Effects of parameterizations of

the drop size distribution with

variable shape parameter on

polarimetric radar moments

Katharina Schinagl, Christian Rieger, Clemens Simmer, Silke Trömel, PetraFriederichs

TR32 Conference – April 6th, 2017

A pattern

Polarimetric radar

horizontal orientation

vertical orientation

→ identify hydrometeor shape/size/type, estimaterain rates, ...

drop size distribution (DSD)polarimetric observables

I horizontal reflectivity ZHI horizontal reflectivity ZVI differential reflectivity ZDRI specific differential phase KDPI cross-correlation coefficient ρHV

data assimilation

→ NWP models need to reproduce physicallyplausible polarimetric moments

www. roc. noaa. gov/ wsr88d/

dualpol/

Polarimetric radar forward operators

polarimetric radar forward operators, e.g.

I horizontal reflectivity ZH(~x , t) =4λ4

radar

π4|Kw |2

∫ Dmax

Dmin

|fHH(π,D,~x , t)|2N(D,~x , t)dD[mm6m−3

]I differential reflectivity

ZDR(~x , t) = 10 logZH(~x , t)

ZV (~x , t)[dB]

I cross-correlation coefficient

ρHV (~x , t) =

∫ Dmax

Dmin

f∗HH(π,D,~x , t)fVV (π,D,~x , t)N(D,~x , t)dD√∫ Dmax

Dmin

fHH(π,D)2N(D,~x , t)dD∫ Dmax

Dmin

fVV (π,D)2N(D,~x , t)dD

N(D, ~x , t) is the DSD in space and time

Role of ZDR

ZDR = 10 logZHZV

[dB]

Dm = 1.619Z0.485DR (Bringi, Chandrasekar 2001)

Florida 1991, S-band weather radar and airborne

particle imaging probe

DSD parameterization

gamma DSD N(D) = N0Dµ exp (−ΛD)

NWP: two-moment-schemes typically predict 0th and 3rd moment of DSDNT (number concentration rain), qr (specific rain content):

NT = M(0) =

∫ ∞0

N(D)dD, ρqr = M(3) =

∫ ∞0

D3N(D)dD

parameterization of DSD given M(0), M(3)?

...while taking into account model-specific challenges (size sorting)

DSD parameter µ diagnosed from D′m =(

M(3)M(0)

)1/3(mean-mass diameter)

mean volume diameter Dm = M(4)M(3)

→ µ-D′m-relations

DSD parameterization: µ− D′m-relations

Seifert, 2008:

µ =

{6 tanh

[(c1(D′m − Deq)

]2 + 1, D′m ≤ Deq

30 tanh[(c2(D′m − Deq)

]2 + 1, D′m > Deq

c1 = 4000m−1, c2 = 1000m−1

Deq = 0.0011m equilibrium diameter

Λ = [(µ + 3)(µ + 2)(µ + 1)]13 D′−1

m

[m−1]

N0 =NT

Γ(µ+1) Λ(µ+1)[m−(µ+4)

]similar relations from e.g. Milbrandtand Yau, 2005 and Milbrandt andMcTaggart-Cowan, 2010

Synthetic polarimetric moments

frequency 9.3e9 (BoXPol)

oblate shape, water phase

Dmin = 0.05e − 3 [m] ,Dmax = 8e − 3 [m] ,Di = 0.05e − 3 [m]

T = 290K

ZH [dBZ] ZH [dBZ]

Synthetic polarimetric moments

frequency 9.3e9 (BoXPol)

oblate shape, water phase

Dmin = 0.05e − 3 [m] ,Dmax = 8e − 3 [m] ,Di = 0.05e − 3 [m]

T = 290K

ZDR [dB] ZDR [dB]

Synthetic polarimetric moments

frequency 9.3e9 (BoXPol)

oblate shape, water phase

Dmin = 0.05e − 3 [m] ,Dmax = 8e − 3 [m] ,Di = 0.05e − 3 [m]

T = 290KρHV ρHV

Synthetic polarimetric moments

frequency 9.3e9 (BoXPol)

oblate shape, water phase

Dmin = 0.05e − 3 [m] ,Dmax = 8e − 3 [m] ,Di = 0.05e − 3 [m]

T = 290K

KDP[degkm−1

]KDP

[degkm−1

]

Synthetic polarimetric moments

frequency 9.3e9 (BoXPol)

oblate shape, water phase

Dmin = 0.05e − 3 [m] ,Dmax = 8e − 3 [m] ,Di = 0.05e − 3 [m]

T = 290K

R[mmh−1

]R[mmh−1

]

Constrained-gamma DSDs

Zhang et al, 2001: µ = −0.016Λ2 + 1.213Λ− 1.957disdrometer observations, east-central Florida (tropical climate), summer 1998

Lam et al, 2015: Λ = 0.041µ2 + 0.310µ+ 1.740disdrometer observations, Kuala Lumpur, Malaysia (equatorial climate), january 1992 -

december 1994

→ derived µ-D′m-relations

ZDR: empirical relations

Dm = 1.619Z 0.485DR (Bringi, Chandrasekar 2001)

Summary

DSDs as used in modelling do not yield fully convincing polarimetricmoments

→ consequences for data assimilationdifferent approaches of radar scientists and modellers

I radar scientists: ’constrained-gamma’ with Λ− µ-relationI modellers: µ-D′m-relations based on mean-mass diameter D′m

DSD parameterization needs further work

3-moment-schemes

finite maximum diameter

Thank you for your attention!Questions?

Bringi, V N and V Chandrasekar: Polarimetric Doppler weather radar: principles and applications.

Cambridge university press, 2001.

Lam, Hong Yin, Jafri Din, and Siat Ling Jong: Statistical and physical descriptions of raindrop size distributions in equatorial malaysia from

disdrometer observations.Advances in Meteorology, 2015, 2015.

Milbrandt, JA and R McTaggart-Cowan: Sedimentation-induced errors in bulk microphysics schemes.

Journal of the Atmospheric Sciences, 67(12):3931–3948, 2010.

Milbrandt, JA and MK Yau: A multimoment bulk microphysics parameterization. part i: Analysis of the role of the spectral shape

parameter.Journal of the Atmospheric Sciences, 62(9):3051–3064, 2005.

Seifert, Axel: On the parameterization of evaporation of raindrops as simulated by a one-dimensional rainshaft model.

Journal of the Atmospheric Sciences, 65(11):3608–3619, 2008.

Xie, Xinxin, Raquel Evaristo, Clemens Simmer, Jan Handwerker, and Silke Trömel: Precipitation and microphysical processes observed by

three polarimetric x-band radars and ground-based instrumentation during hope.Atmospheric Chemistry and Physics, 16(11):7105–7116, 2016.

Zhang, Guifu, Jothiram Vivekanandan, and Edward Brandes: A method for estimating rain rate and drop size distribution from

polarimetric radar measurements.Geoscience and Remote Sensing, IEEE Transactions on, 39(4):830–841, 2001.