Radar-measurement-motivated recent improvements to a ... - Cosmo

Forschungszentrum Karlsruhe 

in der Helmholtz-Gemeinschaft 

Universität Karlsruhe (TH) 

Forschungsuniversität · gegründet 1825 

Radar-measurement-motivated recent 

improvements to a state-of-the-art 2-moment 

cloud microphysical scheme in the framework 

of the COSMO-model 

Ulrich Blahak 1 , Heike Noppel 1 and Axel Seifert 2 

1 IMK, University / Research Center Karlsruhe 

2 DWD Offenbach 

Blahak, Noppel, Seifert 

3.3.2008 

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Table of Contents 

1 Motivation 

2 Two-moment bulk microphysical scheme 

3 Changes to the previous scheme and their effects 

4 Conclusions 


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1 Motivation 



4 Conclusions 


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1 Motivation 



4 Conclusions 


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1 Motivation 



4 Conclusions 


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Cell splitting case, Mannheim, 27.6.2001 

IMK-Radar (C-Band) 

Semi-idealized COSMO run 

(∆X = 1 km) 

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2-moment bulk microphysical scheme 

Cloud droplets, rain, cloud ice, snow, RIME-graupel, 

FRI-graupel (”hail”, Noppel et al., 2006) 

For each hydrometeor category: rate equations for 

1 number density N (0. moment of PSD f (x)) 

2 mass density Q (1. moment of PSD f (x)) 

Parameterizations of microphysical processes based on 

f (x) = N 0 x ν exp(−λ x µ ) 

ν,µ = const., λ = 


[ 

Γ( 

ν+1 

µ ) 

Q 

Γ( ν+2 

µ ) N 

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] −µ 

, N 0 = µ N 

Γ( ν+1 

µ ) λ ν+1 

µ 



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Previous scheme including FRI-graupel 

2D ”warm bubble” simulation, sounding 28.6.2008, Stuttgart 

dBZ after 1 h 

dBZ after 2 h 


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Mean particle size, low CCN case, after 1 h 

D mean cloud D mean ice D mean snow 

D mean rain D mean RIME-graupel D mean FRI-graupel (”hail”) 


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Mean particle size, low CCN case, after 2 h 

D mean cloud D mean ice D mean snow 

D mean rain D mean RIME-graupel D mean FRI-graupel (”hail”) 


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Previous scheme including hail: features/problems 

1 Reflectivities aloft rather small. 

Likely cause: RIME-graupel and FRI-graupel (”hail”) particles 

may be too small, number concentrations too large. 

2 Strong increase of D mean of evaporating rain towards the ground 

(not prominent here, since quite moist PBL) 

3 Strong increase of D mean of melting ice particles towards the 

ground. 

4 No parameterization of ”wet growth” so far, known to be 

important in the formation of large hail. 


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Changes to the previous scheme 

Different ice species compete for available supercooled water. 

=⇒ measures to decrease number concentration and (hopefully) 

increase particle size 

Increase (spherical equivalent) bulk density of small cloud ice 

particles 

=⇒ decrease collision cross section and riming (decrease 

ice-to-graupel conversion) 

Increase bulk density and fall speed of small graupel 

=⇒ slightly increased riming of single particles 

New parameterization of evaporation of number- and 

mass-density of raindrops (Seifert, 2008, submitted) 


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Concerning too small and too many graupel particles: 

Parameterization of graupel growth by riming: 

∂ Q g 

∣ 

π 

= E gc 

∂t 

4 A(ν, µ,a,b,α,β) Q c N g D g (x g ) 2 v g (x g ) 

∂ N g 

∂t 

∣ 

coll,gc 

∣ = 0 

coll,gc 

D g = ax b g , v g = α x β g 

Parameterization of graupel initiation by riming of ice particles: 

∂ Q g 

1 

∂t ∣ = ( ) ∂ Q i 

π6 rime,ic ρ 

α w ρ e D i (x i ) ∂t ∣ 

0 ρe x 

− 1 

coll,ic 

i ∂ N g 

∂t ∣ = 1 ∂ Q g 

∣ 

rime,ic 

x i ∂t 

∣ 

rime,ic 


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Changes in hydrometeor definitions 

ρ-D-relations, v-D-relations (vertical lines = min./max. allowed D mean ) 

ρ eff 

in kg/m 3 

Old hydrometeor definitions 

New hydrometeor definitions 

Diameter−density−relation 

500 

450 

400 

350 

RIME Graupel (prev.) 

FRI Graupel (prev.) 

300 

Snow (prev.) 

Ice (prev.) 

250 

200 

150 

100 

ρ eff 

in kg/m 3 


500 

Graupel (new) 

450 

Hail (new) 

400 

Snow (new) 

Ice (new) 

350 

300 

250 

200 

150 

100 

50 

0 

0 0.5 1 1.5 2 2.5 3 

D in mm 

eff 

50 

0 

0 0.5 1 1.5 2 2.5 3 

D eff 

in mm 

8 

7 

6 

Diameter−fallspeed−relation 



Snow (prev.) 

Ice (prev.) 

8 

7 

6 


Graupel (new) 

Hail (new) 

Snow (new) 

Ice (new) 

5 

5 

v in m/s 

4 

v in m/s 

4 

3 

3 

2 

2 

1 

1 

0 

0 0.5 1 1.5 2 2.5 3 

D eff 

in mm 


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0 

0 0.5 1 1.5 2 2.5 3 

D in mm 

eff 

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Effect of up-to-now changes on profiles 

Space-time average vertical profiles (only QX > 0.001 gm −3 considered) 

Q graupel D mean graupel Q ”hail” D mean ”hail” 


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Actions taken to address these problems 

Observations: 

Now less and only marginally larger graupel, but more hail =⇒ 

more cloud water and rain ”survive” longer in the updraft without 

beeing rimed by graupel, and now rain can freeze to hail 

category more efficiently. 

Scheme most possibly now too ”frozen-drop-friendly” 

(remember: ”hail” = frozen drops). 

Idea: split the outcome of freezing rain into ice, graupel, and hail, 

according to rain size (spectral partitioning). 

Further observation: rain drops originating from melting graupel 

and hail rather small. May be due to overprediction of number 

concentration transfer from ice species to rain during melting. 

=⇒ Time rate of change of number conc. during melting now 

diagnosed in a way that D mean is preserved (all ice species). 


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Observations: 















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”Hail” initiation: Spectral partitioning of freezing rain 


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Statistical description of raindrop freezing (concept of Biggs, 1953): 

1 

f r (x) 

∂ f r (x) 

∂t 

∣ = −x J het (T ) =⇒ 

freeze 

J het (T ) : Probability of freezing of raindrops, depending on T 

f r (x) : underlying generalized gamma mass distribution of rain 

Partitioning into ice species: 

∂ M (k) 

∫ 

x ig 

i 

= − x k ∂ f r 

∫ 

x ig 

∂t ∣ ∂t ∣ dx = J het (T ) x k+1 f r (x)dx 

freeze 

freeze 

0 

0 

∂ M (k) 

x ⎡ 

∫gh 

g 

= − x k ∂ f r 

∫ 

x gh 

x ⎤ 

∫ig 

∂t ∣ ∂t ∣ dx = J het (T ) ⎣ x k+1 f r (x)dx − x k+1 f r (x)dx⎦ 

freeze x freeze ig 0 

0 

⎡ 

∂ M (k) 

∫ 

h 

∞ 

= − x k ∂ f r 

∫ ∞ 

x ⎤ 

∫gh 


freeze x freeze gh 0 

0 


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Statistical description of raindrop freezing (concept of Biggs, 1953): 

1 

f r (x) 

∂ f r (x) 

∂t 

∣ = −x J het (T ) =⇒ 

freeze 

J het (T ) : Probability of freezing of raindrops, depending on T 

f r (x) : underlying generalized gamma mass distribution of rain 

Partitioning into ice species: 

∂ M (k) 

∫ 

x ig 

i 

= − x k ∂ f r 

∫ 

x ig 

∂t ∣ ∂t ∣ dx = J het (T ) x k+1 f r (x)dx 

freeze 

freeze 

0 

0 

∂ M (k) 

x ⎡ 

∫gh 

g 

= − x k ∂ f r 

∫ 

x gh 

x ⎤ 

∫ig 


freeze x freeze ig 0 

0 

⎡ 

∂ M (k) 

∫ 

h 

∞ 

= − x k ∂ f r 

∫ ∞ 

x ⎤ 

∫gh 


freeze x freeze gh 0 

0 


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”Hail” initiation: wet growth (graupel → hail) 

Dividing diameter at which latent heat of freezing due to riming starts 

to no more be transported away fast enough from the particle (based 

on heat budget equation of a spherical particle given by Dennis and 

Musil, 1973) 

0 

Min. diameter in mm for wet growth, P = 800 hPa Q i 

= 1.0 g/m 3 (using Hall/Pruppb./Rasmussen f v 

) 

0.5 0.5 0.5 

1 1 1 1 

4 4 4 4 

3 3 3 3 

5 5 5 

6 6 

88 

2 2 2 

25 

−5 

18 

14 

16 

7 

10 

9 

12 

40 

−10 

50 

20 

7 

T in ° C 

−15 

−20 

30 

25 

40 

50 

graupelhail2test 

−25 

ageo = 1.500e−01 

bgeo = 3.230e−01 

avel = 3.300e+01 

bvel = 1.650e−01 

18 

16 

14 

20 

30 

10 

9 

12 

25 

40 

50 

18 

−30 

1 2 3 4 5 

Q in g/m 3 6 7 8 9 10 

w 

Blahak, Noppel, Seifert IMK Karlsruhe 

8 

16 

14 

6 

20 

30 

10 

7 

9 

12 

25 

18 

8 

16 

14 

5 

6 

20 

10 

7 

9 

12 



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Recent updates to the two-moment scheme 

Space-time-average profiles 

dBZ D mean graupel D mean hail 




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Recent updates to the two-moment scheme 

Total precipitation after 3 h in t/m 

Low CCN case High CCN case 

Previous 1670 1370 

New 1660 1500 


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=⇒ Cell splitting case, Mannheim, 27.6.2001 



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Conclusions and outlook 

Now bigger hail particles aloft due to partitioning in rain 

droplet freezing; however, graupel mean size only 

marginally larger. 

Parameterization of graupel-to-hail conversion due to wet 

growth implemented. 

Simulated reflectivity profile in convective clouds now much 

more realistic in comparison with radar data. 

Parameterization of raindrop evaporation and of number 

conc. treatment for solid particle melting changed which 

considerable decrease the mean rain- and solid particle 

size below freezing level. 

=⇒ Stronger evaporation, stronger cold pools and 

secondary cell generation. 

Further testing in real case studies and in comparison with 

bin microphysical scheme (HUCM) under way. 


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THE END 

Thanks for your attention! 

Questions??? 


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Changes in hydrometeor definitions 

ρ-D-relations, v-D-relations (vertical lines = min./max. allowed D mean ) 

ρ eff 

in kg/m 3 

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

Old hydrometeor definitions 



Snow (prev.) 

Ice (prev.) 


0 

0 5 10 15 20 25 

D in mm 

eff 

ρ eff 

in kg/m 3 

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

New hydrometeor definitions 


Graupel (new) 

Hail (new) 

Snow (new) 

Ice (new) 

0 

0 5 10 15 20 25 

D in mm 

eff 

15 


15 


10 

10 

v in m/s 

v in m/s 

5 



Snow (prev.) 

Ice (prev.) 

0 

0 5 10 15 20 25 

D eff 

in mm 


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5 

Graupel (new) 

Hail (new) 

Snow (new) 

Ice (new) 

0 

0 5 10 15 20 25 

D in mm 

eff 

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Hail initiation in the 2-moment scheme 

Previous scheme 




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Hail initiation in the 2-moment scheme 

New scheme 




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Radar-measurement-motivated recent improvements to a ... - Cosmo

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