some fundamentals of doppler radar velocity analysis l. jay miller (august 2011) using the cedric...
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Some Fundamentals of Doppler Radar Velocity Analysis
L. Jay Miller (August 2011)
Using the CEDRIC program
for wind synthesis
and other analyses
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Acknowledgements of Support Administrative and logistics – Tammy Kepple,
Robert Rilling, and Phillip Stauffer Technical – William Haddon (EOL/CDS) and
Wei-Yu Chang (ASP) Casual appointment and Scientific discussion
Tammy Weckwerth
Jothiram Vivekanandan
Wen-Chau Lee Hosting and paying the bills – NCAR/EOL/RSF
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Custom Editing and Display of Reduced Information in Cartesian space
Software system for the merger, analysis and display of three-dimensional gridded datasets
Primarily for analysis of radar measurements
Unfolding of Doppler radar radial velocities
Synthesis of particle motion (u, v, W=w-Wt)
Computation of Wt = a*(Z^b) * (density correction)
Integration of the mass continuity equation for vertical air motion (w)
Analysis of non-radar measurements
Specialized systems with output in CEDRIC format
Structured as fields
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CEDRIC and CCOPE 1981 Cooperative COnvective Precipitation Experiment
Doppler radars: NCAR CP-2, 3, & 4; NOAA C, D, & E
Aircraft: 13 Mesonet: 80 CEDRIC – merge
radar, aircraft, & mesonet
SPRINT – radar
ACANAL – aircraft
SMANAL - mesonet
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Relevant Publications Mohr, C. G., L. J. Miller, R.L. Vaughn and H.W.
Frank, 1986: The merger of mesoscale datasets into a common Cartesian format for efficient and systematic analysis, J. Atmos. Oceanic Technol., 3, 143-161.
Miller, L. Jay, John D. Tuttle, and Charles A. Knight, 1988: Airflow and hail growth in a severe northern High Plains supercell, J. Atmos. Sci., 4, 736-762.
Miller, L. Jay, John D. Tuttle, and G. Brant Foote, 1990: Precipitation production in a large Montana hailstorm: Airflow and particle growth trajectories, J. Atmos. Sci., 13, 1619-1646.
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Overview of discussion topics
Doppler radial velocity – projection of particle motion (u, v, W = w-w_t) along radar beam
Geometry associated with multiple radars
Inconsistencies or representativeness Two- and three-equation solutions for (u, v, W) Integration of mass continuity equation for w Solution includes variances (u, v, w-w_t) Synthesis quality measures (USTD, VSTD, WSTD)
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Doppler Radar Wind Synthesis Interpolate radar data to common analysis grid
using SPRINT or REORDER Unfold and edit radial velocities for all radars Transform non-orthogonal radial velocities to
orthogonal particle motion
Two- or three-equation solution
Overdetermined two- or three-equation solution Integrate mass continuity for vertical air motion
Upward, downward, or variational
Iterative when two-equation (u,v) winds
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Radar pulse-volume averaging:
Radial velocity and the Cartesian components
of particle motion
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Sources of Errors in Particle Motion Errors in mean radial velocity estimates Inaccuracies in pulse-volume locations
Radar location and/or antenna pointing errors
Ranging errors and propagation effects Inconsistencies of pulse-volume averaging
Mean radial velocity is reflectivity-weighted average
Different pulse-volume shapes and sizes Geometry of transformations from radial
velocities to Cartesian components Non-stationarity of fields during data collection Inadequate spatial and temporal sampling
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Triple Radar
Three equations with four unknowns
Either fallspeed from reflectivity
Or mass continuity
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Linear Equations
Three and two equation solutions
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STEPS 2000 Triple-Doppler Radar NetworkSevere Thunderstorm Electrification
and Precipitation Study
CSU/CHILL KGLD
SPOL
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KGLD DZ Swath 2000.0629
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Three-equation (Triple Doppler) UV
SPOL - G
CHILL - B
UV - Black
KGLD - R
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Two-equation (Dual Doppler) UV
KGLD - R
SPOL - G
CHILL - B
UV - Black
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Three Equation Variances
Standard deviations from normalized
variances
Ustd, Vstd, Wstd
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Two Equation Variances
Standard deviations from normalized
variances
Ustd, Vstd
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Normalized Variances for Dual-Doppler
Hvar
Uvar
Vvar
U
V
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Advection during synthesis
Normal Equations:
Three and two
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SYNTHES Command
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SYNTHES Command (cont'd)
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U,V,W std & EWU EWV
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Fallspeed Define Block
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Fallspeed Correction Define Block
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Reflectivity DZ & Fallspeed VT Comparisons
G – NWS/KGLD S – NCAR/SPOL C – CSU/CHILL
Height = 7 km MSL
UL = DZ S vs G
UR = DZ S vs C
LL = VT S vs G
LR = VT S vs C
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Iterative Integration of Mass Continuity
A
A= Left hand sideB= First term RHSC = Second term RHS
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MassInt Define Block
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MassInt Graphics
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Integration of Mass Continuity Equation
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Upward and Downward Integrations
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Variational and Examples
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Sources of Errors in Vertical Motion when Using Mass Continuity Equation
Inaccuracies in horizontal convergence estimates
Errors in horizontal wind components
Inadequacies of finite difference estimator Incorrect estimates of particle fallspeed Errors in boundary conditions (upper and lower) Deficiencies in numerical integration methods Misrepresentation of air density
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Convergence and Vertical Motion
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Vertical Momentum (w * density)Upward vs Downward
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Convergence and Vertical Motion
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Convergence and Vertical Motion from Random (u,v)
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Vertical Air Motion from Integrations
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DZ_max with UV winds
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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Horizontal Convergence
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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W Integrate Upward
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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W Integrate downward
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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W Variational Integration
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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Cleaner W-3eq Variational Integration
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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Cleaner W-2eq Variational Integration
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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Vector Difference (UV_3 - UV_2)
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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Synthesis – 3eq (W=w-w_t)
DZ_max overlay 30 and 45 dBZ
UL = 3 km UR = 6 km
LL = 9 km LR = 12 km
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“Why you should be critical of results” Radial velocities may not be representative
Radars observe dissimilar spatial volumes
Mean velocities are reflectivity-weighted spatial averages
Vertical component of particle motion typically poorly observed
Cannot be ignored since it is bias error Integration of mass continuity and separating
vertical air motion from fallspeed
Boundary conditions can only be “best guesses”
Intrinsic fallspeeds must be estimated