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.