The Structure of Thermals in Cumulus from Airborne DualDoppler Radar Observations

1
The Structure of Thermals in Cumulus from
Airborne Dual-Doppler Radar Observations
Rick Damiani, UWyo

• Laramie, WY. July 11, 2005

2
Summary

• 1. Why do we study thermals and cumulus?
• 2. How can we efficiently study thermals and
  cumulus?
• Dual-Doppler technique and sources of error
• 3. Observations of Cu kinematics in vertical
  planes
• Cloud microphysical kinematic structure
• Entrainment patterns
• Model of cloud growth
• 4. Observations of Cu kinematics in horizontal
  planes
• Extension of the conceptual model of thermals and
  Cus
• 5. What have we learned? What more do we seek?

3
Why thermals and shallow Cus

• They have been studied for more than 50 years
• first investigations of cumulus Stommel(1947),
  Squires (1958), Warner (1977)
• initial thorough studies on thermals Scorer and
  Ludlam (1953)

• We still know very little about how they really
  work
• Entrainment? Where, what scales, how?
• Model of cloud evolution/growth? Plumes/Thermals?

4
Why thermals and shallow Cus

• Are they not fair weather clouds?
• They rarely produce precipitation or severe
  weather

• Shallow convection and cumulus are the basic
  elements of larger-scale convection, i.e. the
  fundamentals for weather and cloud
  over-development

5
Why thermals and shallow Cus

• Are they not small enough to be ignored?
• Small scale features, mostly rooted on
  local/regional convection scales and micro-scale
  atmospheric phenomena

• They redistribute momentum, heat, and moisture in
  the lower troposhere, impacting energy and
  radiation budgets
• GCMs and NWPs need to take into account the
  effects of shallow cumulus convection
• Relevant to air chemistry and aerosol research
  for mixing of chemical species in the lower
  troposphere and limited scavenging via
  precipitation

6
Why thermals and shallow Cus
For FUN!

• For SAFETY!

7
How can we investigate thermals and
Cus?Airborne Doppler radar in situ
WCR/UWKA

• Increased coverage
• Multidimensional investigation
• Fine resolution
• Direct comparison with flight-level data

8
WCR specs.
9
WCR/UWKA Airborne fine-scale dual-Doppler

• The effective plane of scan also depends on the
  AC attitude

10
WCR Airborne single-Doppler configurations

• Profiling Mode (Up/Dwn) is achieved by
  redirecting the HBDD beam1 upward via mirror
  plate
• Side/dwn mode is achieved using beam 1 from both
  HBDD and VPDD configurations

11
Airborne Dual-Doppler Basic Concept

• Time lag ?t1 - 19 s
• Lifetime of physical features assumed greater
  than ?t
• Plane of the beams determines the resolvable
  components of the velocity

12
Dual-Doppler Technique

• 0. Determine beam directional angles with respect
  to the airframe
• Select the flight segment suitable for a
  dual-Doppler retrieval
• Read synchronize data from WCR and AC data
  system
• Apply calibration and thresholding to the
  reflectivity data
• Correct retrieved Doppler velocities for Aircraft
  motion, via INS (Inertial Navigation System) GPS
  data
• Resolve Doppler aliasing
• Transform each data point from both beams to a
  common coordinate system
• Construct a grid (mesh) onto which the data from
  the two beams will be interpolated. The grid
  advects with the estimated mean wind velocity
  field
• Weight data points from each beam in the vicinity
  of every grid point according to selected
  criteria
• Solve the velocity inverse decomposition (VID)
  problem determine the velocity for each grid
  point from the measured components
• Store grid and processing statistics and
  information parameters

13
Dual-Doppler Technique Gridding

• Straight-leg gridding The grid can be
  constructed in a vertical (VPDD) or horizontal
  (HBDD) plane
• Curtain-leg gridding The grid can be made to
  strictly follow the surfaces scanned by the
  beams, depending on the flight attitude, e.g.

14
Dual-Doppler TechniqueBeam-point assignment

• The generic beam-point (profile,rangegate
  (i.e.,r)), and associated with a curvilinear
  coordinate s, is assigned to a grid cell (i,j)
  according to the following first index guess

Straight-beams Slanted-beams
Dx0 Dh0 initial cell size, i angle between beams
and according to index tolerances depending on
the AC attitude
Index search tolerances
For grid cell size stretching ratiosltgt1 formulas
are more complex (DH05)
15
Dual-Doppler TechniqueBeam-Point Weighting

• The generic beam-point within the cell (i,j) is
  weighted according to SNR, and its geometry
  (EXW,Cressman, IDW, etc.) and/or Beam Skewness
  (BSW)

BSW weighting
EXW
Cressman
IDW
16
Dual-Doppler TechniqueVelocity Inverse
Decomposition Problem
Minimum Norm Least-Square Solution
overdetermined, rank deficient
External guess on the winds
Cross-plane component
17
Dual-Doppler TechniqueError Sources

• The absolute velocity of a scatterer (P) can be
  decomposed as

• INS/GPS

• WCR

I. Errors in the radial velocity

• Beam pointing angle uncertainties

• Beam reciprocal misalignment
• Attenuation/Side-lobe
• Finite pulse-resolution volume (Doppler spectrum
  width)
• Temporal evolution/advection effects

The radial velocity is

• II. Errors affecting the 2D retrieved velocity
• Velocity inverse decomposition (VID) solver
• Wind cross-plane component
• Terminal velocities/ mean advection (in case of
  storm-relative kinematics)

• III. Errors affecting the grid
• Grid orientation
• Feature distortion

18
Dual-Doppler TechniqueRadial Velocity Error
Sources

• Platform motion and beam pointing angles

is the platform ground velocity
beam pointing angle uncertainty
Error in the gradient of a variable q
19
Dual-Doppler TechniqueRadial Velocity Error
Sources

• 2. Beam reciprocal misalignment

Sideslip or aoa deviation from straight level
flight
Slanted-pointing beam radial velocity error
kv (slanted)radial velocity gradient in the
across-track direction
Grid swath and radar volume resolution degrading
with range can partially overcome these errors
20
Dual-Doppler TechniqueRadial Velocity Error
Sources

• 3. LWC attenuation and sidelobe

LWC attenuation
rs rangegate spacing
Attenuation coefficient linear with range
Radial velocity linear with range
Backscattering coeff. linear with range
kv,x0.005s-1, kr,x 0.04dBZm-1
SideLobes
kv,x radial velocity shear across-beam
direction kr,x reflectivity gradient in the
across-beam direction
Kl-20dB dl2º
For typical operational conditions ev,3 , ev,4
lt0.05 m s-1
21
Dual-Doppler TechniqueRadial Velocity Error
Sources

• 4. Finite (pulse) Resolution Volume

Error in the mean Doppler as a fct. of Mpp and
Doppler spectral width (std dev)
shear,fall velocities, platform, turbulence
SNR weighting
(Doviak and Zrnic,1993)
22
Dual-Doppler TechniqueRadial Velocity Error
Sources

• 5. Temporal evolution and advection effects

Dunaccounted displacement of scattererstx(v-vadv
). Shear effect included. tTime lapse between
illuminations 1-19s
Slanted-pointing beam radial velocity error
kv (slanted)radial velocity gradient in the along
or across-track direction

• Lagrangian flight trajectories should help reduce
  the error.
• 5m/s error in the advection could cause up to one
  grid spacing error at rangesgt2Km.
• Limitation on the scale of turbulent features
  resolvable. The DD cannot resolve scales less
  than 2Dg (Nyquist).
• Mitigation due to multiple points within one
  cell.
• A coarser resolution (at larger ranges,i.e.
  stretching) can curb the errors, but decreases
  fine-scale capturing.

23
Dual-Doppler TechniqueError Propagation VID
solver

• Least-squares error upper bound estimates

(1)
(Lawson, 1974)
(2)
Example congestus case
Assumption all the errors in the radial
velocities are root-squared-summed
24
Dual-Doppler TechniqueOther Errors

• 1. Cross-plane component

• Error due to errors in the wind velocity
  estimate along the normal to the solution plane
  propagating into the grid plane
• Estimated w.r.t. std dev AC attitude

2. Terminal velocities and mean advection
(relative kinematics)
25
Dual-Doppler TechniqueErrors Summary
26
Dual-Doppler Technique A case study.
Norm of the residual vector 0.1m/s
expected
upper bounds
27
Dual-Doppler Technique A case study.
Norm of the residual vector 0.1m/s
Average 1.9m/s
28
Dual-Doppler Technique A case study.
29
Terminal velocity
30
Cumulus studies
Cumulus growth model
Observations background

• Cumulus Congestus
• Dry, cold environment (bases 0ºC, tops-25ºC)
• Depth 2-3 km. AR1
• Vertical velocities 10m/s
• Focus on emerging turrets
• Neutrally stable environment over land

• Kinematics and microphysics
• Radar echo vs. velocity fields
• Entrainment patterns
• Length/time scales of the main kinematic
  structures
• Updraft/downdraft arrangement
• Insights in the 3D mechanics of growing turrets

31
Conceptual Model of Cu Growth

• Thermals or plumes?

• Major vorticity structures
• Role on entrainment
• Role of the cross-flow (shear)

32
Conceptual Models of Thermals and Cus
(Scorer, 1957)
Rising Vortex Ring
(Blyth, 1988)
33
Models
Kitchen and Caughey (1981)
Grabowski and Clark (1993)
34
WCR cloud scanning modes
Up/Down profiling mode
Vertical Plane Dual-Doppler
Horizontal Beam Dual-Doppler
35
Up/Down Profiling Mode
Ice (iwc) and liquid water content (lwc100)
gust-probe vertical velocity 1-s gust vectors

• Convergence and lwc drop indicate ambient air
  entrainment driven by the circulation.

AC
WCR retrieved vertical velocity reflectivity
AC
Flight level
36
Up/Down Profiling Mode
Density temperature (Tr) and liquid water content
(lwc100)
gust-probe vertical velocity 1-s gust vectors

• Cloud base thermodynamics (initial stages of
  cloud formation)
• Thermal base convergence and entrainment

WCR retrieved vertical velocity reflectivity
37
VPDD
20030826, 1820UTC

• Toroidal circulation
• Convergence at the base of the thermal
• Hydrometeor recycling at the base of the thermal
• Small scale (nodes) at cloud-top

(Damiani et al., 2005, JAS, submitted)
38
VPDD
s-1
20030826, 1820UTC

• Horizontal component of Vorticity
• Independent of mean advection

39
VPDD
20030826, 1823UTC

• Counter-rotating vortex pair visible at
  cloud-top.
• Multi-thermal nature
• Convergence at the base of the thermal
• Wake flow
• Evidence of intrusions

40
VPDD

• Ambient air intrusion at the base of the thermal
• Hydrometeor recycling

41
Conceptual Model of Cu Growth
asymmetric vorticity structures in stronger winds
(and shear) tilted vortex rings
42
VPDD
20030717, 2142UTC

• Ambient shear effects

43
VPDD

• Ambient shear effects
• Tilted vortex rings?

44
Conceptual Model of Cu Growth Dynamics
45
Conceptual Model of Thermals Cus

• Multi-Thermal Cumulus
• Toroidal thermals
• Convergence at the base of the thermals and
  entrainment/recycling
• Shear? tilting of the main vortical structures,
  asymmetry

46
Extension of the Conceptual Model of Cu Growth
horizontal cross-sections
47
Coupling between vertical and horizontal
kinematics
48
HBDD
20030717, 2050UTC

• Z and v Gradients comparable to those observed in
  the vertical
• Vertical vorticity and hydrometeor distribution
• Entrainment patterns
• Divergence (thermal top?)

49
Divergence/Flux Calculation

• Vertical velocity 5m/s based on cloud
  penetration data
• Radius of the thermal 300-500
• Assuming vertical uniformity in 100m
• ?outgoing flux ? 40-60 incoming flux
• Rate of rise of the thermal ? ½ updraft speed
• (further confirmed by observations of echo-top
  evolution,
• and the findings by Woodward (1959) Turner
  (1962) Zhao and Austin (2005), etc.)

50
Outgoing flux

• Assumed vertical velocity 5m/s
• Thermal radius 370m
• Lateral surface height 45m
• ?outgoing flux 20 incoming
• out/in ltvgt/R.
• height more likely in the order of 100m
• (based on radar scanned volume and AC attitude).
  
• ?Rate of rise of the thermal in the order of 50
  wcore (French99, Telford 1988, Turner 1962)

Aug 26th, 2003
51
In-situ evidence of vertical vorticity

• Analysis of the horizontal flow
• Circulations in the horizontal plane tied to
  those in the vertical?

20030719, 1945UTC
52
Investigating the source of vertical vorticity
20030720, 1903UTC
53
Vertical vorticity generation
20030720, 1906UTC
Mean wind

• Vortical structures in agreement with in situ
  observations
• Reduced horizontal momentum in the updraft core
  (flow against flight-level mean wind direction)

54
Vertical vorticity generation
20030720, 1957UTC
55
Vertical vorticity generation
20030720, 2001UTC
56
Vertical Vorticity Generation
diffusion
transport
wz
tilting
stretching
Core vorticity.08s-1, tilt30º.

• Vortex ring tilting a possible mechanism to
  generate vertical vorticity (wz) in
  counter-rotating vortex pairs (CVP).
• Other mechanisms include CVP forming at the sides
  of a plume in cross-flow, and thermal-to-thermal
  interaction

57
Torques acting on the updraft
MKJ/Msh 1-2
Chang and Vakili(1995)
58
HBDD
59
Conclusions. 1

• Airborne dual-Doppler technique
• High-resolution (30-50m), fine-scale capturing
• Dynamic gridding (close tracking of AC flight
  attitude scanned surface)
• VID stable weighted least-squares solver (smooth
  fields without further filtering)
• Sources of error discussed and quantified for
  WCR/UWKA. They depend on the radar system, data
  collection process, retrieval technique, and
  target aspects.
• Overall accuracy 1-2m/s.

60
Conclusions. 2

• Cumulus studies
• Cumulus formed by sequences of updraft pulses
• 2-3 thermal events per congestus
• Updraft weak reflectivities and liquid droplets.
  Most of ice particles in the downdrafts
• Toroidal thermals as the main building block
  long-lived circulations (seen in 58 of the 41
  cases investigated)
• Convergence at the base of the thermals and
  entrainment, recycling of hydrometeors
• Secondary entrainment sites at cloud outer
  boundaries
• Shear? tilting of the main vortical structures,
  asymmetry

61
Conclusions. 3

• Gradients of Z and v are comparable between
  horizontal and vertical planes
• Reflectivity in the horizontal plane reflects
  multi-thermal nature of Cus and confirms the
  role played by circulations in organizing
  hydrometeor distribution
• Divergence associated with thermal tops lead to
  an estimated rate of rise 0.5max(updraft speed)
• The vortical kinematics is fundamental in driving
  entrainment both in the vertical and horizontal
  plane
• Vertical vorticity present in CVP at the
  periphery of the updrafts ? tilting of vortex
  rings

62
(No Transcript)
63
What else do we need?

• Future investigations will focus on the
  kinematics characteristics shown
• Higher sensitivity
• Multiple scans in alternate modes (3D)
• Background/environmental properties need be
  assessed with more accuracy (local soundings!!)
• Quantification of entrainment (multiple
  platforms)
• Parameterization inputs (Entrainment,
  Detrainment)

Questions?
64
HighPlains Cumulus (HiCu)Field Experiment

• Time and Location
• Summer 2003 Laramie, WY
• (Summer 2002 Flagstaff, AZ)
• Objective
• Investigation of Shallow Cumulus dynamics and
  microphysics interaction
• Tools UWKingAir WCR
• Gordon G., Glover B., Fagerstrom K., Drew T.,
  Kelly R., Snider J., Vali G., Haimov S., Lukens
  D., Ray D., Damiani R.
• Cases presented Aug 26th and Jul 12th,13th 2003

(Telford, 1988)
65
need for straight leveled flight
HBDD
VPDD

• Spatial misalignment
• f(roll,pitch,yaw)
• e.g.5ºroll?260m
• 15ºroll?780m

66
Dual-Doppler in-situ
HiCu03 Aug26th VPDD 182200-182310
67
July 13th HBDD initial stages
68
July 13th HBDD final stages
69
Dual-Doppler Retrieval

• Aircraft motion removal and velocity unfolding
• Data Regridding (advecting grid) and weighting
• Velocity decomposition inverse problem return
  signals associated with two radar antennas are
  combined together to provide independent
  components of the scatterers' mean velocity in a
  given illuminated volume.

System (1) is solved by a weighted least-squares
method using an estimate of the cross-plane'
component, usually derived from in-situ-measured
horizontal winds. The overall uncertainty
associated with the evaluation of the
cross-plane component contribution, beam
pointing angles and removal of the UWKA motion is
in the order of 1 m/s at WCR signal-to-noise
ratio gt 0 dB.
70
Dual-Doppler Velocity retrieval Weighted
Least-Square Method
SVDC
weighting/thresholding
Minimum Norm Least-Square Solution
Cross-plane component