Some Fundamentals of Doppler Radar Velocity Analysis

L. Jay Miller (August 2011)

Using the CEDRIC program

for wind synthesis

and other analyses

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

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

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

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.

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)

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

Radar pulse-volume averaging:

Radial velocity and the Cartesian components

of particle motion

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

Triple Radar

Three equations with four unknowns

Either fallspeed from reflectivity

Or mass continuity

Linear Equations

Three and two equation solutions

STEPS 2000 Triple-Doppler Radar NetworkSevere Thunderstorm Electrification

and Precipitation Study

CSU/CHILL KGLD

SPOL

KGLD DZ Swath 2000.0629

Three-equation (Triple Doppler) UV

SPOL - G

CHILL - B

UV - Black

KGLD - R

Two-equation (Dual Doppler) UV

KGLD - R

SPOL - G

CHILL - B

UV - Black

Three Equation Variances

Standard deviations from normalized

variances

Ustd, Vstd, Wstd

Two Equation Variances

Standard deviations from normalized

variances

Ustd, Vstd

Normalized Variances for Dual-Doppler

Hvar

Uvar

Vvar

U

V

Advection during synthesis

Normal Equations:

Three and two

SYNTHES Command

SYNTHES Command (cont'd)

U,V,W std & EWU EWV

Fallspeed Define Block

Fallspeed Correction Define Block

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

Iterative Integration of Mass Continuity

A

A= Left hand sideB= First term RHSC = Second term RHS

MassInt Define Block

MassInt Graphics

Integration of Mass Continuity Equation

Upward and Downward Integrations

Variational and Examples

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

Convergence and Vertical Motion

Vertical Momentum (w * density)Upward vs Downward

Convergence and Vertical Motion

Convergence and Vertical Motion from Random (u,v)

Vertical Air Motion from Integrations

DZ_max with UV winds

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

Horizontal Convergence

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

W Integrate Upward

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

W Integrate downward

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

W Variational Integration

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

Cleaner W-3eq Variational Integration

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

Cleaner W-2eq Variational Integration

DZ_max overlay 30 and 45 dBZ

UL = 3 km UR = 6 km

LL = 9 km LR = 12 km

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

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

“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