P15R.1 THE DETECTABILITY OF TORNADIC SIGNATURES WITH DOPPLER RADAR:
A RADAR EMULATOR STUDY
Ryan M. May*, Michael I. Biggerstaff and Ming Xue
University of Oklahoma, Norman, Oklahoma
1. INTRODUCTION
The design of a weather radar system, as well
as its scanning strategies, involves various
tradeoffs based upon the goal of observing certain
features of interest. The tradeoffs made in this
design are based on certain assumptions about
the performance of the radar system and on
characteristics of the feature of interest. Often, the
development of algorithms and optimal scanning
strategies requires large datasets to test the range
of operating parameters and find those that yield
the best results. By simulating the operation of a
radar, using a software radar emulator, one can
artificially generate large data sets that span the
range of radar operating characteristics. These
generated datasets are attained much more
quickly and with less effort than would otherwise
be expended in collecting actual data spanning
such characteristics.
Many approaches have been taken previously
in simulating radar data, varying in sophistication
from reflectivity calculation to full simulation of
radar returns from each pulse. Krajewski et al.
(1993) calculated values of reflectivity factor and
differential reflectivity from rainfall rates from a
numerical model, using an assumed drop size
distribution. Similarly, Chandrasekar and Bringi
(1987) looked at the variation of simulated
reflectivity values as a function of raindrop size
distribution parameters. Neither of these studies
was concerned with the Doppler velocity
information. Wood and Brown (1997) evaluated
the effects of WSR-88D (Weather Surveillance
Radar-1988 Doppler) scanning strategies on the
sampling of mesocyclones and tornadoes. The
effects of the scanning strategy were accounted
for by using an effective beamwidth for the radar
that was used to scan an analytic vortex. Capsoni
and D'Amico (1998) simulated the pulse to pulse
time series of radar data by combining the
simulated returns from individual hydrometeors
within a radar volume. Due to the computational
requirements of this approach, the radar data were
generated for only a single range gate, and thus
the aspects of scanning the radar were not
simulated.
This work describes a radar emulator
designed to simulate the returns from a scanning
Doppler radar on a pulse to pulse basis. Starting
with output from a high resolution numerical
simulation of a supercell thunderstorm (Xue 2004),
the emulator generates radar reflectivity, Doppler
velocity, and Doppler spectrum width, based on
the configured radar and scanning strategy. This
emulator is capable of simulating many of the
impacts of radar and scanning strategy design on
the resolution and quality of collected data. The
application of this emulator to studying the
detectability of tornadoes by broad-beam, low
power radars is shown as an example of the utility
of this tool.
2. EMULATOR DESIGN
The operation of the emulator is controlled by
two separate sets of parameters which describe
the radar and the scanning strategy. The
parameters that describe the radar are: location of
the radar relative to the numerical simulation grid,
antenna beamwidth, antenna gain, wavelength,
transmit power, range to the first radar gate, and
the minimum detectable signal. The parameters
that describe the scanning strategy are: pulse
repetition time (PRT), pulse length, antenna
rotation rate, number of pulses to average to
produce a radial, the spacing between radar gates,
and the necessary antenna pointing angles.
Input into the emulator are the numerical grids
from a high resolution numerical simulation. There
is no required resolution for these grids, but the
spatial resolution of the model fields should be
* Corresponding author address: Ryan M. May
Univ. of Oklahoma, School of Meteorology
100 East Boyd St. Suite 1310 Norman, OK 73019
e-mail: rmay@rossby.ou.edu.
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better than the resolution of the radar being
emulated. The meteorological variables used by
the radar emulator are: three dimensional wind
components, density of hydrometeors (rain and
cloud water), and temperature. In this work, the
input used is a simulation of a tornadic
thunderstorm produced by the Advanced Regional
Prediction System (ARPS) (Xue 2004, Xue et al.
2000). This particular simulation used warm-
phase microphysics and was run on a 50m
horizontal grid spacing and a stretched vertical grid
spacing, with 20m the spacing at the surface.
The emulator calculates the power returned to
the radar by a simulated pulse, which is
propagated through the numerical grid, using the
standard radar equation (Doviak and Zrnic 1993):
P r 0=
P t g 22
43 ∑all i
f i4 W i2i V i
l i2r i2
(1)
where Pt is the transmit power, g is the antennagain, λ is the wavelength, f is the normalized
antenna gain, W is the range weighting, η is the
reflectivity, l is the attenuation coefficient, and r is
the range. Quantities with the i subscript represent
individual contributions to the simulated pulse.
The reflectivity is calculated from the model's rain
water and cloud water concentrations, using the
Rayleigh approximation. The rain water is
assumed to have a Marshall-Palmer (1948)
distribution, while cloud water is assumed to be
monodisperse. Attenuation is also calculated
using the extinction cross section from Rayleigh
scattering, including the temperature and
wavelength dependencies of the index of refraction
of water.
From this returned power, and the model's
three dimensional velocity field, the emulator
calculates equivalent reflectivity factor (Ze),Doppler velocity, and Doppler spectrum width. Zeis calculated as (Doviak and Zrnic 1993):
Z e=
210 ln 22r 2P r
3 P t g 212c ∣K w∣2
(2)
where Pr is the returned power, θ1 is the 3dBbeamwidth, c is the speed of light, τ is the pulse
length, and |Kw|2 is approximately 0.93. Doppler
velocity is calculated as the power-weighted
average of the radial velocities within the pules,
while Doppler spectrum width is calculated as the
standard deviation of radial velocities within the
pulse.
The combination of the configuration options
above with the described physics allows for the
simulation of over- and under-sampling in azimuth,
gate spacing, velocity aliasing, range aliasing,
antenna beamwidth with sidelobes, and frequency-
dependent attenuation. As an example of the
basic output from the emulator, Figure 1 shows a
Plan Position Indicator (PPI) of equivalent
reflectivity factor (Ze) from an emulated WSR-88Dradar.
Figure 1: PPI of Ze (in dBZ) for an emulatedWSR-88D radar. Range rings are plotted every
5km from the radar.
2.1 Wavelength and Attenuation
To show the effects of transmit wavelength on
an emulated radar, the emulator was run with the
same WSR-88D parameters as before, but with a
3cm transmit wavelength. A PPI of Ze from thisrun are shown in Figure 2. It is also possible to
look at the difference in Ze between the two runs,which is shown in Figure 3. This figure shows
clearly a region where the values of Ze at 3cm aremuch lower than those at 10cm, with differences
on the order of 10dB in this region.
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Figure 2: PPI of Ze (in dBZ) for an emulatedWSR-88D operating at 3cm wavelength. Range
rings are plotted every 5km.
Figure 3: Ze for WSR-88D minus Ze for 3cmWSR-88D. Range rings are plotted every 5km.
2.2 2nd Trip Echoes
The previous WSR-88D run can be
modified to place the radar 110km from the edge
of the storm and set the unambiguous range to
117km. With these settings, part of the storm lies
beyond the unambiguous range, and 2nd trip
returns are recorded. Such returns are evident in
Figure 4, a PPI of Ze. These returns have muchweaker reflectivity values and are much smaller in
extent than the actual storm. This is due to noise
thresholding based on power, and because
reflectivity is miscalculated from power as a result
of being assigned the incorrect range.
Figure 4: Ze for emulated WSR-88D showing 2ndtrip echoes. Range rings are plotted every
10km.
3. APPLICATION TO DETECTABILITY OF
TORNADOES
The radar emulator described above was
used to examine the impacts of radar and
scanning strategy characteristics on the detection
of tornadic circulations. The input numerical
simulation for the emulator is the same as
described above. This simulated storm produced
a strong tornado 200m across, with a velocity
difference of 160ms-1 across the tornado, which
corresponds to F3 on the Fujita scale.
The study here focuses on the ability to detect
tornadic circulations using low-power, X-band
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radars with 2o beamwidths. Radars of this type are
planned to be deployed as part of a prototype
network in central Oklahoma, through the
Collaborative Adaptive Sensing of the Atmosphere
(CASA) project, a National Science Foundation
Engineering Research Center (Brotzge et al.
2005).
To objectively quantify the impacts of radar
and scanning strategy characteristics, several
metrics have been chosen to measure radar's
detection of the tornado: width (L), change in
velocity across circulation (ΔV), and the vorticity
parameter. The vorticity parameter is defined as
2ΔV/L, and is equal to the vorticity for an
axisymmetric vortex. The baseline values for
these parameters, taken from the simulation itself,
are a value of 200m for L, 160ms-1 for ΔV, and
1.6s-1 for 2ΔV/L.
Unless otherwise specified, the data here was
generated using the parameters specified in Table
1. It should be noted that attenuation is not
actually employed in these runs. However, due to
the viewing angle of the radar to the tornado, the
effects of attenuation would be negligible. A PPI of
Doppler velocity for these parameters is shown in
Figure 5, magnified in to show detail of the
tornadic circulation.
Using the radar characteristics specified in
Table 1, several runs were performed, varying
range to the storm, elevation angle, azimuthal
sampling interval, and Nyquist velocity. The
results from these runs are summarized in Table
2. It was found that a sharp degradation in the
metrics occurred as the range to the tornado
increases. By 20km range, the size of the
circulation measured by the radar is 538m, and the
Table 1: Parameters for emulated CASA radars.
Figures 5: PPI of Doppler velocity for an
emulated CASA radar. Range rings are plotted
every 1km.
vorticity parameter has decreased to 0.14s-1. This
degradation is primarily a result of the mainlobe of
the radar beam being 698m across at this range.
A second feature noticeable in Table 2 is how
fast the metrics degrade from their baseline
values. Even at 3km, the vorticity parameter has
decreased to a value of 0.6s-1. Three kilometers is
close for a fixed-site radar. It is interesting to note
that even at this range, the vorticity parameter has
already degraded to one third of its baseline value.
Overall, it is clear that range is a significant
issue in the ability of broad-beam radars to detect
tornadic circulations. However, the degradation of
these metrics as range increases can be offset
somewhat by azimuthal oversampling, or sampling
with a radial spacing greater than the beamwidth.
This sampling showed some modest gains at
10km, and would probably show even better
improvement over matched sampling at 20km.
It is also important to note that some
preliminary runs were also conducted using a
model simulation time that contained a strong
mesocyclonic circulation, but no tornado. The
emulated CASA radar could easily distinguish
between this case and the case with the tornadic
circulation, which provides some indication that the
radars might be useful in improving false alarm
rates for tornado detection.
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Wavelength 3cm
3dB Beamwidth 2o
Gate Spacing 100m
Nyquist Velocity 18.75ms-1
Unambiguous Range 60km
Radial Spacing 2o
Range to Storm 10km
Elevation Angle 0.5o

Run Max V In Max V Out L ΔV 2ΔV/L
(ms-1) (ms-1) (m) (ms-1) (s-1)
3km Range, 0.0o Elevation 31.6 31.3 229 62.9 0.55
3km Range 31.6 30.6 229 62.2 0.54
3km Range, 1.0o Elevation 28.3 32.7 202 61 0.6
10km Range, 0.0o Elevation 29.7 34.3 368 64 0.35
10km Range 23.3 34.4 368 57.7 0.31
10km Range, 1.0o Elevation 21.1 37.2 368 58.3 0.32
10km Range, 25ms-1 Nyquist 19.6 22.9 363 42.5 0.23
10km Range, 1o Radial Spacing 27.1 34.5 352 61.6 0.35
10km Range, 3o Radial Spacing 19.1 28.8 538 47.9 0.18
20km Range 13.5 35 710 48.5 0.14
30km Range 14 33.4 1080 47.4 0.09
Table 2: Summary of tornadic circulation metrics for set of emulated CASA radars.
4. CONCLUSIONS
A software radar emulator has been created
that is useful for researching the impact of radar
network and scanning strategy characteristics.
The emulator's capabilities include simulating
azimuthal over- and under-sampling, attenuation,
antenna beamwidth with sidelobes, gate spacing,
and 2nd trip echoes. As an example application,
the emulator was used to quantify the ability of low-
power, broad-beam X-band radars to detect
tornadic circulations. Range will be a significant
issue in the detectability, due to their large
beamwidth, but they show some utility in
differentiating between mesocyclonic and tornadic
circulations.
5. ACKNOWLEDGMENTS
Support for this project was provided by
graduate research fellowships sponsored by the
Office of Naval Research through the American
Meteorological Society and by the Army Research
Office through the National Defense Science and
Engineery Graduate Fellowship program. Partial
support was also provided by the National Science
Foundation through the Engineering Research
Center Grant #EEC-0313747.
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