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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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:

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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

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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

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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

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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