WMO International Cloud Modeling Workshop

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Presentation transcript:

WMO International Cloud Modeling Workshop Simulation of Hail using a Triple-moment Microphysics Scheme Jason Milbrandt and M. K. Yau WMO International Cloud Modeling Workshop July 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: BULK METHOD Representation of a hydrometeor size distribution: N(D) D [ m] 100 [m-3  m-1] 20 40 60 80 101 10-1 10-2 ANALYTIC FUNCTION 1 m3 (unit volume) [e.g. Cloud droplets]

Representation of a hydrometeor size distribution: BULK METHOD Representation of a hydrometeor size distribution: GAMMA DISTRIBUTION FUNCTION or, etc.

Representation of a hydrometeor size distribution: BULK METHOD Representation of a hydrometeor size distribution: GAMMA DISTRIBUTION FUNCTION Size Distribution Parameters: Various quantities: N0x : “intercept” lx : “slope” ax : shape parameter Qx : Mass content (Qx = r qx) NTx: Total number concentration Zx : Radar reflectivity Dmx: Mean-mass diameter

Typical double-moment method: BULK METHOD Typical double-moment method: Predict changes to Qx and NTx Implies changes to values of the N0x and lx (ax is held constant)

Alternative bulk methods: 1. Diagnostic-ax (double-moment) - ax = f (Qx, NTx) 2. Prognostic-ax (triple-moment) - a third moment must be predicted e.g. add dZx/dt equation

How important is the shape parameter (x ) 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 ax) x: Predictive variable for hydrometeor category x

Analytic bin model calculation: (1D column) ROLE OF ALPHA: 1. SEDIMENTATION Analytic bin model calculation: (1D column) 10 5 z (km) Mass [g m-3] 1 1. Prescribe Q(z): D log N(D) N0 Di 2. Compute N(Di, z): [from a prescribed distribution] For every size bin i: zi(t) = zi(0) - Vi(Di)  t 3. Compute locations of each particle after sedimentation for time t:

Analytic bin model calculation: (1D column) ROLE OF ALPHA: 1. SEDIMENTATION Analytic bin model calculation: (1D column) Mass Content Total Number Concentration Equivalent Reflectivity Mean-mass Diameter INITIAL 5 min z [km] 10 min 15 min 20 min Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] Contours every 5 min

ROLE OF ALPHA: 1. SEDIMENTATION BULK SCHEMES = number-weighted fall velocity DM = reflectivity-weighted fall velocity TM SM = mass-weighted fall velocity

Mass Content ROLE OF ALPHA: 1. SEDIMENTATION BULK vs. ANALYTIC z [km] Q [g m-3] 5 min 10 min 15 min 20 min INITIAL Analytic model: Mass Content Bulk schemes: Q [g m-3] z [km] DOUBLE- MOMENT Fixed a = 0 SINGLE- Diagnosed a TRIPLE-

ROLE OF ALPHA: 1. SEDIMENTATION BULK vs. ANALYTIC For the prediction of NT, Z, and Dm, the various bulk methods exhibit similar relative abilities for pure sedimentation (as for Q). NOTE: No size-sorting mechanism exists for single-moment schemes For the double-moment scheme with a = 0, excessive size-sorting results in very large Dm and Z

CONTINUOUS COLLECTION ROLE OF ALPHA: 2. GROWTH RATES 2. MICROPHYSICS SOURCES/SINKS CONTINUOUS COLLECTION OF CLOUD WATER (CLcx): ( ) ( )

ROLE OF ALPHA: 2. GROWTH RATES 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)] e.g. The accretion rate for hail (CLch) is proportional to Mh(2.6) HAIL bx  0.6

Analytic bin model calculation for sedimentation: ROLE OF ALPHA: 2. GROWTH RATES RECALL: Analytic bin model calculation for sedimentation: Mass Content Total Number Concentration Reflectivity z [km] Q [g m-3] NT [m-3] Ze [dBZ] Q NT Z } N0 l a {  At each level: M (2.6)_BULK

ROLE OF ALPHA: 2. GROWTH RATES (e.g. CLch) Ratio of Growth Rates: CLch_BULK CLch_ ANAL Mh(2.6)_BULK Mh(2.6)_ANAL = 2 min 10 5 0.8 1.0 1.2 8 min 10 5 0.8 1.0 1.2 z (km) z (km) Mh(2.6)_BULK Mh(2.6)_ANAL ANALYTIC SM DM_FIX_0 DM_FIX_3 DM_DIAG TM Mh(2.6)_BULK Mh(2.6)_ANAL

* Milbrandt and Yau, 2004 [J. Atmos. Sci., accepted] TESTING IN 3D: The New* Microphysics Scheme 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-a relations added for double-moment version* predictive equations for Zx added for triple-moment version* * Milbrandt and Yau, 2004 [J. Atmos. Sci., accepted]

Canadian MC2 mesoscale model - non-hydrostatic, fully compressible CONTROL SIMULATION 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: Nesting Strategy 12-km DOMAIN NOTE: No CPS, perturbation, nudging (or anything else) was used to initiate the convection ALBERTA 3-km DOMAIN 1-km DOMAIN 12 18 00 06 UTC 3 km 12 km 14 JULY 15 JULY Model Nesting Times 1 km

CONTROL SIMULATION: Accumulated Total Precipitation mm 40 30 25 20 16 13 10 8 6 4 RADAR: Accumulated Precipitation N 8:00 pm 50 km RADAR 33 mm 1-km CNTR 8:00 pm 1-km SIMULATION: Accumulated TOTAL Precipitation 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 VIL  27 kg m-2  LARGE HAIL RADAR: Composite of Maximum VIL N 8:00 pm 50 km RADAR 1-km SIMULATION: Accumulated SOLID Precipitation 10 mm 8:00 pm 1-km CNTR 50 km N 10 8 6 4 2 mm

CONTROL SIMULATION: Storm Structure: REFLECTIVITY RADAR: 0030 UTC [6:30 pm] 1-km SIMULATION: 4:30 h [6:30 pm] 40 km 16 km 40 km 16 km dBZ dBZ 65 60 57 54 51 48 45 42 39 36 33 30 Maximum: 60 – 65 dBZ COMPOSITE Maximum: 63.6 dBZ 750 hPa N N

CONTROL SIMULATION: Storm Structure: HOOK ECHO RADAR: 0030 UTC [6:30 pm] 1-km SIMULATION: 4:15 h [6:15 pm] Reflectivity CAPPI (2 km) 10 km Equivalent Reflectivity (750 hPa) 10 km

CONTROL SIMULATION: Hail Sizes How can the maximum hail sizes at the ground be inferred? D * LARGE HAIL log Nh(D) These distributions have identical mean diameters (Dm) D Flux of large of hail (D > D*):

D* = 2 cm OBSERVABLE D* = 3 cm NEGLIGIBLE CONTROL SIMULATION: Simulated Hail Sizes At 5:45 pm (simulation time: 4:45 h): D* = 2 cm Rh*(2 cm) = 5.010-2 m-2 s-1 or, 1 hailstone D  2 cm per 20 m2 every 20 seconds OBSERVABLE D* = 3 cm Rh*(3 cm) = 2.310-4 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 observed MAXIMUM:

ALL RUNS USE DIFFERENT VERSIONS OF THE SAME SCHEME SENSITIVITY EXPERIMENTS List of Runs: 1. TRIPLE-MOMENT (control run) 2. DOUBLE-MOMENT with DIAGNOSED-a 3. DOUBLE-MOMENT with FIXED-a (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

6-h ACCUMLATED TOTAL PRECIPITATION [mm] SENSITIVITY EXPERIMENTS: TOTAL Precipitation 6-h ACCUMLATED TOTAL PRECIPITATION [mm] TRIPLE-MOMENT DOUBLE-MOMENT Diagnosed a 33 34 SINGLE-MOMENT DOUBLE-MOMENT Fixed a 43 28 42 CONTOURS: 5, 10, 20, 30, 40 mm

6-h ACCUMLATED SOLID PRECIPITATION [mm] SENSITIVITY EXPERIMENTS: SOLID Precipitation (HAIL) 6-h ACCUMLATED SOLID PRECIPITATION [mm] TRIPLE-MOMENT DOUBLE-MOMENT Diagnosed a 10 9 9 SINGLE-MOMENT DOUBLE-MOMENT Fixed a 35 25 14 23 34 13 CONTOUR INTERVAL: 2 mm

700 hPa: SENSITIVITY EXPERIMENTS: Equivalent Hail Reflectivity Zeh [dBZ] 700 hPa: Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT DOUBLE-MOMENT Diagnosed a 100 km SINGLE-MOMENT DOUBLE-MOMENT Fixed a

SENSITIVITY EXPERIMENTS: Equivalent Hail Reflectivity, Zeh [dBZ] Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT 63.6 dBZ DOUBLE-MOMENT Diagnosed a 63.6 dBZ SINGLE-MOMENT 68.3 dBZ DOUBLE-MOMENT Fixed a 83.9 dBZ 10 km 0 km 25 km 50 km 75 km 100 km MAXIMUM VALUE

SENSITIVITY EXPERIMENTS: Hail Mass Content, Qh [g m-3] Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT 5.51 g m-3 DOUBLE-MOMENT Diagnosed a 5.58 g m-3 SINGLE-MOMENT 3.71 g m-3 DOUBLE-MOMENT Fixed a 4.91 g m-3 Dashed contour: 0.1 g m-3 MAXIMUM VALUE

SENSITIVITY EXPERIMENTS: Hail Number Concentration log NTh [m-3] Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT 5.18 DOUBLE-MOMENT Diagnosed a 4.07 SINGLE-MOMENT 1.53 DOUBLE-MOMENT Fixed a 5.22 Dashed contour: 1.0 m-3 MAXIMUM VALUE

SENSITIVITY EXPERIMENTS: Mean Hail Diameters, Dmh [mm] Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT 14.9 mm DOUBLE-MOMENT Diagnosed a 11.2 mm SINGLE-MOMENT 6.15 mm DOUBLE-MOMENT Fixed a 67.2 mm MAXIMUM VALUE

SENSITIVITY EXPERIMENTS: Large Hail Concentration, Nh*{1 cm} [m-3] (grape-sized or larger) Local time: 6:30 pm (Simulation time: 4:30 h) TRIPLE-MOMENT 1.03 m-3 DOUBLE-MOMENT Diagnosed a 0.79 m-3 SINGLE-MOMENT 1.76 m-3 DOUBLE-MOMENT Fixed a 0.68 m-3 Dashed contour: 0.01 m-3 MAXIMUM VALUE

SENSITIVITY EXPERIMENTS: Maximum hail sizes (at surface) 3 – 4 cm (Golf ball-sized ) hail was observed [at 5:45 pm, time of maximum hail rate in CONTROL RUN] TRIPLE-MOMENT DOUBLE-MOMENT Diagnosed a 2 – 3 cm (Walnut-sized) 1 – 2 cm (Grape-sized) SINGLE-MOMENT DOUBLE-MOMENT Fixed a 4 – 5 cm (Baseball-sized) 8 – 9 cm (Grapefruit-sized)

CONCLUSIONS    THANK YOU 1. The value of the shape parameter is important in bulk microphysics schemes TRIPLE- MOMENT DOUBLE- Diagnosed a SINGLE- Fixed a    2. For the overall QPF, storm structure, hydrometeor values, and the simulation of hail sizes: THANK YOU

SINGLE-moment bulk scheme (SM): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] ANALYTIC BIN model (ANA): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm]

DOUBLE-moment bulk scheme (FIX0): a = 0 z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] ANALYTIC BIN model (ANA): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm]

DOUBLE-moment bulk scheme (FIX3): a = 3 z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] ANALYTIC BIN model (ANA): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm]

TRIPLE-moment bulk scheme (TM): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] ANALYTIC BIN model (ANA): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm]

DOUBLE-moment bulk scheme (DIAG): a = f(Dm) z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm] ANALYTIC BIN model (ANA): z [km] Q [g m-3] NT [m-3] Ze [dBZ] Dm [mm]