Radar MeteorologyM. D. Eastin 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



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


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


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



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


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



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


Scientific Roles: NCAR Electra Tail Radar

• Used post-flight to construct “detailed” three-dimensional wind analyses for studies of convective storm structure and evolution



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


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…)



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


Aircraft track

Aircraft track


Single Airborne Doppler Radar: Fore-Aft Scanning Technique (FAST)

• Antenna alternates tilts of ~20° fore and ~20° aft between each rotation


• Does not require aircraft to box-off convection

• Permits a “pseudo” dual-Doppler analysis with less concern for storm steadiness


fore radarscan

aftradarscan


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


• Permits a “true” dual-Doppler analysis


Aircraft #2 track

Aircraft #1 track


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



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


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


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


Removing Aircraft Motion:


Raw Data (with navigation corrections applied)


Removing Rings of Bad Data:


Raw Data (with aircraft motion removed)

Rings of bad data


Removing Low-Power and Noisy Data:


Raw Data (with rings of bad data removed)

Low-Power and Noisy Data(large spectral widths)


Removing Sea Clutter:


Raw Data (with low-power and noisy data removed)

Signal from sea clutter(i.e. the ocean surface)


Removing second trip echoes and side-lobe contamination:


Raw Data (with most sea clutter removed – manually)

Some sea clutter remainsSecond trip echoes

Side-lobe contamination


Removing second trip echoes and side-lobe contamination:


Raw Data (with most second trip and side-lobe echoes removed – manually)


Unfolding Radial Velocities: Those not corrected by automated method


Raw Data (with most second trip and side-lobe echoes removed – manually)

Some side-lobe contaminationremains (remove manually)

Folded radial velocities


A “clean” edited radar sweep:


Raw Data (with all corrections applied)


Now repeat the process 150 timesfor a 15 minute

dual-Doppler period!



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


Interpolating Data to a Cartesian GridInterpolation Method: Closest point

Red = Cartesian pointGreen = Points in radar space

Value at this point assigned to Cartesian point


Interpolating Data to a Cartesian GridInterpolation Method: Bilinear interpolation

• Uses eight (8) nearest neighbors in radar space


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


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


Jorgensen et al. 1983


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



1

11

2

12

21 sin

sin

sin

sin

sin

1

RR vv

V


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


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


Traditional Method of Synthesis An Example:

Aircraft #2Track

Aircraft #1Track

Quad Doppler Analysis

A

B

WindsReflectivityz = 3.5 km


Traditional Method of Synthesis An Example:

A

B

B

A


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


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…)



Variational Method of Synthesis


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


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 MeteorologyM. D. Eastin Airborne Weather Radars.

Documents

Transcript of Radar MeteorologyM. D. Eastin Airborne Weather Radars.