Post on 18-Jan-2016
description
Parametric representation of the hydrometeor spectra
for LES warm bulk microphysical schemes.
Olivier Geoffroy, Pier Siebesma (KNMI),Olivier Geoffroy, Pier Siebesma (KNMI),Jean-Louis Brenguier, Frederic Burnet (Météo-France)Jean-Louis Brenguier, Frederic Burnet (Météo-France)
I. Problematic, methodology and measurements
II. Cloud spectrum: results
III. Rain spectrum: results
IV. Sensitivity tests in shallow cumulus simulations.
V. Z-R relationship
To derive other moments from M0 & M3, M0 & M3 it is necessary to make an assumption about the shape of the CDSD and the RDSD
5~ MFcq
2~ MFcN
Cloud Sedim:
Radar reflectivity:
Interaction withradiative transfert:
τ~M2
4~ MFrq
1~ MFrN
Rain Sedim
Problematic
),N,f(q~ cc c
Rain evap:
~M1 & M2
autoconversion:Radar
reflectivity:
Nc (M0) & qc (~M3), Nr (M0) & qr (~M3)
Microphysical processes / variables
Cond/evap:
Bulk prognostics variables =
~SM1 =M6
=M6
))ln
)D/Dln((
2
1exp(
lnD2
1)D( 2
g
g
g
Nn
))D(exp(D)(
)D( 1
Nn
Generalized GammaLognormal
Are Lognormal, Gamma, Gamma in mass suitable ? With which value of the width parameter σg or ν?
Common distributions
ν =1 ν =6ν =11
α=1Size distri = Gamma
α=3Mass distri = Gamma
= Marshall Palmer
σg=? ν =?3 parametersM0, M3 = prognostics
4 parametersM0, M3 = prognosticsα =1 or 3
Observationnal dataData = particule counters in situ Measurements at 1Hz resolution (~ 100 m).
-Sc and Cu spectra - Measurements at each levels in the BL
- ~100 m resolution- Complete hydrometeors spectra : 1 µm to 10 mm
flight plan
RICO : 7 cases of CuACE-2 : 8 cases of Sc
Fast FSSP : ~2 ~50 µmOAP-260-X : 5635 µm2DP-200X: 245 12645 µm
Fast FSSP : ~2 ~40 µmOAP-200-X : 35 310 µm
Instruments
campaign
Cloud Rain D0
MethodologyFor each spectrum:
D0 = 75 µm
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
qc, Nc
Cloud Rain D0
MethodologyFor each spectrum:
D0 = 75 µm
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
σ g Lognormal
M1
qc, Nc
Cloud Rain D0
MethodologyFor each spectrum:
D0 = 75 µm
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
σ g Lognormal
M1 M2 M5 M6
σ g σ g σ g
ν1
qc, Nc
Cloud Rain D0
MethodologyFor each spectrum:
D0 = 75 µm
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
σ g Gamma
Lognormal
M1 M2 M5 M6
ν1 σ g
ν1 σ g
ν1 σ g
ν1
qc, Nc
Cloud Rain
MethodologyFor each spectrum:
D0 = 75 µm
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
σ g
Gamma in mass
Gamma
Lognormal
M1 M2 M5 M6
ν1 σ g
ν1 σ g
ν1 σ g
ν3 ν3 ν3 ν3
D0
ν1
qc, Nc
Cloud Rain D0
MethodologyFor each spectrum:
D0 = 75 µm
Rain:ACE-2 : not used
RICO : 2860 spectra
Cloud:ACE-2 : 19000 spectra
RICO : 8500 spectra
σ g
Gamma in mass
Gamma
Lognormal
M1 M2 M5 M6
ν1 σ g
ν1 σ g
ν1 σ g
ν3 ν3 ν3 ν3
M1 M2 M4 M6
qr, Nr
ν1 σ g
ν1 σ g
ν1 σ g
ν1 σ g
ν3 ν3 ν3 ν3
Plan
I. Methodology and measurements
II. Cloud spectrum: results
III. Rain spectrum: results
IV. Sensitivity tests in shallow cumulus simulations.
Cloud, width parameter=f(M1)
Grey points = value of σg that best represent M1 for each spectrum
Circles = value that minimize the standard deviation of the absolute errors Mmeasure-Manalytic in each moment class
Triangles = value that minimize the standard deviation of the relative errors Mmeasure/ Manalytic in each moment class
Cloud, width parameter=f(Mp)
Circles = value that minimize the standard deviation of the absolute errors Mmeasure-Manalytic in each moment class
Triangles = value that minimize the standard deviation of the relative errors Mmeasure/ Manalyticin each moment class
Value of the width parameter:
32.1g
111
2.13
Lognormal:
Gamma:
Gamma in mass:
Lognormal:
Gamma:
Gamma in mass:
Cloud, width parameter=f(qc)
Parameterization formulation :
1.0))ln((338.2 cg q
4200 4.01 cq
75.080 6.03 cq
Circles = value that minimize the standard deviation of the absolute errors Mmeasure-Manalytic in each LWC class
Triangles = value that minimize the standard deviation of the relative errors Mmeasure/ Manalyticin each LWC class
Gamma in mass:
Gamma:
Lognormal:
Cloud, relative error=f(Mp)
Value of the width parameter:
32.1g
111
2.13
Cloud, relative error = f(qc)
Lognormal:
Gamma:
Gamma in mass:
Parameterizations:
1.0))ln((338.2 cg q
4200 4.01 cq
75.080 6.03 cq
Gamma in mass:
Gamma:
Lognormal:
Cloud, relative error=f(Mp)
Value of the width parameter:
32.1g
111
2.13
Cloud, relative error = f(qc)
Lognormal:
Gamma:
Gamma in mass:
Parameterizations:
1.0))ln((338.2 cg q
4200 4.01 cq
75.080 6.03 cq
Plan
I. Methodology and measurements
II. Cloud spectrum: results
III. Rain spectrum: results
IV. Sensitivity tests in shallow cumulus simulations.
Rain: Gamma, ν=f(Dv)
Seifert (2008)
ν=f(Dv)
Measurements vs Seifert (2008) results:- Some distributions larger than Marshall Palmer at low Dv
- Less narrow distributions at high Dv
1
16
13
10
7
4
Differences:- Measurements at every levels in cloud region- Seifert (2008): distribution at the surface, no condensation
Marshall and Palmer (1948)
Marshall and Palmer (1948)
Stevens and Seifert (2008)
ν=f(Dv)
ν=f(Dv)
Rain : free parameter=f(qr)
Dependance in function of qr Better results
Lognormal:
Gamma:
Gamma in mass:
Parameterizations :
15.054.0 rg q
6.01 /008.0 rq
7.03 /005.0 rq
Circles = value that minimize the standard deviation of the absolute errors Mmeasure-Manalytic in each RWC class
Triangles = value that minimize the standard deviation of the relative errors Mmeasure/ Manalytic in each RWC class
Rain : relative errors
Dependance in function of qr Better results
Lognormal:
Gamma:
Gamma in mass:
Parameterizations:
15.054.0 rg q
6.01 /008.0 rq
7.03 /005.0 rq
Marshall Palmer
Plan
I. Problematic, methodology and measurements
II. Cloud spectrum: results
III. Rain spectrum: results
IV. Sensitivity tests in shallow cumulus simulations.
V. Z-R relationship
Sensivity test: RICO case
LWP (g m-2)
RWP (g m-2)
Rsurface (W m-2)
Ensemble of models
DALES simulationsModels of the intercomparison exercise (black)
ν3c=1, νr=1ν3c=f(lwc), νr=f(lwc)
Deeper BL based on RICO
θl
qt
-0.6 K
+ 2.5 g kg-1
+ 0.5 g kg-1
Colder
Moister-0.6 K
Averaged profilesrestart
Sensitivity to ν3c
ν3c 1 f(qc)
LWP (g m-2) 14.8 17.1
RWP (g m-2) 8.9 4.3
0
22
4
2 ))1(
)(1(
)3)(1(
*20
au
c
c
c
ccccr
N
q
x
k
t
q
υc=1 A=8 υc=2 A=3.75υc=3 A= 2.7
Autoconversion rate :
=A
3 10-8
(Seifert and Beheng, 2006)
Sensitivity to νr
νr 1 f(qc) ( )
νSS08
( )6 11
LWP (g m-2) 15.0 14.8 16.0 18.3 19.0
RWP (g m-2) 7.6 8.9 12.5 20.3 23.1
CB
CT
Processes depending on νr : rain sedim, evap, self-collection and break-up
width
Plan
I. Problematic, methodology and measurements
II. Cloud spectrum: results
III. Rain spectrum: results
IV. Sensitivity tests in shallow cumulus simulations.
V. Z-R relationship
Z-R
Snodgrass (2009)
Z=68 R2
Summary
-Development of a parameterization of the width parameter of the cloud droplet spectra as a function of the LWC.
-Development of a parameterization of the width parameter of the rain drop spectra as a function of the RWC
32.1g
111
2.13
Lognormal:
Gamma:
Gamma in mass:
1.0))ln((338.2 cg q
4200 4.01 cq
75.080 6.03 cq
Lognormal:
Gamma:
15.054.0 rg q
6.01 /008.0 rq
Z-R
Snodgrass: redTRMM: green
Only 2dp
Z-R
Sensitivity to νr
νr 1 f(qc) ( )
νSS08
( )6 11
LWP (g m-2) 15.0 14.8 16.0 18.3 19.0
RWP (g m-2) 7.6 8.9 12.5 20.3 23.1
Without rain evaporation
- Sensivity to νr in sedim process similar results as Stevens and Seifert (2008)- Main sensitivity : sedimentation process. νr in sedim RWP
νr in sedim Vqr evap LWP RWP νr in evap evap LWP
νr 1 f(qc) νSS08 6 11
LWP (g m-2) 12.4 / 13.3 13.2 12.8
RWP (g m-2) 9.5 / 15.1 19.2 21.9
CB
CT
Processes depending on νr : rain sedim, evap, self-collection and break-up
widthFluxprecip
Observational data
ACE-2 : not usedRICO : 2860 spectra
ACE-2 : 19000 spectra RICO : 8500 spectra
Scatterplot all qc-Nc values Scatterplot all qr-Nr values
Large number of spectra typical of Sc and Cu
(RF07, RF08, RF11, RF13)
Measured spectra
ACE-2 : 8 cases of ScFast FSSP : ~2 ~50 µm, 266 bins OAP-260-X : 5635 µm, 63 bins, Δbin~ 10 µm 2DP-200X: 45 12645 µm, 63 bins, Δbin~ 200 µm
Fast FSSP : ~2 ~40 µm, 266 bins OAP-200-X : 15 310 µm, 15 bins, Δbin~ 20 µm
RICO : 7 cases of Cu
- Complete hydrometeors spectra : 1 µm to 10 mm
32.1g
111
2.13
Parameterization formulation :
Cloud, absolute error=f(Mp)
Normalization:M1: 100 µm cm-3
M2 :1000 µm2 cm-3
M5:107 µm5 cm-3
M6 :109 µm6 cm-3
σ: 1 µm
Cloud, absolute error =f(qc)
1.0))ln((338.2 cg q
4200 4.01 cq
75.080 6.03 cq
Parameterization formulation :
Normalization:M1: 100 µm cm-3
M2 :1000 µm2 cm-3
M5:107 µm5 cm-3
M6 :109 µm6 cm-3
σ: 1 µm
ACE 2 - RICO
Only ACE 2
Only ACE 2
Only RICO
Only RICO
Rain sedimentation
))/6001(1(65.9
))/6001(1(65.9)(
)3(
r
r
rsbNr
rsbqr
CV
CV
Terminal velocities parameterization (Stevens and Seifert, 2008) :
Vqr > VNr
V=f(Dv), νr=1 V=f(Dv), νr =6 V=f(Dv), νr =11
Vqr
VNr
Vqr-VNr
Vqr
VNr
Vqr-VNr
Vqr
VNr
Vqr-VNr
broader : νr Vqr ,VNr distribution Vqr-VNr
Size sorting
Rain sedimentation (averaged profiles)
ν width Vqr Rsurf dRWP /dt RWP
ν width RWP evap LWP (positive feedback)
sc / b-up : low impact
Evap : low impact µ evap but larger droplets Rsurf
Sedim
LWP RWP (peaks) RWP , Rsurf
(large drops)
Rain evaporation
0
)()(2
)( dDDnDDFG
t
rnventilatio
a
wevap
r
5.03/1 )Re(DNbaF scvfvfvent
evapr
r
revapevap
r
t
q
q
NC
t
N)()(
Cevap = 1 Dv = constant during evaporation (happens if preence of little drops)Cevap = 0 Nr = constant during evaporation (happens if only large drops)
Rain mixing ratio rr
Rain concentration Nr
Cevap = 0.7 – 1 (A. Seifert personal com)
Cevap sensitivity
Cevap = 0.7 – 1 (A. Seifert personal com)
Cevap=1Cevap=0.7Cevap=0
~2 mm j-1
Cevap = 1 Dv = constant, Nr
Cevap = 0 Nr = constant, Dv
evap LWP and RWP
evapr
r
revapevap
r
t
q
q
NC
t
N)()(
Autoconversion, sensitivity
0
22
4
2 ))1(
)(1(
)3)(1(
*20
au
c
c
c
ccccr
N
q
x
k
t
q
= 8 (υc=1)= 3.75 (υc=2)= 2.7 (υc=3)
kcc= 4.44 E9 m3 kg-2 s-1
10.44 E9 m3 kg-2 s-1
Autoconversion rate :
(Cloud droplet width)Collection efficiency
~2 mm j-1
Sensitivity to the coefficientsυc (cloud droplet spectra width)
The rain drop distribution
),,( rrr Nrf )Dexp(D)(
)D( 1rr
rr
rrN
n
Gamma law :
1 free parameter : νr
Gamma law (rr = 0.2 g kg-1, Nr = 10000 m-3)
νr = 1νr =6νr =11
with :
Dv νr ν Narrowerdistribution
Seifert (2008)
νν=f(Dv)
1
16
13
10
7
4
1-D bin model spectra :
= Marshall Palmer
νr sensivityνr=1
νr=f(Dv) νr=6
νr=11
~2 mm j-1
ν
Width
Size sorting
Vqr
Rsurf
dRWP /dt
RWP
ν
RWP
evap
LWP
Impact due to sedimention
(acrr ~ cste)
Precipitating flights :RF07, RF08, RF12 (low vlues and low number of points , 0.10 g m-3), RF13, RF11
Explicit (bin) scheme
50 – 100 variables High numerical cost
Bulk scheme : only 2 bins
cloud rain
D0 ~ 40 - 100 µm
1 - 5 variables Numerical cost Parameterisations of the microphysical processes
D~ 40 µm
n(D)
~ 1 µm ~ 8 mm
D
n(D)
~ 1 µm ~ 8 mm
dDDnDM pp
0
)(
Warm cloud Bulk parameterisation
Sensivity test: RICO case
LWP (g m-2)
RWP (g m-2)
Psurface (W m-2)
DALES simulations
Rain: Gamma, ν=f(Dv)
Seifert (2008)
ν=f(Dv)
Measurements vs Seifert (2008) results:- Some distributions larger than Marshall Palmer at low Dv
- Less narrow distributions at high Dv
1
16
13
10
7
4
Differences:- Measurements at every levels in cloud region- Seifert (2008): distribution at the surface, no condensation
Marshall and Palmer (1948)
Marshall and Palmer (1948)
Stevens and Seifert (2008)
ν=f(Dv)
ν=f(Dv)
Sensitivity to νr
νr 1 f(qc) ( )
νSS08
( )6 11
LWP (g m-2) 15.0 14.8 16.0 18.3 19.0
RWP (g m-2) 7.6 8.9 12.5 20.3 23.1
CB
CT
Processes depending on νr : rain sedim, evap, self-collection and break-up
width