Simulation of Hail using a Triple-moment Microphysics Scheme Jason Milbrandt and M. K. Yau WMO...

Simulation of Hailusing a

Triple-moment Microphysics Scheme

Simulation of Hailusing a

Triple-moment Microphysics Scheme

Jason Milbrandtand

M. K. Yau

WMO International Cloud Modeling WorkshopJuly 12, 2004

OBJECTIVES OF PRESENTATION:

1. Discuss the role of the shape parameter in bulk microphysics schemes

2. Demonstrate that hail sizes can be simulated using a bulk scheme

3. Compare sensitivity experiments using various bulk methods

Representation of a hydrometeor size distribution:

1 m3

(unit volume)

[e.g. Cloud droplets]

BULK METHOD

N(D)

D [ m]

100

[m-3 m-1]

20 40 60 800

101

100

10-1

10-2

ANALYTIC

FUNCTION

nnn

T

D

D

D

D

D

NDN exp

1)(

1

or,

etc.

BULK METHOD

GAMMA DISTRIBUTION FUNCTION

DDNDN exp)( 0


GAMMA DISTRIBUTION FUNCTION

BULK METHOD

N0x : “intercept”

x: “slope”

x: shape parameter

Qx : Mass content (Qx = qx)

NTx: Total number concentration

Zx: Radar reflectivity

Dmx: Mean-mass diameter

Size Distribution Parameters: Various quantities:

DDNDN xxxx exp)( 0


Typical double-moment method:

BULK METHOD

Predict changes to Qx and NTx

Implies changes to values of the N0x and x

x is held constant)

DDNDN xxxx exp)( 0

BULK METHOD

DDNDN xxxx exp)( 0

1. Diagnostic-x (double-moment)

- x = f (Qx, NTx)

Alternative bulk methods:

2. Prognostic-x (triple-moment)

- a third moment must be predicted

e.g. add dZx/dt equation

ROLE OF ALPHA

How important is the shape parameter (x )

in a bulk scheme?

Continuity equation for x:

Only SEDIMENTATION and SOURCE terms are

affected by the microphysics scheme (and hence by x)

x: Predictive variable for hydrometeor category x

)()()()( xxxxx SOURCESEDIMTURBADV

t

ROLE OF ALPHA: 1. SEDIMENTATION

10

5

0

z(km)

Mass [g m-3]0 1

1. Prescribe Q(z):

D

log N(D)

N0

Di

DeDNDN 0)(

2. Compute N(Di, z): [from a prescribed distribution]

For every size bin i:zi(t) = zi(0) - Vi(Di) t

bii aDDV )(

3. Compute locations of each particle after sedimentation for time t:

Analytic bin model calculation: (1D column)

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

Contours every 5 min

MassContent

Total NumberConcentration

EquivalentReflectivity

Mean-massDiameter

ROLE OF ALPHA: 1. SEDIMENTATION

5 min

10 min

15 min

20 min

INITIAL

Analytic bin model calculation: (1D column)

z

Vq

t

q xqx

SEDI

x

xqV = mass-weighted fall velocity

SM

z

VN

t

N xNx

SEDI

x

xNV = number-weighted fall velocity

DM

z

VZ

t

Z xZx

SEDI

x

xZV = reflectivity-weighted fall velocity

TM

ROLE OF ALPHA: 1. SEDIMENTATION BULK SCHEMES

ROLE OF ALPHA: 1. SEDIMENTATION BULK vs. ANALYTIC

MassContent

Q [g m-3] Q [g m-3] Q [g m-3] Q [g m-3]

z[km]

DOUBLE-MOMENT

Fixed SINGLE-MOMENT

DOUBLE-MOMENT

Diagnosed TRIPLE-

MOMENT

Bulk schemes:

Analytic model:

z[km]

Q [g m-3]

5 min

10 min

15 min

20 min

INITIAL

For the prediction of NT, Z, and Dm, the various

bulk methods exhibit similar relative abilities for

pure sedimentation (as for Q).

ROLE OF ALPHA: 1. SEDIMENTATION BULK vs. ANALYTIC

NOTE:

• No size-sorting mechanism exists for single-moment schemes

• For the double-moment scheme with = 0, excessive size-

sorting results in very large Dm and Z

ROLE OF ALPHA: 2. GROWTH RATES

2. MICROPHYSICS SOURCES/SINKS

0

)()(

dDDNdt

Ddm

dt

dq

CLCL

x

CONTINUOUS COLLECTIONOF CLOUD WATER (CLcx):

xbxx DaDV )(

xbcxccxc

CL

DqEqEDVD

dt

Ddm

2

2

4)(

4

)(

0

2 )(4

dDDNDqEdt

dqxb

cxcCL

x ( )

xbCL

x Mdt

dq 2

0)()( dDDNDpM x

px( )

A scheme’s ability to predict the growth rates

depends on its ability to compute the value of

certain moments [ranging from Mx(bx) to Mx(2+bx)]


xbxx DaDV )(

e.g. The accretion rate for hail (CLch) is proportional to Mh(2.6)

HAILbx 0.6

z[km]

Q [g m-3] NT [m-3] Ze [dBZ]

MassContent

Total NumberConcentration Reflectivity

RECALL:Analytic bin model calculation for sedimentation:


Q

NT

Z} N0

{At each level: M (2.6)_BULK

ROLE OF ALPHA: 2. GROWTH RATES (e.g. CLch)

Mh(2.6)_BULK

Mh(2.6)_ANAL

Mh(2.6)_BULK

Mh(2.6)_ANAL

ANALYTIC

SM

DM_FIX_0

DM_FIX_3

DM_DIAG

TM

z(km)

8 min

10

5

00.8 1.0 1.2

2 min

10

5

00.8 1.0 1.2

Ratio of Growth Rates: CLch_BULK

CLch_ ANAL

Mh(2.6)_BULK

Mh(2.6)_ANAL=

z(km)

• Six hydrometeor categories:– 2 liquid: cloud and rain– 4 frozen: ice, snow, graupel and hail

• ~50 distinct microphysical processes

• warm-rain scheme based on Cohard and Pinty (2000a)

• ice-phase based on Murakami (1990), Ferrier (1994), Meyers et al. (1997), Reisner et al. (1998), etc.

• diagnosed- relations added for double-moment version*

• predictive equations for Zx added for triple-moment version*

* Milbrandt and Yau, 2004 [J. Atmos. Sci., accepted]

TESTING IN 3D: The New* Microphysics Scheme

MODEL:

Canadian MC2 mesoscale model- non-hydrostatic, fully compressible- interfaced with new microphysics scheme (triple-moment version for CONTROL run)

CASE:

14 July 2000 “Pine Lake storm”, Alberta, Canada- long-lasting supercell- F3 tornado - golf ball-sized hail

CONTROL SIMULATION

12-km DOMAIN

3-km DOMAIN

1-km DOMAIN

ALBERTA

CONTROL SIMULATION: Nesting Strategy

NOTE: No CPS, perturbation, nudging (or anything else) was used to initiate the convection

12 18 00 06UTC

3 km

12 km14 JULY 15 JULY

Model Nesting Times

1 km

CONTROL SIMULATION: Accumulated Total Precipitation

mm40

30

25

20

16

13

10

8

6

4

RADAR

33 mm

1-km CNTR

8:00 pm

1-km SIMULATION:Accumulated TOTAL Precipitation

50 km

N

RADAR:Accumulated Precipitation

8:00 pm

50 km

N

30

25

20

15

10

5

mm

CONTROL SIMULATION: Hail Swath

27 26 25 24 23 22 21 20 19 18 17 16

kg m-2

RADAR:Composite of Maximum VIL

8:00 pm

50 km

N

1-km SIMULATION:Accumulated SOLID Precipitation

10 mm 8:00 pm

1-km CNTR

50 km

N

VIL 27 kg m-2 LARGE HAIL

RADAR

10

8

6

4

2

mm

dBZdBZ

CONTROL SIMULATION: Storm Structure: REFLECTIVITY

40 km

16 km

40 km

16 km

Maximum: 60 – 65 dBZ

COMPOSITE

Maximum: 63.6 dBZ

750 hPa

RADAR: 0030 UTC [6:30 pm]

1-km SIMULATION: 4:30 h [6:30 pm]

NN

65

60

57

54

51

48

45

42

39

36

33

30

CONTROL SIMULATION: Storm Structure: HOOK ECHO

Reflectivity CAPPI (2 km)

10 km

Equivalent Reflectivity (750 hPa)

10 km

RADAR: 0030 UTC [6:30 pm]

1-km SIMULATION: 4:15 h [6:15 pm]

CONTROL SIMULATION: Hail Sizes

)()()( ***h

**h DVDNDR T

Flux of large of hail (D > D*):

log Nh(D)

D *

*

)()( **h D

dDDNDN

LARGE

HAIL

D

How can the maximum hail sizes at the ground be inferred?

These distributions have identical mean diameters (Dm)

At 5:45 pm (simulation time: 4:45 h):

D* = 2 cm

Rh*(2 cm) = 5.010-2 m-2 s-1

or,

1 hailstone D 2 cm per 20 m2 every 20 seconds

OBSERVABLE

CONTROL SIMULATION: Simulated Hail Sizes

D* = 3 cm

Rh*(3 cm) = 2.310-4 m-2 s-1

or,

1.4 hailstones D 3 cm per 100 m2 every 1 minute

NEGLIGIBLE

Walnut-sized (2 – 3 cm) hail was simulated

Golf ball-sized (3 – 4 cm) hail was observedMAXIMUM:

List of Runs:

1. TRIPLE-MOMENT (control run)

2. DOUBLE-MOMENT with DIAGNOSED-

3. DOUBLE-MOMENT with FIXED- (2 for r ; 0 for c, i, s, g, h)

4. SINGLE-MOMENT (similar parameters as Lin et al. 1983)

ALL RUNS USE DIFFERENT VERSIONS OF

THE SAME SCHEME

SENSITIVITY EXPERIMENTS

SENSITIVITY EXPERIMENTS: TOTAL Precipitation

TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed

SINGLE-MOMENT DOUBLE-MOMENTFixed

6-h ACCUMLATED TOTAL PRECIPITATION[mm]

CONTOURS: 5, 10, 20, 30, 40 mm

28

3433

4243

10 99

6-h ACCUMLATED SOLID PRECIPITATION[mm]

SENSITIVITY EXPERIMENTS: SOLID Precipitation (HAIL)

CONTOUR INTERVAL: 2 mm

132535

3414

23



Local time: 6:30 pm(Simulation time: 4:30 h)

SENSITIVITY EXPERIMENTS: Equivalent Hail Reflectivity

TRIPLE-MOMENT

SINGLE-MOMENT

100 km

DOUBLE-MOMENTDiagnosed

DOUBLE-MOMENTFixed

Zeh [dBZ]700 hPa:

100 km50 km25 km 75 km0 km

SENSITIVITY EXPERIMENTS: Equivalent Hail Reflectivity,

63.6 dBZ 63.6 dBZ

68.3 dBZ 83.9 dBZ


MAXIMUM VALUE

10 km

TRIPLE-MOMENT

SINGLE-MOMENT

Zeh [dBZ]

DOUBLE-MOMENTDiagnosed

DOUBLE-MOMENTFixed

SENSITIVITY EXPERIMENTS: Hail Mass Content,


SINGLE-MOMENT

MAXIMUM VALUE

5.51 g m-3 5.58 g m-3

3.71 g m-3 4.91 g m-3


DOUBLE-MOMENTFixed

Qh [g m-3]

Dashed contour: 0.1 g m-3

SENSITIVITY EXPERIMENTS: Hail Number Concentration

MAXIMUM VALUE



5.18 4.07

1.53 5.22


log NTh [m-3]

Dashed contour: 1.0 m-3

SENSITIVITY EXPERIMENTS: Mean Hail Diameters,

MAXIMUM VALUE



14.9 mm 11.2 mm

6.15 mm 67.2 mm


Dmh [mm]

SENSITIVITY EXPERIMENTS: Maximum hail sizes (at surface)

2 – 3 cm (Walnut-sized) 1 – 2 cm (Grape-sized)

8 – 9 cm (Grapefruit-sized)4 – 5 cm (Baseball-sized)

3 – 4 cm (Golf ball-sized ) hail was observed[at 5:45 pm, time of maximum hail rate in CONTROL RUN]



CONCLUSIONS

1. The value of the shape parameter is important in

bulk microphysics schemes

THANK YOU

TRIPLE-MOMENT

DOUBLE-MOMENT

Diagnosed

SINGLE-MOMENT

DOUBLE-MOMENTFixed

2. For the overall QPF, storm structure, hydrometeor

values, and the simulation of hail sizes:

SINGLE-moment bulk scheme (SM):

ANALYTIC BIN model (ANA):

z[km]


z[km]


DOUBLE-moment bulk scheme (FIX0): = 0


z[km]


z[km]



DOUBLE-moment bulk scheme (FIX3): = 3

z[km]


z[km]


TRIPLE-moment bulk scheme (TM):


z[km]


z[km]



DOUBLE-moment bulk scheme (DIAG): = f(Dm)

z[km]


z[km]


Simulation of Hail using a Triple-moment Microphysics Scheme Jason Milbrandt and M. K. Yau WMO...

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