30
IMPROVING THE REPRESENTATION OF SNOW IN A BULK SCHEME Christopher P. Woods, Mark T. Stoelinga, John D. Locatelli, and Peter V. Hobbs University of Washington, Seattle, WA
IMPROVING THE REPRESENTATION OF SNOW IN A BULK SCHEME
Christopher P. Woods,Mark T. Stoelinga, John D. Locatelli, and Peter V. Hobbs
University of Washington, Seattle, WA
Why work with a “classic” single-moment 5-class bulk scheme?
[specifically, the Reisner et al. (1998) / Thompson et al. (2004), or “R-T” scheme]:
Intentionally simple
schemes(oper. NWP)
“Classic”SM 5-class
bulk schemes
More classes/More
moments/Gamma dist.
Spectrally explicit “bin”
schemes
Sophistication of Grid-resolved MicrophysicsLow High
As computer power increases, enhanced sophistication in cloud microphysics will always compete with the desire to:
• Increase resolution• Enhance other physics schemes (radiation, PBL, LSM)• Add ensemble members• Improved data assimilation
Why focus on snow?
•For many important classes of precipitation, most of the precipitation mass reaching the ground initiated as snow:
* cold-season extratropical cyclonic storms* cold-cloud orographic precipitation* stratiform precipitation associated with
MCSs
•Yet snow is the most complicated species to represent in terms of the variety of particle shapes, densities, and size distribution
from Reisner et al. (1998)
Three aspects of the representation of snow in bulk schemes:
1. Size distribution2. Shape and density assumptions (i.e., mass-
diameter relationship)3. Velocity-diameter relationship
A case will be made for:
1. Choosing a reasonable/relevant habit2. Enforcing “habit consistency” throughout the
scheme3. Diagnosing (as in Meyers et al. 1997) or predicting
habit variability
1. Size distribution
0ˆ ( ) exp( )s s sN D N D
Integrating the third moment over all sizes yields
0 snowair 04
( , )ss s s
s
Nq f N
qs is predicted;specify N0s, and solve for λs;or alternatively, specify λs, and solve for N0s.
All spectra 0.03 < M < 0.30
y = 0.0875e-0.1181x
R2 = 0.6483
0.01
0.1
1
10
-35 -30 -25 -20 -15 -10 -5 0
Temperature (°C)
No
(cm
-4) CT
CT/DEND
CT/DEN/NEED
CT/DEN/COL
CT/COL
CT/COL/NEED
CT/NEED
Expon. (CT)
All spectra 0.03 < M < 0.30
y = 0.002e-0.0405x
R2 = 0.5442
0.001
0.01
-35 -30 -25 -20 -15 -10 -5 0
Temperature (°C)
Lam
bd
a/10
000
(cm
-1)
CT
CT/DEND
CT/DEN/NEED
CT/DEN/COL
CT/COL
CT/COL/NEED
CT/NEED
Expon. (CT)
(a)
(b)
Best-fit CT only
Houze et al (1979)
N0
(m-4)
106
107
108
109
λ (m
m-1)
100
101
Houze et al (1979)
Intercept (N0s) vs. T
Slope (λs) vs. T
Intercept and slope parameters measured by aircraft particle imagers throughout IMPROVE-1 and IMPROVE-2, as a function of temperature
1 mm
0.1 mm
Global ice particle spectra, Ryan (1996)
Intercept (N0s) vs. T Slope (λs) vs. T
IMPROVE
IMPROVE
R-T scheme
2. Snow particle shape and density
Many bulk schemes (R-T, Tao and Simpson 1993, Ferrier 1994) assume snow particles are spheres of constant density, implying a mass-diameter relationship of:
However, observational and theoretical studies yield more general, habit-dependent power-law relationships of the form
which can also be implemented in bulk schemes (Cox 1988, Meyers et al. 1997).
3snow( ) ( / 6)m D D
( ) ,mbmm D a D
Constants in the m-D power law relationships for various crystal aggregate types (from Locatelli and Hobbs 1974),and for model snow spheres
Habit am (mg mm-bm) bm
Dendrites 0.0141 2.19
Cold-type 0.0370 1.90
Needles 0.0092 2.01
Model spheres 0.0520 3.00
General expression for relationship between qs, N0s, and λs:
0air 1
( 1)m
m s ms b
s
a N bq
Variation of spectral slope with particle habit(for fixed values of N0s and qs)
Particle diameter (mm)
N (m-4)
101
102
103
104
105
106
107
108
NeedlesDendritesCold-type
ColumnsGraupelModel spheres
3. Snow fall speed
Observational and theoretical studies provide habit-dependent power-law relationship between the terminal fall speed of a particle and its diameter (a V-D relationship) of the form
Combining with the exponential size distribution and the appropriate m-D relationship (for the same particle habit) and integrating, one obtains the mass-weighted terminal fall speed for snow particles of that habit:
( ) ,vbvV D a D
v
v m v
m
1
1bs
a b bV
b
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Particle Habit
Fal
l sp
eed
(m s
-1)
qs=0.2 g kg-1
qs=0.4 g kg-1
qs=0.6 g kg-1
Model spheres(with cold-typeV-D reln.)
Dendrites Cold-type Columnar Needle
Mass-weighted terminal fallspeed for various particle habits and snow mixing ratios
Example: Frontal rainband observed off the Washington coast during IMPROVE-1 (1-2 February
2001)
E
B
1-hr accumulated precipitation (mm), 500 mb temperature (ºC)
How does using an empirical mass-diameter relationship for cold-type crystals (not spheres) affect the simulation?
0
Cloud water mixing ratio (g kg-1)
0.05 0.10 0.15 0.20 0.25 0.30
Distance (km)
Precipitation band
Distance (km)
Precipitation band
111112
110104105
103
Control Cold-type crystals
Using M-D relationship from Locatelli and Hobbs (1974) results in:
- more reasonable levels of RHi for band with modest vert. vel.(e.g., Lin et. al 2002)
- reduced CLW above the melting level – eliminated graupel production
B E B E
Tem
perature (°C
)
12km Control
12km Cold-type crystals
0 0.2 0.4-0.2-0.4Precipitation rate
gradient (mm h-1 hPa-1)
Precipitation growth and microphysical processes
Tem
perature (°C
)
12km CTL
12km MD
0 0.2 0.4-0.2-0.4Precipitation rate
gradient (mm h-1 hPa-1)
Precipitation growth and microphysical processes
0
-210
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-410
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10-7
210
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410
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
Profile at x,y= 94.50, 84.50 lat,lon= 46.36,-125.05
200
300
400
500
600
700
800
900
1000
1100
0
-210
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1010
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1210
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Pre
ssur
e (h
Pa)
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300
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
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600
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800
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1000
1100
0
-210
-7
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-610
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-810
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10-7
210
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410
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
400
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700
800
900
1000
1100
0
-210
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10-7
210
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410
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
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1100
0
-210
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10-7
210
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410
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
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500
600
700
800
900
1000
1100
0
-210
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-810
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-10
10-7
210
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410
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610
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810
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1010
-7
1210
-7
1410
-7
Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
-7
-610
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-810
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-10
10-7
210
-7
410
-7
610
-7
810
-7
1010
-7
1210
-7
1410
-7
Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
-7
-610
-7
-810
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-10
10-7
210
-7
410
-7
610
-7
810
-7
1010
-7
1210
-7
1410
-7
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
-7
-610
-7
-810
-7
-10
10-7
210
-7
410
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610
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810
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1010
-7
1210
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1410
-7
200
300
400
500
600
700
800
900
1000
1100
0
-210
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10-7
210
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1010
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1410
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Production (kg kg-1 s-1)
Deposition of snow
Collection of cloud water by snow
Collection of cloud water by rain
Evaporation of rain
Deposition of cloud ice
Primary growth processes
0
-210
-7
-410
-7
-610
-7
-810
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-10
10-7
210
-7
410
-7
610
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810
-7
1010
-7
1210
-7
1410
-7
Pre
ssur
e (h
Pa)
Profile at x,y= 94.50, 84.50 lat,lon= 46.36,-125.05
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
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10-7
210
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
400
500
600
700
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900
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0
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1410
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Pre
ssur
e (h
Pa)
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300
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600
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800
900
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1100
0
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10-7
210
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
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300
400
500
600
700
800
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1000
1100
0
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10-7
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610
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810
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1010
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1210
-7
1410
-7
Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
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-10
10-7
210
-7
410
-7
610
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810
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1010
-7
1210
-7
1410
-7
Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
-7
-610
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-810
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-10
10-7
210
-7
410
-7
610
-7
810
-7
1010
-7
1210
-7
1410
-7
Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
-7
-410
-7
-610
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-810
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-10
10-7
210
-7
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610
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810
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1010
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1210
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1410
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Pre
ssur
e (h
Pa)
200
300
400
500
600
700
800
900
1000
1100
0
-210
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1410
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Production (kg kg-1 s-1)
Deposition of snow
Collection of cloud water by snow
Collection of cloud water by rain
Evaporation of rain
Deposition of cloud ice
Primary growth processes
Collection of cloud water by snow
Control
14-h MM5 forecast of 1-h precip, 12-km grid, R-T microphysics
Cold-type crystals Dendrite
s
Contours: qsnow (g kg-1) qrain (g kg-1) T (ºC)
Control
Cold-type crystals Dendrite
s
0
0
0
0
0 0
Control
Cold-type crystals Dendrite
s
Contours: precip rate (mm h-1) T (ºC)
0
0
0
0
0
0
3
2
1
3
2
1
1
2
3
1
2
3
1
2
3
4
53
2
1
OREGON WASHINGTON
PACIFIC
OCEAN
46.0 °
45.5 °
45.0 °
44.5 °
124 ° 123 ° 122 ° 121 °
Willamette Valley
Cascade Mountains
13-14 Dec 2001 IMPROVE-2
event Control
Cold-type crystals
Contours: qsnow (g kg-1) qrain (g kg-1) qrain (g kg-1)
Recommendations / Future Work:
1. Constant density spheres are not a good representation of most snow particle types.
2. Enforce “habit consistency” for the various habit-dependent aspects of the scheme (size distribution, m-D and V-D relationships, capacitance for depositional growth, etc.)
3. Examine ways to skew the distribution toward smaller particles when ice enhancement is active. Can this be done without going to a double-moment scheme?
4. Implement particle habit diagnosis (Meyers et al. 1997)
5. Develop habit prognosis, to test the effectiveness of the simpler habit diagnosis.
Snow particle images collected by the UW Convair-580 during IMPROVE-1
0 200 400 600 800 1000 1200 1400 1600 1800 200010
-3
10-2
10-1
100
101
10-2
10-1
100
-10 °C spectrum-7 °C spectrum
Size (µm)
No
(cm
-4)
Temperature = -7 °C
Temperature = -10 °C
2D-C particle imagery Particle size distributions
• distribution intercept (Nos) and slope (λs) as temperature increased
• influx of needle-like particles important to distribution shape
snow clw
graupel rain
Precipitation rate (mm h-1)
Summary of observations from Convair-580 flight stack:
In regions where model indicated high ice supersaturation:
• measured RH was generally near ice saturation• Negligible liquid water was detected• Ice crystal habits were generally found to be sub-water-
saturated types, or inconclusive (notably, no dendrites in the dendritic growth zone)
One possible problem with the Rutledge and Hobbs (1983) formulation for growth of snow by deposition
(PSDEP):
Although the RH83 equation uses capacitance for a 2-D plate, it assumes the population is comprised of spherical particles.
For a given supersaturation, the mass of a growing particle as a function of time behaves as follows:
•3-D growth (e.g., spherical particle):
•2-D growth (e.g., plate, dendrite):
•1-D growth (e.g., needle):
(Young 1993)
2/1
2/3
)(s
ttm
s
ttm
2
)(
2/1const
exp)(
s
ttm
Neither formulation for N0S agrees with the “upside-down” behavior of N0S that was observed in Convair-580 flight tracks during the 13-14 Dec 2001 case.(model spectra from 1.3-km MM5 simulation)
N0S(T), N0S obs
6.0 km(-20 °C)
4.9 km(-16 °C)
N0S(qS)
N0S obs
N0S(qS)
N0S(T)
