A New Bulk Microphysical Parameterization in MM5 & WRF

Univ of Washington 03 Apr 2006

A New Bulk Microphysical A New Bulk Microphysical Parameterization in MM5 & WRFParameterization in MM5 & WRF

Greg Thompson,Paul Field, Roy Rasmussen, Bill Hall

and what’s so bad with the old scheme anyway?and what’s so bad with the old scheme anyway?


Microphysics species’ characteristicsMicrophysics species’ characteristics

Raingamma distribution

variable equiv y-intercept:

2 x 109 m-4 (drizzle)

8 x 106 (melted snow)

accurate fallspeed relation

Snowsum of two gamma distributions (Field et al, 2005)

variable y-intercept depends on ice content and temperature

non-spherical geometry (m = aD2)

variable snow density (1/D)

Graupelgamma distribution

variable equiv y-intercept depends on mixing ratio (simulate hail and snow-like graupel):

2 x 106 m-4 (graupel)

1 x 104 (hail)

Cloud icegamma distribution

“pristine” ice (D < 125 microns)

initiation T-dependent (Cooper)

prognosed Ni

slowly sediments at ~10-30 cm/s

Cloud watergamma distribution w/ shape factor dependent on droplet concentration

does not sediment

“autoconverts” to rain using Berry & Reinhardt with dependence on droplet concentration


Microphysical processes (details)Microphysical processes (details)Droplet condensation — removes all supersaturation in single timestep; now using Newton-Raphson iterative technique.

Ice nucleation — primary (>8% supersat w.r.t. ice; T-dependent/Cooper); secondary (rime-splinter); heterogeneous (literal interpretation of Bigg 1953); homogeneous below –40C (implicitly).

Ice depositional growth — T-dependent (Koenig, 1971). When ice grows larger than 125 m, mass moved into snow category by explicit bin method.

Snow depositional growth — integrated from assumed spectra; capacitance=0.3-0.5 (aggregates).

Rain evaporation — integrated from assumed spectra (deposition neglected; grows CLW instead).

Autoconversion — Berry & Reinhardt, 1974 with properly computed characteristic diameters - compares well to Geresdi bin model and K&K scheme.

Rain, snow, and graupel collect cloud water — integrated from assumed spectra and uses Wisner approximation.

Snow collects cloud ice — low collision efficiency; use Wisner approximation. Ignore graupel/ice collisions.

Rain/ice collisions & rain/graupel collisions — pre-compute bin-model style; lookup table. Uses same assumption as bin modelers: when mass of water drop exceeds mass of ice, the drop freezes into graupel; otherwise the ice accretes the water to grow snow.

Sedimentation — rain uses Ferrier modified power law (match Gunn & Kinzer); snow uses power law and Ferrier constants; cloud ice and graupel use power laws.

Melting — cloud ice, instantly; snow and graupel use assumed spectra and thermodynamic equilibrium.


Cloud water - detailsCloud water - detailsGeneralized gamma distribution: N(D) = N0 D e-D

Shape parameter, , depends on droplet concentration, Nt_c [from Martin et al. (1994)]:

= min(15, 1000/Nt_c + 2)

Maritime: Nt_c <= 75 cm-3; = 15; dispersion = 0.25

Continental: Nt_c = 300 cm-3; = 5; dispersion = 0.45

qc = 0.25 g m-3

Future:Will use variable Nt_c in space and time; attempt to initialize from MODIS or other sat data by end of CY2006


Rain - detailsRain - detailsGeneralized gamma distribution: N(D) = N0 D e-D

Autoconversion from Berry & Reinhardt (1974; part 2). Previous implementation followed Walko et al. (1995), but oversimplified characteristic diameters. Current scheme properly implements B&R characteristic diameters:

d(qr)

dt=

€

LWC = m(D)N(D)dD∫Z = m(D)[ ]

2∫ N(D)dD

x f = LWCNc

xg = ZLWC

xb2 = x f xg − x f

2

€

Dc = 6ρ aqc

πρ wNc

⎛ ⎝ ⎜

⎞ ⎠ ⎟1

3

Dg =

Γ(7 + μ)Γ(4 + μ) ⎡ ⎣ ⎢

⎤ ⎦ ⎥1

3

λ

Db = Dc3Dg

3 − Dc6[ ]

16


Rain - details (cont)Rain - details (cont)Y-intercept (equiv exponential distrib), N0, uniquely diagnosed; melted ice versus collision/coalescence. This was done to attempt to simulate freezing drizzle events while not ignoring classical rain (melting ice).

N0r_exp varies from 2 x 109 (drizzle-like) down to 2 x 106 m-4 (convective rain) producing median volume diameters from 50 microns to no larger than 3 mm.

T = 0oCmelting ice mvd=50m

linear increaseto melted equiv (~1-2 mm);then constantN0r_exp below

N0r_exp computed as f(qr) but minimized below

non-classical precip formation

freezing drizzle

drizzlerain

Future:Will add predictive number concentration for rain by end of CY2006


Terminal velocityTerminal velocityPower law for cloud ice, rain, snow, graupel:

€

v t = avxDbvx × e− fvx D

varying N0 causes curvature; greatly reduced “step” from prior (2004) version

(exponential causes the flattening)

Exponential distrib with N 0=8x106 m

-4

Cloud ice:

Snow (Ferrier, 1994):

Graupel:

Rain (Ferrier, 1994):

€

v t = 4854D1 × e−195.0D

€

v t = 900D1

€

v t =18.73D.42

€

v t =130D.7

Snow

Mitchell & Heymsfield


Cloud ice (pristine) - detailsCloud ice (pristine) - detailsGeneralized gamma distribution: N(D) = N0 D e-D

Threshold size for transfer to snow: D0s = 125 micronsDoes not rimeUtilizes explicit size bins to determine mass transfer each timestep (look-up table)Like Harrington et al. (1995), depositional growth of ice for diameters > D0s goes directly into snow category

mass here goes into snow

Initiation: • primary nucleation (when T < -8oC or 8+% supersaturated w.r.t. ice) uses Cooper (1986) curve• freezing of water droplets using literal interpretation of Bigg (1953) temp/volume probabilities (look-up table)• secondary/rime-splinter (Hallet & Mossop 1974)

Bigg, 1953

vapor deposition goes into snow


Ice/snow size spectra (UK-C130 aircraft)Ice/snow size spectra (UK-C130 aircraft)Mid-latitude stratiform cloud around UK

~9000 10 second (~1.1 km) ice particle size distributions

2DC/2DP particle probes (100 m to 6 mm)

N(D)[m-4]

M33

N(D) -----M2

4

re-scaled

M2D -----M3

M2D -----M3

M2D -----M3

M2D ----- M3

D (m)


Moment relations contain lots of scatter until …Moment relations contain lots of scatter until …

stratified by temperature

IWC = m(D) N(D) dD

IWC = 0.069 D2 N(D) dD

M2 = D2 N(D) dD

IWC = 0.069 M2

Mn = a(n,T) M2b(a,T)

Mn = a(n,T) [IWC/0.069]b(a,T)

Sum of exponential + gamma distributions

(Field et al. 2005):

€

N(D) = M 24

M 33 κ 0e

− M2M3

Λ 0D + κ1M 2M 3

D( )μe− M2

M3Λ1D ⎡

⎣ ⎢ ⎤ ⎦ ⎥


Graupel - detailsGraupel - detailsGeneralized gamma distribution: N(D) = N0 D e-D

Y-intercept (equiv exponential distrib), N0, diagnosed as f(qg):

N0 = max(104, min(100*qg, 106))

shifts from snow-like graupel towards hail category using single species

rimed snow converting to graupel remains ad-hoc and needs more research:

Riming:Deposition5 30

% P

rg_s

acw

to g

raup

el

5

75


Collisions between hydrometeorsCollisions between hydrometeors Hydrometeor y collides and collects species x governed by Stochastic Collection Equation (SCE):

Nearly everyone assumes Exy is constant w.r.t. diameter (generally OK except cloud water self-collection).

Next, some processes can apply Wisner (1972) approximation where v(D)x>>v(D)y & Dx>>Dy (example: rain, snow, and graupel collecting cloud water).

When species have similar fallspeeds, Wisner approximation is unacceptable, so Mizuno (1990) pulled velocity difference outside the integral by using abs(vtx-vty) (for rain collecting hail/graupel). Old Reisner et al. (1998) code used this assumption for rain collecting either snow or graupel.

The new scheme uses full SCE for rain collecting either snow or graupel and stores results in look-up table. It creates 100 log-spaced diameter bins of rain, snow, and graupel and sums the full double-integral.

Nearly every researcher including Verlinde et al. (1990) and Gaudet & Schmidt (2005) assume the absolute value of the velocity difference (over diameters ranging from zero to infinity) whereas we “short-circuit” the integral once the diameter causes the velocity difference to become negative.

The process is further complicated in a 3-way process like rain colliding with snow to form graupel. The old code only transferred the mass of snow into graupel, not the mass of rain involved in the collision. The new code converts both species properly to graupel (if mass of water drop exceeds mass of snowflake; alternatively snow accretes the water drop to increase snow mass - identical to how nearly all bin microphysics models are designed).

Example, rain collecting snow…

€

d(ry )dt

= π4

Exy m(Dx ) Dx + Dy( )2

vx (Dx ) − vy (Dy )[ ]0

∞

∫ Nx (Dx ) Ny (Dy )dDxdDy0

∞

∫


Rain collecting snow (and vice-versa)Rain collecting snow (and vice-versa)

old Reisner scheme new scheme

contour lines are production rate of graupel (g kg-1 s-1)


Summary of physical process improvementsSummary of physical process improvements Generalized gamma replaces exponential distributions plus Field et al. (2005) snow distrib. Rain evaporates only after cloud water evaporates. Cloud ice, snow, and graupel sublimate and rain evaporates using more accurate Srivastava & Coen (1992) method. Cloud ice converts to snow using explicit, not ad-hoc method. Collisions between hydrometeors with similar fallspeed use explicit bin method in Stochastic Collection Eqn (SCE). Rain collecting cloud ice or snow properly sums the rain amount into graupel, not just the ice amount. Snow and graupel sublimate when above melting temperature (did not in old scheme). Graupel y-intercept parameter (and terminal velocity) attempt to mimic hail when high mixing ratio (strong updrafts). Rain y-intercept parameter mimics both precip formation mechanisms: classic melting ice & collision/coalescence. Autoconversion uses correctly computed Berry & Reinhardt characteristic diameters. Rimed snow conversion to graupel is no longer “all or nothing” but increases as riming:depositional increases. Sedimentation uses non-zero terminal velocity for “new precipitation cores.” Cloud ice has differential number/mass-weighted terminal velocities.

Summary of code improvementsSummary of code improvements Generalized gamma replaces exponential distributions. Look-up tables implemented for most costly calculations (SCE for rain and snow/graupel collisions). Very simple parameters to change mass-diameter (and other) relations. Rain evaporation only after cloud water evaporates. When skipping timesteps, rain evaporates (and cloud water condenses/evaporates and hydrometeors sediment). Cloud water condensation uses more accurate 1st order iterative Newton-Raphson technique. “Clean slate” approach, no more legacy code, well documented, consistent variable naming, etc.


PlaceholderPlaceholder


Tests in 2-d using MM5 & WRFTests in 2-d using MM5 & WRF

Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis.Mon. Wea. Rev., 132, 519-542.

cloud water

cloud ice& snow

rain

WRF resultsMM5 results


Tests in 3-d using MM5/WRFTests in 3-d using MM5/WRF

• 14 Feb 1990 (WISP)shallow, post-frontal, upslope cloud w/widespread FZDZ.

• 30 Jan 1998 (NASA-SLDRP)shallow stratoCu, primarily CLW w/slight FZDZ.

• 04 Feb 1998 (NASA-SLDRP)deep and dynamic snowstorm w/classic FZRA.

• 01 Feb 2001 (IMPROVE-1)deep PacNW frontal system, abundant precip.

• 28 Nov 2001 (IMPROVE-2)deep PacNW frontal system plus orographics.

• 13 Dec 2001 (IMPROVE-2)deep PacNW frontal system plus orographics.

• plus a series of recent (Feb/Mar 2006) cases and Jim Bresch’s realtime runs

Thompson, et al., 2006: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Case studies. Mon. Wea. Rev., in preparation.


30 Jan 1998 NASA-SLDRP case30 Jan 1998 NASA-SLDRP case

• Very broad and shallow stratus or stratocumulus cloud• High liquid water content but mostly cloud drops• Sporadic surface reports of light freezing drizzle• Numerous pilot reports, generally moderate intensity

Canada

Lake Erie

PennsylvaniaOhio


30 Jan 1998: liquid water comparison30 Jan 1998: liquid water comparison

>95% of water mass in drops less than 30 microns

KCLE ascent (1315z)

KYNG ascent (1400z)KCAK descent (1330z)

KCLE landing (1430z)

dashed lines are MM5 data for same place/time

solid lines are King probe LWC data from Twin Otter aircraft


30 Jan 1998: Old snow/new snow comparison30 Jan 1998: Old snow/new snow comparison

Cloud top temp = -11C

Observed LWC = 0.7 g/m3

Higher (closer to observed) LWC

Green shading = cloud water

Blue contours = snow

Shallow/mostly-water cloud simulation: increased supercooled liquid cloud using new snow scheme versus old!

MM5 simulation using old snow scheme MM5 simulation using new snow scheme


04 Feb 1998 NASA-SLDRP case04 Feb 1998 NASA-SLDRP case• Widespread, deep glaciated cloud (nor’easter)• Classic “warm-nose” with freezing rain near OH/WV border (Parkersburg, WV)• Twin Otter experienced a ‘significant performance degradation’


04 Feb 1998: Temp/Microphysics comparison04 Feb 1998: Temp/Microphysics comparison

>70% of water mass in drops greater than 700 microns

aircraftdataMM5

model

MM5snow

MM5rain

King LWCFSSP LWC

MM5cloudwater

Twin Otter 2d-gray probe indicated snow particles throughout entire depth to surface


04 Feb 1998: Old snow/new snow comparison04 Feb 1998: Old snow/new snow comparison

Deep/mostly-glaciated cloud simulation:

decreased supercooled liquid cloud & decreased RHicealoft using new snow scheme versus old!

MM5 simulation using old snow scheme MM5 simulation using new snow scheme


01 Feb 2001: old/new scheme comparison01 Feb 2001: old/new scheme comparison

Eerily similar results. Was the old scheme not that bad? Is something wrong with the new?

MM5 simulation using entirely new bulk schemeMM5 simulation using old bulk scheme


Future workFuture work• verification and more testing (DTC in next 2 months - ARW&NMM)

• upcoming additions/improvements:

1) 2nd moment for cloud water and rain

2) initial aerosol variable will vary in space/time (connect to Chem module?)

3) aerosol variable will influence cloud water condensation and ice nucleation

4) addition of “Asian dust outbreaks” (for NSF-proposed ICE-L field project)

• needs:

1) testing un-tested aspects (gamma shape parameter)

2) better (and faster) sedimentation

3) improve handling of rimed snow conversion to graupel

4) addition of hail category for convective simulations?


Thank you!Thank you!

[email protected]

mailto:[email protected]

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A New Bulk Microphysical Parameterization in MM5 & WRF