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


D0 = 75 µm


RICO : 8500 spectra

σ g Lognormal

M1

qc, Nc

Cloud Rain D0


D0 = 75 µm


RICO : 8500 spectra

σ g Lognormal

M1 M2 M5 M6

σ g σ g σ g

ν1

qc, Nc

Cloud Rain D0


D0 = 75 µm


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


D0 = 75 µm


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


D0 = 75 µm

Rain:ACE-2 : not used

RICO : 2860 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




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)


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)


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




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)


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





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





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

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


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


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


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 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



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


width

parametric representation of the hydrometeor spectra for les warm bulk microphysical schemes

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