Introduction
The strong radar echoes over polar latitudes during the summer were first
reported by . Since then these echoes, known as
polar mesospheric summer echoes (PMSEs) e.g.,, have
been the subject of active research. Currently there is a general consensus
that they are generated by atmospheric turbulence and require the presence of
free electrons and charged ice particles e.g.,. The scattering theories have been improved in the last
decade to include events that were not supported before. For example,
improved the previous work of
to explain the PMSE observations with the Poker Flat Incoherent Scatter Radar
(PFISR). Namely, they arrived to an expression that shows that PMSE radar
cross section (RCS) depends on electron density when it is much smaller than
ice density. In the reverse case, PMSE RCS is proportional mainly to ice
density.
The connection between noctilucent clouds (NLCs) and PMSEs has been
established by many authors, e.g., , , , and . The common
element in PMSEs and NLCs is the presence of ice particles in the summer polar
mesosphere. A difference is that only the electrically charged population of
the particles have a role in the radar scattering mechanism regardless of
their size. However, only particles of size greater than about
40 nm contribute to the brightness of NLCs regardless of whether they are
charged or not. Another important difference is that NLCs cover a large part
of the sky and they are visible even to the naked eye, which facilitates the
study of their large-scale horizontal behavior with various types of all-sky
cameras. In contrast, PMSEs can be studied only inside a very limited region
determined by the radar antenna beamwidth, typically a few km wide in the
transverse (horizontal) direction using the main beam. Thus, NLCs provide
means to investigate the large-scale behavior of the polar mesosphere.
Observations with a variety of optical instruments have shown that NLCs
present a variety of horizontal scales, from meters to hundreds of
kilometers,
and are typically confined to layers of less than 1 km thickness
e.g.,. From the temporal
and spatial evolution of these structures, atmospheric waves and
instabilities can be studied e.g.,and references
therein.
Given the understanding of PMSE occurrence, recent efforts have been devoted
to study their long-term behavior e.g., and
angular dependence e.g., and using them as tracers for
atmospheric dynamics e.g.,. Following the relation with NLCs,
simultaneous PMSE observations with spatially separated monostatic systems
have been associated to drifting structures e.g.,. However, these previous studies were not
able to determine the size and separation of such drifting structures.
Recently, , using radar imaging, have reported PMSE
horizontal structures with sizes around 1 km, which is not surprising given
that even smaller structures have been observed in NLCs. Moreover, these
findings support the hypothesis of that the radar
cross section of PMSEs does not vary significantly as a function of observing
angle (aspect sensitivity). This implies that the scattering originates from
localized isotropic structures instead of anisotropic horizontally
stratified structures. If the high aspect sensitivity were the norm for PMSEs,
our observations reported here would not have been possible.
In this paper we present the results obtained using the Middle Atmosphere
ALOMAR Radar System (MAARSY) (16.04∘ E, 69.30∘ N) and the
Kilpisjärvi Atmospheric Imaging Receiver Array (KAIRA) (20.76∘ E,
69.07∘ N) in northern Scandinavia. MAARSY is a powerful all-digital
phase array radar that was specially built to study PMSEs and lower
atmospheric dynamics . KAIRA was designed to study
different kinds of atmospheric and ionospheric phenomena
. KAIRA can be used as an
all-sky imaging receiver for cosmic radio emissions to study D-region
absorption and as a phased array radar receiver
for nearby radar and radio transmitters, such as
the EISCAT very high frequency (VHF) radar (European Incoherent Scatter Scientific Association),
MAARSY, or several nearby specular meteor radars.
Our paper is organized as follows. We first cover some aspects of PMSE
scattering theory with special emphasis on meter scales and Bragg wavelength
dependence. Then we describe the experiment configuration and present
important aspects of the bistatic geometry, e.g., the effective Bragg
wavelength. The monostatic and bistatic experimental results are shown and
combined in Sect. . We proceed to discuss the horizontal
sizes and separations of the identified structures and the conservative
angular dependence values derived. Finally we present our conclusions,
emphasizing the possibility of using observations of this kind to both gain
more insight on PMSE spatial–temporal features and potentially use PMSE
scattering as a way of obtaining improved regional wind field measurements.
PMSE scattering theory at meter scales
The expected radar cross section of PMSE has been studied by many authors
trying to explain observations at different radar frequencies under different
natural as well as artificial (ionospheric modification using high-frequency radio waves)
conditions e.g.,. The most recent work in the subject by
, following the work of and
, shows that RCS is a strong function of electron
density only when electron density is much smaller than ice density.
Otherwise it is mainly controlled by ice density. This improvement to
previous theories was motivated by PMSE observations with the Poker Flat
Incoherent Scatter Radar (PFISR) during night and during aurora.
To help in the presentation and interpretation of our results, here we
briefly show expressions relevant for our Bragg wavelengths of interest,
i.e., around 3 m. From Eq. (44) in , the PMSE RCS as
a function of Bragg wavenumber, i.e., kB=2π/λB, is
η(kB)∝kB-3exp-qKκkB2Sc,
where Sc=νa/De is the Schmidt number, Kκ=(νa3/ϵ)1/4 is the Kolmogorov microscale, νa is the
kinematic viscosity of air (m2 s-1), De the diffusion coefficient
of electrons (m2 s-1), and ϵ is the energy dissipation rate of
turbulence (W kg-1). For a turbulent velocity spectrum with a Gaussian
shape and width (or turbulence intensity) σv (m s-1), ϵ=Fσv2, where F is factor that varies typically between 8 and
10,
depending on the actual atmospheric conditions e.g., .
Simulations of PMSE RCS as a function of (a) wavenumber and
(b) turbulence intensity at a λB=2.8 m. In (a) we show two
simulations, one keeping Sc=3 constant and varying σv and the
second one keeping σv=1.1 constant and varying Sc. Two approximate
dependence on λB are shown in black Eq. 44.
In the case of (b), five cases are shown (see text for
details). The two vertical dashed lines represent the wavenumbers of
interest, i.e., bistatic middle point (smaller) and MAARSY monostatic
(larger).
The expected dependence of PMSE RCS at meter scales is shown in
Fig. a. The figure shows the expected PMSE RCS for two
simulations as a function of kB. The simulations have been obtained with a
model used by , which is based on the seminal work of
. Moreover, we have used Model 2 of as
suggested by . In the first simulation, we keep Sc=3
constant and vary the turbulence intensity (σv) (dashed lines). In
the second simulation, we fix σv=1.1 m s-1 and vary Sc. The vertical
dashed-dot-dashed lines represent the lowest and largest (MAARSY monostatic)
wavenumbers we will explore in this study with bistatic and monostatic radar
experiments. The black solid and dashed curves represent Bragg wavenumber
dependence shown in Eq. (). Note that for high Schmidt
number RCS is independent of turbulence intensity, but has a clear dependence
on λB3 for the Bragg wavelengths of interest.
Sketch of PMSE observations with MAARSY as transmitter and KAIRA and
MAARSY as receivers. MAARSY main lobe and side lobes are represented by the
vertical and tilted yellow triangles, respectively. The region of PMSEs is
depicted with clouds of different sizes and colors located in a narrow
region. The white arrows represent the expected Bragg vectors of the
MAARSY–KAIRA detections (see text for more details).
In all cases, the simulations have been conducted for typical PMSE altitudes
(i.e., 85 km). We have assumed Ne=3.×10-9, hH=0.2,
νa=0.567, Dne=0.567, σne=1000, and χ=2.6×1012. Here Ne is electron density in e m-3, σne
scale length of an electron density byte-out in meters, and χ the dissipation
rate of electron density variance in m-6 s-1. hH is the Havnes
parameter given by ZdNd/Ne , where Zd is the
charge dust density and Nd the dust number density.
Figure b shows relative RCSs as a function of turbulence
intensity for different simulations at MAARSY's wavenumber in a monostatic
configuration, i.e., 2π/2.8 m, namely for (a) a large Sc (900)
(green), (b) a small Sc (3) (dashed black), (c) turbulence without ice at
70 km (orange), (d) a fixed σv=1.1 for a wide range of Sc (blue),
and (e) a fixed σ=4.0 for large Sc (from 100 to 5000) (red
triangles). We have intentionally removed the absolute RCS from Fig. b,
since we want to emphasize the qualitative features
of these results.
The salient features at about 2.8 m Bragg wavelength that can be deduced from
Fig. b are as follows:
The RCS varies significantly as a function of Sc when Sc is not
too large (e.g., Sc<100). In our simulation with σv=1.1 (blue) the
variation is more than 6 orders of magnitude.
At low Sc, the RCS varies strongly with turbulence intensity
(dashed black), in a manner similar to turbulence without ice. As a reference,
we are showing the expected RCS with Sc=1 but at 70 km instead of 85 km (orange).
Note the increase of RCS with increasing σv.
Once the Sc is high (e.g., >100), the RCS varies very little
(red triangles).
At high Sc, the RCS decreases with turbulence intensity (green line).
This is an unexpected result, since this behavior cannot be reproduced by
expressions or results shown in previous works e.g.,.
This result indicates that for a given Schmidt number there is a region,
kB≫kT, where the RCS does increase with increasing turbulence intensity,
and kB≪kT, where the RCS decreases with increasing turbulence intensity,
where kT is the Bragg wavenumber of this transition. Note that our
simulations have been obtained by numerically integrating Hill's theoretical
results without approximations.
Experiment description
As mentioned above, the results presented in this paper have been obtained
using MAARSY and KAIRA in northern Scandinavia. The distance between the two
systems is approximately 190 km. MAARSY was used for transmission and
reception operating at 53.5 MHz, i.e., a radar wavelength of 5.61 m. KAIRA
was used for reception only. Figure shows an schematic view
of the experiment. As reference, we show the directions of the Bragg vectors
of the bistatic geometry, i.e., KAIRA receptions, with white arrows, which
all point to the middle point between MAARSY and KAIRA. Note that the Bragg
wavelengths will be different for different vectors, being the largest over
the middle point (i.e., ∼ 4.15 m) and the smallest for a monostatic
configuration (i.e., 2.8 m). Below we describe the specific configuration for
each system as well as the main geometrical parameters of the MAARSY–KAIRA
configuration. In a conventional bistatic configuration without scanning (as
is the case here) neglected antenna side lobes, only one Bragg vector
contributes to the received bistatic signal. The KAIRA data gathered during
this experiment show otherwise, as the received signals at KAIRA have
contributions originating from the MAARSY's antenna side lobes in a wide range
of directions, each with different Bragg wavevectors represented by the white
arrows in Fig. ; see below.
MAARSY configuration
MAARSY consists of 433 crossed-polarized three-element Yagi antennas. On
transmission, right-circular polarization is used, the beam can be steered
from pulse-to-pulse every 1 ms, and different sections of the antenna can be
used. On reception there are 16 complex channels available. One of these
channels receives from all 433 antenna elements, while the other 15 can be
selected to receive from different portions of the antenna. General details
of the system are given by . An example of MAARSY's
flexibility on transmission and reception can be found in
, where narrow and wide beams were used on
transmission, and 15 different groups of 7 antennas each (called hexagons)
were used on reception.
For this campaign MAARSY was run with a complementary code using 2 µs
baud width, 5 % duty cycle of the available power, and an interpulse period of
1 ms. Only one nominally vertically pointing direction was used on both
transmission and reception. Ideally the signal is expected to come from the
main beam; however, depending on the strength of the atmospheric target, echoes
could come also from side lobes (see below). Complex voltages for the added
signal of all 433 elements were recorded. To allow synchronization with
KAIRA, a 1 pulse-per-second GPS pulse and a GPS-disciplined rubidium clock
were used. The data were analyzed offline to obtain spectra and spectral
moments.
KAIRA configuration
KAIRA is a dual array of omnidirectional VHF radio antennas in northern
Finland. It consists of two closely located arrays working in the bands
between 10 and 80 MHz and between 110 and 250 MHz, using LOFAR antenna and
digital signal-processing hardware. Here we have used the former, which is
called the lower band array (LBA). The LBA consists of 48 crossed
inverted-V dipole antennas. Each of the signal channels, i.e., 96 including
the two linear polarizations, is directly sampled. After sampling the
signals are processed and combined in a variety of possibilities that could
combine frequency bands, antenna elements, and antenna pointing directions;
each such configuration is referred to as a “beamlet”. The specific
characteristics of KAIRA and the results, as stand-alone and as receiver
for other transmitters, can be found in .
The part of the experiment that we used in this paper consisted of 5 beamlets
all of them using all 48 LBA antennas pointing over MAARSY, i.e., -80∘
azimuth, and 68.20∘ zenith, with different center frequencies around
53.55 MHz, and a frequency width of 195.312 kHz, allowing an effective
sampling of ∼ 1 µs. Complex voltages for each beamlet were recorded
and later combined, decoded, arranged in range, and spectrally analyzed.
The whole experiment during this campaign consisted of 61 beamlets: 14
beamlets using 7 single selected antennas and 2 subbands around 32.55 MHz, 35
beamlets using the same 7 antennas as before but with 5 subbands around 53.5 MHz,
10 beamlets using two pointing directions over MAARSY and 5 subbands
around 53.5 MHz, and 2 beamlets in riometer mode using two different pointing
directions. The experiment was conducted for almost 3 days around 12 August 2016.
The main purpose of the experiment was to apply the MMARIA
(Multi-static, Multi-frequency Agile Radar Investigations of the Atmosphere)
e.g., in KAIRA, using MAARSY and
the Andenes specular meteor radar working at 32.55 MHz as transmitters,
respectively. Unfortunately, for the purpose of this work, only 5.5 h of the subbands around MAARSY were recorded, mainly due to the high
data volume. There were 14 TB of data recorded during these 3 days. The
results related to the MMARIA approach and the 32.55 MHz will be left for a
future effort.
Antenna patterns and geometric parameters for the MAARSY–KAIRA
multi-static configuration as a function of longitude and latitude at 85 km.
(a) MAARSY one way transmitting pattern, (b) KAIRA narrow beam pointing over
MAARSY, (c) total range, (d) Bragg wavelength, (e) distance with respect to
the middle point, and (f) the resulting zenith angle with respect to local
zenith. The locations of MAARSY and the middle point are indicated with a
square and triangle symbols, respectively.
Bistatic geometry and considerations
The scattering of interest will be given by the Bragg wavelength components,
i.e., λB, where |kB|=2π/λB and kB=ks-ki and ki and ks are the incident and
scattered wavenumbers with magnitudes 2π/λ, where λ is the
radar wavelength. The Bragg wavelength and the radar wavelength are related
by λB=λ/(2cos(θB/2)), where θB is the
scattering angle, i.e., the angle between ki and ks.
In Fig. , we show contour plots of selected parameters of
the bistatic geometry at an altitude of 85 km, as a function of longitude and
latitude. Specifically, we show (a) the normalized antenna gain of MAARSY,
(b) the normalized antenna gain of KAIRA, (c) the total range, (d) the Bragg
wavelength, (e) horizontal distance with respect to middle point, and (f) the
local scattering angle, i.e., the angle with respect to the local coordinate
system taking into account the geoid form of the Earth. By total range we
mean the distance from transmitter to scattering center plus the distance
from scattering center to receiver. In monostatic systems the range to the
scattering center is half the total range. The MAARSY and the middle point
between MAARSY and KAIRA are indicated by a square and a triangle,
respectively. Note that, contrary to monostatic configurations, the contours
are not symmetric with respect to the center point.
A simple version of the radar equation, assuming that the target fills the
radar beam, satisfies the Born approximation, and is located in the
far field, is given by
Pr=PtGt4πRi2VηAr4πRs2sin2δ,
where η is the radar scattering cross section, Pr is the received
power, Pt is the transmitted power, Gt the transmitted antenna pattern,
Ar the receiver effective antenna area, V is the scattering volume,
δ is the polarization angle, and Ri and Rs are the incident and
scattered ranges, respectively. Given that on transmission a right-circular
polarization was used, and on reception the power of two orthogonal linear
polarizations were employed, sin2δ=0.5+0.5cos2θB.
Taking into account the antenna patterns and replacing Ar=Grλ2/(4π), the bistatic backscatter power at a given total range R0 is given
by
Pr(R0)=Ptλ216π218π∫R0-cτ/2R0+cτ/2∫η(kB,h)(1+cos2θB)Gr(θx,θy)Gt(θx,θy)Ri2(Rs)2dΩdR,
where Gr is the receiver antenna pattern, R0=Rs+Ri, θx,θy are the direction cosines with respect to the receiver, c the
speed of light, and τ the pulse width. Note that we are assuming that
η has only a dependence on Bragg vector (kB) and altitude
(h), which is suitable for PMSEs. In addition, we assume that the
transmitted pulse and the receiver bandwidth have perfect square shapes.
Experimental parameters over MAARSY.
MAARSY–
MAARSY–
Parameter
MAARSY
KAIRA
Geometry
Monostatic
Bistatic
Transmitter elements
433
433
Receiving elements
433
48
Peak power
800 kW
800 kW
λB
2.8 m
3.3 m
PMSE mean range
85 km
294 km
Received power
relative to monostatic
0 dB
-26.90 dB
The main characteristics of the monostatic and bistatic observations over
MAARSY are summarized in Table . Note that the expected
difference in sensitivity between monostatic and bistatic, assuming isotropic
scattering and volume filling and considering range differences, is
∼ 26.9 dB.
Experimental results
In this section we present the results of the monostatic
and bistatic observations conducted with MAARSY and KAIRA on 12 August 2016.
In addition, we show the parameters that result from combining both systems.
PMSE height–time observations using MAARSY for transmission and
reception on 12 August 2016: (a) signal-to-noise ratio (SNR), (b) Doppler
shift (Hz), and (c) spectral width (Hz).
MAARSY monostatic observations
Figure shows the spectral parameters of 5.5 h of observations during this campaign: (a) signal-to-noise ratio (SNR)
in decibel scale, (b) mean Doppler shift (Hz), and (c) spectral width. The spectra
have been obtained with 1024 fast Fourier transform (FFT) points and 32 coherent integrations. In all
three measurements, we show only values satisfying a SNR greater than -6 dB.
Each range profile is obtained every 40 s. The Doppler velocities vary
between ±3 m s-1 with periods of a few minutes. The SNR shows a variety of
strong and weak and wide and narrow layers around 85 km. After 08:00 UT
clearly the echoing region gets wider and at least three narrow layers are
observed. The spectral widths show relatively low values with a median of
0.3 Hz and with little variability in both time and altitude, except for larger
values for the layer around 75 km at 04:30 UT, and the layers above
85 km between 06:30 and 07:00 UT.
In general these PMSE observations are typical of monostatic systems, MAARSY
being the most sensitive system able to measure echoes with the lowest RCSs.
In this particular case, the estimated PMSE RCSs are between
1.0×10-17 and 1.0×10-11 m-1. Recently
have reported observations of polar
mesospheric echoes during all seasons and pointed out the type of echoes that
were not observed previously with less sensitive systems, e.g., coexistence
of PMSEs4 with lower mesospheric echoes for a few weeks at the beginning of
PMSE season.
Another important feature in Fig. a is the variability of
SNR in both time and space. We will show later that such variability is
mainly due to horizontal variability and not to in situ temporal variability.
PMSE range–time observations using MAARSY for transmission and KAIRA
for reception on 12 August 2016: (a) signal-to-noise ratio (SNR),
(b) Doppler shift, and (c) spectral width. The approximate height is indicated on
the right, assuming the strongest echoes are observed over MAARSY. In (a) a
black line is plotted around 06:00 UT over a drifting structure (pointed by a
black arrow).
KAIRA bistatic observations
The corresponding KAIRA results are shown in Fig. . The
spectral parameters are similar to those shown for MAARSY in Fig. ,
but instead of altitude they are shown as a function of total
range. This time they were obtained every 20 s, and without any
coherent integration. The spectra have been estimated using 1000 FFT points
and 10 incoherent integrations. In the case of KAIRA we have used two
conservative criteria to select the data, i.e., an SNR threshold of -10 dB
and a coherence threshold of 0.25. By coherence we mean the coherence between
the signals in both linear polarizations without subtracting the noise in the
denominator. As a reference, we are plotting the corresponding height on the
right, assuming that all the echoes are observed over MAARSY. Clearly echoes
below 290 km in range do not come from regions over MAARSY since they would
have come from much lower heights.
To our surprise, we were able to observe echoes from ranges that do not
correspond to PMSEs illuminated overhead MAARSY, i.e., at ranges closer
than 290 km. The echoes, apparently originating from heights lower than the
PMSE heights, are clearly connected to the strongest echoes, which are located
at the true PMSE heights. The only plausible explanation is that these echoes
are normal PMSEs at normal PMSE altitudes, which are illuminated by the
side lobes of the MAARSY transmitter beam and originate from a larger
geographic area. This time the intensity of the echoes is clearly observed to
vary with time. Moreover, in the case of Doppler shift, it is mainly
negative,
varying with time and range. In the case of range, there is a systematic
dependence, being smaller at closer ranges. As in the case of MAARSY, the
spectral widths are relatively small over MAARSY (total range farther than
290 km) and vary significantly at closer ranges, particularly after 07:30 UT.
Around 05:40 UT we are plotting a black parabolic line over the observed KAIRA
PMSEs (pointed by the black arrow). This line has been obtained assuming that
a scattering center was originally located at 85 km in altitude at the middle
point between KAIRA and MAARSY and drifted horizontally at a constant
velocity. The velocity used is 68 m s-1 (from KAIRA to MAARSY), which is
obtained from the Doppler shift measurements (see below). The agreement
between the observed PMSE range–time behavior and this simple model is
excellent, implying that the PMSE structures are drifting with the background
horizontal wind.
Combined MAARSY and KAIRA measurements: (a) median SNR over MAARSY
as observed with MAARSY and KAIRA, and over the middle point; (b) MAARSY
vs.
KAIRA SNR scatter plot; and (c) bivariate distribution of MAARSY SNR
vs.
spectral width. The dashed lines indicate MAARSY's 30 dB SNR as a reference.
In panel (a), the mean horizontal wind over MAARSY in the direction MAARSY–KAIRA is
shown in blue.
Combined KAIRA–MAARSY PMSE measurements
Now we combine both measurements in this section. The peak values in range
after a three-point smoothing in time of the monostatic (MAARSY) and bistatic
(KAIRA) data, obtained from the same volume (overhead MAARSY), are shown in
Fig. a, in red and green, respectively. In the case of
monostatic results, altitudes between 80 and 87 km have been considered, while in the
bistatic case, total ranges between 287 and 297 km were considered. The
horizontal velocity over MAARSY (in the direction KAIRA–MAARSY, being
positive towards KAIRA) is shown in blue (right axis). The horizontal
velocity component in the direction MAARSY–KAIRA has been obtained from
KAIRA's Doppler shift (Fig. b) and MAARSY's vertical
velocity (Fig. b).
We can see that in general there is a good correspondence between the two SNR
time variations, particularly when MAARSY signals are strong. To observe this
feature better, in Fig. b we plot MAARSY vs. KAIRA peak
values in range used in Fig. a. In this plot we can
identify an approximate difference in signal between the two of ∼30 dB,
i.e., where KAIRA SNR is equal to zero, which we have marked with a vertical
dashed line.
Given that the spectral widths shown in Fig. c show a weak
dependence with respect to SNR for the majority of echoes, we present a 2-D
histogram of MAARSY's SNR and spectral widths with the counts in log scale.
The great majority of echoes have a strong variability in SNR with small
changes in spectral width. A smaller but detectable population is
characterized by an SNR that increases with increasing spectral width. Taking
into account the PMSE simulations shown in Fig. b, we
superimpose lines over these two populations and label them as
“ice dominated” (blue) and “turbulence dominated” (black), respectively.
One can argue that the part of Fig. c where spectral
width (proxy for turbulence intensity) increases with increasing RCS agrees
with the part of Fig. b for small Sc (black dashed
line with Sc=3). The other part of Fig. , that
covers the majority population, where narrow spectral widths can produce any
value of RCS, seems to agree with the horizontal line of Fig. b.
From this simple plot, we assume in the remainder of
the paper that most KAIRA detections come from scattering regions with
high Schmidt numbers. We are again marking the SNR threshold of 30 dB
identified before.
Derived PMSE parameters from combining MAARSY and KAIRA
observations, using a SNR threshold of 30 dB in MAARSY observations:
(a) vertical structure, (b) vertical velocity, (c) vertical structure as observed
from KAIRA, and (d) horizontal velocity along MAARSY–KAIRA direction
(positive towards KAIRA). Approximate distances of 100 km are indicated in
panel (a) with white lines. See text for details.
Note that the spectral widths have not been corrected by any effects, like
beam or shear broadening. Therefore, these values represent upper values of
atmospheric turbulence intensity.
Having defined an empirical SNR difference between KAIRA bistatic and MAARSY
monostatic of ∼30 dB, in Fig. we show the parameters
resulting from combining both observations: (a) vertical structure and
(b) vertical velocity after using a MAARSY SNR threshold of 30 dB, (c) vertical
structure over MAARSY as observed with KAIRA, and (d) inferred horizontal
velocity from KAIRA and MAARSY Doppler shifts. The thresholded MAARSY SNR
results show that the echoes come from a narrow region in altitude, appearing
and disappearing in time. After 07:00 UT a second narrow region appears at
lower altitudes, with larger RCS. The corresponding vertical velocity does
not show a distinct altitude dependence. In the case of KAIRA, the observed
structures are wide in range, as expected, due to the convolution of a narrow
layer with a wide receiver beam.
In the case of the horizontal velocity, the estimates are consistent when a
single drifting structure occurs, e.g., between 05:15 and 07:15 UT. When more
structures occur simultaneously, the estimated horizontal velocity gets more
complicated, e.g., at total ranges smaller than 280 km and times around
04:30 and 08:00 UT. Assuming that PMSE structures over MAARSY have horizontally
drifted with the obtained horizontal velocities, we have indicated 100 km
segments in Fig. a with white lines, namely for faster
flows the segments are shorter in time, e.g., around 06:00 UT.
Discussion
We start our discussion by arguing that KAIRA observations come from
scattering regions with high Schmidt numbers. By looking at the PMSE
simulations, a wide range of RCSs (more than 6 orders of magnitude) for a
constant turbulence intensity can be obtained by varying Sc
(see Fig. b). In the 5 h presented, MAARSY's observed PMSE SNR
show a variability of more than 50 dB (i.e., more than 5 orders of magnitude
in RCS). Such variability cannot be attributed to changes in other
parameters, e.g., electron density, atmospheric viscosity, ice density, and
density gradients. However, they can be easily obtained by having coexistent
ice particles with different radii (rA) and therefore generating different
Sc, i.e., rA=Sc/6.5 e.g.,. Therefore, given that KAIRA observations correspond to
MAARSY SNR greater than ∼ 30 dB, i.e., η>5×10-14 m-1,
we claim that such common observations arise from high Sc.
Previous multi-wavelength studies have been also focused on PMSEs with high
Sc e.g.,.
High Sc means that the observations occur in the viscous–convective
subrange and therefore the PMSE RCS will have a kB-3 (or
λB3) dependence at the Bragg wavelengths of interest, i.e.,
λB<3 m. In other words, we are ruling out a higher dependence on
λB at the wavelengths of interest, since such dependence will
require small Sc (see Fig. a). Our PMSE
measurements fall in the region between the green and red continuous lines in
Fig. a, i.e., covering Sc between 100 and 900
within a narrow region of RCS that spans about half an order of magnitude.
The red curve (Sc=900) is still in the power law regime, while the green
curve (Sc=100) is going down into the exponential regime.
Following these considerations, we now discuss the results related to PMSE
drifting structures and to the PMSE angular dependence, separately. In
addition, we briefly discuss other observed features and future plans.
PMSE drifting structures
The half-parabolic structures seen in Fig. a are typical
signatures of horizontally drifting structures. We have verified that this is
the case by overlaying the expected trajectory (total range vs. time) of a
structure drifting at a constant velocity at 85 km altitude, and the match is
perfect. To continue the analogy of a typical drifting echo, e.g., airplanes,
the left half of the parabolic signature is not observed given that the KAIRA
receiver beam points towards MAARSY (see Fig. b).
Therefore the left structures, i.e., between KAIRA and the middle point, are
below KAIRA's sensitivity.
The horizontal distance between the middle point and MAARSY at 85 km is
∼ 90 km. Our results also show that these PMSE structures with high Sc
have a limited volume of approximately 5–15 km of horizontal extent in the
KAIRA–MAARSY direction. Moreover, these PMSE “clouds” (limited-volume
structures) present horizontal separations ranging from 20 to 60 km. These
approximate distances and sizes have been obtained from Fig. a,
specifically from comparing the SNR structures with the
over-plotted 100 km estimated horizontal sections. It is important to stress
that the horizontal structures we have identified are for PMSEs with high
Sc. A more sensitive bistatic radar configuration would have observed
PMSEs all the time, i.e., without spatial gaps, but with varying RCSs.
The obtained horizontal and vertical features of PMSEs with high Sc are
consistent with NLC structures as known from observations with lidar, airglow
imagers, and ground-based NLC photography. For example, using lidars the NLC
half-power full-width in height is approximately 1 km e.g.,. Drifting NLC bright clouds with
horizontal separations between 10 and 40 km are also typical of NLC
observations e.g.,Fig. 2. A sketch of
what we are observing can already be found in Fig. . PMSE
clouds drift from the middle point between KAIRA and MAARSY to MAARSY. These
clouds are of different sizes and have different separations. KAIRA is only
able to observe the light brown clouds (PMSE with high Sc), while MAARSY
alone (i.e., monostatic) can observed the light brown and also the blue
clouds (PMSE with lower Sc). So, the empty regions observed by KAIRA are
not really empty; they are filled by blue clouds that are “invisible” to KAIRA.
NLC observations with high-resolution cameras from the ground imply that even
horizontal features with smaller scales should be measured by radar, less
than 1 km, and even at meter scales e.g.,.
Such scales, less than a kilometer, are not possible in the current configuration.
Recently, have been able to identify horizontal
structures with sizes around 1 km using radar imaging and antenna compression
techniques. We are planning to improve this resolution by using a combination
of compressed sensing and multi-input multiple
output (MIMO) techniques .
The drifting nature of PMSE structures has been hypothesized before and
sometimes characterized by simultaneous measurements at sites separated by
100–150 km e.g.,. Our
measurements are the first to show directly such drifting PMSE structures
with high Sc as well as the limited-volume horizontal sizes and
separations of few tens of kilometers between them.
Although our results are encouraging to further understand the temporal and
spatial characteristics of PMSEs and their relation to atmospheric dynamics
and chemistry responsible of such characteristics, more detailed observations
are needed. In our particular case, the whole PMSE region has experienced
almost the same horizontal wind with a strong component in the KAIRA–MAARSY
direction. This is not necessarily always the case; sometimes strong wind
shears are observed. For example using an EISCAT VHF tristatic experiment,
observed that the upper part of PMSE moved in the
opposite direction from the lower part. In that case, our observations would
have shown the left–right part of the parabola for structures going towards
KAIRA–MAARSY, assuming that the limited-volume structures are maintained and move
primarily in the KAIRA–MAARSY direction.
PMSE angular and wavelength dependence
A byproduct of our observations is the possibility of studying the angular
dependence of PMSE. As indicated in Fig. f, our bistatic
configuration allows for measurements with zenith angles ranging from
0∘ (middle point) to ∼ 33∘ (over MAARSY). To follow the
previous literature, here we also characterized the angular dependence as
follows
η(θ)∝exp-sin2θ2sin2θS.
Before 2014, we would not have expected to observe these echoes given the
high aspect sensitivity values reported in the literature, i.e.,
θS = 2–3∘, particularly when so-called spaced antenna methods were employed
e.g.,. Using a combination of
vertical and oblique beams, the resulting values vary significantly, i.e.,
θS=5–15∘ e.g.,. , using many
months of MAARSY multi-beam data, have hypothesized that PMSEs are
statistically due to localized isotropic scattering structures. Moreover,
their hypothesis has been supported by who observed
PMSE structures with sizes around 1 km, i.e., smaller than the illuminated
volume. Encouraged by the latter observations, we decided to add the MAARSY
PMSE observations to the originally planned MMARIA campaign with KAIRA, i.e.,
the results we present here.
To determine the angular dependence, first we calculate the expected angular
dependence, assuming isotropic scattering. Moreover, we are assuming a narrow
layer in altitude, centered at 85 km with a Gaussian width of 1 km. The
expected received power is obtained after numerically integrating Eq. (),
taking into account a range sampling of 300 m and
kB-3 dependence in η. We have simulated two scenarios: (a) assuming
ideal antenna patterns like those shown in Fig.
(Model 1) and (b) using a MAARSY antenna pattern with a random uniformly
distributed amplitude varying from 0.2 to 1 in all 433 elements (Model 2).
Model 2 simulates an extreme case of an antenna array with unmatched antenna
elements. Measuring the actual power levels of the antenna side lobes is not
an easy task. In both cases the range dependence has been already considered.
(a) Normalized power cuts as a function of total range for three
different time periods in Fig. a in red, green, and blue.
The expected relative power for an isotropic scattering is indicated in
black. (b) Power ratio between measurements and isotropic power. Fitted
curves centered at 0∘ are indicated in dashed-dotted lines.
In Fig. a we show the resulting normalized received
power as a function of total range for Model 1 and Model 2 with black solid
and dashed lines, respectively. The main difference between the two is the
expected received power arising from the side lobes, i.e., the closer ranges.
We compare the model profiles with three power profiles obtained from
measurements: measurement 1, along the black curve shown in Fig. a;
measurement 2, average power between 06:40 and 07:25 UT; and
measurement 3, average power between 07:30 and 08:30 UT. The resulting
measurement profiles are shown in red, green, and blue, respectively. In all
three cases, the profiles have been self-normalized to their peak value, which
corresponds to measurements over MAARSY.
Assuming that the same scattering center drifts from KAIRA to MAARSY and
remains unchanged during this time (a few tens of minutes), we proceed to
analyze their angular dependence by comparing the measurements to the model
outputs. The received power ratios, measurements over models, are shown in
Fig. b, with Model 1 in solid lines and with Model 2
in dashed lines. The color represents, as before, which measurements were
used. On top of the ratios with Model 1 we plot the
fits to Eq. () with dashed-dotted lines. The resulting θs values are
12.10, 12.80, and 13.19∘ for measurements 1, 2, and 3,
respectively. In the case of Model 2, θs is greater than 20∘,
but the obtained ratio profiles do not behave like Eq. ().
Using the same procedure in Model 1 (ideal antenna gain) for a MAARSY–MAARSY
configuration (monostatic), we found that the expected power ratio of MAARSY
measurements over KAIRA's measurements is 27 dB. Comparing this difference to
the empirically determined difference of 30 dB, the difference in power with
respect to isotropic scattering at 33∘ zenith angle is -3 dB, i.e., an
equivalent θs ∼ 27.55∘. In the case of MAARSY–MAARSY
configuration using Model 2 (imperfect antenna gain), the expected ratio is
21.39 dB, i.e., a difference of 8.61 dB at 33∘ and
θs ∼ 15.87∘. In both cases, the actual values could be a few dB less if the
real antenna pattern of the KAIRA dipoles were included.
As one can see, we obtained different values of θs depending on what
portion of the data we use and which assumptions we make. From a simple
inspection, Model 2 qualitatively has a better agreement with observations,
i.e., power levels are almost constant at large zenith angles. However, when
compared to the angular dependence of Eq. (), the agreement is
better with Model 1. We have assumed that the same PMSE structure drifts
without changing much from KAIRA to MAARSY. Moreover, the PMSE clouds are
elongated in the north–south direction and drift mainly in the zonal
direction. In reality this might not be the case, since we cannot measure
the horizontal velocity transverse to the KAIRA–MAARSY direction, and PMSE
RCSs might have changed, spatially and temporarily, during the drifting
process. Typically, correlation times of 2.8 m PMSE irregularities are on the
order of seconds, while the observed kilometer-scale drifting structures
appear to be frozen for a few tens of minutes. The deviation from our
assumptions, i.e., the spatial and temporal evolution of PMSE RCS, might be
the main reason for the lack of consistency of the angular dependence using
different methodologies.
In general, the results are not perfectly consistent; i.e., we cannot
explain all the observations with the simple Gaussian model of Eq. ().
However, we can conservatively conclude that our
measurements indicate that by using the simple Gaussian model, the true
θs for this event is greater than 12∘; i.e., the scattering
cannot be considered highly aspect sensitive. These results are in general
consistent not only with previous multi-beam experiments but also with the
suggestion by ; i.e., PMSE scattering is in general
not highly aspect sensitive as previously reported, but instead the
scattering is due to limited-volume (localized) isotropic structures.
The small differences between our estimates and the suggestion of
, i.e., between slightly isotropic and isotropic,
might be due to (a) unknown behavior of the antennas at the side lobe levels
and/or (b) selection of PMSEs with high Sc. For the former, estimating the
actual gain of side lobes is not trivial given that the mutual coupling of closely
located neighboring antennas is hard to characterize. In case of the latter,
included all PMSE measurements during a month, with
varying Sc; therefore the structures with larger Sc could be less
isotropic than structures with lower Sc.
Other features and future plans
In our results, we have used existing PMSE scattering theories, all of them
showing a well-defined kB-3 for the meter-scale irregularities at high
Sc (viscous–convective subrange) and an exponential decay at smaller
scales (viscous–diffusive subrange) (see Eq. ). In the
viscous–diffusive subrange all theories show that RCS increases with
turbulence intensity. However, in the viscous–convective subrange, our
simulations show that PMSE RCS decreases with increasing turbulence intensity
(see Fig. b) in the viscous–convective subrange. Such
behavior is not reproducible using the expressions provided by
and . Although difficult to
validate observationally, unless the other parameters are measured (e.g.,
electron density, density and ice gradients), we think it is worth
investigating such behavior, both theoretically and experimentally.
In Fig. c, we show two well-separated populations of polar
mesospheric echoes in the summer based on their SNR vs. spectral width
behavior, i.e., RCS vs. turbulence intensity. The ice-dominated population
belongs to the majority of PMSE events previously reported. The
turbulence-dominated echoes correspond to (a) echoes occurring below the
typical PMSE altitudes, in our case around 75 km, and (b) echoes occurring at
the top of PMSEs, presumably with small particles sizes, i.e., small Sc. A
similar behavior has been shown using EISCAT 224 MHz by
. In the case of the echoes occurring around 75 km,
they might not strictly speaking be called PMSEs, but their existence,
besides enhanced turbulence, might require a way to reduce their diffusion
time. The altitude is too low for ice, though. Its existence might be related
to some of the mesospheric echoes observed at equatorial latitudes
e.g., and polar mesospheric echoes observed in
winter e.g., that cannot be explained by
pure turbulence arguments.
In future experiments, we plan to improve the measurements by focusing on
PMSEs and making better use of MAARSY and KAIRA capabilities. For example, we
plan to steer MAARSY in different directions towards KAIRA and generate also
different KAIRA beams towards MAARSY simultaneously. In this way, we would
improve the quality of the observations, the spatial coverage, and the
angular dependence. This type of observations would be a good complement to
current NLC studies from the ground, since they can be done independently of
weather conditions as long as there are some electrons and sufficient ice
particles with relative large radius (i.e., high Sc). Moreover, the MAARSY
observations close to overhead bring the additional advantage that it allows
for the observations of echoes due to ice particles with smaller sizes than
those responsible of NLCs. Besides the improved PMSE characteristics, the
proposed improved experiments would also allow wind field measurements around
the summer polar mesopause with unprecedented temporal and spatial
resolutions. Instead of specular meteor echoes, one could applied the MMARIA
approach e.g., to PMSE
observations at multiple locations and from different observing angles.