Introduction
Radars have proven to be important tools for investigating dynamic processes
of different temporal and spatial scales in the lower and middle atmosphere
e.g.,. Frequencies ranging
from MF (medium frequency – 3 MHz) to UHF (ultrahigh frequency – 3 GHz) are
the most common for studying dynamic processes and structures in the neutral
atmosphere.
In general, VHF (very high frequency) and UHF stratosphere–troposphere (ST)
clear-air radar returns are sensitive to electromagnetic refractive index
fluctuations, which depend primarily on variations of the atmospheric
parameters temperature (T), relative humidity (RH), and pressure (P) at Fourier
scales of half the radar wavelength e.g.,. Radar returns
can be due to isotropic fluctuations in T and RH associated with active
turbulent mixing or anisotropic sheets of stable stratification at a scale
of several meters . Coupled with typical radar
vertical resolutions (100–200 m) that are large compared to the vertical
scales of these disparate phenomena, it has been difficult to infer what
phenomena the radar returns represent. Frequency-modulated continuous-wave (FM-CW) radars are high-resolution and
highly sensitive instruments that allow the study of the
fine-structure atmosphere with typical resolution of 1 m but only up to
1–2 km. There have been other studies or campaigns that aim to detect
turbulent layers in the troposphere and stratosphere with reasonable
resolution: used high-resolution pulse scanning to improve
the range resolution (∼ 30 m), detected turbulent layers
above the tropopause with a 20 m radar resolution, and
used digital deconvolution to achieve wind profiler measurements with 60 m
resolution
Additional measurements are clearly needed, both at higher resolution and
with complementary sensitivities to the phenomena of interest.
examined the conversion from structure function parameter
of refractive index (Cn2) to kinetic eddy dissipation rates (ϵ)
from Buckland Park radar data by using in situ high-resolution thermosonde
data (∼1 m) to optimize the measurement accuracy.
Other work has compared the backscatter echo received by radar (at 50 m
resolution and corrected for range attenuation effects) with the square of
the mean vertical gradient of the generalized potential refractive index
(obtained from high-resolution radiosonde balloons) and references
therein. These have produced excellent correspondence
under particular atmospheric conditions with persistent horizontal structure,
where the large (many km) separation between an advected balloon and the
radar beam are inconsequential.
In the present work, we describe significant improvements in measurement
resolution and coincidence between VHF radar returns and in situ measurements
in the lower troposphere.
The SOUSY (SOUnding SYstem) VHF radar is a powerful tool with which to study the
troposphere and stratosphere ,
and its observations include wind fields, frontal zones and tropopause
height, cumulus convection, gravity wave source mechanisms, and
jet-stream-generated dynamic instabilities and turbulence. After its installation
at the Jicamarca Radio Observatory (JRO), there have been two main
modifications to the SOUSY system : first, the antenna
size and shape were modified to enable two fixed-beam pointing directions.
Second, the control and data acquisition modules were upgraded with a digital
receiver system to take full advantage of the wide power-stage bandwidth
(4 MHz), resulting in a high spatial resolution (37.5 m).
Coincident in situ measurements of the atmosphere were obtained using a small
unmanned aircraft system (sUAS) developed at the University of Colorado,
called the DataHawk . This system consists of a
GPS-controlled, battery-operated aircraft (1 m wingspan), programmed to fly
70 m diameter circles ascending or descending entirely in the radar beam,
while measuring temperature, humidity, and winds at 8.1 Hz. Through
post-processing of these data, it can also measure ϵ (turbulent
energy dissipation rate) and structure functions CT2
(temperature); Cq2 (humidity); and, as used here, Cn2 (refractive
index) . In order to reach the altitudes above the 1 km
radar ground clutter, the DataHawk was dropped from a conventional weather
balloon and flown under permission from The Peruvian Corporation of
Commercial Airports and Aviation Inc. (CORPAC) air traffic control.
The present work describes the results of this unique coordinated
observational campaign where the DH flies on a tight spiral up and down
inside the high-resolution SOUSY radar antenna beam over an altitude overlap
range of 1.2–4.2 km. This provides the first comparisons using 8.1 Hz
colocated in situ measurements of pressure, humidity, and temperature
acquired with the DH and scaled to the 37.5 m SOUSY radar resolution. The
paper is structured as follows: Sect. describes the theoretical
basis for estimating Cn2 from both in situ DH and radar backscatter
measurements. Section provides details on the experimental setup. In
Sect. , the data collection is described along with the Cn2
comparison results. Finally, in Sect. , conclusions and future work
are outlined.
Theoretical background
In situ and remotely sensed observations are compared on the basis
of the structure function parameter of refractive index Cn2 that is
briefly reviewed here. Its estimation from the DH and SOUSY instruments is
discussed in separate subsections below.
The energy spectrum of turbulence
E(κ) proposed by can be classified into three
regions: the energy-containing range, the inertial subrange (ISR), and the dissipation
range. Under this hypothesis, the rate of energy
transfer from large scales in the energy-containing
range is equivalent to the energy dissipation
rate at small scales in the dissipation range
. In the inertial subrange,
the bulk of energy transfers from larger to smaller scales following a
wave number slope of -5 / 3. This is also known as the energy cascade
assumption or Kolmogorov -5 / 3 turbulence spectrum for
isotropic turbulence, where the turbulence has
the same variance in all directions . In the troposphere, ISR typically
spans large eddy scales of 200 m down to small eddy sizes of 1 cm
.
Considering that these turbulent eddies contain air parcels with variations
in temperature and humidity, and hence also in the refractive index n, and
assuming that the turbulence is both
isotropic and in the inertial
subrange, Cn2 (m-2/3) parameterizes the refractive index
structure function Dn as follows :
Dn(δ)=n(r+δ)-n(r)2,Dn(δ)=Cn2(r)|δ|2/3,Cn2=n(r+δ)-n(r)2|δ|2/3,
where 〈⋅〉 denotes the spatial average over a volume within which the
n irregularities are assumed to be statistically
isotropic and homogeneous.
Here, r represents the position vector, δ
denotes the spatial separation over which the structure function is being
computed, and δ=|δ|.
Estimations of Cn2 obtained from the DataHawk and the SOUSY radar are
detailed in the following subsections. The measured parameters from the DH
are obtained at different separations δ due to the constant temporal
sampling rate, the variable wind speed, and the different vertical ascent and
descent rates. Details on the methodology to compare estimates obtained at
different turbulent scales (or from DH and SOUSY instruments) are discussed
below.
In situ DH measurement of Cn2
If the background atmospheric pressure profile is in hydrostatic balance,
then the refractivity N=(n-1)×106 can be
found directly from the following equations of state
:
dlnP=-gRTdz,es=6.112exp17.6TT+243.5,e=RHes100,N=77.6T+273.11P+4811eT+273.11,
where P is total atmospheric pressure (hPa), es is the saturated vapor
pressure (hPa), RH is the relative humidity (%), e is the partial
pressure of water vapor (hPa), P0 represents the pressure at z = 0 m
(1000 hPa), g is the gravitational acceleration (9.81 m s-2), R is
the gas constant for dry air (287 J kg-1 K-1), and T is the
temperature (∘C). The electron density term has been omitted in
Eq. () due to its influence being only in the ionosphere.
The DH provides in situ measurements of P, e, and T at 8.1 Hz. With a
vertical ascent rate of 1.0 m s-1 and descent rate of 2.0 m s-1,
refractivity N (or equivalently refractive index n) can be estimated
along the helical path at each of the measured points.
The structure function parameter Cn2 can be estimated at separation
δ along the helix path (see black points and solid black line in
Fig. ) using Eq. (). From now on, this method will
be called “DH direct”. However, as stated by and
, it is important to account for the advection of turbulence
past the DH platform. To account for this, Taylor's hypothesis of frozen
turbulence is utilized . So, instead of calculating δ
as the separation of two measurement locations, an effective separation
distance δE, which considers the advection of frozen turbulence, can
be defined as
Δt=tj-ti,Δx=xj-xi-uΔt,Δy=yj-yi-vΔt,Δz=zj-zi-wΔt,δE=Δx2+Δy2+Δz2,
where x, y, and z are the zonal, meridional, and vertical separation
distances between the i and j measurements, respectively; u, v, and w are zonal,
meridional, and vertical wind, respectively; and Δt is the time between measurements. Estimates
of measured n are obtained at each irregular separation (black dots in
Fig. ) and then resampled at the desired uniform separation
δE to obtain Cn2 by interpolating using the six closest points.
For comparisons with the SOUSY radar, Cn2 estimations from the DH must be
at the radar Bragg scale δE=∼ 2.8 m @ 53.5 MHz as follows
:
Cn2=(Δn)2δE2/3,
where Δn represents the refractive index
difference over the Bragg scale δE.
Another approach for calculating Cn2 is adapted from the work of
and , where estimates of the
structure function parameters are calculated from circular trajectories at
constant heights to account for horizontal variations of n. Here, estimates
of (Δn)2 are calculated for a set of possible separations δE
in each turn of the helical trajectory (shown by different colored lines in
Fig ); then these estimates are separated into δE length bins
to estimate Dn=(Δn)2‾. Finally, Cn2 and the
ISR are estimated, where Cn2 is constant and
independent of δE, at the average altitude of that turn. Direct use
of this method may not be suitable for the helical patterns, because it
highly depends on the ascent and descent rate, and on the vertical variations of
n over one helix turn. In the end, these variations cause a bias in the
estimates Dn that needs to be accounted for. A solution to remove the bias
in Δn and thereby improve the estimate of Dn is to calculate Dn
as the variance of Δn at each 10 m bin. This modified approach will
be referred to as “DH ISR”.
SOUSY radar measurement of Cn2
Radars transmit pulses at high power in order to maintain the required
sensitivity to detect reflections from weak targets at a desired maximum
range. The radar equation is used to determine the returned power Pr
based on multiple parameters from a single target with backscattered
cross section σb .
Pr=PavgG2λ2σbf4(θ,ϕ)(4π)3r4l2
Here Pavg is the averaged transmitted power, G2 represents the gain
of the combined transmitting and receiving antennas for the monostatic case,
and λ is the radar wavelength. The range to the target is r, l
represents the attenuation losses, and f4(θ,ϕ) is the two-way
normalized power density pattern. The radar equation for a volume filled with
targets is more
appropriate for atmospheric scattering:
Pr=PtdG2λ2(4π)3r02l2×cτw2×πθ128ln2×η,
where Pavg=Pt×d, Pt is the peak transmitted power, d is
the duty cycle, and r0 is the range to the center of the resolution
volume. The radar resolution volume size is the minimum separation between
two volume targets that permits them to be distinguished by a radar. The
second term on the right-hand side of the equation represents the range
resolution Δr=cτw/2, where τw is the transmitting pulse
width. The third term on the right-hand side represents the transmitting
beamwidth, where θ1 is the 3 dB width (in radians) of the one-way
pattern . Finally, the radar
reflectivity η, or average backscatter
cross section per unit volume , is a
measurement of the radar scattering intensity in units of m-1.
The radar reflectivity for clear-air
radars is a measure of the scattering intensity caused
by refractive index fluctuations present in the
radar resolution volume. If the radar half-wavelength (Bragg
scale λB=λ/2) lies within the inertial
subrange, the radar
reflectivity can be represented as
η=0.379Cn2λ-1/3.
The received radar power Pr is proportional to the radar
reflectivity η, which is a measure of the
radar scattering intensity (see Eq. ). Also, η is
proportional to Cn2 (see Eq. ). If the radar is calibrated, Cn2 can be
obtained by the above from measurements of return power at every radar dwell
time (at the sampling volume resolution Δr= 37.5 m).
Unfortunately, an accurate radar calibration can be complex, requiring
detailed measurements of the various radar parameters (see
Eq. ), such as the transmitted peak power Pt, duty
cycle d, antenna gain G, antenna efficiency, and radar beamwidth θ1,
among others. After combining Eqs. ()
and (), and grouping all the radar parameters that are hard to
measure or quantify in a calibration constant C, a simplified equation for
the estimation of Cn2 can be expressed as
logCn2=log(Pr×r02)-logd-logτw+C,
where Pr×r02 represents the total range-corrected power.
Estimates of Cn2 from the DH and the SOUSY radar have been calculated at
two different scales: the Bragg scale (2.8 m) and the radar range resolution
(37.5 m). From radar theory, the received power is due to the convolution of
the eddies within the radar resolution volume with the range-weighting
function e.g.,. A similar analogy can be
applied to the Cn2 estimates obtained from the DH for fair comparison
between the two instruments, which is an approximation of the convolution for
Gaussian pulses:
Cn2=1M∑m=1MCn2(m)×Wr(m),
where m indexes the contribution of each individual eddy of the total of
M eddies encountered by the DH within the resolution volume centered at the
range r0.
The range-weighting function Wr represents
the convolution between the impulse response of the receiver with the
transmitted pulse and is described by and as
Wr(m)=exp-(r(m)-r0)22σr2,
where r(m) represents range of the m eddy and σr=0.35cτw/2.
Experimental setup
Site description
The SOUSY radar is installed at JRO,
located at 511 m above sea level approximately 25 km from the city of Lima,
Peru. The location of the DataHawk launch site was approximately at 0.8 km
northeast from the SOUSY radar because it is both close to the radar site
and far away from possible sources of interference during preflight
calibration. See Fig. .
The Jicamarca Radio Observatory (JRO) is the experimental site for
the observational campaign. JRO is located approximately 25 km from the city
of Lima. The DataHawk launch site is on the JRO property 400 m from the
main antenna (marked in yellow). The SOUSY radar is located next to the main
antenna (marked in red). A picture of the SOUSY antenna elements is presented
in the top left corner of the dash rectangle.
SOUSY radar
The SOUSY radar was donated by the Max-Planck-Institut für Aeronomie to the
Instituto Geofísico del Perú in 2000 and installed at
JRO to complement JRO studies due to SOUSY's large bandwidth (4 MHz compared
to 700 kHz from the Jicamarca radar), which provides atmospheric measurements
with high spatial resolution (37.5 m). SOUSY specifications and parameters
are presented in Table .
SOUSY radar specifications.
Quantity
Value
Radar type
Pulsed
Frequency
53.5 MHz
Wavelength
5.6 m
Beamwidth
∼ 4.9∘
Bandwidth
4 MHz
Transmitter peak power
20 kW
Receiver
Digital based on AD6620 chip
Processing type
Spectra
Number of FFT points
8
Number of coherent integrations
4096
Number of incoherent integrations
1
Dwell time
12.5 s
Unambiguos velocity
1.1 m s-1
Mode 1
Characteristics
Inter pulse period (IPP)
57.2062 km
Pulse width
300 m
Code
Complementary 8 baud
Range resolution
37.5 m
Duty cycle
0.5244%
Mode 2
Characteristics
Inter pulse period (IPP)
57.2062 km
Pulse width
37.5 m
Code
None
Range resolution
37.5 m
Duty cycle
0.0655 %
Shortly after its installation at Jicamarca, a new digital acquisition system
was developed using an off-the-shelf AD6620 digital receiver board to take
full advantage of SOUSY's wide bandwidth
. For the upgrade to be fully functional, it
included a radar controller and direct digital synthesizer.
Initial results confirmed SOUSY's ability to provide high range resolution,
which proves that it is a valuable tool with which to study the morphology of turbulent
layers under statistically stable stratified conditions .
During the present campaign the beam was set to point vertically, to be
coincident with vertical DataHawk helix profiles.
DataHawk
The DataHawk is a sUAS that was specifically designed for high-resolution,
multiple-variable, state-of-the-art atmospheric sensing measurements
. The atmospheric regions targeted by the DataHawk are the
atmospheric boundary layer (ABL) and lower troposphere (up to 10 km).
(a) Balloon lifting the DataHawk for the afternoon data set on 10 July 2014.
(b) DataHawk flying towards the landing site for the same data set at an
approximate altitude of 50 m. (c) Helical trajectory of the
DataHawk descending from approximately 3.75 km to 500 m over the SOUSY
radar (indicated in blue).
DataHawk sensing system characteristics and capabilities (extracted
from ).
Value
Value
Wingspan
1 m
Alt. (balloon drop)
> 9 km m.s.l.
Mass
0.7 kg
Alt. (bungee launch)
>2 km a.g.l.
Design
Flying wing, rear propeller
Turning radius
> 50 m
Telemetry
IEEE 802.15.4 at 2.4 GHz
Climb rate
< 5 m s-1
Propulsion
Electric motor, folding propeller
Downlink throughput
> 1500 bytes s-1
Autopilot
CU custom design (CUPIC)
Downlink update rate
10 Hz
Control
Auto-helix, balloon drop
Sensor sampling
> 100 Hz
Power
11-V LiPo battery, 2600 mA h-1
Data storage (on board)
16 MB
Sensing capabilities
Type
Resolution
Accuracy; range
Time const.; cadence
Notes
Location (GPS)
0.1 m
10 m; worldwide
1 s; 4 Hz
Real time
In situ temperature
0.1 ∘C
2 ∘C; -60 to +40∘
5 s; 8.1 Hz
Real time
Relative humidity
0.01 %
2 %; 0–100 %
5 s; 8.1 Hz
Real time
Cold-wire temperature
< 0.003 ∘C
2 ∘C; -60 to +40 ∘C
0.5 ms; 81 Hz
Real time;
postflight calibration
Airspeed
0.01 m s-1
0.2 m s-1; 0–30 m s-1
0.3 ms; 81 Hz
Real time
The maximum altitude reached by the DH depends on the launch method: when
launched from the ground (bungee launch), it can reach up to 2.5 km at a
2 m s-1 rise rate. Higher altitudes (up to 10 km) can be reached when it
is launched by a balloon drop (see Fig. a), in which the DH detaches
at a prescribed altitude and then flies back upwind to the desired region
(Fig. b). Upon reaching the study region, the DH descends (or
ascends depending on the launch method) in a helix trajectory as shown in
Fig. c. A detailed list of the capabilities, sensors, and system
characteristics of the DataHawk is provided in Table .
SOUSY and DataHawk coordinated events.
Date
Period
Max. Altitude
Radar Mode
10 July 2014
11:05–11:30 UTC-5
2800 m
Mode 2
10 July 2014
15:21–15:46 UTC-5
3850 m
Mode 1
SOUSY daytime calibrated range-corrected received power for 10 July 2014
shows distinct turbulent layers from 500 m up to 7 km. The dropout of data
between 14:00 and 15:00 was due to upgrades in the radar system that allowed
for discrimination of echo returns bellow 1 km. DataHawk flights over the
radar were easily detected as an increase of the radar returns between 11:05
and 11:30 and between 15:21 and 15:46.
Daytime vertical velocity for 10 July 2014 shows stratified layers in the
morning evolving into updrafts and downdrafts in the afternoon with a
periodicity of approximately 10 min. The propagation of the updrafts reached
altitudes close to 7 km.
The black line represents the DataHawk altitude as a function of time plotted
on top of the calibrated range-corrected received power for the morning
flight (11:05–11:30). The DataHawk was dropped by a tethered balloon at an
approximate altitude of 2.25 km. In this case, there is an ascent from its
initial altitude to 3 km, followed by a descent over SOUSY down to 1.5 km.
Results
A campaign for coordinated observations using the DataHawk and the
SOUSY radar was conducted between 5 and 10 July 2014. The first few days
were used to set up the instruments, test launch and recovery at the site,
and conduct test flights. The main observations were made on 10 July 2014.
There were two flights that reached the desired altitude within the radar
beam (see Table ).
Corresponding radial velocity for the morning flight (same period as Fig. ).
The DataHawk trajectory is indicated by the red line. Vertical wind cannot be
determined by the radar along the DH path due to strong returns from the DH
vehicle.
Two radar pulse configurations were tested with SOUSY and are outlined in
Table . The main difference between the two modes is the average
transmitted power: mode 1 transmits 8 times the power of mode 2 and uses
pulse compression to keep the same range resolution.
Radar returns for 10 July 2014 between 09:10 and 17:30 LT are presented in
Fig. . Data between 09:10 and 13:50 were acquired using mode 2, while
data between 14:40 and 17:30 were acquired using mode 1. The gap observed
between 13:50 and 14:40 was due to a change in the T/R switch. This change
gave a better recovery time of the signal, which allowed the detection of
layers down to 500 m range, in comparison with the old design that only
allowed discrimination of turbulent layers from ranges above 1.2 km. For
better comparison of both modes, the power is corrected by range and the
difference in the average transmitted power.
Different layers are clearly observed throughout the day especially between 2 and 4 km
(see Fig. ), which shows SOUSY's potential for turbulence
studies. Both DH flights over SOUSY are seen in the radar data as straight
lines relating altitude and time, with an increase in the returned power (see
the saturated red lines between 11:05 and 11:30, and between 15:20 and
15:45). In addition to the increase in the returned power from DataHawk
reflections, the vertical velocity signatures of the DH flights can be
observed in Fig. . The evolution of the updrafts and downdrafts
throughout the day and their propagation to altitudes up to 6.5 km can also
be observed.
Results from 10 July 2014, flight starting at 10:03:46 LT
The morning flight over the SOUSY radar was a balloon drop using a tethered
balloon that reached approximately 2 km altitude from the launch site. Right
after the drop, the DH flew over the SOUSY radar and started its spiral
ascent up to 2.8 km, which was limited because of battery life. After
reaching its maximum altitude, it descended down to 500 m and returned to the
launch site for landing. The total time of the flight over SOUSY was
approximately 25 min. A close-up of the calibrated range-corrected received
power is presented in Fig. . The black line presented on top of the
radar data represents the altitude measured directly by a pressure sensor on
the DataHawk. Not only can the DH ascent and descent be clearly observed in
the radar data, but the agreement in time and altitude between these instruments
is within the resolution of the data (37.5 m in altitude, 12.5 s in
time).
Estimations of Cn2 (DH direct) along the helical path were calculated by
first calculating N at each of the measured points (see black dots in
Fig. ) and then calculating δE for each of the measured points
(see red thick line in Fig. ) after correcting for advection. The
horizontal winds u and v were obtained from the DH
and are presented in Fig. . The vertical wind w was measured
directly from the radar and is presented in Fig. . However, due to the
strong return signal caused by the DH as seen by the radar, estimates of w
were clearly contaminated, and it was impossible to retrieve these estimates
at the exact altitude of the DH. However, their values at other altitudes
were bounded by [-0.4, 0.4] m s-1 and will be neglected in the
calculations of δE. Estimates of Cn2 were obtained at Bragg scale
(2.8 m), but their contributions were integrated over the radar resolution
(37.5 m).
Horizontal winds obtained from the DataHawk for the morning flight.
(a) Zonal wind. (b) Meridional wind. The red line indicates
the ascent portion of the flight, while the black line indicates the descent
portion of the flight.
Illustration of a method for evaluating Cn2 (adapted from )
for a helical trajectory. The different distances δE are represented
by the lines with different colors. The measured points are indicated by the
black dots. The smallest distance used in the DH direct method is indicated
by the thick red line. (a) 3-D view of the trajectory for a portion
that covers at least one half circle. (b) Top view of the
trajectory.
Procedure followed for the evaluation of Cn2 in the inertial subrange (ISR)
for the portion of the ascent trajectory similar to the one presented in
Fig. . (a) Refractivity as a function of height that
corresponds to an average height of 2362.50 m with a span of 18.75 m.
(b) Variations for δN with separation distance. Data clearly
present a bias due to the helical (non-flat) trajectory.
(c) Variations of (δn)2‾ with separation
evaluated with 10 m bin. (d) Variation of Cn2 with distance.
The red lines mark the bounds of the ISR, where the
turbulence is constant and independent of δE, and the blue line is
the corresponding Cn2 value.
A second method to estimate Cn2 (DH ISR) that follows the modifications
discussed earlier of the method of and
was implemented only for the ascent part of the trajectory.
Reflectivity N was divided into small portions of 18.75 m that contained at
least one half rotation on the helix trajectory to reduce the contribution of
vertical variability of N.
A sample of the N portion centered at 2362.50 m is presented in Fig. a.
The variability of N (δN) with respect to the set of δE is presented
in Fig. b, where the bias caused by the vertical variability of N can be
clearly observed, as the distribution shifts to negative values while δE
increases. Dn or (δn)2‾ is instead calculated as the variance
of (δN) at each 10 m bin and presented in Fig. c. The use of the variance removes the
mean of the bias observed in the calculations. Finally, estimates of Cn2 for each δE are
presented in Fig. d. From inspection the ISR, where Cn2 is constant
and independent of δE, is bounded between 60 and 100 m.
Structure parameter of refractive index obtained during the ascent
(a) and descent (b) portions of the morning flight over the SOUSY radar. The
light-gray lines represent the multiple Cn2 profiles obtained from SOUSY
for the corresponding flight. The thick dark-gray line is the radar average
over the same period. The thick black line represents the Cn2 obtained
from the radar around the closest times after the DH signature is removed.
The thick red line represents Cn2 obtained from the DataHawk estimated
for a distance corresponding to the Bragg scale (λB = 2.8 m).
Finally, the thick blue line represents Cn2 estimated within the ISR
but only estimated for the ascent portion of the
flight.
Similar to Fig. but during the afternoon flight (15:21–15:46).
In this case, the DataHawk was dropped by a “free” balloon at an altitude
of approximately 8 km. However, due to the strong winds, the DataHawk was
advected 4 km from the SOUSY radar, which caused a 3 km drop during the time
it took to regain its position over the radar.
Similar to Fig. but for the afternoon flight. Estimates of the vertical
wind cannot be estimated from radar returns along the DataHawk path due to
its high reflectivity.
Horizontal winds for the afternoon flight (15:21–15:46) estimated from the
DataHawk. (a) Zonal wind. (b) Meridional wind.
Similar to Fig. but during the afternoon flight (15:21–15:46),
which only had a descent trajectory.
Estimation of Cn2 from the two instruments is presented in
Fig. . Estimates from ascending and descending flights are presented
in Fig. a and Fig. b, respectively. In both figures,
instantaneous Cn2 estimated profiles obtained from the radar are
presented in thin light-gray lines, one for every dwell time (12.5 s)
over the time period corresponding to the colocated DH flight. All these
radar estimates of Cn2 have the segments of increased power from the DH
reflections removed. The time average of these radar instantaneous profiles
at each altitude is presented as the thick dark-gray line, exhibiting rather
stationary gross features over this time period but with significant
variability in the details of the profiles over time.
In contrast, the DataHawk measurements are not averaged over this 25 min
interval but are instantaneous at a given altitude and time. So a more
direct comparison would be obtained by extracting the radar returns at the
altitude and time occupied by the DataHawk. As the DataHawk itself
obliterates the radar returns there, due to is larger reflectivity, the
next-best comparison is to use an average of the radar returns just before and
after the DataHawk reflection. This is presented by the thick black line.
Turbulent layers are identified by a relative increase in the Cn2 values
at those altitudes. The agreement between the directly corresponding
measurements (DH direct – red; SOUSY – black) is remarkable, especially during
the ascent portion of the morning flight and above 1.75 km in the descent
portion, where the radar data not only agree with the DH data in magnitude of
Cn2 but clearly follow each other in all the main layered features.
Below 1.75 km on the descent the main variations becomes smaller, and the
degree of detailed correspondence between the red and blue lines breaks down,
although the averages over altitude continue to track well. The order of
magnitude of Cn2 profiles in these data is consistent with experimental
observations , and according to a category
defined by , the level of turbulence varies from intermediate
to moderate.
Comparisons of Cn2 obtained from the DH ISR estimate (blue) and the other
estimates are only presented for the ascent part (Fig. a). The
agreement is observed above 2.5 km, where all the estimates have the same
order of magnitude. Possible causes for the overestimation of DH ISR below
2.5 km are, first, vertical variability of the refractive index (clearly
observed in Fig. b). Second, the identified inertial subrange lies at
separations higher than the Bragg scale (2.8 m) in Fig. d. Third, the
radar Bragg scale is only represented by the first point in Fig. d,
which clearly misrepresents the radar measure of turbulence. Finally, we
consider the DH direct method to be the best way to capture the
turbulence at the radar Bragg scale.
The DH ISR method was not implemented in the descent portion due to the
higher descent rate (2 m s-1), which will increase the size of the
portion that will complete the half helix, thereby increasing
the vertical variability of the refractive index.
Results from 10 July 2014, DH flight starting at 14:42:12
The afternoon DH flight was a balloon drop from an altitude of 6.7 km,
several kilometers south of the SOUSY radar. At approximately 4 km during the descent
the DH arrived over the radar and started the helical descent at
2 m s-1, continuing down to an altitude of 600 m before returning to the
launch site. The calibrated radar returns during the flight are presented in
Fig. , while the radial velocities are presented in Fig. .
Note the small kink in the descent trajectory where the DH was inadvertently
commanded to climb for a short period. Again the similarities in the
altitudes of both trajectories (obtained from DH and detected by SOUSY) are
excellent. As in the previous case, comparisons of Cn2 were computed for
both DH and SOUSY, and are presented in Fig. . Again the δE
was corrected for advection with zonal and meridional winds presented in
Fig. , and the vertical velocity was neglected. For this case, there
is only a descending flight over the radar, beginning at an altitude of
∼ 4.2 km. The location of the turbulent layers and their morphology are
similar from both SOUSY and the DH data for the DH direct method to those in the
morning flight.
Radar calibration constant
In each of the two cases above, the radar returns were calibrated by applying
the appropriate calibration constant C to bring the DH and SOUSY Cn2
estimates into general agreement. If this constant takes into account all the
major factors, and the theory is adequate to describe the general conditions
of interest, then this one constant should provide a correspondence that
holds up over time and over variations in conditions within those of
interest. Finally, introducing the different parameters in
Eq. (), the “best” value of the calibration constant C
for the morning flight in the data shown above was 6×10-26 m-5/2 mW-1 and 7×10-26 m-5/2 mW-1
for the afternoon flight. The small discrepancies observed in the calibration
constant for both flights might be caused by the change in the T/R switch,
which might have introduced a change in the sensitivity in the returned
signal, and by the peak transmitted power, which might not have remained
constant due to changes in the operational modes. After combining both
(morning and afternoon) estimates, C=6.5×10-24 m-5/2 mW-1 was estimated for the whole
day.
Conclusions and future work
Radar profiling of atmospheric turbulence and associated fine-structure atmosphere
has the potential to unravel important details of mixing and transport processes,
owing to its instantaneous profiling capabilities near the boundary layer up
into the stratosphere and its ability to provide continuous measurements
over extended periods. Unfortunately, radar return power is a complex
function of difficult-to-measure radar parameters and various turbulent
atmospheric scattering phenomena.
This paper showed how the measurement of the turbulent structure function
parameter of refractive index Cn2 obtained from the radar can be
calibrated using a small unmanned aircraft system (the DataHawk) to provide
coincident in situ measurements inside the radar beam. This one-time
calibration enables the radar to provide quantitative estimates of this
turbulence parameter continuously thereafter, in turn enabling more detailed
studies of these structures and their evolution.
Since turbulence can have a complex and evolving character, radar returns
alone, by their dependence on refractive index alone, are not likely to
suffice for study of turbulence processes in general, without information
from other sources. Accordingly, future work will include periodic
observational campaigns (every 3 months) that will include the DataHawk,
SOUSY, and probably additional radars. A different flight trajectory should
be tested in order to account for only the horizontal variations of the
refractive index n at different heights. These campaigns will seek to add
estimates of the structure parameters of temperature CT2 and
turbulent energy dissipation rates ϵ. Another addition might be the
recently installed Advanced Modular Incoherent Scatter Radar (AMISR) at JRO
that operates at 450 MHz. AMISR has a pulse-to-pulse beam steer capability
that could allow us to compare and validate horizontal wind estimates
obtained from the DataHawk.