Some Fundamentals of Doppler Radar Velocity Analysis

Some Fundamentals of Doppler Radar Velocity Analysis

L. Jay Miller (May 2011)

Data Preparation and Gridding for Wind Synthesis

Using REORDER, SPRINT, and CEDRIC PROGRAMS

TRADITIONAL FORMULATION Radial velocity is projection of particle motion

(u,v,w+Vt) onto radar beam (A,E) at several ranges [Vr = (u*sinA + v*cosA)*cosE + W*sinE]

Map measurements from (R,A,E) to Cartesian (x,y,z) or coplane (r,s,c) analysis domain

Correct each radar for fallspeed contribution

Vt = a*(Z^b) * (density correction) Solve 2 or 3 equations Vr = Vr(u,v) or Vr(u,v,w) Include mass continuity equation to obtain the

vertical air motion

Specify boundary conditions (upper and lower)

Considerations before Gridding Develop overview of radar scans in context of

research goals

Display with SOLOII or CIDD or similar program Select radar(s) to be used in wind synthesis Operations in radar sample space before

gridding (asymmetries in pulse volume shape)

Preliminary Range-Angle filling and filtering

Correct for fall-speed contribution to Vr Formats readable by NCAR gridders

REORDER – Universal and Dorade sweep files

SPRINT – Older RP2-7, Universal, Dorade, and NEXRAD Level II (Build 9, MSG1; pre-MSG30)

STEPS 2000 Triple-Doppler Radar NetworkSevere Thunderstorm Electrification

and Precipitation Study

CSU/CHILL KGLD

SPOL

Central Plains Composite 2000.0629.2330

Tornadic (F1) Storm

KGLD DZ Swath 2000.0629

Considerations for Gridding Identify characteristics of radar scans

Azimuth-Elevation angle bounds and increments

Range-Height bounds Determine fields to be interpolated

Radar measured fields (DZ, VE, SW, …)

Ancillary fields (AZ, EL, TIME, …) Determine latitudes, longitudes of origin and

radar(s) to obtain their grid locations Decide on output grids common to radars

Considerations for Gridding (cont'd) Issues that control fields to be gridded

Degree of space-time overlap of radar scans

Types and durations of scans (ppi, rhi, …)

Radars (ground-based research, operational, and airborne)

CEDRIC formulation of wind synthesis

Advection needs time field

Airborne needs azimuth and elevation angles

Gridder to be used (SPRINT or REORDER)

Local ENU-ECEF

ENU – local tangent plane

ECEF – Center of the Earth

X along prime meridian (0 deg reference dividing East and West longitudes at the equator)

Z points to North Pole

Lambda – longitude of local point

Phi – latitude of local point

Spherical Earth with 4/3 radius

*Convert radar lat-lon-height to Cartesian coordinates of common output grid

REORDER ALGORITHM Region of influence (box)

Cartesian (xyz radii or box half-dimensions)

Spherical (rae radii dependent on slant range)

Hybrid (Cartesian until exceeded by Spherical) Filter or distance-weighting scheme applied to

all measured values inside the box

Cressman (Rsq – rsq)/(Rsq + rsq)

Exponential [exp(-a*rsq/Rsq)Big Rsq – sum of box radii squared

Little rsq – squared distance (RAE sample – XYZ grid)

Uniform weighting and closest point

REORDER RADII of INFLUENCE Cartesian radii: (xradius, yradius, zradius)

If xradius = 0, then xradius = yradius

Map into cartesian (dx, dy, dz) box Spherical radii: (rgradius, azradius, elradius)

Always map into cartesian (dx, dy, dz) box

User inputs (azradius, elradius) in degrees

dy (dz) = range*[azradius (elradius) in radians]

If rgradius = 0, dx = range*(azradius in radians)

If rgradius > 0, then dx = constant rgradius km Hybrid radii: Uses cartesian radii until spherical

radii are bigger, then shifts to spherical

ORIENTATION of GRIDDING BOXESREORDER* Prefer SPRINT-LIKE

*Inner (outer) box – Fixed (range-dependent) size

KGLD – REORDER (part 1)

DATA LOCATION & RADAR

XYZ Grid

LAT/LON/ALT

Grid (G)Radar (R)


XYZ Radii

BOX Dimensions

WEIGHTS

RAE Radii


Fields to be Interpolated

Data Quality

Study VolumeTime Interval

SPRINT ALGORITHM Successive linear

interpolations in the R, A, E directions

Uses 8 RAE sample gates surrounding the output grid point

Two ranges

Two azimuths

Two elevations XYZ, XYE, XYC, LLZ,

or LLE

KGLD – SPRINT Input (part 1)

INPUT DATA LAT/LON/ALT

2D FILTER Range-Angle

KGLD – Sprint Input (part 2)

DATE-TIME

VE PassVE Pass

DZ Pass

Regions Influencing Output FieldsXY output grid

(Big +s)

RA sampling locations (Little +s)

REORDER circles for

Cartesian radii

SPRINTRA Cells

LOCAL UNFOLDING & QUALNOTE: Currently Reorder and Sprint use standard deviation rather than velocity variance and output 100*Q. M below is the number of range gates in a range slab (for Sprint M = 2). QUAL includes only those velocities used for individual output grid point.

NOTE

Va = 2*Vn

Ue = Local estimate atoutput XYZ

COordinated coPLANar ScanningModify elevation angle: tan (E) = tan (coplan angle) * abs [sin (A -Ab)]

COPLAN Interpolation with SPRINT and Winds with CEDRIC

Two-dimensional Winds: Orthogonalize V1 and V2 into Ur and Us

SPOL – REORDER Scan Information

Elevation Angles

Azimuthal Spacing

SPOL – SPRINT Scan Table

SPOL Scan Characteristics

CSU/CHILL – REORDER Scan Info

Azimuthal Spacing

Elevation Angles

CSU/CHILL – SPRINT Scan Table

CSU/CHILL Scan Characteristics

KGLD – REORDER Scan Information

Elevation Angles

Azimuthal Spacing

KGLD – SPRINT Scan Table

KGLD Scan Characteristics

SPOL - PPI (RAE) vs CEDRIC (XYE)

DZ @ E=0.5 deg

XYE - Threshold at LDR < -6

VE @ E=0.5 deg

Both – Threshold at LDR < -6

SPOL -Sprint vs Reorder (DZ)Z = 2.5 km MSL

UL = SPRINT

UR = REORDERCRE-XYZ radii0.5-0.5-1.0 km

LL = REORDEREXP-RAE radii

0.2-1.0-1.0 km-dg

LR = REORDERCRE-RAE radii0.0-1.0-1.0 deg

SPOL – Sprint vs Reorder (DZ)Z = 7.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL – Sprint vs Reorder (DZ)Z = 13.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


Global Unfolding with CEDRICTemplate creation and cleanup

Preliminary unfold with vertical profile of VE Additional steps to further unfold

AUTO – Decimate, global fill, and unfold AUTOTEMP – Propagate away from LEVEL AUTOFILL – Like AUTOTEMP, propagate and fill

Unfold VE → VEUF using the above template Decimate, filter, and fill with multiple PATCHER

SPOL – Sprint vs Reorder (VE)Z = 2.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL – Sprint vs Reorder (VEUF)Z = 2.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL – Sprint vs Reorder (VE)Z = 7.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL-Sprint vs Reorder (VEUF)Z = 7.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL – Sprint vs Reorder (VE)Z = 13.5 km

UL = SPRINT



0.2-1.0-1.0 km-dg


SPOL – Sprint vs Reorder (VEUF)Z = 13.5 km MSL

UL = SPRINT



0.2-1.0-1.0 km-dg


Horizontal-Vertical Resolutionfrom Range-Elevation Angle Resolution

Elevation dR*sinE RdE*cosE dR*cosE - RdE*sinE

90 1.00*dR 0.00 0.00 - 1.00*RdE

75 0.97*dR 0.24*RdE 0.24*dR - 0.97*RdE

60 0.87*dR 0.50*RdE 0.50*dR - 0.87*RdE

45 0.71*dR 0.71*RdE 0.71*dR - 0.71*RdE

30 0.50*dR 0.87*RdE 0.87*dR - 0.50*RdE

20 0.34*dR 0.94*RdE 0.94*dR - 0.34*RdE

10 0.17*dR 0.98*RdE 0.98*dR - 0.17*RdE

0 0.00 1.00*RdE 1.00*dR 0.00

Z = R*sinEdZ = dR*sinE + RdE*cosE

H = R*cosEdH = dR*cosE - RdE*sinE

dZ ~ RdE @ 0 to dR @ 90 dH ~ dR @ 0 to RdE @ 90

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Summary Comparison of Reorder and Sprint

REORDER SPRINT

SCHEME: DISTANCE-WEIGHTING TRI-LINEAR INTERPOLATION CLOSEST POINT CLOSEST POINT UNIFORM-WEIGHTING

REGION OF INFLUENCE: USER-SPECIFIED RADII LOCALLY ADAPTIVE XYZ-ORIENTED RAE-ORIENTED

CONSEQUENCES: CONSTANT LINEAR SCALE UNEQUAL LINEAR SCALE UNEQUAL ERROR CONSTANT ERROR

GROUND-BASED (AIRBORNE) OUTPUT GRID ORIENTATION: USER SPECIFIES + X AZIMUTH USER SPECIFIES + X AZIMUTH (USER-SPECIFIES + X AZIMUTH) (+ X – OUT RIGHT SIDE)

(+ Y – FLIGHT DIRECTION)

(ROTATE TO SPECIFIED + X AZIMUTH)

Some Fundamentals of Doppler Radar Velocity Analysis

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