A Doppler Radar Emulator with an Application to the Detectability of
Tornadic Signatures
RYAN M. MAY AND MICHAEL I. BIGGERSTAFF
School of Meteorology, University of Oklahoma, Norman, Oklahoma
MING XUE
School of Meteorology, and Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma
(Manuscript received 14 June 2006, in final form 3 April 2007)
ABSTRACT
A Doppler radar emulator was developed to simulate the expected mean returns from scanning radar,
including pulse-to-pulse variability associated with changes in viewing angle and atmospheric structure.
Based on the user’s configuration, the emulator samples the numerical simulation output to produce
simulated returned power, equivalent radar reflectivity, Doppler velocity, and Doppler spectrum width. The
emulator is used to evaluate the impact of azimuthal over- and undersampling, gate spacing, velocity and
range aliasing, antenna beamwidth and sidelobes, nonstandard (anomalous) pulse propagation, and wave-
length-dependent Rayleigh attenuation on features of interest.
As an example, the emulator is used to evaluate the detection of the circulation associated with a tornado
simulated within a supercell thunderstorm by the Advanced Regional Prediction System (ARPS). Several
metrics for tornado intensity are examined, including peak Doppler velocity and axisymmetric vorticity, to
determine the degradation of the tornadic signature as a function of range and azimuthal sampling intervals.
For the case of a 2° half-power beamwidth radar, like those deployed in the first integrated project of the
Center for Collaborative Adaptive Sensing of the Atmosphere (CASA), the detection of the cyclonic shear
associated with this simulated tornado will be difficult beyond the 10-km range, if standard metrics such as
azimuthal gate-to-gate shear from a single radar are used for detection.
1. Introduction
The design of a weather radar system and its scan-
ning strategy involves trade-offs based upon features to
be observed and the cost of building and deploying the
radar system. Design trade-offs are often difficult to
quantify in terms of their impacts on detecting and
tracking features of interest. Moreover, the develop-
ment of optimal scanning and the refinement of radar-
based algorithms require large datasets to test the full
range of environmental conditions and radar operating
parameters to yield robust results. Recent advances in
numerical modeling have made it possible to simulate
convective storms at very fine scales over a broad range
of environmental conditions (e.g., Wicker and Wil-
helmson 1995; Lewellen et al. 1997). Coupling a soft-
ware radar emulator with high-resolution numerical
simulations, one can generate large sets of simulated
radar data that span a wide range of radar operating
characteristics. These simulated datasets can be used to
quantify the impact of radar design and operational
mode on the diagnosis of storm features by automated
algorithms.
Many approaches have been taken previously in
simulating radar data, varying in sophistication from
simple time series simulation (Zrnic 1975) to reflectiv-
ity calculation (Chandrasekar and Bringi 1987; Krajew-
ski et al. 1993) to full simulation of radar returns from
each pulse (Capsoni and D’Amico 1998; Capsoni et al.
2001). Zrnic (1975) generated simulated time series ra-
dar data and Doppler spectra using an assumed Gauss-
ian distribution of velocities within the resolution vol-
ume. Chandrasekar and Bringi (1987) looked at the
variation of simulated reflectivity values as a function
of raindrop size distribution parameters. Similarly, Kra-
Corresponding author address: Ryan May, National Weather
Center, 120 David L. Boren Blvd., Suite 5900, Norman, OK
73072-7307.
E-mail: rmay@ou.edu
VOLUME 24 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y DECEMBER 2007
DOI: 10.1175/2007JTECHA882.1
© 2007 American Meteorological Society 1973
JTECH2106

jewski et al. (1993) calculated values of reflectivity fac-
tor and differential reflectivity using rainfall rates from
a numerical model, with an assumed drop size distribu-
tion. Neither of these studies was concerned with
Doppler velocity or the impacts of scanning strategies.
Wood and Brown (1997) evaluated the effects of
Weather Surveillance Radar-1988 Doppler (WSR-88D;
Crum and Alberty 1993) 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, which was used to
scan an analytic vortex with a uniform reflectivity field.
Capsoni and D’Amico (1998) simulated the pulse-to-
pulse time series of radar data by combining the simu-
lated returns from individual hydrometeors within a ra-
dar volume. This work was extended to generate po-
larimetric signatures by Capsoni et al. (2001). Because
of the computational requirements of this approach,
the radar data were generated for only a single range
gate only, and thus many aspects of the scanning radar
were not simulated.
This work describes a radar emulator designed to
simulate the expected average returns from a scanning
Doppler radar. Starting with output from a high-
resolution numerical simulation, the emulator gener-
ates fields of power, equivalent reflectivity factor,
Doppler velocity, and Doppler spectrum width based
on the radar configuration and scanning strategy used.
Here we show that the emulator is capable of simulat-
ing several radar data characteristics, including range
resolution, azimuthal over- and undersampling, non-
standard (anomalous) propagation, Rayleigh attenua-
tion, antenna sidelobes, velocity aliasing, and range
aliasing.
As an example of its use for research, the emulator is
applied to output from a numerical simulation of an F3
intensity (Fujita 1971) supercell tornado simulated by
the Advanced Regional Prediction System (ARPS; Xue
et al. 2000, 2001) to evaluate the ability of 2° beamwidth
radars to directly detect the circulation associated with
the tornado. This application is motivated by the first
integrated project of the Center for Collaborative
Adaptive Sensing of the Atmosphere (CASA; Brotzge
et al. 2005), which recently deployed four such radars in
the Oklahoma test bed.
2. Radar emulator design
a. Emulator configuration and input
The behavior of the radar emulator is controlled by
specifying radar characteristics and scanning strategy
(Table 1). Note that the antenna beamwidth, gain, and
wavelength are treated independently to allow for vari-
ous types of antennas. The minimum detectable signal
is used as a threshold to compensate for the lack of
incorporation of noise (subgrid-scale turbulence and
hardware electronic signals) on the quality of the emu-
lated radar measurements. Hence, regions where sig-
nal-to-noise ratios would be expected to be low are
deleted. The pulse repetition time and pulse length are
given independently, but, in reality, they are usually
constrained by the duty cycle of the transmitter. The
antenna pointing angles can be specified for either full
or sector plan position indicator (PPI) scans or range–
height indicator (RHI) scans. The emulator allows for
oversampling in both azimuth (or elevation for RHI
scans) and range.
The input data to the radar emulator are three-
dimensional gridded fields that describe the state of the
atmosphere. Wind components and mixing ratios of rel-
evant precipitation-sized hydrometeors are required
fields. Other water species can be included and used for
additional scattering or attenuation. Water vapor, along
with temperature and pressure, are needed for calcu-
lating the atmospheric index of refraction, which is used
for anomalous propagation. Temperature is also used
in determining the backscatter cross section of hydro-
meteors.
b. Scattering
For computational efficiency, backscattering and ex-
tinction cross sections per unit volume of air are pre-
calculated at each model grid point. Moreover, only
Rayleigh scattering by liquid hydrometeors is currently
included. According to Battan (1973) and Doviak and
Zrnic (1993), the Rayleigh approximation implies the
following relationships for the backscattering cross sec-
tion
b and the extinction cross section
e of a sphere of
liquid water with diameter D:

b 

5

4 | Kw | 2D6, 1

e 

2D3

Im

Kw 
2
3

b, 2
TABLE 1. Emulator control parameters.
Radar parameters
Scanning strategy
parameters
Location PRT
Antenna beamwidth Pulse length
Antenna gain (including sidelobes) Antenna rotation rate
Wavelength No. of pulses per radial
Transmit power Radar gate spacing
Range to first gate Scan fixed angle
Minimum detectable signal Scan start and end angles
1974 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24

Kw 
m2  1
m2  2
, 3
where  is radar wavelength, and m is the complex
index of refraction for liquid water. The emulator cur-
rently assumes a monodisperse distribution of cloud
droplets and a Marshall and Palmer (1948) distribution
of raindrops, which is consistent with the microphysics
scheme used in many numerical models, including the
ARPS. The use of a more general gamma distribution
(Ulbrich 1983) would be possible. These assumed dis-
tributions permit the calculation of the total backscat-
tering and extinction cross sections per unit volume
from the cloud water c, and rainwater r concentra-
tions (in kg m3) at each grid point:

b
V


5

4 | Kw | 2
6!N0
r
lN0


74

48
l
Rm
3
c,
4

e
V

6
l
Im

Kwr  c, 5
where l is the density of liquid water; Rm is the median
radius for the cloud droplets; and N0 is the Marshall–
Palmer distribution intercept parameter; Rm and N0 are
assumed to have values of 50
m and 8000 drops m3
mm1, respectively. The Debye formula, shown by Sax-
ton (1946, 278–325) to be applicable for the microwave
region, is used to calculate the complex index of refrac-
tion explicitly. The Debye formula is
m2 
1  2
1  i

0


 2, 6
where 1 is the static dielectric constant, 2 is the optical
dielectric constant, 0 is the transition wavelength, and
i equals1. Values of 0, 1, and 2 as a function
of temperature were taken from Kerr (1951) and are
based on Ryde and Ryde (1945). This formulation of
m2 allows the emulator to capture the temperature and
wavelength dependencies of Kw.
It is important to note that the Rayleigh approxima-
tion has been assumed for both scattering and attenu-
ation. The range where the Rayleigh approximation is
accurate for attenuation is much more limited than
that for backscatter (Battan 1973). Therefore, at wave-
lengths shorter than approximately 10 cm, the attenu-
ation simulated here will grossly underestimate the ac-
tual attenuation. This limitation will be addressed in
future work by using scattering parameters calculated
using Mie theory for spherical scatterers (Mie 1908)
and/or the T-matrix method for nonspherical scatterers
(Waterman 1965).
c. Sampling of input fields
To sample the virtual model atmosphere, the emula-
tor calculates radar variables along the path of indi-
vidual pulses at the interval specified by the pulse rep-
etition time (PRT). This allows the input model fields,
as well as the state of the radar (such as antenna point-
ing angle), to change for individual pulses. While the
emulator is currently configured for a mechanically
scanning antenna, pulse-by-pulse calculation can be
used to emulate measurements for phased-array radar
as well. The pulse generated within the emulator de-
fines the volume of space that contributes to a sample
taken along the radar beam. It is bound in elevation and
azimuth by a fixed multiple of the half-power beam-
width. This multiple is chosen based on the number of
sidelobes that are desired for simulation in the antenna
pattern. The pulse is bound in range by the specified
pulse length. This volume of space is subdivided into
individual pulse elements defined in angular coordi-
nates such that, at the maximum range from the radar,
the dimensions of each pulse element are 10% smaller
than the model grid spacing at that range. While there
is flexibility in how many subdivisions are made in the
pulse element, having too many increases the compu-
tation requirements without changing the results. Sub-
dividing the pulse volume into subelements that be-
come larger than the grid spacing at the maximum
range of the radar will result in undersampling of the
model input fields and will change the emulator output.
Each pulse element is assigned values of extinction
cross section, backscattering cross section, and radial
velocity that correspond to the grid point nearest to the
element’s location in space. Nearest-neighbor sampling
is chosen over interpolation to improve the computa-
tional efficiency of the emulator. Because the pulse el-
ements are generally much smaller than the grid cells,
this sampling method provides sufficient accuracy.
The radial velocity is calculated by the projection of
the total wind velocity vector onto the radar beam:
Vr  u sin   cos cos  w  wt sin , 7
where Vr is the radial velocity, u is the x component of
the wind,
is the y component of the wind, w is the z
component of the wind, wt is the average terminal fall
speed for the hydrometeors,  is the azimuth angle mea-
sured clockwise from north, and  is the elevation
angle. The average hydrometeor terminal fall speed for
the grid box is calculated as a backscatter cross-section
weighted average given by
DECEMBER 2007 M A Y E T A L . 1975

wt 

1

0


0.5


b DVtDND dD, 8
where  is the total grid reflectivity, is the air density
of the grid box, 0 is the reference density, N(D) is the
drop size distribution, and Vt(D) is the terminal fall
speed as a function of diameter, which is calculated
using the fitted relationship of Brandes et al. (2002):
VtD  0.1021  4.932D  0.9551D
2
 0.079 34D3
 0.002 362D4, 9
where Vt is in meters per second and D is in millimeters.
The weighting by backscatter cross section makes the
terminal fall speed more representative of the velocity
seen by the radar than a simple mass-weighted average.
The pulse itself is propagated through the numerical
grid using a ray-tracing technique. For each range gate,
the height of each pulse element is determined sepa-
rately by taking into account the atmospheric index of
refraction experienced by that particular ray element.
This allows for differential propagation across the radar
beam. The change in the height above ground h and
change in range from the radar (along the surface of the
earth) r can be calculated from the incremental
change in range along the path s as
h 


h2  s2  2hs

1 
C2
n2h2


12


12
,
10
FIG. 1. Emulator antenna pattern for a 1° half-power
beamwidth radar.
FIG. 2. Model rainwater mixing ratio (qr) and vector velocity fields at 13 500 s into the
simulation and 20-m height. The black dots represent radar locations at ranges of 3 and 10 km.
The inverted triangle represents the location of the tornado.
1976 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24

r  a sin1


Cs
nh

h  h
, 11
C  n0a cos , 12
where a is the radius of the earth, h is the previous
height of the element above ground, n is the index of
refraction at height h, n0 is the index of refraction at the
radar, and  is the initial elevation angle of the element
(Doviak and Zrnic 1993). The index of refraction is
calculated from the model temperature T, water vapor
pressure e, and air pressure p, using the relation pro-
vided by Bean and Dutton (1966):
FIG. 3. PPIs of (a) returned power (dB relative to 1 W), (b) equivalent reflectivity factor
(Ze), (c) Doppler velocity, and (d) spectrum width for control experiment CNTL.
TABLE 2. Configuration parameters for each experiment.
Expt

(cm)
Beamwidth
(°) PRF (Hz)
Pulse
length (
s)
Rotation
rate (° s1)
Pulses
per radial
Gate
length (m)
Az
(°)
VNYQ
(m s1)
Ra
(km)
CNTL 10 1 1500 1.5 20 75 250 1.0 37.50 100
EXP2 10 1 1500 1.5 15 50 250 0.5 37.50 100
EXP3 10 1 1500 .75 20 75 125 1.0 37.50 100
EXP4 10 1 1500 1.5 20 75 250 1.0 37.50 100
EXP5 10 1 1000 1.5 20 50 250 1.0 25.00 150
EXP6 10 2 1500 1.5 20 75 250 1.0 37.50 100
EXP7 10 1 1500 1.5 20 75 250 1.0 37.50 100
EXP8 3 1 1500 1.5 20 75 250 1.0 11.25 100
DECEMBER 2007 M A Y E T A L . 1977
Fig 3 live 4/C

n 

Cdp
T

Cw1e
T

Cw2e
T2

 106  1, 13
where Cd, Cw1, and Cw2, have values of 0.776 K Pa
1,
0.716 K Pa1, and 3.7  103 K2 Pa1, respectively. The
element’s range from the radar along the surface of the
earth is then converted to standard two-dimensional
Cartesian coordinates, which are used to determine the
location of the element on the model grid.
The pulse volume is allowed to propagate through
the environment as far as twice the unambiguous
range Ra,
Ra 
cTs
2
, 14
where Ts is the PRT, and c is the speed of light. Allow-
ing the pulse to propagate 2Ra from the radar means
that after one PRT from the time the radar is started
there are two pulses propagating through the model
field at any given instant. Thus, when a sample is taken,
the returns from both pulses are assigned to the gate,
producing the effects of range aliasing. Range aliasing
can be disabled if desired.
d. The calculation of returned power
The entire pulse volume is stepped forward in range
while keeping track of the total extinction cross section
along the path. This running total is kept for each pulse
element, which allows for the calculation of differential
attenuation across the pulse. As the pulse is propagated
through the model grid of the simulated atmosphere, it
is periodically sampled at an interval in range dictated
by the specified gate spacing. This allows for the gate
and pulse lengths to be independent. When a pulse
sample is taken, three values are calculated: power,
power-weighted average radial velocity, and power-
FIG. 4. As in Fig. 3, but magnified to show more details in the region of mesocyclone and
tornado.
1978 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 4 live 4/C

weighted radial velocity variance. The power weight-
ings are performed over all of the pulse elements as
follows:
Vr 

i
PiVi

i
Pi
, 15

vr 

i
PiVi
2

i
Pi
 Vr
2, 16
where Vr is the power-weighted average radial velocity,

vr is the power-weighted variance of radial velocities,
Pi is the power for a particular pulse element, and Vi is
the radial velocity for a particular pulse element. The
estimate of variance here,
vr, is not unbiased but is
chosen to simplify the computations. Since values from
thousands of pulse elements are used in the calculation,
the difference between biased and unbiased estimates is
negligible.
As given in Doviak and Zrnic (1993), the power P for
a sample taken at range r0 is given by
P

r0  
rIr0, rdV, 17
where
I

r0, r 
Ptg
2

2f 4

,  | Wr0, r | 2

43l2rr4
, 18
dV  r2dr sin d d, 19
and Pt is the transmitted power, g is the system gain, 
is the wavelength, r is range from the radar, l is the
FIG. 5. As in Fig. 4, but for experiment EXP2, showing the effects of azimuthal
oversampling.
DECEMBER 2007 M A Y E T A L . 1979
Fig 5 live 4/C

attenuation factor, f2 is the normalized antenna pat-
tern,  is the reflectivity (backscattering cross section
per unit volume),  is the azimuth angle relative to the
beam center,  is the elevation angle relative to beam
center, and W is the range-weighting function. The
emulator approximates this integral with a sum over the
finite elements within the pulse volume,
P

r0 
Ptg
2

2

43 i
f i
4Wi
2

iVi
li
2ri
2 , 20
where V is the volume of a pulse element, and all
quantities subscripted with i are values for a particular
pulse element. The emulator assumes a Gaussian
range-weighting function and a normalized antenna
pattern with the following form (Doviak and Zrnic
1993):
f 2

 


8J2Da sin

Da sin
2 
2
, 21
where J2 is the second-order Bessel function of the first
kind,  is the angular offset from boresight, and Da is
the diameter of the antenna, which for (21) above can
be calculated from the half-power beamwidth 1 as
Da 
1.27
1
, 22
where  is the wavelength. Doviak and Zrnic (1993)
state that (21) describes the antenna pattern for the first
few sidelobes quite well for a parabolic antenna. How-
ever, (21) is limited in that it gives sidelobes of a fixed
level and location (e.g., Fig. 1), prohibiting configura-
tion of sidelobes with arbitrary magnitude.
e. Moment calculation
The sampling of model data is repeated for the num-
ber of pulses that are to be averaged for a radial of data,
as specified by the scanning strategy. Moment data
FIG. 6. As in Fig. 4, but for experiment EXP3, showing differences due to a shorter gate
spacing and shorter pulse duration.
1980 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 6 live 4/C

(power, Doppler velocity, and Doppler spectrum
width) are then generated at each range gate along the
radial. Power is calculated as the average of all power
samples for the specified number of pulses at that range
gate. Note that this is the expected mean power that an
actual weather radar would produce if random power
fluctuations were successfully removed by the pulse av-
eraging and the radar system had no noise.
Radial velocity is calculated as the power-weighted
average of all velocity samples (one per pulse) at that
range gate. To emulate velocity aliasing, this average is
restricted to a value within the Nyquist interval and is
given by
Va  Vr  2nVNYQ, 23a
where
n  0 for | Vr |  VNYQ, 23b
n 
VNYQ  Vr
2VNYQ
 1 for Vr
VNYQ, 23c
n 
VNYQ  Vr
2VNYQ
 1 for Vr   VNYQ,
23d
where Va is the aliased velocity value; Vr is the original
(unaliased) radial velocity; VNYQ is the Nyquist (or
aliasing) velocity; and n, an integer, is the number of
Nyquist intervals by which the Va differs from Vr. One
advantage of emulated data is that the unaliased Dopp-
ler velocity is known. Spectrum width is calculated as
the power-weighted average of the variance for each
sample, which is the variance of all velocity values
within the pulse. Initial attempts at emulating spectrum
width used only the variance of the individual velocity
samples that were themselves an average over the en-
tire pulse. That approach produced unreasonably low
spectrum width. By taking into account the variance of
all velocity values within all pulses, the spectrum width
takes into account the effect of antenna rotation and
wind shear across the radar beam. However, we have
neglected subgrid-scale atmospheric turbulence. More-
over, since the emulator does not generate a true power
spectrum at each range gate, the emulated spectrum
width does not take into account a limited Nyquist in-
terval or the pulse-to-pulse variability associated with
random phase changes from scatterers moving relative
to the transmitted wavelength. In addition to the three
moments above, equivalent reflectivity factor (Ze) is
calculated from the average power Pr, using
Ze 
210

ln22r2Pr

3Ptg
2
1
2c | Kw | 2
, 24
where  is the pulse duration.
FIG. 7. PPI of returned power difference between CNTL and
EXP4 (CNTL subtracted from EXP4), showing overall minimal
differences due to sidelobes. Areas where EXP4 has less returned
power are due to numeric instability in the computations.
FIG. 8. As in Fig. 7, but for Doppler velocity difference, showing
the small impact of sidelobes on measured Doppler velocity.
DECEMBER 2007 M A Y E T A L . 1981
Fig 7 and 8 live 4/C

3. Demonstration of emulator capabilities
Emulated data were generated for different radar
characteristics to illustrate the emulator’s capabilities
and to demonstrate the impact of radar design on data
quality. The input is from a numerical simulation of a
supercell thunderstorm produced using the Advanced
Regional Prediction System (ARPS; Xue et al. 2000,
2001). The ARPS is a fully compressible and nonhy-
drostatic prediction model, and its prognostic state vari-
ables include wind components u,
, w; potential tem-
perature ; pressure p; the mixing ratios for water vapor
q

; cloud water qc; rainwater qr; cloud ice qi; snow qs;
and hail qh; plus the turbulent kinetic energy used by
the 1.5-order subgrid-scale turbulent closure scheme.
For the current simulation, only liquid-phase Kessler
(1969) microphysics is used. The simulation had a hori-
zontal grid spacing of 50 m over a 48 km by 48 km
domain and a vertically stretched grid that goes from
the surface to 16 km. The stretching is specified by a
hyperbolic tangent function, having a minimum spacing
of 20 m at the surface, 380-m spacing at the top of the
model, and a mean spacing of 200 m (Xue et al. 1995).
The model thunderstorm was initiated by a thermal
bubble in a horizontally homogeneous environment de-
fined by the 20 May 1977 Del City, Oklahoma, super-
cell sounding reported in Ray et al. (1981). Detailed
analysis of the simulated storm is unimportant here as
the simulation serves only as input to the emulator.
Furthermore, only a single time step taken during the
most intense portion of the tornadic stage of the simu-
lated storm is used. The impact of storm evolution on
radar-derived storm structure will be the subject of fu-
ture studies.
Figure 2 shows the rainwater mixing ratio and storm-
relative velocity at the surface at 13 500 s into the simu-
lation, the time used to produce the emulated data. An
intense supercell thunderstorm with characteristic v-
FIG. 9. As in Fig. 3, but for experiment EXP5, showing the impacts of reducing the PRF.
1982 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 9 live 4/C

notch and hook (Lemon and Doswell 1979) in the rain-
water field is evident. The simulated tornado vortex is
about 200 m in diameter, with maximum winds of about
75 m s1.
Table 2 lists the parameters used to define the radar
and scanning strategy in each of the experiments dis-
cussed below.
a. Control experiment for S-band radar with 1°
beamwidth
The control experiment (CNTL), against which other
radar configurations are compared, assumes character-
istics similar to those of the U.S. National Weather Ser-
vice WSR-88D (Crum and Alberty 1993) operational
weather radars. The WSR-88Ds operate at a nominal
wavelength of 10 cm with a peak power of 750 kW and
have a nominal half-power beamwidth of 1°. The cur-
rent operational scanning strategy uses a 1° azimuthal
sampling interval (which is close to the beamwidth),
with range gates spaced 250 m apart. For these experi-
ments, the radar is located 20 km north of the southern
edge of the model domain and 31 km east of the west-
ern edge of the domain, or about 10 km northeast of the
center of the tornadic circulation. Except where noted,
the antenna has no sidelobes but is restricted to the
area between the first nulls in the antenna pattern,
keeping the full main lobe of the antenna. The width of
this region for a 1° half-power beamwidth antenna is
approximately 3°. PPIs of emulated power, equivalent
reflectivity factor Ze, Doppler radial velocity, and spec-
trum width (Fig. 3) for this experiment show the famil-
iar reflectivity structure (Fig. 3b) of a supercell thun-
derstorm, with a pronounced hook echo (magnified in
Fig. 4). A pronounced mesocyclone circulation (Figs.
3c, 4c), with a small region of high gate-to-gate shear
FIG. 10. As in Fig. 4, but for experiment EXP6, showing the impacts of changing the
half-power beamwidth.
DECEMBER 2007 M A Y E T A L . 1983
Fig 10 live 4/C

corresponding to the tornado, was found at the tip of
the hook echo. The spectrum width (Figs. 3d, 4d) was
relatively low, 1–3 m s 1, for most of the storm. How-
ever, the spectrum width was higher (4 m s1) in the
region of the mesocyclone, reaching a maximum of 20
m s1 around the tornado. It should also be noted that
the Doppler velocity field for this experiment exhibits
almost no aliasing, except for a single velocity gate,
because of the high Nyquist velocity (37.5 m s1) of the
CNTL run. Even at this range, the 75 m s1 flow in the
simulated tornado was significantly reduced by averag-
ing across the 1° half-power beamwidth. Similar reduc-
tion in vortex strength by beam averaging was noted by
Wood and Brown (1997).
b. Oversampling in azimuth
Experiment EXP2 (Table 2) is identical to CNTL,
except that fewer pulses (50 instead of 75) are used to
generate a radial, and the antenna is rotated at 15° s1
instead of 20° s1, yielding data that are azimuthally
oversampled relative to the beamwidth. This difference
in azimuthal sampling resulted in differences in the ob-
served structure of the storm, especially in the tornadic
region (Fig. 5). Overall, azimuthal oversampling
yielded finer-scale structure of the storm (cf. Fig. 4). Of
particular interest are the velocity measurements
around the tornado; the oversampled data produce
higher inbound and outbound velocities than the beam-
matched CNTL case. These increases in velocity values,
though minimal, are due to the decreased region that is
averaged, which allows the peak velocity values in the
tornado to contribute more to the sampled Doppler
velocity value. Wood et al. (2001) and Brown et al.
(2002) report a similar result for an idealized Rankine
vortex flow and a simpler radar emulator. Using time
series data taken from a WSR-88D during a tornadic
FIG. 11. As in Fig. 3, but for experiment EXP7, showing second-trip echoes. The scale has
been changed to allow both first- and second-trip echoes to be shown.
1984 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 11 live 4/C

supercell, Wood et al. (2001) demonstrated that over-
sampling by a factor of 2 increased the observed meso-
cyclone strength by 10%–50% relative to standard azi-
muthal sampling for one-third of the mesocyclones de-
tected.
c. Effects of gate length
Experiment EXP3 (Fig. 6) differs from CNTL by us-
ing a smaller gate length, 125 m instead of 250 m, and a
correspondingly smaller pulse length, 0.75
s instead of
1.5
s, resulting in a higher range resolution. As in
experiment EXP2, the shorter sampling interval in the
radial direction results in the elucidation of finer-scale
flow, especially in the region of the tornado. Due to the
smaller region sampled (and averaged) in range, higher
inbound and outbound velocity values are obtained,
though not as high as the azimuthally oversampled
case. The latter is expected because azimuthal oversam-
pling is more effective in capturing the extreme values
of inbound and outbound velocities in quasi-
axisymmetric flow. This fact was also the motivation of
the work of Xue et al. (2007).
d. Effects of sidelobes
Experiment EXP4 repeated the CNTL experiment
with the pulse expanded to 6° in azimuth, which in-
cluded the first two antenna sidelobes. For the antenna
pattern used here, the first sidelobe had a one-way gain
that was 28 dB less than the peak of the main lobe.
Since ground clutter was not included, this experiment
exhibited only minor differences from CNTL (Figs. 7
and 8). Regions with the strongest reflectivity gradients
exhibited a few tenths of a decibel change in returned
power and a few tenths of a meter per second differ-
FIG. 12. As in Fig. 3, but for experiment EXP8, highlighting the storm structure observed
at X band.
DECEMBER 2007 M A Y E T A L . 1985
Fig 12 live 4/C

ence in wind speed. The area around the tornado had
almost no change in diagnosed velocity, suggesting that
the WSR-88D velocity measurements in such storms
are not strongly affected by sidelobes in the absence of
ground clutter.
While the increase in volume contributing to re-
turned power in EXP4 should have led to consistently
higher values, there are a few places where less power
was found. The lower power results from slight changes
in the antenna gain weighting assigned to individual
grid elements illuminated by the radar beam between
the two runs. In essence, the center of the beam is not
located in exactly the same place because of truncation
in the numerical calculations of the beam projection
through the model grid. These small errors led to places
in which the sidelobes’ run had lower power than the
CNTL run without sidelobes. We speculate that once
ground clutter is included the enhanced return from the
ground will overwhelm this numerical artifact and re-
sult in higher reflectivity uniformly across the radar do-
main at small elevation angles.
e. Experiment with PRF and effects on velocity
aliasing
In experiment EXP5, the pulse repetition frequency
(PRF) was set to 1000 Hz instead of the 1500 Hz in
FIG. 13. PPI of returned power difference between CNTL and EXP8, showing clearly the
range propagation effect of Rayleigh attenuation at X band.
TABLE 3. Configuration parameters for CASA radars.
Radar parameter Matched sampling Oversampled
 (cm) 3 3
Beamwidth (°) 2 2
PRF (Hz) 2000 2000
Rotation rate (° s1) 40 40
Pulses per radial 100 50
Pulse length (
s) 0.5 0.5
Gate length (m) 100 100
Az (°) 2 1
1986 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 13 live 4/C

CNTL, and 50 pulses were used for each radial instead
of 75, to keep the azimuthal sampling interval the same
(1°). This changes the Nyquist velocity from 37.5 m s1
for CNTL to 25 m s1 for EXP5. Figure 9c shows a PPI
of the Doppler velocity for this case. The reduced
Nyquist velocity causes more velocity aliasing, espe-
cially in the mesocyclone and tornado region. There are
also subtle differences in the Ze (Fig. 9b) and spectrum
width (Fig. 9d) fields, which are caused by the change to
a lower PRF and using fewer samples to generate a
radial of data. This experiment illustrates the advantage
of using high PRFs to reduce velocity aliasing. This
becomes particularly important at shorter wavelengths,
since the Nyquist velocity scales linearly with the trans-
mitted wavelength.
f. Experiment with beamwidth
In EXP6 the half-power beamwidth was increased
from 1° to 2° (effectively halving the diameter of the
dish) while keeping the azimuthal sampling interval the
same. This effectively yields azimuthally oversampled
FIG. 14. PPIs of (a) equivalent reflectivity factor, (b) spectrum width, (c) aliased Doppler
velocity, and (d) nonaliased Doppler velocity for a radar located 3 km from the tornado using
matched sampling. The black circle indicates the location and size of the tornado in the model.
TABLE 4. Calculated tornado parameters for emulated CASA
radars.
Expt (radar range,
oversampling)
Vmax
(m s1)
V
(m s1)
D
(m)
2 V/D
(s1)
3 km, matched 49.1 93.3 216 0.864
3 km, oversampled 55.7 110.6 216 1.024
10 km, matched 35.2 57.6 705 0.163
10 km, oversampled 36.3 62.7 529 0.237
30 km, matched 31.8 33.4 1047 0.064
30 km, oversampled 32.3 42.7 1047 0.082
50 km, matched 27.5 29.5 1749 0.034
50 km, oversampled 28.5 38.6 1749 0.044
DECEMBER 2007 M A Y E T A L . 1987
Fig 14 live 4/C

data, since the 1° azimuthal sampling interval is smaller
than the antenna’s half-power beamwidth (Fig. 10).
Comparing the data with those from CNTL (Fig. 4), it
is clear that the broader beam decreases the peak ve-
locities retrieved by the emulator within the tornado
(Fig. 10c). Specifically, the maximum outbound velocity
is decreased from 38 to 31 m s1. Changing the half-
power beamwidth also increases the spectrum width in
the entire region of mesocyclone, which is a conse-
quence of the larger sampling volumes.
g. Second-trip echoes and range aliasing
The purpose of EXP7 was to demonstrate the emu-
lator’s ability to simulate range aliasing. In this case, the
radar is located approximately 100 km from the storm’s
mesocyclone. Otherwise, the scanning strategy is the
same as CNTL, which had an unambiguous range of
100 km. With this scanning strategy, part of the storm is
located beyond the unambiguous range, resulting in
second-trip echoes from 0- to 35-km range (Fig. 11).
These echoes look very narrow as a result of the fixed
angular resolution of the data, which causes distortion
since the data are assigned to a much closer range than
their actual location. It is important to note that cur-
rently the velocities from the second-trip echoes are
determined by assuming a fixed-phase transmitter, like
a klystron, which makes the Doppler velocities and
spectrum widths of the second-trip echoes coherent.
Emulation of a random phase transmitter, like a mag-
netron, could be accomplished by assigning a random
value of velocity for each sample of the radar pulse for
the second-trip echo.
h. Radar wavelength and effects on attenuation and
velocity aliasing
EXP8 was identical to CNTL, except that the trans-
mitted wavelength of the radar was changed from 10 cm
(S band) to 3 cm (X band). Comparing the returned
FIG. 15. As in Fig. 14, but for the radar azimuthally oversampling by a factor of 2.
1988 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 15 live 4/C

power in EXP8 (Fig. 12a) to that in CNTL (Fig. 3a)
reveals the effects of Rayleigh attenuation at X band.
On the radar side of the storm, the X-band returned
power is approximately 10 dB greater than that of the S
band (Fig. 13), as expected from the dependence of
returned power on the transmitted wavelength [Eq.
(16)]. On the opposite side of the storm from the radar,
this difference decreases to 3 dB, corresponding to
7 dB decrease in the returned power at X band due to
Rayleigh attenuation. As previously mentioned, the
Rayleigh approximation underestimates attenuation at
shorter wavelengths, so the actual attenuation at X
band for such a storm would be much greater. Here we
are merely demonstrating the ability of the emulator to
properly handle the propagation effects. The current
algorithm could easily incorporate extinction cross sec-
tions from Mie (1908) or T-matrix (Waterman 1965)
calculations. In addition to non-Rayleigh attenuation,
the model does not include ice microphysics. Hence,
wet hail, a strong attenuator (Battan 1971), is not in-
cluded.
Another significant difference between S band and X
band is the amount of velocity aliasing (Fig. 12c). At X
band, the Nyquist velocity for a given PRF is 30% of
that at S band; in EXP8, the Nyquist velocity is 11.25
m s1. Consequently, the EXP8 Doppler velocity field
shows a large amount of aliasing, with some regions,
such as the storm’s mesocyclone, exhibiting aliasing by
more than one Nyquist interval.
4. Application to tornado detection
To illustrate the research and operational value of
the radar emulator, the detectability of tornadic signa-
tures is examined as a function of the radar range from
the tornado and the azimuthal sampling interval. The
emulated radar characteristics (Table 3) follow those of
the Integrated Project 1 (IP1) radars deployed by the
FIG. 16. As in Fig. 14, but for a radar located 10 km from the tornado.
DECEMBER 2007 M A Y E T A L . 1989
Fig 16 live 4/C

CASA Engineering Research Center (Brotzge et al.
2005). To keep cost low, these radars have a broad
beam (2° half-power beamwidth), use relatively low
power (25 kW), and operate at X band. One of the
goals of CASA is to improve the detection of low-level
hazardous weather, such as tornadoes, by placing the
radars close to each other and by performing collabo-
rative adaptive sampling of the lowest 3 km of the at-
mosphere. The average radar spacing of the IP1 net-
work is about 30 km.
Using the known location and intensity of the tor-
nado in the model as a baseline, this study examines the
values of several tornado intensity metrics, including
maximum velocity Vmax, maximum radial velocity dif-
ference V, diameter D, and axisymmetric vorticity a,
as determined directly from the emulated radial veloc-
ity data. They are examined as functions of range (3, 10,
30, and 50 km) from the tornado, using both azimuth-
ally matched sampling (2° intervals) and oversampling
(at 1° intervals). The axisymmetric vorticity, defined as
the vorticity for an axisymmetric vortex having the
same V and diameter as the tornado, is given by
a 
2V
D
. 25
The intensity parameters are used to quantify the range
dependency of tornado detection by 2° beam X-band
radars. To eliminate the impact of dealiasing algo-
rithms, this quantitative analysis assumes perfectly
dealiased Doppler velocities and, hence, represents the
best-case scenario. Furthermore, the known location of
the tornado is used to choose the gates for the calcula-
tion of the parameters, as opposed to choosing a loca-
tion based on the position of the velocity maxima in the
data. The values of these parameters for all cases, with
different range and azimuthal sampling combinations,
are listed in Table 4. It should also be noted that the
FIG. 17. As in Fig. 16, but for a radar azimuthally oversampling by a factor of 2.
1990 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 17 live 4/C

viewing angle chosen here (from northeast) minimizes
the impact of attenuation at X band.
At 3-km range, the tornado can be clearly identified
in both the matched and oversampled moment data
(Figs. 14 and 15). The tornado resides in the tip of a
well-defined hook echo in a region of enhanced spec-
trum width. At this range, the strong flow within the
tornado can be diagnosed even in the aliased Doppler
radial velocity field, especially when the storm is azi-
muthally oversampled by the radar beam. Indeed, the
oversampled unaliased velocity field (Fig. 15d) shows
separated inbound and outbound velocity maxima in
the tornado vortex. Separation between maximum ra-
dial velocities is a useful criterion for resolving a tor-
nadic circulation. Even at this close range, however, the
peak Doppler velocity of the tornado measured by the
radar (Table 4) is greatly decreased from the true value
of 78 m s1. The distance between peak Doppler ve-
locities, 216 m, agrees well with the 200 m distance
between velocity maxima in the model field. Axisym-
metric vorticities of 0.864 and 1.024 s1 for the matched
and oversampled cases, respectively, further indicate
that the tornadic circulation is well resolved by the 2°
half-power beamwidth radar at 3-km range.
Moving the radar to 10 km away from the tornado
resulted in degradation of the radar-derived structure
as the geometric width of the beam increased (Figs. 16
and 17). While the hook echo and maxima in spectrum
width were still fairly well resolved in the matched sam-
pling case, the peak Doppler velocities associated with
the tornado were located much farther apart (705 m),
with the peak velocity down to 35.2 m s1. Conse-
quently, the estimated vorticity decreased to 0.163 s1,
or 20% of the value obtained at 3-km range. It should
be noted that the peak inbound velocity measured with
the tornado was only 22.4 m s1, less than the 24.1
m s1 inbound velocity associated with the mesocy-
clone. It is only when the storm was azimuthally over-
FIG. 18. As in Fig. 14, but for a radar located 30 km from the tornado.
DECEMBER 2007 M A Y E T A L . 1991
Fig 18 live 4/C

sampled that the tornadic circulation was resolved at
10-km range with the current radar system. With 1°
azimuthal sampling (Fig. 17), the distance between the
velocity maxima decreased to 529 m, which was the
main factor for the increase in the axisymmetric vortic-
ity to 0.237 s1.
At 30-km range with matched sampling, the structure
of the hook echo and spectrum width field is so de-
graded that the location of the tornado is no longer well
diagnosed by the radar parameters (Fig. 18). Even the
nonaliased velocity field no longer shows separate ve-
locity maxima for the tornado and mesocyclone. In-
stead, a single maximum is located several gates away
from the known location of the tornado. The tornado-
scale flow is no longer resolved because the half-power
beamwidth is over 1 km wide at this range, roughly 5
times the diameter of the tornado. Also at this range,
the poor resolution of the data makes distinguishing
storm shear from regions of aliased velocity a challenge
(Fig. 18c). Using the known location of the tornado, a
vorticity estimate of 0.064 s1 is calculated for this cir-
culation. Such a low vorticity estimate would likely not
be associated with a strong tornadic mesocyclone. It
should be noted that the inbound velocity measured
and used in the calculation is only 1.6 m s1. Even when
oversampling is performed (Fig. 19) the tornadic circu-
lation is still not resolved by a 2° beamwidth radar when
it is located 30 km away. While the separation between
the maximum inbound and outbound velocities in the
mesocyclone and a region of enhanced spectrum width
exists, there is no indication of a tornado vortex signa-
ture (Brown et al. 1978). Furthermore, dealiasing the
X-band radial velocity field becomes challenging, as the
beam containing the tornado appears to be embedded
in a broad-scale region of aliased inbound velocities. In
reality, the minimum in radial velocity associated with
the tornado separates aliased inbound velocities from
the true receding flow.
FIG. 19. As in Fig. 18, but for a radar azimuthally oversampling by a factor of 2.
1992 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 19 live 4/C

At 50-km range, the half-power beamwidth is 1.7 km
across, reducing even the mesocyclone-scale circulation
to gate-to-gate shear and completely obscuring the tor-
nado-scale flow (Figs. 20, 21). It would be very difficult
to detect reliably a tornado with the size and intensity
as in the simulation using only the moment data at this
range.
5. Conclusions
A Doppler radar emulator based on Rayleigh scat-
tering has been developed that simulates a wide range
of radar operating characteristics, including range and
azimuthal oversampling, velocity and range aliasing,
Rayleigh attenuation, second-trip echoes, antenna side-
lobes, and anomalous propagation. The emulator cal-
culates returned power, equivalent radar reflectivity
factor, Doppler velocity, and Doppler spectrum width
from cloud model output containing fields of wind,
temperature, moisture, and hydrometeor species. The
capabilities of the emulator are demonstrated using a
high-spatial-resolution simulation of a tornado embed-
ded within a supercell thunderstorm. It is shown that
the emulator is a useful tool for evaluating the capa-
bilities and trade-offs in the design, deployment, and
operation of radar systems. Given that the emulator
can produce numerous synthetic datasets for a wide
range of storm types and radar characteristics, we be-
lieve that such a tool can be a significant aid in the
development of radar algorithms. Such realistically
emulated data can also be used in observing system
simulation experiments (OSSEs) such as those of Xue
et al. (2006) for examining the potential impact of radar
data on thunderstorm analysis and prediction.
Using the output from a 50-m horizontal-resolution
simulation of a supercell storm that explicitly resolves
FIG. 20. As in Fig. 14, but for a radar located 50 km from the tornado.
DECEMBER 2007 M A Y E T A L . 1993
Fig 20 live 4/C

an F3 intensity tornado of about 200 m in diameter, the
basic capabilities of the emulator are first tested in a set
of experiments that examines the effects of radar wave-
length, beamwidth, azimuthal oversampling, gate
length, sidelobes, pulse repetition frequency, and the
effects of velocity and range aliasing. Results consistent
with theory are observed from the simulated data.
As an example of the emulator’s many potential ap-
plications, the detection of the simulated tornado de-
scribed above by a 2° half-power beamwidth X-band
radar is examined. The emulated data show that the
strength of the diagnosed tornado circulation decreases
rapidly with range, with the tornado-scale flow becom-
ing unresolved at and beyond 30 km. Azimuthal over-
sampling improves the ability to diagnose the tornado
vortex, especially from the 10- to 30-km ranges. At
shorter ranges, the 2° beam-matched azimuthal sam-
pling is sufficient. It is important to note that the simu-
lated tornado examined here represents the top 10% of
tornadoes occurring in nature in terms of intensity. The
much more prevalent weaker and/or smaller tornadoes
will be even harder to detect.
A significant problem demonstrated by the emulator
is the impact of velocity aliasing at X band on the po-
tential diagnosis of the circulations. Correct dealiasing
is crucial to tornado detection when the detection al-
gorithm mainly relies on the radial velocity data (e.g.,
Burgess et al. 1993; Liu et al. 2007). Any method that
can increase the effective Nyquist velocity, such as the
use of staggered PRT (Gray et al. 1989), would likely be
helpful.
Future studies will include more radar operating pa-
rameters as well as the use of objective algorithms to
evaluate tornado detection for broad-beam X-band ra-
dars. This work is motivated by the Integrated Project
I (IP1) of the Collaborative Adaptive Sensing of the
Atmosphere (CASA; Brotzge et al. 2005) Engineering
Research Center that recently deployed four 2° half-
FIG. 21. As in Fig. 20, but for a radar azimuthally oversampling by a factor of 2.
1994 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24
Fig 21 live 4/C

power beamwidth X-band radars in central Oklahoma.
One of the goals of such inexpensive networks is tor-
nado detection, based on the promise of being able to
observe at low altitudes (0–3 km) and at short ranges
(less than 30 km), and do so in a collaborative and
adaptive manner. In the future, the radar emulator will
be further enhanced to include Mie scattering, as well
as scattering from ice-phase hydrometeors, and the an-
tenna routine will be modified to allow for emulation
(using many model time steps) of electronically steered
phased-array radars that can point the beam in arbi-
trary directions on a pulse-to-pulse basis. This will en-
able applied research in the phased array radar (For-
syth et al. 2005) program and further enhance the edu-
cational utility of the radar emulator.
Acknowledgments. This work was supported by
graduate research fellowships sponsored by the Office
of Naval Research through the American Meteorologi-
cal Society and by the Army Research Office through
the National Defense Science and Engineering Gradu-
ate Fellowship program. Partial support was also pro-
vided by NSF Grant EEC-0313747 to the CASA ERC.
M. Biggerstaff was supported by NSF Grants ATM-
0619715, ATM-0410564, and ATM-0618727, while M.
Xue was supported by NSF Grants ATM-0129892,
ATM-0331594, ATM-0331756, and ATM-0530814. The
authors would also like to thank two anonymous re-
viewers whose many comments helped improve the
quality of this work.
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