ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-35-393-2017High-resolution coherent backscatter interferometric radar images of equatorial spread F using Capon's methodRodriguesFabiano S.fabiano@utdallas.edude PaulaEurico R.ZewdieGebreab K.W. B. Hanson Center for Space Sciences, The University of Texas at Dallas, Richardson, TX, USAInstituto Nacional de Pesquisas Espaciais – INPE, São José dos Campos, SP, BrazilFabiano S. Rodrigues (fabiano@utdallas.edu)14March20173533934029August201620February201723February2017This 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/35/393/2017/angeo-35-393-2017.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/35/393/2017/angeo-35-393-2017.pdf
We present results of Capon's method for estimation of in-beam images of
ionospheric scattering structures observed by a small, low-power coherent
backscatter interferometer. The radar interferometer operated in the
equatorial site of São Luís, Brazil (2.59∘ S, 44.21∘ W,
-2.35∘ dip latitude). We show numerical simulations that evaluate
the performance of the Capon method for typical F region measurement
conditions. Numerical simulations show that, despite the short baselines of
the São Luís radar, the Capon technique is capable of distinguishing
localized features with kilometric scale sizes (in the zonal direction) at
F region heights. Following the simulations, we applied the Capon algorithm
to actual measurements made by the São Luís interferometer during a
typical equatorial spread F (ESF) event. As indicated by the simulations, the
Capon method produced images that were better resolved than those produced by
the Fourier method. The Capon images show narrow (a few kilometers wide) scattering
channels associated with ESF plumes and scattering regions spaced by only a
few tens of kilometers in the zonal direction. The images are also capable of
resolving bifurcations and the C shape of scattering structures.
Radio science (interferometry; ionospheric physics; instruments and techniques)Introduction
Equatorial
spread F (ESF) refers to a broad spectrum of electron density irregularities
occurring in the equatorial and low-latitude F region ionosphere. ESF is
associated with interchange plasma instabilities, which can create large-scale (tens
of kilometers) sizes plasma density perturbations. Secondary plasma
instabilities then create smaller-scale (down to centimeter) irregularities
. While the overall features of ESF are well-understood,
we still seek a better understanding of the processes leading to the
variability in the generation, development and decay of ESF events. In
addition to the scientific aspect of studying instabilities in space plasmas,
the investigation of ESF is also motivated by its impact on the propagation of
trans-ionospheric radio waves such as those used for remote sensing,
navigation and communication e.g.,.
Ground-based ionospheric radars have contributed significantly to our
understanding of ionospheric plasma and irregularities. Ionospheric radars
are used to measure the scatter from electron density irregularities matching
the Bragg scatter condition. Because these radars usually operate in the VHF
and UHF bands, the scatter comes from irregularities in scale sizes ranging
from a few meters down to a few tens of centimeters.
Incoherent scatter radars are high-power, large-aperture systems that can
measure extremely weak echoes produced by thermal electron density
fluctuations. Coherent scatter radars, on the other hand, are smaller systems
capable of measuring echoes produced by non-thermal electron density
fluctuations, that is, fluctuations caused by plasma instabilities.
Conventional coherent radar measurements are capable of providing
information about the altitudinal distribution of irregularities, as a
function of time, as well as the mean radial phase velocity of the
irregularities producing the echoes. Additionally, conventional coherent
radars provide information about the strength of plasma turbulence at the
wavelength matching the Bragg condition.
Radar measurements made using spaced antennas can provide additional
information about the irregularities causing echoes e.g.,.
Using multiple baselines, one can estimate the two-dimensional distribution
(zonal distance versus height) of the scatterers responsible for the observed
echoes using interferometric imaging techniques. Coherent scatter radar
(in-beam) images can help us understand the underlying plasma processes
responsible for ionospheric disturbances, including those associated with ESF.
Radar images can also be used to help validate theoretical predictions of
equatorial spread F e.g.,.
Coherent backscatter radar imaging has been used for investigations of
equatorial spread F. These investigations have been performed, predominantly,
in the Peruvian longitude sector using measurements made by the radar and
antenna modules of the Jicamarca Radio Observatory
e.g., with only a couple of
exceptions . Initial studies used
Fourier-based analyses of the measurements . More advanced
techniques, using the maximum entropy algorithm (MaxEnt), were implemented by
. Since then, the MaxEnt technique has been improved, well
tested and is now commonly used at Jicamarca. and
have also proposed that the Capon method can be used to create
interferometric images of scattering structures producing coherent scatter
echoes. The implementation of the method is simple, not computationally
intensive and produces images of the scattering regions with a much higher
spatial resolution than those produced by the Fourier method. Despite the
encouraging results of and , limited efforts
have been made to use the Capon method in ionospheric studies. An exception
is the work of , which used the Capon method and other techniques
to create radar images of electrojet irregularities.
In the present study, we revisit the Capon method and investigate its
performance when applied to measurements made by a small, low-power coherent
backscatter radar interferometer located at the equatorial site of São
Luís, Brazil. We show that the method can produce high-resolution images,
which reproduce features predicted by numerical simulations and previous
observations of interchange plasma instabilities. This report is presented as
follows: Sect. 2 describes the setup used by the São Luís radar for
interferometric measurements. Section 3 provides information about the
Fourier and Capon methods for interferometric imaging. In Sect. 4, we present
and discuss the results of analyses. Numerical simulations are used to
evaluate the performance of the Capon method. We also present and discuss the
results of applying the Capon algorithm to actual measurements made by the
São Luís radar during a typical pre-midnight ESF event. The features in
the scattering structures resolved by the Capon method are discussed in light
of our current understanding of ESF. Finally, Sect. 5 summarizes the main
results of our study.
Measurements
The measurements available for this study were made by a 30 MHz coherent
backscatter radar interferometer. The radar was installed at the equatorial
site of São Luís, Brazil (2.59∘ S, 44.21∘ W,
-2.35∘ dip latitude) and operated between 2000 and 2012. The São
Luís radar is a low-power radar system that was used for studies of
equatorial ionospheric irregularities in the E and F regions
. Starting in 2005, the radar was
equipped with four independent antenna sets connected to four receivers.
Each antenna set is formed by an array of four by four Yagi antennas. The
arrays have been placed non-uniformly in the magnetic zonal direction for
radar imaging studies of scattering layers. Figure
shows the distribution of the antennas in the magnetic zonal direction. The
longest baseline is 150 m, that is 15λ, where the λ is the
wavelength of the 30 MHz radar signal. Two 4 kW transmitters are available
for observations and were normally used for F region measurements.
Diagram describing the distribution of the antenna sets used for the
interferometric observations. Each antenna set is formed by a four by four array of Yagi antennas. A, B, C and D represent the antenna sets.
Transmissions are made with sets A and B. Reception is made with all of the
antenna sets. The magnetic declination is approximately
21∘ W.
For F region observations, we used 28 bit coded pulses, with a 9.33 ms
inter-pulse period (IPP). The baud length and sampling were 2.5 km. A total
of 250 samples were collected per IPP. This observation setup allowed us to
make measurements of the F region from 200 to 825 km altitude with a range
resolution of 2.5 km.
Analysis
Coherent scatter radar imaging techniques have been used to determine the
distribution of scatterers as a function of height and zenith angle (ψ)
e.g.,. The real-valued,
continuous function representing this distribution is referred to as
Brightness distribution B(ψ), and it is computed for each range gate.
The brightness distribution is closely related to the cross correlation of
scattered signals received by antennas spaced by a distance d. A commonly
used estimator for the normalized cross correlation of signals measured by
spaced antennas 1 and 2 is given by
V(kd)=v1v2*|v1|2-N1|v2|2-N2,
where the angle brackets represent an ensemble average. In practice, time
averages are used, with v1 and v2 being complex-valued voltage samples
measured by antennas 1 and 2, respectively. N1 and N2 are estimates of
the noise power in each receiver, and k=2πλ with
λ is the wavelength of the radar signal.
In imaging, the spatial cross-correlations V(kd) are referred to as
visibility measurements. For the case of ionospheric imaging, where the
scatters are assumed to be two-dimensional due to the nature of field-aligned
irregularities, the relationship between visibility and brightness is given
by
V(kd)≈∫-∞+∞B(ψ)ejkdψdψ.
The visibility is the correlation of the scattered signals received by
antennas spaced by a distance d.
One can recognize that Eq. (2) represents a Fourier-type integral, and,
therefore, the brightness can be estimated from the visibility function using
the inverse Fourier transform:
B(ψ)=∫-∞+∞V(kd)e-jkdψd(kd).
In the practical case of a finite number of receivers (n), the Fourier
transform estimate of the brightness distribution (B^f) can
be obtained from B^f(ψ)=wfHVwf,
where H denotes the Hermitian operator, V is the n×n
visibility matrix, and wf is the weight (or pointing)
vector given by
wf=ejkd1ψejkd2ψ…ejkdnψT,
where di is the distance of receiver i to a reference point and T
denotes the transpose operator.
Ionospheric radar images are obtained by computing the brightness function
for each range gate independently. The images, therefore, represent the
distribution of ionospheric irregularities causing echoes, as a function of
range and zenith angle. The brightness functions can also be obtained for
different Doppler shifts adding a new dimension to the images. A sequence of
images can be used to track the appearance, development and decay of
scattering regions and to understand the dynamics of the irregularity
structures.
The Capon method
The angular resolution of the
images obtained with the Fourier method is limited by the length of the
longest baseline. proposed a new technique to obtain images
with higher angular resolution than those provided by the Fourier method. The
technique is based on the spectral analysis approach proposed by
. The method selects the set of weights
(wc) that
will not only provide a high-resolution spectrum but will also suppress the
effects of interfering signals. The set of weights is obtained by setting the
search for the brightness distribution as a constrained optimization problem.
The Capon weights are such that they minimize interference from signals
outside the direction of interest. A detailed description of the derivation of
the Capon method is given by and . They show
that the Capon set of weights is given by
wc=V-1eeHV-1e,
where e=ejkd1ψejkd2ψ…ejkdnψT. Note that, unlike the conventional Fourier
transform, the Capon weights depend on the visibility data. Therefore, the
Capon technique can be described as an adaptive method. The Capon weights
lead to an estimate of the brightness function given by
B^c(ψ)=1eHV-1e.
Despite being a technique that is computationally simple to implement and to
execute and despite the encouraging results obtained by and
, the Capon method has not yet been widely used in
ionospheric irregularity studies. The potential of the technique and
availability of measurements motivated our investigation of the performance
of the Capon method when applied to measurements made by a low-power,
short-baseline radar interferometer such as those provided by the São
Luís radar.
Results and discussionNumerical simulations
Before obtaining imaging results from actual measurements, we investigated
the ability of the Capon method to produce accurate estimates of the
distribution of the irregularities. We considered the specific case of the
São Luís baseline setup and created synthetic visibility distributions
for different scattering geometries (brightness distributions) under
different levels of measurement errors.
Numerical simulations of the Fourier and Capon methods under
different SNR conditions. The simulated brightness
function is described by a Gaussian function centered at 1.5∘ with an angular width of 2∘.
Measurement errors for normalized correlations were taken into account
considering typical SNR values
observed during ESF events and the number of incoherent integrations (K)
used in the ESF observations made by the São Luís radar.
The expected value for the error variances of the normalized correlation
functions (ρ) are given by e.g.,|ρ^-〈ρ^〉|2≈1KS+NS2[1+12|ρ^|21+SS+Nρ2-2SS+N|ρ|2],
where K=800, for typical F region observations made with the São
Luís interferometer. For this analysis, we assumed that the errors in noise
estimation were negligible and that the errors in the visibility estimates
were statistically independent.
In order to evaluate the potential of the Capon method, two scenarios were
considered in our simulation analysis. These two scenarios illustrate the
weaknesses and strengths of the Capon method.
Numerical simulations of the Fourier and Capon methods under
different SNR conditions. The simulated brightness
function is described by two Gaussian functions centered at ±1.5∘
and an angular width of 0.2∘.
The first simulation scenario considered a broad distribution of scatterers
(brightness) that is described by a Gaussian function, centered at
1.5∘ zenith angle. The Gaussian function has an angular width
(σ) of 2∘. Figure shows the results of the
inversions of this simulated brightness function using the Capon method for
different SNR conditions. It also shows results of the inversion using the
Fourier method and the true brightness function. Each panel only shows the
result of a single realization of the inversion for the SNR condition
indicated at the top of each panel. The results shown in
Fig. indicate that, for the São Luís setup and a broad
brightness distribution function, the Fourier and Capon methods have similar
performances for most of the SNR values considered in the simulations. Both
methods are capable of retrieving adequate information about the brightness
distribution, at least for conditions of SNR >-5 dB. For
SNR ≤-5 dB, little similarity (low correlation) was found
between the inversions and the true brightness distribution.
The second simulation scenario presented here considered a scattering region
that is described by two Gaussian distributions centered at ±1.5∘
off zenith. In this case, the ability of the Capon method to resolve closely
spaced, narrow features was investigated, and the angular width of each
scattering center was set to 0.2∘. Figure shows
the results of the simulations for the narrow brightness distributions. In
this simulation scenario, the Capon technique shows its strength, that is,
the high resolution. The Capon method was able to better resolve the narrow
structures than the Fourier method even under conditions of very low SNR
(∼-5 dB). The length of the longest baseline (15λ) of the
São Luís interferometer, on the other hand, severely limits the angular
resolution of the Fourier inversions, and the narrow spectral features cannot be
properly resolved even under high SNR conditions.
Figure summarizes our simulation results and our
evaluation of the performance of the Capon and Fourier methods as a function
of SNR. The performance of the inversion is quantified by the normalized
correlation (Pearson correlation coefficient) of the inverted brightness and
the true brightness. It shows the average value of the normalized
correlation of inversions with the true brightness distribution as a function
of SNR conditions. The average for each SNR is the result of 1000
realizations. The results are shown for the two scattering distribution
scenarios described above. The top panel shows the results for one single
broad brightness distribution and the bottom panel shows the results for two
narrow brightness centers.
Simulation results describing the performance of the Fourier and
Capon methods as a function of SNR conditions for two scattering
distribution scenarios: (a) the brightness distribution is described
by a single wide Gaussian function and (b) by two narrow Gaussian
functions. Each correlation estimate is an average of correlations obtained
for 1000 simulations.
Figure a shows that, for a broad scattering distribution
and the setup of the São Luís interferometer, the Capon method does not
outperform the Fourier method. In fact, its ability to recover the correct
brightness distribution is slightly inferior for most SNR conditions. At
very low SNR conditions (SNR < 0 dB), the ability of the Capon
method to recover the brightness distribution decreases substantially, and is
more clearly outperformed by the Fourier method. Both methods, nevertheless,
are capable of recovering the correct brightness with high accuracy given
echoes with adequate SNR. The normalized correlations are greater than 0.9
for SNR ≥ 0 dB.
Figure b shows simulation results for the case of two
narrow scattering structures. The results show that, for this case, the Capon
method provides more accurate inversions than the Fourier method for SNR
levels greater than -5 dB. The accuracy of the inversion does not exceed a
correlation of approximately 0.72 even for SNR = 20 dB. The accuracy,
however, could be improved further by reducing the error in the correlation
estimates. The error can be reduced, for instance, by adjusting the IPP and increasing the number of incoherent integrations
(K).
Panel (a) shows the range–time–intensity map of F region
observations made by the São Luís radar on 24 November 2005.
Panels (b, c) show the images obtained with the Fourier
transform (b) and Capon methods (c) for observations from
21:14:31 LT. Zonal distance is positive to the east. The estimated images
are scaled by the SNR of the echoes. The Doppler information is encoded in
the pixel colors. The green components represent small mean Doppler
velocities. Red and blue components represent irregularities moving away and
towards the radar, respectively.
The results shown in Fig. confirm the inferences we made
based on simulations presented in Figs. and
. The Capon method shows its strength when estimating the
brightness distribution of localized scatterers. It is capable of identifying
multiple structures with widths that are just a fraction of a degree and
that cannot be adequately retrieved with the Fourier method. The ability of
the Capon method to produce high-resolution radar images agrees with results
of previous studies e.g.,. , in particular,
found that even an interferometer with a limited number of short baselines
can produce estimates of the brightness distribution that are highly
correlated with the true distribution. Similar to our results, they also
found that, for localized scatterers, the Capon method outperforms the
Fourier method especially when conditions of SNR > 0 dB are
considered. showed that, even for conditions of high SNR and
a large number of well-spaced receivers, the correlations between Capon and
true brightness distributions can be significantly less than 1. We also found
that even for SNR = 20 dB the normalized correlation is around 0.72.
Finally, also found that the performance of the Fourier method
does not change much for SNR >-5 dB.
In-beam radar images
We have also analyzed the results of the Capon method applied to actual
interferometric measurements made by the São Luís radar. We applied our
Fourier and Capon algorithms to ESF measurements made by the São Luís
radar. For this study, we present results of our analysis of a well-developed
ESF event observed by the São Luís radar on the night of
24 November 2005. We present and discuss some of the features of the
scattering structures resolved by our Capon algorithm.
Capon and Fourier inversions
Figure a shows the
range–time–intensity (RTI) map of the echoes observed on 24 November 2005.
The RTI map shows bottom-type irregularities starting around 19:15 LT at
approximately 250 km altitude. Topside irregularities start to be observed
around 20:45 LT, with echoes reaching as high as 650 km altitude.
The São Luís data consisted of cross-spectral measurements for four
spectral bins, which allowed us to infer information about the line-of-sight
Doppler velocity of the scatterers, in addition to their location.
Two-dimensional in-beam radar images are constructed by stacking
one-dimensional brightness distributions B(ω,ψ) estimated for each
range gate e.g.,.
Figure b and c show the in-beam
images produced by our algorithms for measurements made at 21:14:31 LT. The
left panel shows the image produced by the Fourier method, while the right
panel shows the image produced by the Capon method.
The estimated images are scaled by the SNR of the echoes. The Doppler
information is encoded in the pixel colors. The green components represent
small mean Doppler velocities. Red and blue components represent
irregularities moving away and towards the radar, respectively.
Both images show a topside ESF structure that, as will be shown later,
drifts from west (left-hand side) to east. The images also show that the
structure is tilted to the west, and this is, presumably, caused by height
variations in the zonal plasma drifts. More importantly, one can see that the
Capon method produces a better-resolved image than the Fourier method. In
some range gates, the Fourier images show artifacts in the brightness that
are intrinsic to the method. For instance, the simulations in Fig. 3 show an
increased brightness outside the scattering region produced by the sidelobes
of the Fourier estimates even under high SNR conditions.
Panel (a) shows the RTI map of
F region observations made by the São Luís radar on 24 November 2005.
Panel (b) shows a sequence of images obtained with the Capon method
and interferometric observations. The time for each image is indicated above
each panel and as vertical white lines in the RTI map.
The Capon image shows the scattering region is narrower (in the zonal
direction) than what is presented by the Fourier image. The Fourier image
shows scattering features that are broad and diffuse; a result of the short
baselines used for visibility functions. This is particularly true for the
strong scattering channel seen above 350 km altitude. The colors also
indicate that irregularities are ascending with large velocities within the
scattering structure.
Finally, we must point out that the images were produced with the same number
of incoherent integrations used in our simulations (K=800). This requires
an integration time of approximately 30 s. The zonal motion of the
irregularities during the integration time can affect the resolution of the
images. Considering a zonal irregularity velocity of about 100 m s-1,
the spatial resolution in the zonal direction will be limited to 3 km, or
approximately 0.5∘ in the zenith angle for scatterers at 300 km
altitude. Note, however, that the effects of irregularity zonal drifts in the
angular resolution will be reduced at higher altitudes. Slower zonal drifts
at lower altitudes (bottom-side F region) associated with the evening vortex
e.g., will also reduce the degradation in the angular
resolution.
Zonal motion and multiple plumes
Figure shows a sequence of images created using the Capon
method for measurements made between 20:50 and 21:03 LT. The sequence serves
to illustrate the ability of the Capon method to produce images that provide
accurate information about the dynamics of ESF irregularities. The images
show, initially, a scattering structure entering the field of view of the
radar moving from the west. The sequence of images shows that the scattering
structure moves in the zonal direction at a rate of about 130 m s-1.
The scattering structure is thought to be embedded within (or along the walls
of) large-scale plasma depletions. Therefore, its motion reflects the motion
of the underlying large-scale depletion, which has been suggested to be a good
tracer of the zonal plasma motion . We found that the
direction and magnitude of the irregularity drift matches expectations based
on previous observations. Measurements of the background plasma zonal drifts
made by the Jicamarca incoherent scatter radar show average values around
120 m s-1 for similar times (21:00 LT) and solar flux conditions
(∼ 90 SFU) e.g.,.
Panel (a) shows the RTI map of
F region observations made by the São Luís radar on 24 November 2005.
Panel (b) shows a sequence of images obtained with the Capon method
and interferometric observations. The time for each image is indicated above
each panel and as vertical white lines in the RTI map.
At 20:59:59 LT one can start to identify two vertically developed ESF
structures, spaced in the zonal direction, within the radar field of view.
The two structures are more clearly seen at 21:01:45 LT. The first
(easternmost) structure reaches about 400 km altitude, while the second
structure reaches over 500 km altitude. The measurements were made during
low solar flux conditions when the altitudinal reach of ESF structures is
limited e.g.,. Previous studies suggest that the zonal
wavelength of the initial perturbation (seed wave) controls the spacing
between plumes e.g.,. These studies
focused, in general, on scale sizes of a few to several hundreds of kilometers.
, on the other hand, suggested that a collisional shear
instability operating in the bottom-side equatorial F region can produce
transient plasma perturbations with deca-kilometric zonal scale sizes. Our
results show that ESF channels spaced by approximately 50 km (see
Fig. at 21:01:45 LT) can be detected, and these scale
sizes should be taken into consideration in theories explaining the
initiation and morphology of ESF structures.
We point our that the multiple structures seen in the in-beam images could
not be inferred from the RTI map. The RTI map alone would suggest that a
single radar plume passed over the radar site around 21:00 LT. Also,
the detection of multiple plumes within the radar field of view is possible
because of the large east–west beamwidths of the antennas used by the São
Luís interferometer.
Bifurcation and C-shaped structures
Figure shows another sequence of images obtained with the
Capon algorithm but now for times between 21:03 and 21:13 LT. As shown in
the previous sequence, the scattering region continues to move in the
eastward direction. Around 21:07 LT, the imaging results allow us to
identify a bifurcation of the scattering structure starting at about 375 km
altitude. Bifurcation in ESF structures is thought to be caused by a
secondary interchange instability occurring on the leading “head” of the
ESF plasma depletion as it rises into the main F region and topside
e.g.,. One can see regions of large upward
flows (red spots) within the first (east) branch of the bifurcation between
21:03 and 21:06 LT. Then, echoes are mostly broad and weaker. By 21:12 LT
there are no echoes associated with the first branch. As the structure moves
to the east, the images also show the development of the second (west)
branch. Well-defined, large flows (red and blue spots) are seen again within
the west channel as it reaches higher altitudes. By 21:12 LT, only the west
branch is seen in the images.
In addition to bifurcation, the images produced by the Capon method are
capable of resolving the C-shape structure of the ionospheric perturbation,
which has been predicted by numerical models of ESF e.g.,
and observed using the ALTAIR steerable radar e.g.,. The
sequence in Fig. shows that the scattering structure is
tilted to the east from about 200 to 300 km altitude. Then, above 300 km,
the tilt is westward. This is clearer in the image at 21:08:30 LT. The
tilt is a signature of complexities in the height variation of the zonal
plasma velocity. It suggests a maximum in the zonal velocity around 300 km.
This variability in the zonal drifts is caused by height variations in the
vertical component of the electric field (EL), which in turn is controlled
by variations, as a function of apex height, of flux-tube integration
parameters such as Hall and Pedersen conductivities (ΣH and
ΣP), conductivity-weighted zonal wind velocity
(UϕP), and equatorial zonal electric field
(Eϕ) and currents (JL) :
EL=ΣHΣPEϕ-BUϕP+JLΣP,
where B is the geomagnetic field intensity, which also varies with height.
Conclusions
We investigated the application of the Capon method
to obtain in-beam images of scattering regions
from measurements made by a small (maximum baseline of 15λ),
low-power (maximum transmitter power of 8 kW) coherent backscatter radar
interferometer.
Numerical simulations were used to evaluate the performance of the Capon
method. The numerical simulations show that, for broad scattering structures
and the São Luís antenna configuration, the Capon method does not
outperform the simple Fourier method. The simulations also show, however,
that the strength of the Capon method lies in its ability to identify
localized (narrow) scattering structures. We found that images with an angular
resolution of a fraction of a degree can be obtained for typical equatorial
spread F (ESF) measurement conditions found with the São Luís radar setup
using the Capon algorithm. In practice, the resolution is also controlled by
the magnitude of zonal irregularity drift during the integration time.
Following the simulation analyses, we applied the Capon method to actual
measurements made by the São Luís interferometer during a typical ESF
event detected on 24 November 2005. The Capon technique produces sharper
images than those created by the Fourier method and better resolves the
actual widths of the scattering structures.
Sequences of images show consistency from one inversion to the next
indicating the robustness of the method. The sequence of images also shows the
occurrence of ionospheric phenomena with better spatial and temporal
resolution than would be possible with other types of instruments (e.g.,
scanning radars or airglow imagers). The images show scattering channels with
zonal widths of a few kilometers. As expected from previous observations, the
scattering structures move to the east as they evolve in time. Scattering
channels spaced by only a few tens of kilometers in the zonal direction can be
resolved, and their occurrence should be taken into consideration in theories
and the description of ESF. The Capon images are also able to reveal the
occurrence of bifurcation in ESF structures as well as variations in the
zonal tilt of the scattering channels.
It is believed that the MaxEnt technique can produce images with more
accuracy than the Capon method, particularly for conditions of low SNR
. The Capon method, however, is computationally inexpensive
with the potential to be used in near real-time observations, needed, for
instance, during scientific rocket campaigns. Future work includes the
implementation of compressed sensing e.g., and MaxEnt
algorithms for comparison with Capon inversions given the São Luís
interferometer setup.
The interferometric radar data used in this study are available
upon request from Fabiano Rodrigues (email: fabiano@utdallas.edu).
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported by NSF (AGS-1261107) and AFOSR (FA9550-13-1-0095).
Eurico R. de Paula acknowledges the support from CNPq under process number
310802/2015-6. The authors would like to thank A. Cunha for their efforts in the operation and maintenance of the São Luís radar. The topical editor, P. J. Erickson, thanks two anonymous
referees for help in evaluating this paper.
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