Raindrop size distribution retrieval

• Rain estimation affected by rain type, stage,climatology; fundamentally DSD

• Microphysical parameterization depends assumedDSD for characterizing precipitation microphysicalprocesses

• Weather radar polarimetry makes obtaining 3/4-Drain DSDs possible

• ReferenceZhang, G., J. Vivekanandan, and E. Brandes, A method for estimating rain rate and drop size

Distribution form polarimetric radar measurements. IEEE Trans. on Geoscience andRemote Sensing, 39, 831-841, 2001

Gorguchi, E, V. Chandrasekar, V. N. Bringi, and G. Scarchilli, Estimation of raindrop sizedistribution parameters from polarimetric radar measurements. J. Atmos. Sci., 59, 2373-2384, 2002.

Polarimetric variables for

DSD retrieval

• Polarimetric observables: ZDR, KDP, !hv, LDR

depend on drop shape while the shape is

directly related to size. Consequently, the

measurements contain rain DSD information

• Limitations of each measurement

• Number of independent information for rain

estimation is limited; hence, ZH and ZDR are

used for rain estimation

• A two-parameter DSD model needed

Two parameter retrieval

• Reflectivity

• Differential reflectivity

• Two parameter DSD models:

– Exponential DSD model:

– Contrained-Gamma DSD model:

!

Zhh =4"4

# 4|Kw |

2fhh (#,D)

2

$ N(D)dD

!

ZDR

=10logZhh

Zvv

!

µ = a"2 + b" + c!

N(D) = N0 exp("#D)

!

N(D) = N0Dµexp("#D)

Procedure to retrieve DSD

parameters(ZH, ZDR and µ-" relation) (N0, µ, ")

i) ZDR, and the µ-" relation! µ and "

ii) ZH, retrieved µ and " !N0

A parameterized approach

• Parameterized scattering amplitudes

• Reflectivity

• Solve " from Zdr

• Solve N0 from Zhh

!

Zhh

=4"4

# 4|K

w|2N0$a

2%&(2' a +µ +1)((2'a

+ µ +1)

!

Zdr

= "#2($ a #$ b )%(2$

a+ µ +1)

%(2$b

+ µ +1)

!

fa ="aD# a

!

fb ="bD# b

Data quality-control and calibration

•Agree well

September 17, 1998

• to match well

• larger range for disdrometer, common with a smaller sampling volume

Verification with disdrometer measurementsPhysical parameters

September 17, 1998September 17, 1998

• Other physical parameters: Nt, D0 and #m retrieved accurately

• Nt is usually difficult to retrieve (zero moment from high moments)

Spatial distribution of retrieved rain DSDsConvective case: 19:26:46 UTC

Spatial distribution of retrieved rain DSDsStratiform case: 22:21:54 UTC

Comparison with Beta–MethodGorgucci et al. (2001 & 2002) and Bring et al. (2002)

1.03r D!= "

Issues related to DSD retrieval

• Selection of radar measurements: Z, and ZDR

• Shape model: fixed axis ratio relation, density relation

is needed for snow

• Constrained gamma DSD model: a µ-" relation

• Hydrometeor classification should be applied before

rain DSD retrieval