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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
Representation of a hydrometeor size distribution:
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
Representation of a hydrometeor size distribution:
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)]
ROLE OF ALPHA: 2. GROWTH RATES
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:
ROLE OF ALPHA: 2. GROWTH RATES
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
TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed
SINGLE-MOMENT DOUBLE-MOMENTFixed
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
Local time: 6:30 pm(Simulation time: 4:30 h)
MAXIMUM VALUE
10 km
TRIPLE-MOMENT
SINGLE-MOMENT
Zeh [dBZ]
DOUBLE-MOMENTDiagnosed
DOUBLE-MOMENTFixed
SENSITIVITY EXPERIMENTS: Hail Mass Content,
TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed
SINGLE-MOMENT
MAXIMUM VALUE
5.51 g m-3 5.58 g m-3
3.71 g m-3 4.91 g m-3
Local time: 6:30 pm(Simulation time: 4:30 h)
DOUBLE-MOMENTFixed
Qh [g m-3]
Dashed contour: 0.1 g m-3
SENSITIVITY EXPERIMENTS: Hail Number Concentration
MAXIMUM VALUE
TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed
SINGLE-MOMENT DOUBLE-MOMENTFixed
5.18 4.07
1.53 5.22
Local time: 6:30 pm(Simulation time: 4:30 h)
log NTh [m-3]
Dashed contour: 1.0 m-3
SENSITIVITY EXPERIMENTS: Mean Hail Diameters,
MAXIMUM VALUE
TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed
SINGLE-MOMENT DOUBLE-MOMENTFixed
14.9 mm 11.2 mm
6.15 mm 67.2 mm
Local time: 6:30 pm(Simulation time: 4:30 h)
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]
TRIPLE-MOMENT DOUBLE-MOMENTDiagnosed
SINGLE-MOMENT DOUBLE-MOMENTFixed
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]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
DOUBLE-moment bulk scheme (FIX0): = 0
ANALYTIC BIN model (ANA):
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
ANALYTIC BIN model (ANA):
DOUBLE-moment bulk scheme (FIX3): = 3
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
TRIPLE-moment bulk scheme (TM):
ANALYTIC BIN model (ANA):
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
ANALYTIC BIN model (ANA):
DOUBLE-moment bulk scheme (DIAG): = f(Dm)
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]
z[km]
Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]