Measurements of Measurements of raindrop-size raindrop-size

distributions fromdistributions from dual-polarization dual-polarization

spectral observationsspectral observations

Dmitri Moisseev and V. Dmitri Moisseev and V. ChandrasekarChandrasekar

Colorado State UniversityColorado State University

The research is supported by the National Science Foundation

MotivationMotivation There is a great importance in mapping There is a great importance in mapping

naturally occurring drop-size naturally occurring drop-size distributions.distributions.

Being able to do this with scanning Being able to do this with scanning radars expands the scope of DSD radars expands the scope of DSD mapping tremendously because of the mapping tremendously because of the inherent large space / time sampling inherent large space / time sampling capability of scanning radars.capability of scanning radars.

This paper presents a novel approach This paper presents a novel approach combining the advantages of a combining the advantages of a traditional dual-polarization radar and traditional dual-polarization radar and the DSD capabilities of a vertical the DSD capabilities of a vertical profiler. profiler.

Dual-polarization spectral Dual-polarization spectral measurementsmeasurements

profiler

+

v

h=

v

h

v

v

dual-pol radar

30-60 deg

ZZdr dr as a function of elevation as a function of elevation angleangle

0 10 20 30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

Elevation angle (degrees)

Zd

r [dB

]

De = 4 mm

De = 3 mm

De = 2 mm

Dual-polarization slant profile Dual-polarization slant profile observationsobservations

If measurements are If measurements are taken at a high taken at a high elevation angle, elevation angle, optimally between 30 optimally between 30 and 60 deg, both and 60 deg, both Doppler and dual-Doppler and dual-polarization polarization measurements can be measurements can be utilized to retrieve utilized to retrieve microphysical microphysical properties of properties of precipitation precipitation

Spectral differential Spectral differential reflectivityreflectivity

Spectral differential reflectivity is Spectral differential reflectivity is the ratio of the ratio of hhhh and and vvvv power spectra. power spectra.

In absence of spectral broadening, e. In absence of spectral broadening, e. g. due to turbulence, and wind the g. due to turbulence, and wind the ZZdrdr(v)(v) can directly be related to a can directly be related to a ratio of ratio of hh, vvhh, vv radar cross-sections radar cross-sections defined as functions of defined as functions of equivolumetric diameter.equivolumetric diameter.

Spectral differential Spectral differential reflectivityreflectivity

a) Spectral a) Spectral differential differential reflectivity for reflectivity for different axis ratio different axis ratio relations.relations.

b) influence of b) influence of spectral spectral broadening on broadening on ZZdrdr(v).(v).

-5 -4 -3 -2 -1 00

0.5

1

1.5

2

2.5

3

3.5

4

Zdr

(v)

[dB

]

-5 -4 -3 -2 -1 00

0.5

1

1.5

2

2.5

3

3.5

4

Doppler velocity [m/s]

Zdr

(v)

[dB

]

Beard & Chuang (1987)Brandes et al (2002)Andsager et al (1999)Pruppacher & Beard (1970)

D = 0.5 mm

D = 4 mm

b = 0 ms-1

b = 0.25 ms-1

b = 1 ms-1

a)

b)

) ( * )( )( 0vvSvSvS bprobs

Spectrum modelSpectrum model

) 2

( exp 2

1)(

2

2

bb

b

vvS

) ms / m ( )()()( 1 -3

dv

dDDNDvS pr

Observed spectrum can be represented as

Ambient wind velocity

Precipitation spectrum Broadening kernel

To retrieve a DSD, N(D), one needs to estimate ambient wind velocity, v0, and spectrum broadening kernel width, b

MethodologyMethodologyAt the first step of the procedure wind velocity At the first step of the procedure wind velocity component and spectrum broadening are component and spectrum broadening are estimated from estimated from ZZdrdr(v),(v), by minimizing the by minimizing the following function following function

Here is obtained from deconvolved is obtained from deconvolved Doppler power spectra. Doppler power spectra. represents the quiet air spectral differential represents the quiet air spectral differential reflectivity. reflectivity. WWhvhv(v) (v) is the co-polar coherency is the co-polar coherency spectrum. spectrum.

otherwise ,0

95.0)( ,1)(

)(

)()( )(),(

max

00

2

,0

vWvM

D

DvZvMvSSR

hv

v

vvv

hh

v

decdrb

b

)(vZ decdr)(/)( DD vvhh

At the second step of At the second step of the procedure the procedure precipitation precipitation specrum is specrum is calculated.calculated.

This figure shows This figure shows estimated estimated precipitation precipitation spectrum.spectrum.

Simulation input :Simulation input :NNww = 8000 m = 8000 m -3-3mmmm-1-1

DD00 = 1.2 mm = 1.2 mmb b = 0.5 m/s= 0.5 m/svv00 = 0 m/s = 0 m/s

Example of spectral broadening and Example of spectral broadening and deconvolutiondeconvolution

At the third At the third step of the step of the procedure the procedure the N(D) is N(D) is calculated.calculated.

Example of the retrieved DSDExample of the retrieved DSD

Error analysisError analysis

Simulation results. Dependence of Simulation results. Dependence of the Dthe D00 errors on input D errors on input D00 values. values.

Error analysis; effect of a size-Error analysis; effect of a size-shape relationshape relation

Result of 100 simulations. For simulation axis ration were assumed to follow Andsager et al. (1999). Retrieval was carried out assuming Pruppacher and Beard (1971) relation.

Nw = 8000D0 = 1.2 mm

Correction of the Zdr bias was carried out by including a Zdr bias as a free parameter in the optimization procedure.

Error analysis; ZError analysis; Zdr dr bias influencebias influenceNw = 8000D0 = 1.2 mm

ZZdrdr bias correction bias correction

Deconvolved Zdr(v) after optimization with and without Zdr bias

-6 -5 -4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Doppler velocity [m/s]

Zdr

(v)

[dB

]

True Zdr

(v)

Zdr

bias = - 0.5 dB

Zdr

bias corrected

(est. bias -0.5 dB)

DSD retrieval from CSU-CHILL DSD retrieval from CSU-CHILL measurementsmeasurements (30 degrees) (30 degrees)

-10 -5 0 50

10

20

30

Po

wer

[d

B]

Observ. spectra

log

N(D

)lo

g N

(D)

log

N(D

)lo

g N

(D)

log

N(D

)

-10 -5 0 50

10

20

30

Po

wer

[d

B]

-10 -5 0 50

10

20

30

Po

wer

[d

B]

-10 -5 0 50

10

20

30

Po

wer

[d

B]

-10 -5 0 50

10

20

30

Radial velocity [m/s]

Po

wer

[d

B]

-10 -5 0 50

10

20

30

velocity [m/s] Eq. diameter [mm]

-10 -5 0 50

10

20

30-10 -5 0 50

10

20

30-10 -5 0 50

10

20

30-10 -5 0 50

10

20

30Deconv. spectra

0 2 4 6-5

0

5Retr. DSD

0 2 4 6-5

0

5

0 2 4 6-5

0

5

0 2 4 6-5

0

5

0 2 4 6-5

0

52000 m

2500 m

3000 m

3500 m

4000 m

ConclusionsConclusions

A New Dual-polarization spectral A New Dual-polarization spectral methodology to retrieve Non-methodology to retrieve Non-Parametric DSD from scanning radars.Parametric DSD from scanning radars.

Retrieval errors are comparable to Retrieval errors are comparable to ones from profiler techniques.ones from profiler techniques.

ZZdrdr bias can also be estimated. bias can also be estimated. Knowledge of underlying raindrop Knowledge of underlying raindrop

shapes is required for an accurate shapes is required for an accurate retrieval.retrieval.