1. Radar MeteorologyM. D. Eastin Airborne Weather Radars

2. Radar MeteorologyM. 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

3. Radar MeteorologyM. 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 ParameterLFTA Frequency5.37 GHz9.32 GHz Wavelength5.6 cm (C-band)3.2 cm (X-band) Radial resolution250 m125 m Maximum PRF200 s -1 1600 s -1 Transmitted power70 kW60 kW Pulse duration6.0 μs0.5 μs Beam width1.1°1.5° Gain37.5 dB40.0 dB Rotation period30 s6 s Maximum Range371 km93 km

4. Radar MeteorologyM. 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

5. Radar MeteorologyM. 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

6. 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 MeteorologyM. D. Eastin Airborne Weather Radars ParameterTA (both antenna) Frequency9.40 GHz Wavelength3.2 cm (X-band) Radial resolution150 m Maximum PRF2000 s -1 Transmitted power50 kW Pulse duration1.0 μs Beam width1.8° Gain38.7 dB Rotation period5.5 s Maximum Range70 km

7. Radar MeteorologyM. 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

8. Radar MeteorologyM. 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 1Radar 2 Actual wind VR Radar 1 VR Radar 1

9. Radar MeteorologyM. 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

10. Radar MeteorologyM. 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

11. Radar MeteorologyM. 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 radar scan aft radar scan

12. Radar MeteorologyM. 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

13. Radar MeteorologyM. 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

14. Radar MeteorologyM. 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

15. Radar MeteorologyM. 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

16. Radar MeteorologyM. 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

17. Radar MeteorologyM. D. Eastin Removing Aircraft Motion: Editing Doppler Radar Data Raw Data (with navigation corrections applied)

18. Radar MeteorologyM. D. Eastin Removing Rings of Bad Data: Editing Doppler Radar Data Raw Data (with aircraft motion removed) Rings of bad data

19. Radar MeteorologyM. 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)

20. Radar MeteorologyM. 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)

21. Radar MeteorologyM. 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 remains Second trip echoes Side-lobe contamination

22. Radar MeteorologyM. 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)

23. Radar MeteorologyM. 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 contamination remains (remove manually) Folded radial velocities

24. Radar MeteorologyM. D. Eastin A “clean” edited radar sweep: Editing Doppler Radar Data Raw Data (with all corrections applied)

25. Radar MeteorologyM. D. Eastin Now repeat the process 150 times for a 15 minute dual-Doppler period! Editing Doppler Radar Data

26. Radar MeteorologyM. D. Eastin Interpolating Data to a Cartesian Grid Coordinate 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 (v r ) 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

27. Radar MeteorologyM. 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

28. Radar MeteorologyM. D. Eastin Interpolating Data to a Cartesian Grid Interpolation Method: Bilinear interpolation Uses eight (8) nearest neighbors in radar space

29. Radar MeteorologyM. 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 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 weightingArithmetic mean of all points within radius of influence R Cressman weightingwhere r is the distance from the Cartesian point to the point in spherical coordinates Exponential weightingwhere a is the “e-folding” distance defined by the user

30. Radar MeteorologyM. D. Eastin Traditional Method of Synthesis Calculation of Horizontal Winds: A two “view” example Relations between Radial and Cartesian velocities: where: v R = Doppler radial velocity U, V, W = X, Y, Z velocities V T = Hydrometeor terminal velocity Jorgensen et al. 1983

31. Radar MeteorologyM. D. Eastin Traditional Method of Synthesis Calculation of Horizontal Winds: A two “view” example If we neglect the (W + V T ) cos θ 2 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…)

32. Radar MeteorologyM. 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 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)

33. Radar MeteorologyM. 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 field composed of random noise Upward Variational Downward

34. Radar MeteorologyM. D. Eastin Traditional Method of Synthesis An Example: Aircraft #2 Track Aircraft #1 Track Quad Doppler Analysis A B Winds Reflectivity z = 3.5 km

35. Radar MeteorologyM. D. Eastin Traditional Method of Synthesis An Example: A B B A

36. Radar MeteorologyM. 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 +V T | > 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 Winds No Winds Winds

37. Radar MeteorologyM. 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 V T at all grid locations using analytic Z-V T 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

38. Radar MeteorologyM. 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

39. Radar MeteorologyM. 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-V T 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!