight collapse or rapid descent of
the F peak driven by meridional tidal winds and wind shears in the
thermosphere .
This paper informs the aforementioned debates with new, comprehensive
observations from the Arecibo Radio Observatory. New analytic tools permit
neutral diagnostics and stability analysis in the neutral mesosphere-lower–thermosphere (MLT) region. A new simulation code elucidates a heretofore
neglected instability mechanism in the midlatitude F region. Below, the
data, tools, and simulation are presented and evaluated in a common context.
Observations
The period from 10 to 12 July 2015 was moderately disturbed, with the Kp index
exceeding 4 for three contiguous 3 h periods at the start of 11 July. The
F10.7 solar flux index was approximately 120. Ionospheric irregularities were
observed in turn over Arecibo on the evening of 11 July through the morning
of 12 July.
The digisonde in San Juan, Puerto Rico, was detecting a sporadic E layer
with a blanketing frequency of 6.5 MHz and a top frequency of 7.25 MHz by
16:15 LT on 11 July 2015. The gap between the two frequencies increased
steadily thereafter. By 19:45 LT, the top frequency of what had become a
patchy layer was approximately 9 MHz. The sporadic E layer traces would
remain strong and variable until about 03:00 LT the following morning. In
addition, strong ionosonde spread F emerged at about 23:30 LT. The spread
F was strongest through 01:30 LT the following morning and persisted until
sunrise.
Incoherent scatter observed by the line feed system at the Arecibo
Radio Observatory on 11/12 July 2015. Grayscales represent range-corrected
power, which serves as a proxy for electron number density. The top panel
shows E- and F-region data, whereas the bottom panel shows E-region
data in more detail.
Arecibo observations for 11/12 July 2015, are shown in Fig. . For
these experiments, data were collected using both the line feed and Gregorian
feed systems. The former was pointed at zenith, and the latter was pointed at
a 15∘ zenith angle and scanned in azimuth between west and north.
Dual-beam data such as these permit inferences about vector plasma and
neutral drifts in three spatial dimensions (see below).
Data were acquired using the coded long-pulse (CLP) mode developed by
. This represents a departure from synoptic experiments
run in the recent past at Arecibo, which usually divided time between the CLP
mode and a multi-frequency mode optimized for F-region plasma drift
estimation . The change was made to facilitate the
acquisition of more plasma-line data. F-region plasma drifts can still be
estimated from CLP data, albeit at a lower cadence. The cadence for the
processed data shown here is once per minute.
Incoherent scatter (ion-line) power profiles acquired with the line feed
system are shown in Fig. . The backscatter power has been
corrected for range and serves as a proxy for electron density. The upper
panel spans the E and F regions, whereas the lower panel presents an
exploded view of the E region.
Between 19:00 and 21:30 LT, the F-region densities at all altitudes
underwent quasiperiodic modulation with a dominant period of a little less than
1 h. The phenomenon suggests the passage of medium-scale traveling
ionospheric disturbances (MSTIDs).
Beginning about 30 min after midnight, the F region fell rapidly. This is
suggestive of the midnight collapse, a recurring dynamical feature in
Arecibo datasets e.g.,and references therein. We
will not focus attention on the midnight collapse but refer to it to
establish context for some other dynamical events.
Starting 1 h before midnight, the height of the bottom side fell and then
rose even more sharply. The sharp rise is also a recurring feature over
Arecibo that can be regarded as preconditioning for eventual collapse. Just
before midnight on this occasion, a narrow, depleted channel extending from
the bottom side to the topside passed over the observatory. For a period of
about 1 h after the passage of the depleted channel, the bottom-side F
region exhibited considerable structuring at scale sizes down to the finest
that could be resolved by this observing mode. The depleted channel and the
fine structure that followed were morphologically similar to what is observed
at the magnetic equator during periods of equatorial spread F. Later in the
paper, we will explicitly link the depleted channel to the large-density
perturbation that preceded it.
Irregular layers in the E region that appear concurrently are highlighted
in the lower panel of Fig. . A sporadic E layer was present
through sunset on 11 July. After sunset, as very often occurs in the summer
months, the sporadic E layer persisted but became irregular. Between
20:00 and 21:30 LT, the layer became patchy and vertically developed. Its
billowy appearance suggests a connection with neutral dynamic instability, as
demonstrated by . As mentioned above, coherent scatter
radar observations in a common volume have shown that ionized patches like
these are usually organized along elongated wavefronts with wavelengths of a
few tens of kilometers e.g.,. In this case, the
patchy layer was observed at about the same time as the MSTIDs which preceded
it by about 1 h. Note that previous investigations at Arecibo have not
revealed a universal relationship between patchy sporadic E layers and
MSTIDs. In the event documented by , for example,
MSTIDs and patchy Es layers occurred on the same night but were
mutually exclusive in time. In the present case, the MSTIDs and Es
layers exhibit dissimilar periodicities.
Whereas the aforementioned feature was a typical example of sporadic E
layer morphology, the feature in evidence between 00:00 and 02:00 LT is
unusual. The feature was more than 10 km thick at times and morphologically
suggestive of a single roll. The feature was moreover precisely coincident
with the elevation of the F layer and the most intense period of
midlatitude spread F.
Density profiles from the Gregorian feed (not shown) are substantially
similar to Fig. except for modulation in time due to azimuth
swinging. The modulation is barely detectable in the F region before
23:30 LT but severe thereafter. This indicates that horizontal fine
structuring on the scale of the beam separation was largely absent before the
emergence of spread F and widespread afterward. The second Es-layer patch was also free of modulation, implying that the sporadic E layer
blob was relatively unstructured on these scales.
Detailed examination of the Arecibo dataset from 11/12 July 2015.
The panels are described in the text.
More comprehensive measurements and derived parameters are shown in
Fig. . Panels a and b show line-of-sight plasma drift
estimates from line feed data acquired in the E and F regions,
respectively. The estimates are based on weighted averages of the phases of
the first few lags of the incoherent scatter radar autocorrelation functions. Whereas the E-region estimates
are range resolved, the F-region estimates are altitude averaged (to
improve statistical confidence). Altitude variations in panel a reflect the
varying influence of winds, Pedersen drifts, and Hall drifts in different
strata.
Similar remarks hold for panels c and d, which represent Gregorian feed
(off-zenith) plasma drift estimates. Regular modulation in the drift
estimates is a consequence of strong zonal flows combined with azimuth
steering. Additional altitude variations in the Gregorian-feed drifts
indicate shear flow.
Detailed examination of the Arecibo dataset from 11/12 July 2015.
The focus here is on the first patchy sporadic E layer. The panels are
described in the text. Note that panels (a) through (d) in
Fig. 2 apply to the entire experiment and are not reproduced in Figs. 3 and
4.
Plasma temperature and composition are estimated from the autocorrelation
functions using the procedure described by . A
simple composition model that allows for O+, NO+, and O2+ ions and
used temperature-dependent rate coefficients is incorporated in the parameter
fitting process iteratively. The resulting temperature estimates are shown in
panel e. These estimates are expected to be valid in the sunlit E region
but not in the sporadic E layers, which are reanalyzed differently below.
Between 16:00 and 18:00 LT, there is the suggestion of significant dynamics
and mixing in the E layer, i.e., the isotherms are not vertically
stratified.
Figure f presents F-region plasma drift estimates derived
from the line feed and Gregorian line-of-sight drift measurements. Here, an
inverse method incorporating a forward model of the (anisotropic) plasma
mobility along with regularization is used to estimate drifts in the
parallel-to-B, perpendicular-east, and perpendicular-north directions, which
are consistent with the available line-of-sight drifts while having minimal
curvature. The method is described in detail in and
is similar to that introduced by . Two main features
are present in the drifts. The first feature is a sharp ascent anti-parallel to
B peaking at 23:30 LT followed by a rapid descent along B peaking broadly
at 01:00 LT. The ascent followed a brief plunge in the F-layer height. The
descent is consistent with the apparent midnight collapse of the F-layer
height.
The second feature is rapid westward plasma advection between 23:30 and
01:30 LT. Notably, this is nearly coincident with the appearance of the
sporadic E layer blob.
Lastly, Fig. g–i show estimates of the zonal, meridional,
and vertical winds in the sunlit E region from 16:00 to 18:30 LT. The
winds are also estimated using an inverse method that incorporates a forward
model of the plasma mobility together with regularization and curvature
minimization, as described by . The electric fields
deduced from the F-region analysis are assumed to be representative of the
E region as well and incorporated into the wind-estimation problem. Strong
zonal and meridional shear is indicated, with the shear node being closely
collocated with the thin sporadic E layer. Atypically large vertical winds
with a periodicity of about 1 h are also indicated in the highest
altitudes at which the wind analysis could be carried out.
Detailed examination of the Arecibo dataset from 11/12 July 2015.
The focus here is on the second patchy sporadic E layer.
Panels (e)–(i) are described in the text.
Figure presents data in a manner similar to
Fig. but focuses on the first patchy sporadic E layer.
The incoherent scatter data were processed differently in two respects.
First, no composition modeling was performed. Instead, the composition was
assumed to be a combination of iron and magnesium ions, and temperature and
composition were estimated through ordinary nonlinear least-squares fitting
of the autocorrelation functions. Second, to accommodate the sparseness of
the sporadic E echoes in range, a global fitting strategy was used, similar
to that described by (see also
). In this strategy, state parameters for all
altitudes are fit simultaneously, and an additional penalty for the curvature
of the parameters with altitude is imposed. This produces parameter profiles
that are consistent with all available data while varying gradually with
altitude. Continuity in time is not enforced in the global fitting.
Figure e shows temperature profiles within the patchy sporadic
E layers, where the aforementioned methodology is expected to be
applicable. (Ion temperatures are what have been measured, but we equate
these with neutral temperatures; the ion cooling time due to nonresonant
collisions with neutrals is much shorter than the timescale for modifying the
ion temperature dynamically.) Temperatures within the first patch are almost
uniform or slightly increasing with altitude. Within the second patch,
however, the temperatures appear to decrease with altitude much of the time.
Panels g–i show wind estimates within the first patchy sporadic E layer
between 20:12 and 21:15 LT. The methodology used here was the same as described
above and in except that conductivities for
metallic ions based on collision frequency formulas found in
were utilized in the inversion. The panels reflect
planar shear flow, with winds reversing from southwest at low altitudes to
northeast at high altitudes. Vertical winds are very small, as is usually the
case. The flows are consistent over time. Little turning shear is present.
Lastly, Fig. focuses on the second patchy sporadic E layer.
The new information here is in panels g–i, which show the wind estimates
between 23:55 and 01:15 LT. The winds are rapid and toward the southeast for
the most part. Shear is evident but is not particularly strong except toward
the end of the event. Vertical winds are again small.
State-parameter estimates within the sporadic E layer patch seen
between 20:12 and 21:15 LT. Left: zonal winds. Middle: meridional winds.
Right: temperatures. The change in color, from black to red to green to
blue, indicates the passage of time. The violet curves are models reflecting
conditions at 20:24 LT used in subsequent analysis.
Same as Fig. except for 23:50–01:20 LT. The violet
curves are models reflecting conditions at 00:12 LT.
Figures and present measurements within the
first and second Es layers (respectively) in still greater detail.
The figures show the progression over time of the zonal (U) and meridional
(V) winds. Different colors, progressing from black to red to green to
blue, represent different times in the given intervals. The violet curves are
models selected to represent typical profiles in analyses carried out in the
next section of the paper. Also shown in Figs.
and are temperatures averaged over the intervals in question.
Lines through the plotted points are sample variances. In the case of the
first patch, there is little natural variability, and the sample variances
reflect mainly statistical uncertainty in the measurement. Variability is
greater in the second patch, and the sample variances are consequently
larger.
The zonal and meridional winds are similar in shape in the first patch,
meaning that the shear, which is significant, is planar as opposed to turning
shear. The temperatures increase throughout the layer at a rate of
2–3 K km-1. The layer is convectively stable but possibly dynamically
unstable. The case of the second layer is more unusual. The zonal and
meridional wind profiles have rather different shapes. The shear is
relatively modest except at first when U varied strongly with altitude.
Most remarkably, the temperature profile is inverted. Around 100 km
altitude, the lapse rate is even comparable to the adiabatic lapse rate of
∼ 9.5 K km-1. This suggests the possibility even of convective
instability and all but guarantees dynamic instability.
Analysis
We focus our analysis on two aspects of irregularities in the Arecibo
dataset: the patchy sporadic E layers and the spread F plume. For the
first, we analyze the possible role of neutral dynamic instability. For the
second, we consider the possibility of plasma convective instability. These
are the avenues of investigation with the most support in the available data.
Es layers
We solve the Miles–Howard problem to assess
the dynamical stability of the MLT region in the vicinity of the two
Es-layer patches observed over Arecibo. This is a boundary value
problem that derives from the linearized equations of mass and momentum
conservation in a vertically stratified, non-Boussinesq fluid. The inputs to
the problem are horizontal wind profiles spanning the strata of interest and
the local Brunt–Väisälä frequency. Dirichlet boundary conditions
are imposed at the upper and lower altitude limits. The eigenvalue sought is
the complex phase speed. Real solutions imply propagating waves, and imaginary
solutions imply growing mode shapes. The problem is solved numerically using
a relaxation method . Details regarding the problem
and its solution are given by .
Figure shows results of the analysis for the first of the
two Es-layer patches. For this analysis, the
Brunt–Väisälä period is taken to be 5 min. The model wind
profiles used to represent the conditions in the patch are plotted in the
lower-left panel. The upper-left panel shows the minimum Richardson number
(Ri) for those profiles as well as the propagation angle (in the
horizontal plane measured in degrees east of north) for which Ri is a
minimum. The curve suggests that a necessary condition for dynamic instability,
viz., Ri<14, is satisfied, if just barely, in a narrow stratum.
The upper-right panel of the figure shows the growth rate for dynamical
instability for different wave vectors. Here, x and y denote eastward and
northward directions, respectively. Unstable solutions exist for
northeast–southwest propagating modes with wavelengths of about 20 km. The
e-folding time for the fastest-growing modes is of the order of 15 min.
Marginal instability, limited by the stabilizing effect of buoyancy, is
therefore indicated.
The three sets of curves superimposed in the upper-right panel are mode
shapes calculated at the three points indicated. The mode shapes are
concentrated close to the strata of maximum shear, implying only shallow
mixing. The phase velocities for the unstable modes are small, as indicated
by the lower-right panel in the figure. Rolls caused by the instability would
be expected to drift with the winds at the shear node, which were small in
this case.
Eigenfunction analysis for wind profiles in first patchy
Es layer. (a) Minimum Richardson number parameter and
propagation angle at which the minimum occurs. (b) Linear growth
rate of the fastest-growing eigenmode with some representative mode shapes.
(c) Zonal (solid) and meridional (dashed) wind profiles.
(d) Phase speed of fastest-growing mode.
Same as Fig. except for the second
Es-layer patch.
Figure shows the results of a similar analysis applied to
the second Es-layer patch. In view of the lapse rate within this
patch, which approaches the adiabatic rate over some spans of altitude, the
Brunt–Väisälä period is taken to be very long for this analysis.
The removal of the buoyancy stabilization gives rise to a number of families
of fast-growing solutions that would not otherwise be present. The
upper-right panel of the figure reveals growing modes propagating in all
directions.
The fastest-growing waves have e-folding times of about 2 min and
wavelengths of 20–30 km. This is considerably shorter than predictions for
Es-layer instability or its variants under the same forcing
conditions e.g.,. The mode
shapes for the most unstable waves span large vertical distances, implying
the possibility of deep overturning, particularly in the case of waves
propagating in the meridional directions. The predicted phase speeds for the
fastest-growing modes are again small. Irregularities are expected to drift
with the background winds, which are mainly eastward in this case.
Spread F plume
Numerical simulations of midlatitude spread F. The left, center,
and right columns depict simulation times of 0, 20, and 37.5 min,
respectively. The top panels of each column show plasma number density in the
plane perpendicular to B in the meridional center of the simulation. The
colors indicate the abundances of molecular ions (blue), atomic oxygen ions
(green), and protons (red). The middle panels show vector current density in
the same plane according to the indicated color legend (full
scale: 20 µA m-2). For clarity, contributions from
diamagnetic currents are not shown. Equipotential curves in kilovolt are
superimposed. The bottom panels show current density in a magnetic meridional
plane at a 50 km zonal ground distance according to the indicated color legend
(full scale: 200 µA m-2).
The introductory discussion about midlatitude F-region plasma instability
focused on mechanisms involving motions of planar slabs of ionization. Such
mechanisms are easy to visualize, amenable to linear, local analysis, and
were prime candidates for explaining midlatitude spread F when it was first
being observed at Arecibo. However, contemporary computational tools permit
the exploration of a wider range of candidate mechanisms that can tap the
free energy in the unstably stratified nighttime ionosphere.
Aside from the depletion plume observed at 23:30 LT, the most prominent
feature in the F region in Fig. is the zone of enhanced
ionization in the bottom side at about 300 km altitude that immediately
preceded the plume. According to the F-region drift estimates in
Fig. , this feature was accompanied by rapid, widespread
motion of ionization up and down magnetic field lines. The displacement of
ionization along the magnetic field lines at middle latitudes signifies a
drastic redistribution of conductivity. The enhancement in Fig.
represents a bulge in field-line-integrated Pedersen conductivity with
significant dynamical consequences. It could well have been the seed for
instability and midlatitude spread F onset.
We have used a 3-D numerical simulation to examine the effects of a
conductivity bulge in the midlatitude ionosphere. The simulation code is a
modified version of the one described by . It evolves
the number density of four ion species (O+, O2+, NO+, and H+) in
time, incorporating the effects of background electric fields, winds,
pressure gradients, gravity, and recombination chemistry. Initial conditions
for the plasma number density and composition are derived from a combination
of empirical models. The code solves for the electrostatic potential fully in
three dimensions by enforcing quasi-neutrality. The code is cast in tilted
magnetic dipole coordinates (see , for discussion). The
simulation space encompasses the E and F regions in the Northern Hemisphere in the American sector and is bounded by p∈[1.03,1.08], q∈[0,0.24], and ϕ∈[-2.0,2.0] where q≡cosθ/r2, p≡r/sin2θ, θ is magnetic co-latitude, and ϕ is
degrees longitude. The simulation space therefore spans a zonal distance of
just over 400 km at the magnetic equator and L shells from 1.03 to 1.08.
For this simulation, a zonal wind profile with a hyperbolic-tangent profile
shape drives eastward plasma drifts approaching 100 m s-1 at the top
of the simulation volume. Note that the direction of the winds is immaterial
and that the phenomena described below occur given eastward or westward winds
and background plasma drifts. A constant background zonal electric field
drives plasma ascent at 30 m s-1. Ascent in the plane perpendicular to
B is required for instability in the scenario depicted. The drifts in the
v⟂n direction were positive most of the time in the hours before
the appearance of the spread F plume and so consistent with this
assumption.
The left column of Fig. depicts the initial conditions. The
upper panel shows the plasma number density in the plane perpendicular to B
in the meridional midpoint of the simulation. Red, green, and blue tones
represent molecular ions, atomic oxygen ions, and hydrogen ions,
respectively. The panel reflects the addition of an ellipsoidal blob of
enhanced density in the bottom side. The plasma density is doubled where the
blob is densest.
The middle panel shows the current density in the same perpendicular-to-B
plane. Superimposed on the current density are equipotential contours in
units of kV. These are approximate streamlines of the transverse-to-B flow.
The streamlines indicate the well-known behavior of plasma dynamics in the
vicinity of a Pedersen conductivity enhancement or blob. The effects are
twofold. First the blob drifts with the zonal wind faster than the background
plasma. Second, the blob descends in the background plasma frame of
reference. Since the background plasma is ascending, the net effect is that
the blob nearly maintains its altitude.
Since the transverse-to-B flow is nearly incompressible, the plasma flow
surrounding the blob is deflected around it. The resulting vertical motion
perturbs the background plasma density gradient, producing depletions to the
east and west of the blob. These depletions are subsequently prone to normal
E×B instability. After 37.5 min of simulation time, the
depletion on the leading edge of the enhancement exhibits vertical drifts in
excess of 200 m s-1 in this simulation. The ascent rate moreover
increases rapidly toward the end of the simulation as the depletion channel
becomes more narrow and structured. Our simulation was terminated as the
depletion propagated outside of the simulation space. In nature, the
depletion would be expected to propagate well into the topside F region.
We can estimate a growth rate for the instability by dividing the ascent
speed of the depletion by the vertical density gradient scale length L∼ 20 km. The corresponding e-folding time of 100 s is much shorter
than can be expected from the Perkins instability or its variants.
The bottom panel in the right column of Fig. shows the
current density in the plane of the magnetic meridian. The particular plane
shown here is coincident with the westward wall of the depletion. Very strong
downward field-aligned currents are seen to flow on the meridional edges of
the depleted region. The currents close in the E region. We can speculate
that the currents would provide the free energy for secondary instabilities
in sporadic E layers sharing magnetic field lines with similar depletions
in nature. Details regarding the secondary instabilities in question are
provided by .
The spread F event described by was similar to
the one described here in several respects. It occurred between sunset and
midnight and was preceded by a sharp, downward displacement of plasma along
B and an attendant density enhancement. The major difference was that the
earlier event produced an ascending plume of enhanced rather than depleted
plasma, something that is never observed at equatorial latitudes. We argue
that the mechanism proposed here could account for that event if (1) the
initial conductivity enhancement occurred in the topside and (2) the
background plasma was descending rather than ascending. (These conditions
were met in the earlier event.) In that case, the deflection of plasma around
the blob would tend to pull dense ionization from the F peak upward and
push more rarefied plasma from the topside downward. The dense plasma would
then continue to ascend in the topside and become unstable under the action
of the westward background electric field. The phenomenology is almost
symmetric with that observed in the present event albeit more slowly growing.
Enhanced density plumes are inherently less unstable than depleted ones, and
the corresponding mechanism is not as robust. Both mechanisms appear to be
viable, however.
Summary and conclusions
We have presented observations from the Arecibo Observatory of the E- and
F-region ionosphere during moderately disturbed conditions. The
observations exhibit the most common manifestations of space weather at
middle latitudes: patchy Es layers, MSTIDs, and spread F
depletions. Although the phenomena occurred at about the same time, clear
connections between them are not obvious. Indeed, a conclusion of the paper
is that there appear to be viable instability mechanisms in the midlatitude
E and F regions that are not directly coupled.
Detailed analysis of the Arecibo data involving statistical inverse methods
allow the inference of neutral dynamics in the MLT and the thermosphere.
Neutral dynamics appears to play a key role in ionospheric instability at
middle latitudes. Significant shear flow appears to be nearly ubiquitous in
the midlatitude E region. In the patchy Es layers examined here,
the neutral flow was marginally or robustly unstable in the Richardson number
sense. In the latter case, instability benefited from regions of less stable
lapse rates, which negated the stabilizing effect of buoyancy. The predicted
e-folding time for the stratum in question was only about 2 min and much
shorter than what is anticipated for plasma instability acting alone. Once
patchy Es layers have been induced, fast-growing secondary plasma
instabilities should be able to function and produce irregularities on intermediate and small scales.
An interesting feature of the observations presented here is the occurrence
of temperature profiles with lapse rates close to the adiabatic value.
Adiabatic or near-adiabatic lapse rates are common in the mesosphere where
the ambient lapse rate is generally negative. Relatively small perturbations
associated with passing wave motions or various types of heating or cooling
can easily change the lapse rate, making it more negative and at times
getting close to or exceeding the adiabatic value. At altitudes above 100 km
where the background lapse rate is generally isothermal or the temperature increases with height, perturbing the temperature profile sufficiently to
reach the adiabatic value is difficult, however. With increasing height in
the thermosphere, diffusive effects and radiational cooling effects become
more important, but in the lower thermosphere such effects are still
relatively small. This suggests that the flow is, at least to a fairly good
approximation, nearly adiabatic in that part of the atmosphere. One way to
produce an adiabatic layer is therefore to have strong upwelling in the
layer, due to mechanical forcing, for example. The motion has to be nearly or
entirely vertical since slantwise convection will not lead to an adiabatic
lapse rate. The general assumption is often made that the vertical winds in
the thermosphere are small because of the highly stable stratification, i.e.,
the positive or isothermal lapse rates in that part of the atmosphere, but a
number of studies have shown that not to be the case.
summarized a large number of ground-based and
in situ vertical wind measurements and found that vertical winds exceeding
10 m s-1 are common and often extend over large altitude ranges and
over periods of 1 h or more. With respect to observations specifically from
Arecibo, presented observations of a number of
overturning events in the lower thermosphere, including some from Arecibo.
The more recent vertical neutral wind measurements
obtained with the Arecibo incoherent scatter radar showed large vertical
motions throughout the multi-hour observing period, consistent with the
conclusions of . The forcing
responsible for the observed thermospheric vertical winds is not clear, but
the occurrence of layers with near-adiabatic lapse rates is to be expected,
given that the large vertical winds are there.
In the F region, large-scale plasma irregularities in the bottom side appear
to be induced by thermospheric motion with a component parallel to the
geomagnetic field in the manner suggested by . Once
present, the irregularities seed additional irregularities and provide the
conditions necessary for plasma convective instability leading to spread F.
The e-folding time for this process appears to be much shorter than that
predicted for Perkins instability.
An analytic formulation of the equations for an instability is always
attractive, in part because it makes the instability mechanism easier to
understand and in part because the stability boundaries can often be
identified more easily. The various midlatitude spread F instability
theories that have been proposed have either relied entirely on analytic
theories or used the analytic theories as a starting point for further
numerical calculations. The results presented here are not represented in a
simple analytic form but nonetheless show the existence of a robust and
fast-growing instability mechanism that appears to account for the observed
characteristics of the midlatitude F-region plumes that were observed.
Data availability
The data used for this study are available from the NSF Madrigal Database
(http://madrigal.haystack.mit.edu/madrigal/).
Acknowledgements
This work was supported by awards AGS-1360718 and AGS-1360594 from the
National Science Foundation to Cornell University and Clemson University. The
Arecibo Observatory is part of the National Astronomy and Ionosphere Center
which is operated under a cooperative agreement with the National Science
Foundation. The topical editor,
D. Pallamraju, thanks two anonymous referees for help in evaluating this
paper.
ReferencesBehnke, R. A.: F layer height bands in the nocturnal ionosphere over
Arecibo, J. Geophys. Res., 84, 974–978, 1979.
Bernhardt, P. A.: The modulation of sporadic-E layers by Kelvin-Helmholtz
billows in the neutral atmosphere, J. Atmos. Sol.-Terr. Phy., 64, 1487–1504,
2002.Bernhardt, P. A., Selcher, C. A., Siefring, C., Wilkens, M., Compton, C.,
Bust, G., Yamamoto, M., Fukao, S., Takayuki, O., Wakabayashi, M., and Mori,
H.: Radio tomographic imaging of sporadic-E layers during SEEK-2, Ann.
Geophys., 23, 2357–2368, 10.5194/angeo-23-2357-2005, 2005.
Bernhardt, P. A., Werne, J., and Larsen, M. F.: Modeling of Sporadic-E
Structures from Wind-Driven Kelvin-Helmholtz Turbulence, in: Characterising
the Ionosphere, Meeting Proceedings RTO-MP-IST-056, Neuilly-sur-Seine,
France, 34, 31-1–31-14, 2006.
Cabrit, B. and Kofman, W.: Ionospheric composition measurement by EISCAT
using a global fit procedure, Ann. Geophys., 14(12), 1496–1505, 1996.Chu, Y. H. and Wang, C. Y.: Interferometry observations of 3-dimensional
spatial structures of sporadic E using the Chung-Li VHF radar, Radio
Sci., 32, 817–832, 1997.
Chu, Y. H., Wang, C. Y., Su, S. L., and Kuong, R. M.: Coordinated sporadic
E layer observations made with Chung-Li 30 MHz radar, ionosonde and
FORMOSAT-3/COSMIC satellites, J. Atmos. Sol.-Terr. Phy., 73, 883–894,
2011.Cosgrove, R. B.: Generation of mesoscale F layer structure and electric
fields by the combined Perkins and Es layer instabilities, in
simulations, Ann. Geophys., 25, 1579–1601, 10.5194/angeo-25-1579-2007,
2007.Cosgrove, R. B. and Tsunoda, R. T.: A direction-dependent instability of
sporadic-E layers in the nighttime midlatitude ionosphere, Geophys. Res.
Lett., 29, 1864, 10.1029/2002GL014669, 2002.Cosgrove, R. B. and Tsunoda, R. T.: Instability of the E–F coupled
nighttime midlatitude ionosphere, J. Geophys. Res., 109, A04305,
10.1029/2003JA010243, 2004.
Crary, D. J. and Forbes, J. M.: The dynamic ionosphere over Arecibo: A
theoretical investigation, J. Geophys. Res., 91, 249–258, 1986.Didebulidze, G. G. and Lomidze, L. N.: Double atmospheric gravity wave
frequency oscillations of sporadic E formed in a horizontal shear flow,
Phys. Lett. A, 374, 952–959, 2010.Duly, T. M., Huba, J. D., and Makela, J. J.: Self-consistent generation of
MSTIDs within the SAMI3 numerical model, J. Geophys. Res., 119,
6745–6757, 10.1002/2014JA020146, 2014.
Fukao, S., Kelley, M. C., Shirakawa, T., Takami, T., Yamamoto, M., Tsuda, T.,
and Kato, S.: Turbulent upwelling of the midlatitude ionosphere: 1.
Observational results by the MU radar, J. Geophys. Res., 96, 3725–3746,
1991.Fukao, S., Yamamoto, M., Tsunoda, R. T., Hayakawa, H., and Mukai, T.: The
SEEK (Sporadic-E Experiment over Kyushu) campaign, Geophys. Res. Lett., 25,
1761–1764, 1998.Fukushima, D., Shiokawa, K., Otsuka, Y., and Ogawa, T.: Observation of
equatorial nighttime medium-scale traveling ionospheric disturbances in
630-nm airglow images over 7 years, J. Geophys. Res., 117, A10324,
10.1029/2012JA017758, 2012.Gong, Y., Zhou, Q. H., Zhang, S. D., Aponte, N., Sulzer, M., and Gonzalez,
S.: Midnight ionosphere collapse at Arecibo and its relationship to the
neutral wind, electric field, and ambipolar diffusion, J. Geophys. Res., 117,
A08332, 10.1029/2012JA017530, 2012.Haldoupis, C. and Schlegel, K.: Observation of the modified two-stream plasma
instability in the midlatitude E region ionosphere, J. Geophys. Res., 99,
6219–6226, 1994.Hamza, A.: Perkins instability revisited, J. Geophys. Res., 104,
22567–22575, 10.1029/1999JA900307, 1999.Hecht, J. H., Liu, A. Z., Bishop, R. L., Clemmons, J. H., Gardner, C. S.,
Larsen, M. F., Roble, R. G., Swenson, G. R., and Walterscheid, R. L.: An
overview of observations of unstable layers during the Turbulent Oxygen
Mixing Experiments (TOMEX), J. Geophys. Res., 109, D02S01,
10.1029/2002JD003123, 2004.Helmboldt, J. F., Lazio, T. J. W., Intema, H. T., and Dymond, K. F.:
High-precision measurements of ionospheric TEC gradients with the Very
Large Array VHF system, Radio Sci., 47, RS0K02, 10.1029/2011RS004883,
2012.
Howard, L. N.: Note on a paper by John W. Miles, J. Fluid Mech., 10,
509–512, 1961.Hysell, D. L., Chau, J. L., and Fesen, C. G.: Effects of large horizonbtal
winds on the equatorial electrojet, J. Geophys. Res., 107, 1214,
10.1029/2001JA000217, 2002.Hysell, D. L., Larsen, M. F., and Zhou, Q. H.: Common volume coherent and
incoherent scatter radar observations of mid-latitude sporadic E-layers and
QP echoes, Ann. Geophys., 22, 3277–3290, 10.5194/angeo-22-3277-2004,
2004.Hysell, D. L., Nossa, E., Larsen, M. F., Munro, J., Sulzer, M. P., Aponte,
N., and González, S. A.: Sporadic E layer observations over Arecibo
using coherent and incoherent scatter radar: Assessing dynamic stability in
the lower thermosphere, J. Geophys. Res., 114, A12303,
10.1029/2009JA014403, 2009.Hysell, D. L., Nossa, E., Larsen, M. F., Munro, J., Smith, S., Sulzer, M. P.,
and González, S. A.: Dynamic instability in the lower thermosphere inferred
from irregular sporadic layers, J. Geophys. Res., 117, A08305,
10.1029/2012JA017910, 2012.Hysell, D. L., Nossa, E., Aveiro, H. C., Larsen, M. F., Munro, J., Sulzer,
M. P., and González, S. A.: Fine structure in midlatitude sporadic E
layers, J. Atmos. Sol.-Terr. Phy., 103, 16–23,
10.1016/j.jastp.2012.12.005, 2013.Hysell, D. L., Jafari, R., Milla, M. A., and Meriwether, J. W.: Data-driven
numerical simulations of equatorial spread F in the Peruvian sector, J.
Geophys. Res., 119, 3815–3827 10.1002/2014JA019889, 2014a.Hysell, D. L., Larsen, M. F., and Sulzer, M. P.: High time and height
resolution neutral wind profile measurements across the mesosphere/lower
thermosphere region using the Arecibo incoherent scatter radar, J. Geophys.
Res., 119, 2345–2358, 10.1002/2013JA019621, 2014b.Kelley, M. C.: On the origin of mesoscale TIDs at midlatitudes, Ann.
Geophys., 29, 361–366, 10.5194/angeo-29-361-2011, 2011.Kelley, M. C. and Miller, C. A.: Electrodynamics of midlatitude spread F 3.
Electrohydrodynamic waves? A new look at the role of electric fields in
thermospheric wave dynamics, J. Geophys. Res., 102, 11539–11547, 1997.Krall, J., Huba, J. D., Ossakow, S. L., and Joyce, G.: Why do equatorial
bubbles stop rising?, Geophys. Res. Lett., 37, L09105,
10.1029/2010GL043128, 2010.Krall, J., Huba, J. D., Ossakow, S. L., Joyce, G., Makela, J. J., Miller,
E. S., and Kelley, M. C.: Modeling of equatorial plasma bubbles triggered by
non equatorial traveling ionospheric disturbances, Geophys. Res. Lett., 38,
L08103, 10.1029/2011GL046890, 2011.
Larsen, M. F.: A shear instability seeding mechanism for quasi-periodic radar
echoes, J. Geophys. Res., 105, 24931–24940, 2000.Larsen, M. F.: Winds and shears in the mesosphere and lower thermosphere:
Results from four decades of chemical release wind measurements, J.
Geophys. Res., 107, 1216, 10.1029/2001JA000218, 2002.Larsen, M. F. and Meriwether, J. W.: Vertical winds in the thermosphere, J.
Geophys. Res., 117, A09319, 10.1029/2012JA017843, 2012.Larsen, M. F., Fukao, S., Yamamoto, M., Tsunoda, R., Igarashi, K., and Ono,
T.: The SEEK chemical release experiment: Observed neutral wind profile
in a region of sporadic-E, Geophys. Res. Lett., 25, 1789–1792, 1998.Larsen, M. F., Liu, A. Z., Gardner, C. S., Kelley, M. C., Collins, S.,
Friedman, J., and Hecht, J. H.: Observations of overturning in the upper
mesosphere and lower thermosphere, J. Geophys. Res., 109, D02S04,
10.1029/2002JD003067, 2004.Larsen, M. F., Hysell, D. L., Zhou, Q. H., Smith, S. M., Friedman, J., and
Bishop, R. L.: Imaging coherent scatter radar, incoherent scatter radar, and
optical observations of quasiperiodic structures associated with sporadic E
layers, J. Geophys. Res., 112, A06321, 10.1029/2006JA012051, 2007.Layzer, D.: The Turbulence Criterion in Stably Stratified Shear Flow and The
Origin of Sporadic E, in: Ionospheric Sporadic E, edited by: Smith,
E. K. and Matsushita, S., Pergamon Press, Oxford, NY, 258–275, 1962.Mathews, J. D.: Sporadic E: Current views and recent progress, J. Atmos.
Sol.-Terr. Phy., 60, 413–435, 1998.
Miles, J. W.: On the stability of heterogeneous shear flows, J. Fluid Mech.,
10, 496–508, 1961.Miller, E. S., Makela, J. J., and Kelley, M. C.: Seeding of equatorial plasma
depletions by polarization electric fields from middle latitudes:
Experimental evidence, Geophys. Res. Lett., 36, L18105,
10.1029/2009GL039695, 2009.Miller, K. L. and Smith, L. G.: Incoherent scatter radar observations of
irregular structure in mid-latitude sporadic E layers, J. Geophys. Res.,
83, 3761–3775, 1978.Ogawa, T., Nishitani, N., Otsuka, Y., Shiokawa, K., Tsugawa, T., and
Hosokawa, K.: Medium-scale traveling ionospheric disturbances observed with
the SuperDARN Hokkaido radar, all-sky imager, and GPS network and their
relation to concurrent sporadic E irregularities, J. Geophys. Res., 114,
A03316, 10.1029/2008JA013893, 2009.Otsuka, Y., Onoma, F., Shiokawa, K., Ogawa, T., Yamamoto, M., and Fukao, S.:
Simultaneous observations of nighttime medium-scale traveling ionospheric
disturbances and E region field-aligned irregularities at midlatitudes, J.
Geophys. Res., 112, A06317, 10.1029/2005JA011548, 2007.Otsuka, Y., Tani, T., Ogawa, T., and Saito, A.: Statistical study of
relationship between medium-scale traveling ionospheric disturbance and
sporadic E layer activities in summer night over Japan, J. Atmos.
Sol.-Terr. Phy., 70, 2196–2202, 2008.Otsuka, Y., Shiokawa, K., Ogawa, T., Yokoyama, T., and Yamamoto, M.: Spatial
relationship of nighttime medium-scale traveling ionospheric disturbances and
F region field-aligned irregularities observed with two spaced all-sky
airglow imagers and the middle and upper atmosphere radar, J. Geophys. Res.,
114, A05302, 10.1029/2008JA013902, 2009.Perkins, F.: Spread F and Ionospheric Currents, J. Geophys. Res., 78,
218–226, 1973.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.:
Numerical Recipes in C, Cambridge University Press, New York, 1988.Riggin, D., Swartz, W. E., Providakes, J., and Farley, D. T.: Radar studies
of long-wavelength waves associated with mid-latitude sporadic E layers, J.
Geophys. Res., 91, 8011–8024, 1986.Saito, S., Yamamoto, M., Hashiguchi, H., and Maegawa, A.: Observation of
three-dimensional signatures of quasi-periodic echoes associated with
mid-latitude sporadic-E layers by MU radar ultra-multi-channel system,
Geophys. Res. Lett., 33, L14109, 10.1029/2005GL025526, 2006.Saito, S., Yamamoto, M., Hashiguchi, H., Maegawa, A., and Saito, A.:
Observational evidence of coupling between quasi-periodic echoes and medium
scale traveling ionospheric disturbances, Ann. Geophys., 25, 2185–2194,
10.5194/angeo-25-2185-2007, 2007.
Schunk, R. W. and Nagy, A. F.: Ionospheres: Physics, Plasma Physics, and
Chemistry, Cambridge University Press, 2004.Shiokawa, K., Otsuka, Y., Ihara, C., Ogawa, T., and Rich, F. J.: Ground and
satellite observations of nighttime medium-scale traveling ionospheric
disturbance at midlatitude, J. Geophys. Res., 108, 1145,
10.1029/2002JA009639, 2003.Smith, L. G. and Miller, K. L.: Sporadic-E layers and unstable wind shears,
J. Atmos. Sol.-Terr. Phy., 42, 45–50, 1980.
Sulzer, M. P.: A phase modulation technique for a sevenfold statistical
improvement in incoherent scatter data-taking, Radio Sci., 21, 737–744,
1986a.
Sulzer, M. P.: A radar technique for high range resolution incoherent scatter
autocorrelation function measurements utilizing the full average power of
klystron radars, Radio Sci., 21, 1033–1040, 1986b.Sulzer, M. P., Aponte, N., and González, S. A.: Application of linear
regularization methods to Arecibo vector velocities, J. Geophys. Res., 110,
A10305, 10.1029/2005JA011042, 2005.Suzuki, S., Hosokawa, K., Otsuka, Y., Shiokawa, K., Ogawa, T., Nishitani, N.,
Shibata, T. F., Koustov, A. V., and Shevtsov, B. M.: Coordinated observations
of nighttime medium-scale traveling ionospheric disturbances in 630-nm
airglow and HF radar echoes at midlatitudes, J. Geophys. Res., 114, A07312,
10.1029/2008JA013963, 2009.Swartz, W. E., Kelley, M. C., Makela, J. J., Collins, S. C., Kudeki, E.,
Franke, S., Urbina, J., Aponte, N., Sulzer, M. P., and Gonzalez, S.: Coherent
and incoherent scatter radar observations during intense mid-latitude spread
F, Geophys. Res. Lett., 27, 2829–2832, 2000.
Swisdak, M.: Notes on the dipole coordinate system, Cornell University
Library, arXiv:physics/0606044 [physics.space-ph], 2006.Tsunoda, R. T.: On the coupling of layer instabilities in the nighttime
midlatitude ionosphere, J. Geophys. Res., 111, A11304,
10.1029/2006JA011630, 2006.Whitehead, J. D.: The structure of sporadic E from a radio experiment,
Radio Sci., 7, 355–358, 1972.Whitehead, J. D.: Recent work on mid-latitude and equatorial sporadic E, J.
Atmos. Sol.-Terr. Phy., 51, 401–424, 1989.Woodman, R. F., Yamamoto, M., and Fukao, S.: Gravity wave modulation of
gradient drift instabilities in mid-latitude sporadic E irregularities,
Geophys. Res. Lett., 18, 1197–1200, 1991.Yamamoto, M., Fukao, S., Woodman, R. F., Ogawa, T., Tsuda, T., and Kato, K.:
Mid-latitude E region field-aligned irregularities observed with the MU
radar, J. Geophys. Res.-Space, 96, 15943–15949, 1991.Yamamoto, M., Fukao, S., Ogawa, T., Tsuda, T., and Kato, S.: A morphological
study of mid-latitude E-region field-aligned irregularities observed with
the MU radar, J. Atmos. Sol.-Terr. Phy., 54, 769–777, 1992.Yamamoto, M., Fukao, S., Tsunoda, R. T., Pfaff, R., and Hayakawa, H.: SEEK-2
(Sporadic-E Experiment over Kyushu 2) – Project Outline, and Significance,
Ann. Geophys., 23, 2295–2305, 10.5194/angeo-23-2295-2005, 2005.
Yokoyama, T., Otsuka, Y., Ogawa, T., Yamamoto, M., and Hysell, D. L.: First
three-dimensional simulation of the Perkins instability in the nighttime
midlatitude ionosphere, Geophys. Res. Lett., 35, L03101,
10.1029/2007GL032496, 2008.Yokoyama, T., Hysell, D. L., Otsuka, Y., and Yamamoto, M.: Three-dimensional
simulation of the coupled Perkins and Es layer instabilities in
the nighttime midlatitude ionosphere, J. Geophys. Res., 114, A03308,
10.1029/2008JA013789, 2009.