Parametric representation of the hydrometeor spectra for LES warm bulk microphysical schemes.
description
Transcript of Parametric representation of the hydrometeor spectra for LES warm bulk microphysical schemes.
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:
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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:
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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:
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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
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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
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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