A New Bulk Microphysical
Parameterization in MM5 & WRF
and what’s so bad with the old scheme anyway?
Greg Thompson,
Paul Field, Roy Rasmussen, Bill Hall
Univ of Washington 03 Apr 2006
Microphysics species’ characteristics
Cloud water
Cloud ice
gamma distribution w/ shape factor
dependent on droplet concentration
gamma distribution
“pristine” ice (D < 125 microns)
does not sediment
initiation T-dependent (Cooper)
“autoconverts” to rain using Berry &
Reinhardt with dependence on
droplet concentration
Rain
gamma distribution
variable equiv y-intercept:
2 x 109 m-4 (drizzle)
8 x 106 (melted snow)
accurate fallspeed relation
prognosed Ni
slowly sediments at ~10-30 cm/s
Snow
sum of two gamma
distributions (Field et al,
2005)
variable y-intercept depends
on ice content and
temperature
non-spherical geometry
(m = aD2)
Univ of Washington 03 Apr 2006
variable snow density (1/D)
Graupel
gamma distribution
variable equiv y-intercept
depends on mixing ratio
(simulate hail and snowlike graupel):
2 x 106 m-4 (graupel)
1 x 104 (hail)
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 –40C (implicitly).
Ice depositional growth — T-dependent (Koenig, 1971). When ice grows larger than 125 mm, 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.
Univ of Washington 03 Apr 2006
Cloud water - details
Generalized gamma distribution:
N(D) = N0 Dm e-lD
Shape parameter, m, depends on droplet concentration, Nt_c [from Martin et al. (1994)]:
m = min(15, 1000/Nt_c + 2)
Maritime: Nt_c <= 75 cm-3; m = 15; dispersion = 0.25
Continental: Nt_c = 300 cm-3; m = 5; dispersion = 0.45
qc = 0.25 g m-3
Univ of Washington 03 Apr 2006
Future:
Will use variable Nt_c in
space and time; attempt to
initialize from MODIS or
other sat data by end of
CY2006
Rain - details
Generalized gamma distribution:
N(D) = N0 Dm e-lD
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 
Z
 m(D)N(D)dD
 m(D) N(D)dD
2
=
1
 6  q  3
Dc   a c 
 w N c 
1
LWC
xf 
Nc
Z
xg 
LWC
x b2  x f x g  x 2f
Dg 
(7  m)  3


(4  m)
l
Db  Dc3 Dg3  Dc6  6
1

Univ of Washington 03 Apr 2006
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.
non-classical precip formation
freezing drizzle
N0r_exp
computed as
f(qr) but
minimized
below
T = 0o C
melting ice
drizzle
Univ of Washington 03 Apr 2006
rain
mvd=50mm
linear increase
to melted equiv
(~1-2 mm);
then constant
N0r_exp below
Future:
Will add predictive number
concentration for rain by
end of CY2006
Terminal velocity
Power law for cloud ice, rain, snow, graupel:
v t  av x Dbvx  e fvx D
v t  900D1
Snow (Ferrier, 1994):
(exponential causes the flattening)

Cloud ice:



v t  18.73D.42
Graupel:
v t  130D.7
Rain (Ferrier, 1994):
v t  4854D1  e195.0D
Snow

varying N0 causes curvature; greatly reduced “step” from prior (2004) version
Mitchell & Heymsfield
Univ of Washington 03 Apr 2006
Cloud ice (pristine) - details
Generalized gamma distribution:
N(D) = N0 Dm e-lD
Threshold size for transfer to snow: D0s = 125 microns
Does not rime
Like Harrington et al. (1995), depositional growth of ice for
diameters > D0s goes directly into snow category
Bigg, 1953
mass here goes into snow
Univ of Washington 03 Apr 2006
• 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)
Utilizes explicit size bins to determine mass transfer each
timestep (look-up table)
vapor deposition goes into snow
Initiation:
• secondary/rime-splinter (Hallet & Mossop 1974)
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 mm to 6 mm)
re-scaled
N(D)
[m-4]
M3 3
N(D) -----4
M2
D (mm)
Univ of Washington 03 Apr 2006
M
M
M
222
D
----DD--------M
M
M333
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):
  MM23  0 D
N(D)  M 3  0e
 1
3 
M 24
Univ of Washington 03 Apr 2006


M2
M3

m  M2  1 D
M
D e
3



Generalized gamma distribution:
N(D) = N0 Dm e-lD
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
75
% Prg_sacw
to graupel
Graupel - details
5
rimed snow converting to graupel remains ad-hoc and needs more research:
5
30
Riming:Deposition
Univ of Washington 03 Apr 2006
Collisions between hydrometeors
Hydrometeor y collides and collects species x governed by Stochastic Collection Equation (SCE):
d(ry )
dt


4
 
 E
0
m(Dx ) Dx  Dy  v x (Dx )  v y (Dy )N x (Dx ) N y (Dy ) dDx dDy
2
xy
0
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…
Univ of Washington 03 Apr 2006
Rain collecting snow (and vice-versa)
old Reisner scheme
contour lines are production rate of graupel (g kg-1 s-1)
Univ of Washington 03 Apr 2006
new scheme
Summary 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 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).
st order iterative Newton-Raphson technique.
 Cloud water condensation uses more accurate 1
 “Clean slate” approach, no more legacy code, well documented, consistent variable naming, etc.

Univ of Washington 03 Apr 2006
Placeholder
Univ of Washington 03 Apr 2006
Tests in 2-d using MM5 & WRF
MM5 results
WRF results
cloud water
cloud ice
& snow
rain
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.
Univ of Washington 03 Apr 2006
Tests 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.
Univ of Washington 03 Apr 2006
30 Jan 1998 NASA-SLDRP case
•
•
•
•
Canada
Very broad and shallow stratus or stratocumulus cloud
High liquid water content but mostly cloud drops
Erie
Sporadic surface reports of light freezingLake
drizzle
Numerous pilot reports, generally moderate intensity
Ohio
Univ of Washington 03 Apr 2006
Pennsylvania
30 Jan 1998: liquid water comparison
dashed lines are MM5 data for same place/time
KCLE ascent (1315z)
KCAK descent (1330z)
KYNG ascent (1400z)
KCLE landing (1430z)
solid lines are King probe LWC data from Twin Otter aircraft
>95% of water mass in drops less than 30 microns
Univ of Washington 03 Apr 2006
30 Jan 1998: Old snow/new snow comparison
MM5 simulation using old snow scheme
Cloud top temp = -11C
MM5 simulation using new snow scheme
Higher (closer to observed) LWC
Observed LWC = 0.7 g/m3
Green shading = cloud water
Blue contours = snow
Shallow/mostly-water cloud simulation:
increased supercooled liquid cloud using new snow scheme versus old!
Univ of Washington 03 Apr 2006
04 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’
Univ of Washington 03 Apr 2006
04 Feb 1998: Temp/Microphysics comparison
MM5
model
aircraft
data
Twin Otter
2d-gray
probe
indicated
snow
particles
throughout
entire depth
to surface
MM5
cloud
water
MM5
rain
MM5
snow
King LWC
FSSP LWC
>70% of water mass in drops greater than 700 microns
Univ of Washington 03 Apr 2006
04 Feb 1998: Old snow/new snow comparison
MM5 simulation using old snow scheme
MM5 simulation using new snow scheme
Deep/mostly-glaciated cloud simulation:
decreased supercooled liquid cloud & decreased RHicealoft using new
snow scheme versus old!
Univ of Washington 03 Apr 2006
01 Feb 2001: old/new scheme comparison
MM5 simulation using old bulk scheme
MM5 simulation using entirely new bulk scheme
Eerily similar results. Was the old scheme not that bad? Is something wrong with the new?
Univ of Washington 03 Apr 2006
Future 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?
Univ of Washington 03 Apr 2006
Thank you!
gthompsn@ucar.edu
Univ of Washington 03 Apr 2006