Airborne Weather Radars
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Outline
• Research radars on NOAA and NCAR aircraft
• Scientific “roles”
• Sampling considerations for wind field analysis
• Basic Idea
• Single-Doppler
• Dual-Doppler
• Quad-Doppler
• Editing Doppler radar data
• Synthesizing Doppler radar data
• Interpolating data to Cartesian grid
• Traditional Method
• Variational Method
• Remain aware of potential errors and assumptions
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Research Radars: NOAA WP-3D Research Aircraft
Parameter
LF
TA
Frequency
5.37 GHz
9.32 GHz
Wavelength
5.6 cm (C-band)
3.2 cm (X-band)
Radial resolution
250 m
125 m
Maximum PRF
200 s-1
1600 s-1
Transmitted power
70 kW
60 kW
Pulse duration
6.0 μs
0.5 μs
Beam width
1.1°
1.5°
Tail (TA)
Gain
37.5 dB
40.0 dB
• Doppler
• Single antenna with adjustable tilt
• Scans in “vertical” plane normal
to the aircraft track during periods
of level flight
Rotation period
30 s
6s
Maximum Range
371 km
93 km
Lower Fuselage (LF)
• Non-Doppler
• Scans at a single elevation angle
in the “horizontal” plane during
periods of level flight
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Scientific Roles: NOAA WP-3D Lower Fuselage Radar
• Data used in real-time to “guide”
scientists to desired study locations
(each flight has specific goals)
• Images sent back to the National
Hurricane Center (NHC) at regular
real-time intervals to help forecasters
deduce relevant storm structure
(symmetric vs. asymmetric)
(single vs. multiple eyewalls)
(intensity of convection)
• Used post-flight to document storm
precipitation content and structure
for research purposes
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Scientific Roles: NOAA WP-3D Tail Radar
• Data use in real-time to construct a “first-order” three-dimensional wind analysis
• Assimilated into mesoscale forecast models (HWRF and GFDL) to provide
basic storm structure for “bogus” vortex
• Sent to NHC so forecasters can deduce basic storm structure
• Used post-flight to construct “detailed” three-dimensional wind analyses for studies
of convective storm structure and evolution
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Research Radars: NCAR Electra Research Aircraft
Parameter
TA
(both antenna)
Frequency
9.40 GHz
Wavelength
3.2 cm (X-band)
Lower Fuselage (LF)
Radial resolution
150 m
• None
Maximum PRF
2000 s-1
Transmitted power
50 kW
Pulse duration
1.0 μs
Beam width
1.8°
Gain
38.7 dB
Rotation period
5.5 s
Maximum Range
70 km
Tail (TA)
• Doppler
• Two antenna fixed at 18.5° fore and aft
• Scan in “vertical” plane normal to the
aircraft track during periods of level flight
Note: This aircraft and its radar design
built upon the successes of the
prototype NOAA aircraft radars
Radar Meteorology
M. D. Eastin
Airborne Weather Radars
Scientific Roles: NCAR Electra Tail Radar
• Used post-flight to construct “detailed” three-dimensional wind analyses for studies
of convective storm structure and evolution
Radar Meteorology
M. D. Eastin
Sampling Considerations
Basic Idea:
• In order to construct a three dimensional wind field from Doppler radar data, multiple
“views” of the same location within a given storm are required
• One “view” provides only along beam wind component (two- or three-dimensional
wind field is then qualitatively inferred from careful examination – NEXRAD)
• Two “views” provide two unique along-beam wind components that can be used
to calculate the three-dimensional wind (with a few assumptions…)
VR
Radar 1
VR
Radar 1
Actual
wind
Radar 1
Radar 2
• More than two “views” provide a set of over-sampled unique winds from which
a more accurate three-dimensional wind can be estimated (with assumptions…)
Radar Meteorology
M. D. Eastin
Sampling Considerations
Assumptions associated with the construction of Doppler wind analyses:
• Winds and storm structure are steady during the sampling period between unique views
(which can be 1-2 minutes…)
• Storm motion is constant during the sampling period
• Difference in contributing volumes for the two radar views are negligible
• Application of Z-R relationships can effectively remove precipitation fall velocities
at all altitudes (…usually one for ice particles and one for water particles)
• All remaining radial velocity measurements are representative of actual air motions
(i.e. all non-meteorological returns must be removed…)
Radar Meteorology
M. D. Eastin
Sampling Considerations
Single Airborne Doppler Radar: Normal-plane scanning
• Antenna rotates through plane at 90°
to the flight track
• Aircraft must “box-off” target convection
by flying adjacent leg over a short period
and then turning 90 and flying a second
leg of similar length
Aircraft
track
• Provides two views over 10-20 minutes
at typical aircraft speeds
• Permits a “pseudo” dual-Doppler analysis
Aircraft
track
Radar Meteorology
M. D. Eastin
Sampling Considerations
Single Airborne Doppler Radar: Fore-Aft Scanning Technique (FAST)
• Antenna alternates tilts of ~20° fore
and ~20° aft between each rotation
• Provides two views over 1-2 minutes
at typical aircraft speeds
• Does not require aircraft
to box-off convection
aft
radar
scan
fore
radar
scan
• Permits a “pseudo” dual-Doppler
analysis with less concern for
storm steadiness
Radar Meteorology
M. D. Eastin
Sampling Considerations
Dual Airborne Doppler Radar: Normal-plane scanning
• Two aircraft flying coordinated orthogonal
patterns near target convection
• Both antenna rotate through plane at 90°
to the flight track
Aircraft #1
track
• Provides two views over 1-2 minutes
at typical aircraft speeds
• Permits a “true” dual-Doppler analysis
Radar Meteorology
Aircraft #2
track
M. D. Eastin
Sampling Considerations
Dual Airborne Doppler Radar: Fore-Aft Scanning Technique (FAST)
• Two aircraft fly coordinated parallel
patterns near target convection
• Both antenna alternates tilts of ~20° fore
and ~20° aft between each rotation
• Provides four views over 1-2 minutes
at typical aircraft speeds
• Permits “quad” Doppler analyses
with less concern of storm steadiness
and an over-sampling of the wind
vectors for better accuracy
Radar Meteorology
M. D. Eastin
Constructing Doppler Wind Analyses
Four Basic Steps:
1. Edit raw radar data to remove navigation errors, aircraft motion, sea clutter,
second-trip echoes, side-lobe contamination, low-power (or noisy) returns,
and unfold any folded radial velocities
2. Interpolating the radar reflectivity and radial velocities from each radar view
to a common Cartesian grid
3. Calculation of the horizontal wind components at each grid point from the
multiple Doppler views
4. Calculation of the vertical wind component through integration of the continuity
equation with height
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Navigation Errors:
• The aircraft’s navigation system has
inherent uncertainties:
Drift angle
Pitch angle
Roll angle
Altitude
Horizontal velocity
Vertical velocity
± 0.05°
± 0.05°
± 0.05°
± 10 m
± 2.0 m/s
± 0.15 m/s
Drift
• The radar antenna may also contain
systematic (e.g. mounting) errors:
Tilt angle
Spin angle
± 1.0°
± 1.0°
• Environmental considerations:
Surface is not flat (terrain)
Surface is not stationary (ocean currents)
Testud et al. 1995
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Navigation Errors:
• Discussed by Testud et al. (1995) and Bosart et al. (2002) in detail (on course website…)
• Determined during periods of “straight” and “level” flight in “clear air” regions
Testud et al. 1995
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Aircraft Motion:
Raw Data (with navigation corrections applied)
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Rings of Bad Data:
Raw Data (with aircraft motion removed)
Rings of bad data
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Low-Power and Noisy Data:
Raw Data (with rings of bad data removed)
Low-Power and Noisy Data
(large spectral widths)
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing Sea Clutter:
Raw Data (with low-power and noisy data removed)
Signal from sea clutter
(i.e. the ocean surface)
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing second trip echoes and side-lobe contamination:
Raw Data (with most sea clutter removed – manually)
Some sea clutter remains
Second trip echoes
Side-lobe contamination
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Removing second trip echoes and side-lobe contamination:
Raw Data (with most second trip and side-lobe echoes removed – manually)
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Unfolding Radial Velocities: Those not corrected by automated method
Raw Data (with most second trip and side-lobe echoes removed – manually)
Folded radial velocities
Radar Meteorology
Some side-lobe contamination
remains (remove manually)
M. D. Eastin
Editing Doppler Radar Data
A “clean” edited radar sweep:
Raw Data (with all corrections applied)
Radar Meteorology
M. D. Eastin
Editing Doppler Radar Data
Now repeat the process 150 times
for a 15 minute
dual-Doppler period!
Radar Meteorology
M. D. Eastin
Interpolating Data to a Cartesian Grid
Coordinate transformation:
Raw (edited) Radar Data
• The edited radar data location
references a spherical grid
Tilt angle (τ, ψ)
Pitch angle (β)
Drift angle (α)
Roll angle (φ)
Azimuth angle (λ)
Elevation angle (θ)
Range (r)
X – distance
Y – distance
Z – distance
• Requires a transformation matrix
• Requires a lot of trigonometry
Testud et al. 1995
Transformed Radar Data
• Radial velocities (vr) are transformed
to Cartesian velocities (u, v, w)
• Details are in Lee et al. (1994)
(on the course website…)
Lee et al. 1994
Radar Meteorology
M. D. Eastin
Interpolating Data to a Cartesian Grid
Interpolation Method: Closest point
Red = Cartesian point
Green = Points in radar space
Value at this point
assigned to Cartesian point
Radar Meteorology
M. D. Eastin
Interpolating Data to a Cartesian Grid
Interpolation Method: Bilinear interpolation
• Uses eight (8) nearest neighbors in radar space
Radar Meteorology
M. D. Eastin
Interpolating Data to a Cartesian Grid
Interpolation Method: Weighting Functions
• Uses “radius of influence” concept
• All points within sphere of radius R about
the Cartesian point will be used to obtain
the value at the Cartesian point
R  x2  y 2  z 2
• Each point within the sphere is then weighted according to its distance from the
Cartesian point → the weighting function (W) acts as a filter, allowing certain
spatial scales while suppressing others
Equal weighting
W 1
Arithmetic mean of all points
within radius of influence R
Cressman weighting
R2  r 2
W 2
R  r2
where r is the distance from the
Cartesian point to the point in
spherical coordinates
Exponential weighting
  ar 2 
W  exp  2 
 R 
where a is the “e-folding” distance
defined by the user
Radar Meteorology
M. D. Eastin
Traditional Method of Synthesis
Calculation of Horizontal Winds: A two “view” example
• Relations between Radial and Cartesian velocities:
vR 1  U sin  1 sin  1  V cos  1 sin  1  W  VT  cos  1
vR2  U sin  2 sin  2  V cos  2 sin  2  W  VT  cos  2
where:
vR
U, V, W
VT
= Doppler radial velocity
= X, Y, Z velocities
= Hydrometeor terminal velocity
Jorgensen et al. 1983
Radar Meteorology
M. D. Eastin
Traditional Method of Synthesis
Calculation of Horizontal Winds: A two “view” example
vR 1  U sin  1 sin  1  V cos  1 sin  1  W  VT  cos  1
vR2  U sin  2 sin  2  V cos  2 sin  2  W  VT  cos  2
• If we neglect the (W + VT) cos θ2 terms and restrict elevation angles to ±45° from horizontal,
the horizontal winds at ranges > 10 km from the aircraft can be determined throughout the
storm depth (up to 15 km):
 vR1 cos  2 vR 2 cos  2 
U



sin 1   2   sin 1
sin  2 
1
 vR 2 sin 1 vR1 sin 1 
V



sin 1   2   sin  2
sin 1 
1
• See Jorgensen et al. (1983) for details (on the course website…)
Radar Meteorology
M. D. Eastin
Traditional Method of Synthesis
Calculation of Vertical Winds:
Recall:
Vertical and horizontal velocities are linked through the continuity equation :
 u v 
w
     
z
 x y 
where ρ = density of air (which decreases exponentially with height)
Three options:
1. Integrate the continuity equation upward from the surface specifying a lower
boundary condition (e.g. w = 0 at sea level)
2. Integrate the continuity equation downward from the echo top specifying an
upper boundary condition (e.g. w = 0 at echo top)
3. Perform a variational integration by specifying lower and upper boundary
conditions (e.g. w = 0 at sea level and echo top)
Radar Meteorology
M. D. Eastin
Traditional Method of Synthesis
Calculation of Vertical Winds:
Which method is better?
• Error analysis suggests the variational
method performs the best throughout
the depth → minimizes errors from
upward and downward integration
Errors associated with a wind field
composed of random noise
Upward
Variational
• Downward integration is second best
(performs poorly near the surface)
• Upward integration is the worst
(performs poorly at upper levels)
Downward
Radar Meteorology
M. D. Eastin
Traditional Method of Synthesis
An Example:
Quad
Doppler
Analysis
Winds
Reflectivity
z = 3.5 km
A
Aircraft #1
Track
B
Radar Meteorology
Aircraft #2
Track
M. D. Eastin
Traditional Method of Synthesis
An Example:
A
B
A
Radar Meteorology
B
M. D. Eastin
Traditional Method of Synthesis
Limitations:
• Assumes radial velocities contain no vertical motion
• Only valid for horizontal radar beams
• Other elevation angles have |W +VT| > 0
No Winds
Winds
• Prevents wind synthesis near the radar (aircraft)
• Horizontal winds are not estimated
well at elevations angles > 45°
Winds
No Winds
• Difficult to resolve storm top close to radar (aircraft)
No Winds
• Difficult to perform wind synthesis when aircraft must
fly through the target convection (e.g. a hurricane)
Winds
Winds
No Winds
Radar Meteorology
M. D. Eastin
Variational Method of Synthesis
Simultaneous Calculation of 3-D Winds:
• Uses same relations between Radial and Cartesian velocities as the Traditional Method:
vR 1  U sin  1 sin  1  V cos  1 sin  1  W  VT  cos  1
vR2  U sin  2 sin  2  V cos  2 sin  2  W  VT  cos  2
• Then it performs the following:
• Removes VT at all grid locations using analytic Z-VT relationships
• Calculates a “first guess” horizontal wind field at all grid locations
• Calculates a “first guess” vertical wind field at all grid locations using mass continuity
 Begins an iterative process, by which the total domain difference between the
observed U-V-W fields and the “mass-balanced” U-V-W fields is minimized
 When the total domain difference reaches some minimum threshold, the
mass-balanced U-V-W fields are output as the final wind synthesis
• See the Appendix of Reasor et al. (2009) for details (on the course website…)
Radar Meteorology
M. D. Eastin
Variational Method of Synthesis
Advantages:
• Uses radial velocities at large elevations angles (i.e. above and below the aircraft)
• Permits quality wind syntheses when aircraft are flying near or through convection
An example:
W
Note: Analysis is a
mirror image
of raw data
Radar Meteorology
M. D. Eastin
Remain Aware!
Multiple Doppler analyses can be a powerful technique to recover wind fields, but
the user must remain aware of the errors that may impact the analyses!
Factors:
• Uncertainty in raw radial velocity measurements (spectral width)
• Attenuation can affect signal-to-noise power ratio
• Uncertainty in aircraft location and orientation relative to a flat surface
• Uncertainty in radar orientation relative to the aircraft (mounting errors)
• Assumption of steady wind field and storm structure over sampling period
• Assumption of a constant storm motion over sampling period
• Effective removal of sea clutter, side-lobes, and second-trip echoes?
• Geometric assumptions associated with coordinate transforms
• Assumption of boundary conditions (Is w = 0 at surface and echo top?)
• Assumption of air density profile
• Assumption of Z-VT relationships to remove hydrometeor fall velocity
Nevertheless, many quality Doppler wind analyses have provided meteorologists with
very comprehensive views of flow structure and evolution within convective storms!
Radar Meteorology
M. D. Eastin