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Weather Radar Data. Doppler Spectral Moments Reflectivity factor Z Mean Velocity v Spectrum width  v Polarimetric Variables Differential Reflectivity Z DR Specific Differential Phase Correlation Coefficient  hv Linear Depolarization Ratio L DR.

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Weather Radar Data

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Weather Radar Data

  • Doppler Spectral Moments

    • Reflectivity factor Z

    • Mean Velocity v

    • Spectrum width v

  • Polarimetric Variables

    • Differential Reflectivity ZDR

    • Specific Differential Phase

    • Correlation Coefficient hv

    • Linear Depolarization Ratio LDR

Contributors to Measurement Errors*1) Widespread spatial distribution of scatterers(range ambiguities)*2) Large velocity distribution (velocity ambiguities)3) Antenna sidelobes 4) Antenna motion*5) Ground clutter (regular and anomalous propagation)*6) Non meteorological scatterers (birds, etc.)*7) Finite dwell time 8) Receiver noise*9) Radar calibration *--- these can be somewhat mitigated

Mitigation of Range Ambiguities

Uniform PRTs

Alternate batches of long (for Z) and short

(for velocity) PRTS.

El = 19.5o

Long PRTs (first PPI scan) for reflectivity ra>460 km;

Short PRTs (second PPI scan) for velocity, ra <200km; typically 150 km

7 Scans

= 5.25

= 4.3

5 Scans

= 2.4

= 1.45

4 Scans

= 0.5

Reflectivity Field of Widespread Showers(Data displayed to 460 km)

Velocity Field: Widespread Showers (5dB overlaid threshold; data displayed to 230 km)

Spectrum Width Field: Widespread Showers (20 dB threshold)

Echoes from Birds leaving a Roost; Spectrum Width Field

Measurements of Rain

  • R(Z) relations

  • Error sources

  • Procedure on the WSR-88D

Reflectivity Factor

Rainfall Rate Relations


Z = 200 R1.6

Z(mm6 m-3); R(mm h-1)

For WSR-88D:

Z = 300 R1.4 - convective rain

Z = 200 R1.2 - tropical rain

Rain Rate Error Sources

  • *1) Radar calibration

  • 2) Height of measurements

  • *3) Attenuation

  • 4) Incomplete beam filling

  • *5) Evaporation

  • *6) Beam blockage

  • 7) Gradients of rain rate

  • 8) Vertical air motions

  • *9) Variability in DSD

DSDs, R(Z), and R(disdrometer)

Sep 11, 1999



DSD’s, R(Z), and R(disrometer)

Dec 3, 1999


Locations of Z Data used in the WSR-88D for Rain Measurement

Applications of Polarization

  • Polarimetric Variables

  • Measurements of Rain

  • Measurements of Snow

  • Classification of Precipitation

Polarimetric Variables

  • Quantitative - Zh, ZDR, KDP

  • Qualitative - |hv(0)|, , LDR, xv, hv

  • Are not independent

  • Are related to precipitation parameters

  • Relations among hydrometeor parameters allow retrieval of bulk precipitation properties and amounts

Rainfall Relation R(KDP, ZDR)

R(KDP, ZDR) = 52 KDP0.96 ZDR-0.447

- is least sensitive to the variation of the median drop diameter Do

- is valid for a 11 cm wavelength

Scatergrams: R(Z) and R(KDP, ZDR)vs Rain Gauge

Sensitivity to Hail


Area Mean Rain Rate and BiasR(gauges)-R(radar)



Fundamental Problems in Remote Sensing of Precipitation

  • Classification - what is where?

  • Quantification - what is the amount?

Weighting Functions

Partitions in the Zh, ZDR Space into Regions of Hydrometeor Types

Weighting Function forModerate Rain WMR(Zh, ZDR)

Scores for hydrometeor classes

Ai= multiplicative factor 1

Wj = weighting function of two variables assigned to the class j

Yi= a variable other than reflectivity (T, ZDR, KDP, hv, LDR)

j = hydrometeor class, one the following: light rain,

moderate rain, rain with large drops, rain/hail mixture,

small hail, dry snow, wet snow, horizontal crystals,

vertical crystals, other

Class j for which Sj is a maximum is chosen as the correct one






Fields of classified Hydrometeors - Florida

Fields of classified Hydrometeor - Florida

Fields of classified Hydrometeors - Florida


  • Data quality - develop acceptance tests

  • Anomalous Propagation - consider “fuzzy logic” scheme

  • Classify precipitation into type (snow, hail, graupel, rain, bright band) even if only Z is available

  • Calibrate the radar (post operationally, use data, gauges, ..anything)

Specific Differential Phase at short wavelengths (3 and 5 cm)

  • Overcomes the effects of attenuation

  • Is more sensitive to rain rate

  • Is influenced by resonant scattering from large drops

Suggestions for Polarimetric measurements at =3 and 5 cm

  • Develop a classification scheme

  • Develop a R(KDP, ZDR) or other polarimetric relation to estimate rain

  • Correct Z for attenuation and ZDR for differential attenuation (use DP)

  • Use KDP to calibrate Z

Radar Echo Classifier

  • Uses “fuzzy logic” technique

  • Base data Z, V, W used

  • Derived fields (“features”) are calculated

  • Weighting functions are applied to the feature fields to create “interest” fields

  • Interest fields are weighted and summed

  • Threshold applied, producing final algorithm output

AP Detection Algorithm

  • Features derived from base data are:

    • Median radial velocity

    • Standard deviation of radial velocity

    • Median spectrum width

    • “Texture” of the reflectivity

    • Reflectivity variables “spin” and “sign”

      • Similar to texture

  • Computed over a local area


mean V


texture Z


mean V


texture Z

Investigate data “features”

  • Feature distributions

    • AP Clutter

    • Precipitation

  • Best features have good separation between echo types

AP Weighting Functions

Median Radial Velocity

Median Spectrum Width



“Texture” of Reflectivity

Standard Deviation of Radial Velocity



“Reflectivity Spin”

F) Spin


0 50

G) Sign

“Reflectivity Sign”

-10 -0.6 0 0.6


Field of Weights for AP Clutter

AP Clutter

AP Clutter

For median velocity field,

the weighting function is:


Interest Field

Radial Velocity


Radial Velocity

+3 m/s

+3 m/s




Weighting functions are

applied to the feature field

to create an “interest” field

Values scaled between 0-1


Radial Velocity

Example of APDA

using S-Pol data

from STEPS

Polarimetric truth field

given by the

Particle Identification

(PID) output

APDA is thresholded

at 0.5

Good agreement between PID clutter

and APDA





20 June 2000, 0234 UTC 0.5 degree elevation

Storm-Scale Prediction

  • Sample 4-hour forecast from the Center for Analysis and Prediction of Storms’ Advanced Regional Prediction System (ARPS) – a full-physics mesoscale prediction system

  • For the Fort Worth forecast

    • 4-hour prediction

    • 3 km grid resolution

    • Model initial state included assimilation of

      • WSR-88D reflectivity and radial velocity data

      • Surface and upper-air data

      • Satellite and wind profiler data

7 pm

8 pm

6 pm

4 hr

3 hr

2 hr

Forecast w/Radar


7 pm

8 pm

6 pm


4 hr

3 hr

2 hr

Fcst w/o Radar

R(Z) for Snow and Ice Water Content

Snow fall rate:

Z(mm6m-3) =75R2 ; R in mm h-1 of water

Ice Water Content:

IWC(gr m-3)= 0.446 (m)KDP(deg km-1)/(1-Zv/Zh)

Vertical Cross Sections





In Situ and Pol Measurements

T-28 aircraft

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