1 March 2004 University of Missouri-Columbia Dept. of Soils, Environmental, and Atmospheric Science 1 Quantifying the effect of wind drift on radar-derived

1 March 20041 March 2004 University of Missouri-Columbia DeUniversity of Missouri-Columbia Dept. of Soils, Environmental, and Atmpt. of Soils, Environmental, and Atmospheric Scienceospheric Science

11

Quantifying the effect of wind drift Quantifying the effect of wind drift on radar-derived surface rainfall on radar-derived surface rainfall

estimationsestimations

Steve LackSteve Lack

NATR 410: SeminarNATR 410: Seminar


22

MotivationMotivation

Flooding causes more deaths than both Flooding causes more deaths than both tornadoes and lightning strikestornadoes and lightning strikes

30 yr national average for flooding deaths is 30 yr national average for flooding deaths is 127 as opposed to 65 and 73 for the others127 as opposed to 65 and 73 for the others

Worldwide there are many who live in areas Worldwide there are many who live in areas susceptible to flash floodingsusceptible to flash flooding

Property damage can be intense ($20 billion Property damage can be intense ($20 billion for Mississippi River flood of 1993)for Mississippi River flood of 1993)


33

Motivation (cont.)Motivation (cont.)

Flood warnings need to be issued on time so that Flood warnings need to be issued on time so that proper measures can be takenproper measures can be taken

Flood warnings rely on accurate observations, rain Flood warnings rely on accurate observations, rain gauge networks do satisfactorily, but new radar gauge networks do satisfactorily, but new radar technology with increased temporal and spatial technology with increased temporal and spatial resolution is the present and futureresolution is the present and future

Precipitation estimates to be useful in hydrological Precipitation estimates to be useful in hydrological models need to be within 10-20% accurate (Collier models need to be within 10-20% accurate (Collier 1985)…radars currently cannot meet this criteria 1985)…radars currently cannot meet this criteria without correctionswithout corrections


44

OutlineOutline

Errors in Radar MeasurementsErrors in Radar Measurements Data Sets Data Sets Methodology- Program Structure Methodology- Program Structure

AssumptionsAssumptions Results from convective and stratiform Results from convective and stratiform

casescases ConclusionsConclusions Future WorkFuture Work


55

Errors in Radar MeasurementsErrors in Radar Measurements

Most errors exist aloft and are not carried to Most errors exist aloft and are not carried to the surfacethe surface

Error in radar returns aloft eventually must Error in radar returns aloft eventually must be carried down to the surface in some way, be carried down to the surface in some way, correcting aloft does not do justice for the correcting aloft does not do justice for the spatial accuracy needs of hydrological spatial accuracy needs of hydrological modelsmodels


66

Calibration ErrorsCalibration Errors

Like any other instrument, radars are Like any other instrument, radars are sensitive to calibration errorssensitive to calibration errors1) Variability in transmitter power1) Variability in transmitter power

2) Poorly known antenna and other component 2) Poorly known antenna and other component characteristics characteristics

All lead to sources of error that are generally All lead to sources of error that are generally ignored or corrected by gauge ignored or corrected by gauge measurements, or solar calibrationmeasurements, or solar calibration


77

AttenuationAttenuation

Attenuation is simply the reduction is power Attenuation is simply the reduction is power that is caused when electromagnetic that is caused when electromagnetic radiation passes through a medium of any radiation passes through a medium of any density and materialdensity and material

Gas attenuation is easily corrected for Gas attenuation is easily corrected for Cloud and precipitation non-uniform…large Cloud and precipitation non-uniform…large

errors (S-band less error than X-band) errors (S-band less error than X-band) (radome wetting)(radome wetting)


88

Bright Band and Mixed PrecipBright Band and Mixed Precip

The bright band is a result of enhancement The bright band is a result of enhancement of reflectivity resulting from frozen of reflectivity resulting from frozen precipitation falling through a melting layer, precipitation falling through a melting layer, thus yielding an artificial high reflectivity in thus yielding an artificial high reflectivity in this region aloft this region aloft

Hail also causes problems in estimating Hail also causes problems in estimating precipitation amounts…overestimationprecipitation amounts…overestimation

(hail spikes and flares)(hail spikes and flares)


99

Bright Band ExampleBright Band Example

Taken from KOUN radar during JPOLE Taken from KOUN radar during JPOLE


1010

Misc ErrorsMisc Errors

Beam blockage due to mountainous areaBeam blockage due to mountainous area Anomalous propagation caused by radar Anomalous propagation caused by radar

beam ducting and intercepting surface beam ducting and intercepting surface targetstargets

Beam filling, overestimation on storm tops Beam filling, overestimation on storm tops and edges, especially at higher elevations, and edges, especially at higher elevations, wider beamswider beams


1111

Reflectivity to Rainfall ratesReflectivity to Rainfall rates Marshall and Palmer (1948) first empirical Marshall and Palmer (1948) first empirical

relationships relating reflectivity to rainfall relationships relating reflectivity to rainfall rates (Z-R relationships)rates (Z-R relationships)

RELATIONSHIP Optimum for: Also recommended for:

Marshall-Palmer

(Z=200R1.6) General stratiform precipitation

East-Cool Stratiform

(Z=130R2.0) Winter stratiform precipitation - east of continental divide Orographic rain - East

West-Cool Stratiform

(Z=75R2.0) Winter stratiform precipitation - west of continental divide Orographic rain - West

WSR-88D Convective

(Z=300R1.4) Summer deep convection Other non-tropical convection

Rosenfeld Tropical

(Z=250R1.2) Tropical convective systems


1212

New RelationshipsNew Relationships

Increased accuracy in measuring drop size Increased accuracy in measuring drop size distributions, and new radar technology, distributions, and new radar technology, dual-polarization radars…enhanced dual-polarization radars…enhanced relationshipsrelationships

R R c(h) 1.06 Z c(h) 1.06 Zeheh0.30.3 K KDPDP

0.500.50 Z Zdrdr-0.84-0.84

Reduces error to 20-40% rangeReduces error to 20-40% range Still not acceptable for hydro apps (10-20%)Still not acceptable for hydro apps (10-20%)


1313

Spatial Accuracy?Spatial Accuracy?

All of the previous correction schemes plus All of the previous correction schemes plus the Z-R relationships and relationships the Z-R relationships and relationships based on advanced radars attempt to based on advanced radars attempt to quantify rainfall aloftquantify rainfall aloft

The problem is getting accurate results to The problem is getting accurate results to the surface…evaporation, the surface…evaporation, collision/coalescence, and wind-drift come collision/coalescence, and wind-drift come into playinto play


1414

Wind Drift ConsiderationsWind Drift Considerations

Gunn and Marshall (1955): parabolic Gunn and Marshall (1955): parabolic trajectory of raindrops in a constant wind trajectory of raindrops in a constant wind shear environment, lateral advection along shear environment, lateral advection along the ground could be quite large from the the ground could be quite large from the original location of the droplet aloft.original location of the droplet aloft.

Atlas and Plank (1953): drop sorting, same Atlas and Plank (1953): drop sorting, same size drops come from two different spots size drops come from two different spots aloftaloft


1515

Data UsedData Used

Sydney 2000 World Weather Research Sydney 2000 World Weather Research Programme’s (WWRP) Forecast Programme’s (WWRP) Forecast Demonstration Project (FDP) (Keenan et al., Demonstration Project (FDP) (Keenan et al., 2003) 2003)

CPOL radar 40km west of SydneyCPOL radar 40km west of Sydney 45 x 45 km Cartesian grid of reflectivity, 45 x 45 km Cartesian grid of reflectivity,

horizontal, and vertical velocitieshorizontal, and vertical velocities Dates used: Convective- 11-03-00, Dates used: Convective- 11-03-00,

Stratiform 11-18-00 (3 hour time frame)Stratiform 11-18-00 (3 hour time frame)


1616

Horizontal VelocitiesHorizontal Velocities

Radar assimilation into an adjoint model Radar assimilation into an adjoint model (Sun and Crook 1995)(Sun and Crook 1995)

Adjoint model is based off of sensitivity…Adjoint model is based off of sensitivity…data is inserted where needed data is inserted where needed

Near real-time output from modelNear real-time output from model


1717

Adjoint ExampleAdjoint Example


1818

Cartesian Horizontal VelocitiesCartesian Horizontal Velocities

Sample U Component Sample V Component


1919

Vertical VelocitiesVertical Velocities

M.W. Sleigh (2002): derived w wind field from the u and M.W. Sleigh (2002): derived w wind field from the u and v components using the continuity equation, matched to v components using the continuity equation, matched to reflectivity fieldsreflectivity fields


2020

Program BackgroundProgram Background

MATLAB: matrix based program language, MATLAB: matrix based program language, graphical displaygraphical display

Input Cartesian grids of reflectivity (CAPPIs Input Cartesian grids of reflectivity (CAPPIs in this case) and velocityin this case) and velocity

Generates images and movies of corrected Generates images and movies of corrected rainfall rate, reflectivity, and accumulation rainfall rate, reflectivity, and accumulation errorserrors


2121

MethodologyMethodology

2 schemes used2 schemes used– Bulk AdvectionBulk Advection– Drop SortingDrop Sorting

Experimental ResolutionsExperimental Resolutions– Native: 1.5km CAPPI height/ 2.5km horizontal Native: 1.5km CAPPI height/ 2.5km horizontal

resolutionresolution– Change in horizontal resolution: 1.5km and Change in horizontal resolution: 1.5km and

0.5km run0.5km run– Change in CAPPI to 0.75kmChange in CAPPI to 0.75km


2222

Bulk Advection SchemeBulk Advection Scheme

From reflectivity, solve for fall speed, which From reflectivity, solve for fall speed, which is a function of approx. mean drop diameter is a function of approx. mean drop diameter (Lacy, 1977)(Lacy, 1977)

Fall speed, calculations of time of fall to sfc, Fall speed, calculations of time of fall to sfc, multiply by u,v components (parabolic multiply by u,v components (parabolic trajectory avg) to get drifttrajectory avg) to get drift

Sum up contribution from pixels to new Sum up contribution from pixels to new reflectivity gridreflectivity grid

)9/1(5.4 RV f


2323

Bulk Advection Scheme (cont.)Bulk Advection Scheme (cont.)


2424


(Convective bulk advection)

590.145 1839.145 0 0 0

1839.145 5731.565 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

(Stratiform bulk advection)

565.9306 1812.999 0 0 0

1812.999 5808.071 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

Starting with 40 dBZ (10000 mm6m3) in upper left, using u,v wind 6 ms-1


2525


Summary of scheme…Summary of scheme…– This only uses a mean drop size diameterThis only uses a mean drop size diameter– Stratiform fall speed slower, more spread than Stratiform fall speed slower, more spread than

convectiveconvective– Z-R relationships based on ROC criteria Z-R relationships based on ROC criteria

(Z=200R(Z=200R1.61.6 and Z=300R and Z=300R1.41.4))– Dimensions of the wind drift grid are conserved Dimensions of the wind drift grid are conserved

“bulk-advection” of grid“bulk-advection” of grid


2626

Drop Sorting SchemeDrop Sorting Scheme

More complex (computational time More complex (computational time increases), than simplified BA schemeincreases), than simplified BA scheme

Divided drop distributions into 25 size bins Divided drop distributions into 25 size bins depending on strat/conv storm typedepending on strat/conv storm type

Each bin has unique fall speed given by its Each bin has unique fall speed given by its sizesize

Drop numbers in different bins calculated by Drop numbers in different bins calculated by adjusted M-P relationshipsadjusted M-P relationships


2727

Drop Sorting Scheme (cont.)Drop Sorting Scheme (cont.)Adjusted M-P relationships for drop sortAdjusted M-P relationships for drop sort

6

00

0869.00

0617.00

205.02095.0

6.14.1

0

(6)

)()( (5)

(strat)405.44 (conv);869.99 (4)

(strat)1.4(conv); 1.4 (3)

200 (conv);300 (2)

(1)

DNZ

eNeNN

eNeN

RR

RZRZ

eNN

d

DDd

ZZ

Dd

lu

Integrate (1) to yield (5) and substitute, (6) solves for reflectivity Integrate (1) to yield (5) and substitute, (6) solves for reflectivity contribution from bin (every 0.3mm from 0-7.5mm (conv) every 0.2mm contribution from bin (every 0.3mm from 0-7.5mm (conv) every 0.2mm from 0-5mm (strat)from 0-5mm (strat)


2828

Drop Sorting Scheme (cont.)Drop Sorting Scheme (cont.)

Summary of scheme…Summary of scheme…– Uses 25 drop size binsUses 25 drop size bins– Uses adjusted M-P relationships and different Uses adjusted M-P relationships and different

fall speed calculations than BA schemefall speed calculations than BA scheme– Spread of reflectivity from one cell greater Spread of reflectivity from one cell greater

extent than bulk advection schemeextent than bulk advection scheme– Original grid square spreads out more than its Original grid square spreads out more than its

original dimensionoriginal dimension– Longer Computational TimeLonger Computational Time


2929

Topography ConsiderationsTopography Considerations

5 min res of NSW, 5 min res of NSW, smoothed out to match smoothed out to match the res of the native the res of the native reflectivity and wind reflectivity and wind grids (2.5km x 2.5km)grids (2.5km x 2.5km)

High terrain…less wind High terrain…less wind drift effect evident over drift effect evident over western part of imagewestern part of image

Take CAPPI height-Take CAPPI height-terrainterrain


3030

Convective CaseConvective Case

November 3November 3rdrd, 2000 (3hr, 10 minute intervals), 2000 (3hr, 10 minute intervals) Severe Convective Case, dBZ>53 are reduced to Severe Convective Case, dBZ>53 are reduced to

53 dBZ and converted to rainfall rate, hail 53 dBZ and converted to rainfall rate, hail contamination contamination

Series of supercellular storms moving through the Series of supercellular storms moving through the region of interestregion of interest

First images are uncorrected, followed by some First images are uncorrected, followed by some corrected rainfall totals, and accumulation error corrected rainfall totals, and accumulation error imagesimages


3131

Original Reflectivity/Rainfall LoopOriginal Reflectivity/Rainfall Loop


3232

Original vs. Bulk Advection Rainfall Original vs. Bulk Advection Rainfall Totals at Native ResolutionTotals at Native Resolution


3333

Original vs. Drop Sort at Native Original vs. Drop Sort at Native ResolutionResolution


3434

Accumulation Errors for BA and DS Accumulation Errors for BA and DS at Native Resolutionat Native Resolution


3535

Accumulation Error (BA) Movie at Accumulation Error (BA) Movie at Native ResolutionNative Resolution


3636

Accumulation Error for BA and DS at Accumulation Error for BA and DS at CAPPI height of 1500m and CAPPI height of 1500m and

Horizontal Resolution of 500m Horizontal Resolution of 500m


3737

Selected Error Statistics (Conv)Selected Error Statistics (Conv)

Conv BA scheme at z=1.5km and r=2.5km Conv BA scheme at z=1.5km and r=2.5km – Max Error ~17mm after 3hr accumulationMax Error ~17mm after 3hr accumulation– Max R is ~69mm while Max Corr R is ~65mm Max R is ~69mm while Max Corr R is ~65mm

(divergence)(divergence)

Conv BA scheme at z=1.5km and r=0.5kmConv BA scheme at z=1.5km and r=0.5km– Max Error ~47mm after 3hr accumulationMax Error ~47mm after 3hr accumulation– Max Corr R is ~70mm (slight convergence in Max Corr R is ~70mm (slight convergence in

grid)grid)


3838

Selected Error Statistics (Conv)Selected Error Statistics (Conv)

Conv DS scheme at z=1.5km and r=2.5km Conv DS scheme at z=1.5km and r=2.5km – Max Error ~16mm after 3hr accumulationMax Error ~16mm after 3hr accumulation– Max R is ~69mm while Max Corr R is ~64mm Max R is ~69mm while Max Corr R is ~64mm


Conv DS scheme at z=1.5km and r=0.5kmConv DS scheme at z=1.5km and r=0.5km– Max Error ~52mm after 3hr accumulationMax Error ~52mm after 3hr accumulation– Max Corr R is ~72mm (convergence in grid)Max Corr R is ~72mm (convergence in grid)


3939

Stratiform CaseStratiform Case

November 18November 18thth, 2000 (3hr, 10 min interval), 2000 (3hr, 10 min interval) Typical stratiform case with a mass of light Typical stratiform case with a mass of light

showers hanging around the regionshowers hanging around the region Rainfall totals are really low, making the Rainfall totals are really low, making the

errors less between the original and errors less between the original and correctionscorrections

Follows similar order to the convective Follows similar order to the convective slidesslides


4040

Original Reflectivity/Rainfall LoopOriginal Reflectivity/Rainfall Loop


4141

Original vs. Bulk Advection Rainfall Original vs. Bulk Advection Rainfall Totals at Native ResolutionTotals at Native Resolution


4242

Original vs. Drop Sort at Native Original vs. Drop Sort at Native ResolutionResolution


4343

Accumulation Errors for BA and DS Accumulation Errors for BA and DS at Native Resolutionat Native Resolution


4444

Accumulation Error (BA) Movie at Accumulation Error (BA) Movie at Native ResolutionNative Resolution


4545

Accumulation Error for BA and DS at Accumulation Error for BA and DS at CAPPI height of 1500m and CAPPI height of 1500m and

Horizontal Resolution of 500m Horizontal Resolution of 500m


4646

Selected Error Statistics (Strat)Selected Error Statistics (Strat)

Strat BA scheme at z=1.5km and r=2.5km Strat BA scheme at z=1.5km and r=2.5km – Max Error ~3mm after 3hr accumulationMax Error ~3mm after 3hr accumulation– Max R is ~22mm while Max Corr R is ~21mm Max R is ~22mm while Max Corr R is ~21mm


Strat BA scheme at z=1.5km and r=0.5kmStrat BA scheme at z=1.5km and r=0.5km– Max Error ~9mm after 3hr accumulationMax Error ~9mm after 3hr accumulation– Max Corr R is ~21mm (divergence)Max Corr R is ~21mm (divergence)


4747

Selected Error Statistics (Strat)Selected Error Statistics (Strat)

Strat DS scheme at z=1.5km and r=2.5km Strat DS scheme at z=1.5km and r=2.5km – Max Error ~2mm after 3hr accumulationMax Error ~2mm after 3hr accumulation– Max R is ~22mm while Max Corr R is ~21mm Max R is ~22mm while Max Corr R is ~21mm


Strat DS scheme at z=1.5km and r=0.5kmStrat DS scheme at z=1.5km and r=0.5km– Max Error ~8mm after 3hr accumulationMax Error ~8mm after 3hr accumulation– Max Corr R is ~21mm (divergence)Max Corr R is ~21mm (divergence)


4848

Including Topography to Convective Including Topography to Convective CaseCase


4949

ConclusionsConclusions

Increasing the horizontal resolution increases the Increasing the horizontal resolution increases the error (significant when dealing with sub-watershed error (significant when dealing with sub-watershed (urban-hydrology) scales)(urban-hydrology) scales)

Errors are reduced when incorporating terrain into Errors are reduced when incorporating terrain into wind-drift or using lower beam elevations or wind-drift or using lower beam elevations or CAPPIs (introduce clutter, beam blockage)CAPPIs (introduce clutter, beam blockage)

Schemes implicitly handle convergence and Schemes implicitly handle convergence and divergencedivergence

Both schemes give similar results however drop Both schemes give similar results however drop sort has longer computational timesort has longer computational time

Radar is a give and take device in many waysRadar is a give and take device in many ways


5050

Future WorkFuture Work

Wind-drift is only one portion of gaining spatial Wind-drift is only one portion of gaining spatial accuracy for surface rainfall estimation…need to accuracy for surface rainfall estimation…need to account for evaporation of drops and changes in account for evaporation of drops and changes in DSDs…develop enhanced schemeDSDs…develop enhanced scheme

Incorporate more vertical levels of wind field data Incorporate more vertical levels of wind field data to get a more accurate vertical profile instead of to get a more accurate vertical profile instead of assuming parabolic trajectoryassuming parabolic trajectory

More case studies (local)More case studies (local) Apply results in a simple hydrological model to Apply results in a simple hydrological model to

examine changes in streamflow based on examine changes in streamflow based on correctionscorrections


5151

AcknowledgementsAcknowledgements

Alan Seed from the BoM Alan Seed from the BoM

Andrew Crook from NCARAndrew Crook from NCAR

Documents

1 March 2004 University of Missouri-Columbia Dept. of Soils, Environmental, and Atmospheric Science 1 Quantifying the effect of wind drift on radar-derived