Towards parameterization Towards parameterization of cloud drop size of cloud drop size
distribution for large distribution for large scale modelsscale modelsWei-Chun Hsieh Wei-Chun Hsieh
Athanasios NenesAthanasios Nenes
Image source: NCAR
MotivationMotivationCurrent General Circulation Models (GCMs) treat cloud Current General Circulation Models (GCMs) treat cloud microphysics as bulk properties, i.e., one-single sizemicrophysics as bulk properties, i.e., one-single size
Ignore cloud drop size distribution would bias the Ignore cloud drop size distribution would bias the estimate of indirect effect which is subject to the largest estimate of indirect effect which is subject to the largest uncertainty in climatic forcing assessment (IPCC 2007)uncertainty in climatic forcing assessment (IPCC 2007)
The estimated indirect decrease 10-80 % as considering The estimated indirect decrease 10-80 % as considering size distribution effect, i.e., droplet dispersion [Liu and size distribution effect, i.e., droplet dispersion [Liu and Daum, NATURE, 2002]Daum, NATURE, 2002]
Uncertainty in estimate of indirect effect is related to Uncertainty in estimate of indirect effect is related to cloud microphysical schemes, especially autoconversion cloud microphysical schemes, especially autoconversion parameterizationparameterization
More CCNLess CCN
Indirect effectEffective radius (μm)
West coast (California)
Aerosol act as Cloud Condensation Nuclei (CCN).Anthropogenic emissions increase their levels Decreases cloud droplet size more reflection of sunlight (“first” indirect effect) cloud precipitation decreases (“second” indirect effect)
Rosenfeld, Kaufman, and Koren, ACPD, 2005
Estimate of Indirect effect is subject to the largest uncertainty for climatic forcing assessment (IPCC, 2007)
ObjectiveObjective
Developing parameterization to explicitly compute Developing parameterization to explicitly compute droplet growth (i.e., evolution of droplet size droplet growth (i.e., evolution of droplet size distribution properties). Then important cloud distribution properties). Then important cloud microphysical properties such as LWC, effective microphysical properties such as LWC, effective radius, droplet spectrum width can be obtained radius, droplet spectrum width can be obtained
With these droplet size distribution characteristics, With these droplet size distribution characteristics, we can also compute autoconversion rates with we can also compute autoconversion rates with existing parameterizationsexisting parameterizations
• Based on Fountoukis and Nenes, 2005
• We assume that the droplets ascend in an updraft and evolve within a Lagrangian frame of reference.
• The model explicitly computes growth of droplet population by condensation of excess water vapor generated by cooling as raising air parcel adiabatically.
The FrameworkThe Framework
cloud base
cloud top
Droplet growth and development of collision- coalescence(New framework)
Droplet activation
smax
updraft
Algorithm for computing droplet size distribution.Input: P, T, updraft velocity, aerosol & gas phase characteristics.
dt
dWV
dt
ds
Initial conditions at smax : Droplet Size Distribution, DSD, nd(Dp)
• The rate change of supersaturation ds/dt is given by
i
n
ipiw NDW
1
3
6
= W’ ??
• Droplets growth is continuously computed until the integrated LWC
reach LWC W’ predicted from large scale model.
Photo source: CSTRIPE imagery
eqpi
pi ssD
G
dt
dD
V: updraft velocity dW/dt: rate change of liquid water content (LWC), W
• The equation of droplet growth
Output: DSD as a function of time (height) nd(Dp) = f(t)
Dpi: droplet size of section i; G: growth factor seq is the equilibrium s of the droplet
Evaluation of droplet growth parameterization
clouds sampled during NASA CRYSTAL-FACE and CSTRIPE (Meskhidze et al., 2005).
CRYSTAL-FACE is for cumulus clouds in Key West, Florida (2002).
CSTRIPE is for stratecumulus clouds in Monterey, California (2003).
Evaluation of droplet growth parameterization
0
5
10
15
20
25
30
0 5 10 15 20 25 30
Dpavg (Parcel model)
Dp
av
g (
Par
amet
eriz
atio
n)
CRYSTAL-FACECSTRIPE
1 m deviation line
0
0.05
0.1
0.15
0.2
0.25
0 0.05 0.1 0.15 0.2 0.25Relative dispersion (Parcel model)
Rel
ativ
e di
sper
sion
(P
aram
eter
izat
ion)
CRYSTAL-FACECSTRIPE
0.05 deviation line
• Lower relative dispersion predicted by parameterization is mainly due to the underestimation of spectrum width and not mean droplet size • This deviation is small suggesting that using the activation parameterization provides a good boundary condition for subsequent growth.
Evaluation with in-situ observations Evaluation with in-situ observations
0
20
40
60
80
100
120
140
1 10 100
Droplet diameter (m)
dN/d
Dp (
cm-3
m-1)
Predicted
Measured
•We focus on spectra without drizzle and are relatively narrow to avoid entrainment effect•The narrow spectrum observed in near adiabatic regions is still broader than the predicted adiabatic spectrum
Spectra Broadening
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Relative dispersion (Measured)
Rat
io o
f re
lativ
e di
sper
sion
(P
redi
cted
/Mea
sure
d)
Average updraft (CRYSTAL-FACE)
PDF updrafts (CRYSTAL-FACE)Average updraft (CSTRIPE)
PDF updrafts (CSTRIPE)
0.320.09
0.200.07
0.160.1
Average ratiosAverage ratios
• Broadening of the DSD is in part from variability of updraft in clouds• This variability is accounted for by averaging spectra over the PDF of updraft velocity
relative dispersion (defined as standard deviation over mean radius of cloud drop distribution)
Prediction of autoconversion
• Liu and Daum (2004)
cRRHLNP 663/73/1
66
3/2662
2
6 4
3
N
Lk
w
6/1
22
222
6 211
514131
R6 and R6c: mean and critical radius of 6th moment of cloud droplet distributionk2 and 6 : Stokes constant and coefficient related to cloud drop dispersion.N and L: cloud drop number and cloud liquid water content.H: threshold function which specifies the onset of autoconversion when R6 > R6c
: relative dispersion (=/rm)
cloud drop number
cloud liquid water content
Linking growth with autoconversionLinking growth with autoconversion Autoconversion rates are computed using the P6 formulation of Liu and Daum (2004):
PP66 autoconversion rates autoconversion rates(Predicted relative dispersion)(Predicted relative dispersion)
PP66 autoconversion rates autoconversion rates(Adjusted relative dispersion)(Adjusted relative dispersion)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-12
10-11
10-10
10-9
10-8
10-7
10-6
P6 Measured [kg m-3 s-1]
P6 P
redi
cted
[kg
m-3
s-1
]
Parcel model (CRYSTAL-FACE)
Parameterization (CRYSTAL-FACE)Parcel model (CSTRIPE)
Parameterization (CSTRIPE)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-12
10-11
10-10
10-9
10-8
10-7
10-6
P6 Measured [kg m-3 s-1]
P6 P
redi
cted
[kg
m-3
s-1
]
Parcel model (CRYSTAL-FACE)
Parameterization (CRYSTAL-FACE)Parcel model (CSTRIPE)
Parameterization (CSTRIPE)
Uncertainty of autoconversion rates
-80
-60
-40
-20
0
20
40
60
80
4.37
x10-5
5.40
x10-5
1.05
x10-4
1.16
x10-4
1.29
x10-4
1.30
x10-4
1.37
x10-4
1.41
x10-4
1.43
x10-4
1.49
x10-4
1.66
x10-4
1.67
x10-4
1.77
x10-4
1.78
x10-4
1.91
x10-4
2.01
x10-4
2.22
x10-4
2.32
x10-4
2.54
x10-4
2.86
x10-4
3.86
x10-4
3.94
x10-4
4.42
x10-4
4.62
x10-4
LWMR (kg/kg)
Unc
erta
inty
ofau
toco
nver
sion
(%)
Relative dispersionCloud drop number
Autoconversion errors come from errors in droplet number and relative dispersion.
Errors in droplet number tend to partially cancel errors from relative dispersion.
On average, autoconversion uncertainty was -41.1% and +3.4% from the predicted relative dispersion and cloud drop number concentration for CRYSTAL-FACE and -58.4% and +5.6% in CSTRIPE.
Summary ISummary I• The growth parameterization framework links drop
activation with collision-coalescence and predicts evolution of cloud droplet distributions
• Good agreement between parameterization and detail numerical model indicates the framework is capable to provide cloud microphysics and is feasible to implement in general circulation models (GCMs).
• Evaluation of framework with in-situ observations show an underestimation of spectrum dispersion.
• Considering PDF updrafts has the effect to broaden the droplet distribution. However, we still systematically underpredict spectrum dispersion; this suggests we are in the “right direction” but still need to include additional broadening mechanisms. For the time being, we can apply the framework with the systematic correction of spectral dispersion.
Summary IISummary II• This underestimation would cause 50%
underestimation of computed autoconversion rates and this uncertainty may amplify due to errors in predicting cloud drop number concentration.
• Our study shows drop spectra has significant influence in predicting autoconversion rates and this may have crucial impacts in assessment of second aerosol indirect effect and distribution of precipitation.
Thank youThank youThank youThank youQuestions?Questions?
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
80
Droplet diameter (m)
dN/d
Dp (
cm-3
m
-1)
0.26334
0.345020.30858
0.53466
• Overall, underestimation of relative dispersion by framework is seen for majority of the data and this is due to adiabatic assumption in the framework. We only consider droplets whose growth is controlled by diffusion of water vapor which tend to narrow the droplet spectra.
• The underestimation is about a factor of 5.
y = 0.2145x
R2 = 0.1825
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Relative dispersion (Measured)
Rel
ativ
e di
sper
sion
(Pre
dict
ed)
CRYSTAL-FACE (Parcel model)CRYSTAL-FACE (Parameterization)CSTRIPE (Parcel model)CSTRIPE (Parameterization)
Trendline
