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Radar Meteorology M. D. Eastin
Airborne Weather Radars
Radar Meteorology M. D. Eastin
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
Airborne Weather Radars
Radar Meteorology M. D. Eastin
Research Radars: NOAA WP-3D Research Aircraft
Lower Fuselage (LF)
• Non-Doppler• Scans at a single elevation angle in the “horizontal” plane during periods of level flight
Tail (TA)
• Doppler• Single antenna with adjustable tilt• Scans in “vertical” plane normal to the aircraft track during periods of level flight
Airborne Weather Radars
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°
Gain 37.5 dB 40.0 dB
Rotation period 30 s 6 s
Maximum Range 371 km 93 km
Radar Meteorology M. D. Eastin
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
Airborne Weather Radars
Radar Meteorology M. D. Eastin
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
Airborne Weather Radars
Research Radars: NCAR Electra Research Aircraft
Lower Fuselage (LF)
• None
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
Parameter TA (both antenna)
Frequency 9.40 GHz
Wavelength 3.2 cm (X-band)
Radial resolution 150 m
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
Radar Meteorology M. D. Eastin
Scientific Roles: NCAR Electra Tail Radar
• Used post-flight to construct “detailed” three-dimensional wind analyses for studies of convective storm structure and evolution
Airborne Weather Radars
Radar Meteorology M. D. Eastin
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…)
• 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…)
Sampling Considerations
Radar 1 Radar 2
Actualwind
VRRadar 1
VRRadar 1
Radar Meteorology M. D. Eastin
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…)
Sampling Considerations
Radar Meteorology M. D. Eastin
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
• Provides two views over 10-20 minutes at typical aircraft speeds
• Permits a “pseudo” dual-Doppler analysis
Sampling Considerations
Aircraft track
Aircraft track
Radar Meteorology M. D. Eastin
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
• Permits a “pseudo” dual-Doppler analysis with less concern for storm steadiness
Sampling Considerations
fore radarscan
aftradarscan
Radar Meteorology M. D. Eastin
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
• Provides two views over 1-2 minutes at typical aircraft speeds
• Permits a “true” dual-Doppler analysis
Sampling Considerations
Aircraft #2 track
Aircraft #1 track
Radar Meteorology M. D. Eastin
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
Sampling Considerations
Radar Meteorology M. D. Eastin
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
Constructing Doppler Wind Analyses
Radar Meteorology M. D. Eastin
Removing Navigation Errors:
• The aircraft’s navigation system has inherent uncertainties:
Drift angle ± 0.05° Pitch angle ± 0.05° Roll angle ± 0.05° Altitude ± 10 m Horizontal velocity ± 2.0 m/s Vertical velocity ± 0.15 m/s
• The radar antenna may also contain systematic (e.g. mounting) errors:
Tilt angle ± 1.0° Spin angle ± 1.0°
• Environmental considerations:
Surface is not flat (terrain) Surface is not stationary (ocean currents)
Editing Doppler Radar Data
Testud et al. 1995
Drift
Radar Meteorology M. D. Eastin
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
Editing Doppler Radar Data
Testud et al. 1995
Radar Meteorology M. D. Eastin
Removing Aircraft Motion:
Editing Doppler Radar Data
Raw Data (with navigation corrections applied)
Radar Meteorology M. D. Eastin
Removing Rings of Bad Data:
Editing Doppler Radar Data
Raw Data (with aircraft motion removed)
Rings of bad data
Radar Meteorology M. D. Eastin
Removing Low-Power and Noisy Data:
Editing Doppler Radar Data
Raw Data (with rings of bad data removed)
Low-Power and Noisy Data(large spectral widths)
Radar Meteorology M. D. Eastin
Removing Sea Clutter:
Editing Doppler Radar Data
Raw Data (with low-power and noisy data removed)
Signal from sea clutter(i.e. the ocean surface)
Radar Meteorology M. D. Eastin
Removing second trip echoes and side-lobe contamination:
Editing Doppler Radar Data
Raw Data (with most sea clutter removed – manually)
Some sea clutter remainsSecond trip echoes
Side-lobe contamination
Radar Meteorology M. D. Eastin
Removing second trip echoes and side-lobe contamination:
Editing Doppler Radar Data
Raw Data (with most second trip and side-lobe echoes removed – manually)
Radar Meteorology M. D. Eastin
Unfolding Radial Velocities: Those not corrected by automated method
Editing Doppler Radar Data
Raw Data (with most second trip and side-lobe echoes removed – manually)
Some side-lobe contaminationremains (remove manually)
Folded radial velocities
Radar Meteorology M. D. Eastin
A “clean” edited radar sweep:
Editing Doppler Radar Data
Raw Data (with all corrections applied)
Radar Meteorology M. D. Eastin
Now repeat the process 150 timesfor a 15 minute
dual-Doppler period!
Editing Doppler Radar Data
Radar Meteorology M. D. Eastin
Interpolating Data to a Cartesian GridCoordinate transformation:
• The edited radar data location references a spherical grid
Tilt angle (τ, ψ) Pitch angle (β) Drift angle (α) X – distance Roll angle (φ) Y – distance Azimuth angle (λ) Z – distance Elevation angle (θ) Range (r)
• Requires a transformation matrix• Requires a lot of trigonometry
• Radial velocities (vr) are transformed to Cartesian velocities (u, v, w)
• Details are in Lee et al. (1994) (on the course website…)
Raw (edited) Radar Data
Transformed Radar Data
Lee et al. 1994
Testud et al. 1995
Radar Meteorology M. D. Eastin
Interpolating Data to a Cartesian GridInterpolation Method: Closest point
Red = Cartesian pointGreen = Points in radar space
Value at this point assigned to Cartesian point
Radar Meteorology M. D. Eastin
Interpolating Data to a Cartesian GridInterpolation Method: Bilinear interpolation
• Uses eight (8) nearest neighbors in radar space
Radar Meteorology M. D. Eastin
Interpolating Data to a Cartesian GridInterpolation 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
• 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 Arithmetic mean of all points within radius of influence R
Cressman weighting where r is the distance from the Cartesian point to the point in spherical coordinates
Exponential weighting where a is the “e-folding” distance defined by the user
222 zyxR
22
22
rR
rRW
2
2
expR
arW
1W
Radar Meteorology M. D. Eastin
Traditional Method of Synthesis Calculation of Horizontal Winds: A two “view” example
• Relations between Radial and Cartesian velocities:
where: vR = Doppler radial velocity U, V, W = X, Y, Z velocities VT = Hydrometeor terminal velocity
111111 cossincossinsin TR VWVUv
222222 cossincossinsin TR VWVUv
Jorgensen et al. 1983
Radar Meteorology M. D. Eastin
Traditional Method of Synthesis Calculation of Horizontal Winds: A two “view” example
• 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):
• See Jorgensen et al. (1983) for details (on the course website…)
2
22
1
21
21 sin
cos
sin
cos
sin
1
RR vv
U
111111 cossincossinsin TR VWVUv
222222 cossincossinsin TR VWVUv
1
11
2
12
21 sin
sin
sin
sin
sin
1
RR vv
V
Radar Meteorology M. D. Eastin
Traditional Method of Synthesis Calculation of Vertical Winds:
Recall: Vertical and horizontal velocities are linked through the continuity equation :
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 anupper boundary condition (e.g. w = 0 at echo top)
3. Perform a variational integration by specifying lower and upper boundaryconditions (e.g. w = 0 at sea level and echo top)
y
v
x
u
z
w
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
• Downward integration is second best (performs poorly near the surface)
• Upward integration is the worst (performs poorly at upper levels)
Errors associated with a wind fieldcomposed of random noise
Upward
Variational
Downward
Radar Meteorology M. D. Eastin
Traditional Method of Synthesis An Example:
Aircraft #2Track
Aircraft #1Track
Quad Doppler Analysis
A
B
WindsReflectivityz = 3.5 km
Radar Meteorology M. D. Eastin
Traditional Method of Synthesis An Example:
A
B
B
A
Radar Meteorology 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
• Prevents wind synthesis near the radar (aircraft)• Horizontal winds are not estimated well at elevations angles > 45°
• Difficult to resolve storm top close to radar (aircraft)
• Difficult to perform wind synthesis when aircraft must fly through the target convection (e.g. a hurricane)
No Winds
No Winds
WindsWinds
No Winds
No Winds
WindsWinds
Radar Meteorology M. D. Eastin
Simultaneous Calculation of 3-D Winds:
• Uses same relations between Radial and Cartesian velocities as the Traditional Method:
• 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…)
111111 cossincossinsin TR VWVUv
222222 cossincossinsin TR VWVUv
Variational Method of Synthesis
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!
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