Clouds strongly influence th earth's energy budget. They control th amount of solar radiative energy absorbed by the climate system, partitioning the energy between the atmosphere and the earth's surface. They also control the loss of energy to space by their effect on thermal emission. Cirrus and altostratus are the most frequent cloud types, having an annual average global coverage of 35 and 40 percent, respectively. Cirrus is composed almost entirely of ice crystals and the same is frequently true of the upper portions of altostratus since they are often formed by the thickening of cirrostratus and by the spreading of the middle or upper portions of thunderstorms. Thus, since ice clouds cover such a large portion of the earth's surface, they almost certainly have an important effect on climate. With this recognition, researchers developing climate models are seeking largely unavailable methods for specifying the conditions for ice cloud formation, and quantifying the spatial distribution of ice water content, IWC, a necessary step in deriving their radiative characteristics since radiative properties are apparently related to IWC. A method is developed for specifying IWC in climate models, based on theory and measurements in cirrus during FIRE and other experiments

Donner, Leo J.

Heymsfield, Andrew J.

English

NASA Technical Reports Server

N90-
A SCHEME FOR PARAMETERIZING CIRRUS CLOUD ICE WATER CONTENT
IN GENERAL CIRCULATION MODELS
by
Andrew J. Heyms_.eld
National Center for Atmospheric Research
P.O. Box 3000
Boulder, Colorado 80307
Leo J. Donner
Department of Geophysical Sciences
University of Chicago
Chicago, Illinois 60637
1. INTRODUCTION
Clouds strongly influence the earth's energy budget.
They control tile amount of solar radlatl.zC energy
al,u.rhcd by the eli.rote ,y_tv, h partitiottin 8 the energy
I,ctwcc, the atltL,._phctc at.l tile eull, h'tt nuifrtce. 'l'liey
also control tile loss of energy to space by their effect
on thermal emission. Cirrus mad altostratus are the
most frequent cloud types, having an annual average
glol_al coverage of 35% and 't0%, respectively. (Compiled
from llahn, et al., 1984, who used surface synoptic
observations for the period 1971-1980). Cirrus is
composed almost entirely of ice crystals and the same is
frequently true of the upper porilons of Mtostratus since
they are often formed by the thickening of cirrostratus
and by the spreading of the middle or upper portions of
thunderstorms. Thus, since ice clouds cover such a large
portion of the e_rth'_ surface, they almost certainly have
an important effect on' climate. With this recognition,
researchers developing climate models are seeking largely
unavailable methods for specifying the conditions for ice
cloud formation, and quantifying the spatial distribution
of ice water content, IWC, a necessary step in deriving
their radiative characteristics since radiative properties
are apparently related to IWC (e.g. Grifflth, st. al.,
1980). This study develops a method for specifying
ice water content in climate models, based on theory
and measurements in cirrus during FIRE and other
experiments.
2. APPROACH
A conceptual model of the production of ice within
a lifting layer is illustrated in Fig. 1. The horizontal
extent of the layer is commensurate with one GCM
grid, _> 100 kin, and in the vertical it is i kin.
The parameterization will generate mean IWC for this
layer, whose horizontal dimensions do not enter the
parameterization, and whose vertical dimensions enter
only weakly. The layerliftsat constant velocity,w (taken
as the large-scale vertical velocity prognoscd by the
GCM or obtained from aircraft data in the vcri_cation
experiments), from some initialstate characterized by
temperatures Ti and _'i, and pressures Pi and /3i, at
its base and top, respectively. The relative humidity in
assumed to be at ice saturation. After lifting for time
t, the layer contains an ice water content given by the
difference between the vapor mass sublimated onto the
ice crystals and the net fallout of ice mass from the
layer. Fallout must be considered since ice crystals have
terminal velocities of tens of cm s -I, much more than
synoptic scale vertical velocities.
In this section the theoretical development of this
conceptual view is given, and a discussion of aircraft
flights used to characterize the ice mass distribution in
deep ice clouds will be presented. The IWC's from the
uircraft nteasureln('llts arc enhattced in _O[lle iustarlces
by hotiz.ntM advrcti,m uf its f.t:ncd ,b,vt: and outaitle
of Lkg. layers in cirrus convective cells, a factor which
must be considered in comparing the measurements to
the model results.
A. Theoretical Development
The total water mass in a layer undergoing ascent
and cooling isconstant, except for the accumulated mass
which settlesout of the layer:
. X..(l + S.) + X. =C-F, (1)
where X.. is the mixing ratio of the vapor at saturation
with respedt to the solid (ice), X° is the ice mass mixing
ratio, S, is the supersaturation with respect to ice, C is
the initial water mass, and F is the mass mixing ratio of
ice which has settled out of the layer.
The mass settled out of the layer (in a Lagrangian
framework) is given by the vertical divergence of the ice
mass nfixing ratio integrated over the time of the parcel's
ascent:
°- 1F= -_-ff'_ N(D,t')m(D,t')V,(D,t')dD dt'
= _ [pX.V,] (p,,r)d",
(2)
where p is the density of air, z is the height, p is the
pressure, t is the time, N, m, and V, the concentration,
mass and terminal velocity of ice crystals of dimension D,
and Vi the mean mass-weighted terminal velocity. The
bracketed term on the right-hand side of Eq. (2) is the
precipitation mass flux (or precipitation rate) relative to
the lifting layer.
Taking the time dlffercntiM of Eq. (2), using
the Clausius-Clapeyron and hydrostatic equations, and
taking a_ = wJA; ' where w is the layer ascent velocity,
the following is obtained 2:
2 We have denoted Lagrangian derivates as total deriva-
tives, although strictly speaking these are partial time
derivatives with the initial position of the layer held
constant, as noted explicitly in Eq. (2).
1 The National Center for Atmospheric Research is sponsored 10y the N ationld Science Foundalion.
411
PRECEDING PACE BLANK NOT FILMED
https://ntrs.nasa.gov/search.jsp?R=19900018976 2020-03-19T21:09:10+00:00Z
ICE PRODUCTION IN LIFTING LAYER
liiiiiiiiiiiiiiiiiii::,il;.:;i ,:.:,:,; :,: :iiiiiiiiii!i!!!ii!il/
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
t
I
Col.len_t_oa
SeLhlllcl_t&tl_ll
"|'ranspott _oHt Oul6ide the Vulume
I llotilont&l
2. Vertical
\I T(O). p(O). IWC = 0 1 /
Figure 1. A conczptual model of the production of condensate in an ice cloud.
dX. (1 + S,)wX, R----_--_-- + -X.,dt dz _aT
Y
• uppl II
-- [ 1 dV, I dX. I dT g ]
-XsV, [ _tt-_- z + X. dz T dz R-aT j '
s_edlmentation
(3)
where L, is the latent heat of sublimation, R, and R_
are the ideal gas constants for water vapor and dry air,
T is the air temperature, and g is the gravitational
acceleration constant. The change in temperature is
computed on the basis of dry adiabatic ascent and latent
heat released due to vapor deposition onto ice crystals:
dT g L, d
d_ = cp c, d-- [(1 + S.)X..}. (4)
If supersaturation with respect to ice S, is known *
as a function of z, Eq. (4) provides an expression for
for use in Eq. (3).
The Vt is evaluated from calculations of the ice mass
precipitation rate in deep ice clouds by Heymsfield (1977).
Converting to the terms used here,
V, = a.o9(px,) TM, (5)
where Vt is in units ofm s -l, p is in units ofg m -3, and
X, is unitless. Values predicted from this equation are in
accord with estimated particle terminal velocities of 0.3
to 2.0 m s -l in virga falling from ice and snow generating
cells (e.g., cirrus uncinus).
Our calculations assume an ice-saturated mixing ratio
through the cloud depth.
Fig. 2 illustrates the ice water content for several
layers undergoing ascent for t=10,000 see., obtained by
solving Eq. (3). Temperatures indicated are those at
the end of the time period, and vertical velocity is held
constant throughout. A common characteristic is a phase
during which IWC increases with time, followed by a
phase during which it decreases. Ice mass first increases
in the layer by condensation; as the ice content increases,
settling becomes increasingly important in removing ice,
eventually dominating as the layer continues to cool moist
adiabatically and the condensation rate decreases. Thus,
i0-1
U
iO_S
10-7
IOo
A
'E 10-2
10_4
A, w * Icm S-I
I I I
-- No Settling
.... Settling
I I I
8, w * 20cms -I
_ 1 I _ A
i
T 255°K _
f T - 215°K 2
iO -s I I I
0 IO00 2000 3000 4000
TIME ( s )
Figure 2. The ice water content as a function of
time for several layers undergoing ascent for various
temperatures (at the end of the ascent) and vertical
velocities. A: w = 1 cm s -l. B: w = 20 cm s -1
412
the ice content of a layer depends on its ascent time.
In later comparisons with aircraft measurements the ice
content for a fully developed ice cloud will be taken as
the maximum value during the layer ascent. These
contents are appropriate for comparison with ice contents
measured in clouds by aircraft which typically sample the
densest regions of clouds undergoing penetration.
Later in this paper we will be comparing data from
aircraft taken at particular temperatures and pressures
with those predicted from Eq. (3). The comparison
should be for the time the maximum IWC is reached
in the parcel. Therefore, the history of parcel ascent
must be reconstructed so that the initial conditions of
the parcels ascent can bc deduced. An estimat_of.the
ascent time to maximum ice content for the conditions
at the end of the parcel's ascent is made by tracing a
parcels ascent backwards in time. The estlmatcd initial
temperature and pressure is iterated using the ascent
times to maximum ice content until the cycle does not
change the ice content significantly.
B. Aircraft Data Collection
Data were collected by aircraft in cold clouds
over the continental United States in the mid-1970's
during the Environmental Definition Program (EDP)
(Heymsficld, 1977) and from the FIRE cirrus IFO.
Measurements in the twenty EDP flightswcrc acqnircd
in the densest (visually) regions of deep winter- and
springtime ice clouds associated with warm frontal
overrunning systems, warm frontal occlusions, closed lows
aloft,and jet stream bands. Sampling patterns consisted
of 25-kin-long constant altitude legs oriented parallel to
the wind direction, beginning at the cloud top (8.5 to
II.0 kin), and descending in 600-m steps to below cloud
base (I to 5 kin). Four of the flights were coincident
with single Doppler radar measurements. The FIRE data
reported here were collected during eight flightsby the
NCAR King Air aircraft in visually dense cloud during
spiral descents which began near cloud top (8 to 9 kin)
and ended st or below cloud base (5 to 6 kin). The
aircraft drifted with the wind and descended at a rate
of about 2 m s-l to follow approximately the fallout of
the ice particles. The flightsoccurred on 19 October, 22
October, 25 October (2 flights), 28 October (2 flights), 1
November, and 2 November 1986. Horizontal distances
covered by each loop of the spiral were from 5 to 10
km. Synoptic systems sampled were the same as those
discussed above for the EDP data.
Aircraft size spectra measurements were used in
conjnm:tion with the ice crystal shape data to calculate
the ice water content and precipitation rate. Vertical air
velocity was calculated by equating the change in the
calculated precipitation rate between two sampling levels
to the vertical flux of moisture producing this change
(Heymsfleld, 1977).
3. RESULTS
The variation of ice water content with temperature
and vertical velocity from the paramctcrization is illus-
trated by the lines in Fig. 3. These curves arc computed
by assuming ice-saturated ascent in Eq. (4) over tlmcs
required for condensation and settling to balance (about
1800 to 4000 seconds). Pressure at the end of the
ascent time istaken as the average for a specified vertical
velocity from the aircraft data. The IWC depends
primarily upon T, varying by four orders of magnitude
over temperatures found in the troposphere. Increasing
I
E
v
¢..)
3:
H
I00
lO-t
10-Z
10-3
10-4
lO-S
210 270
EDP
I I I I cI s-tw_,50 m
o Oo°o
5o_' o
×
× × X
X
I × 1 I I I
220 2:50 240 250 260
T (°K)
Figure 3. IWC values for each constant altitude penetration from the EDP data,
plotted against temperature and partitloncd into vertical air velocity intervals. Curves
for the mid-point of the vertical velocity intervals from the paramctcrizatlon arc shown
with dashed lines. Crosses: 0 to 2.5 cm s-l; triangles: 2.5 to 10 cm s-l; circles: 10
to 33 cms-1; squares: >33 cms -1.
413
I00
10_1
vm 10-2
H 10 -3
F-
10-4:
225
FIRE
-= I I I I I
w • 50._m s-J---"-'--
. / 2o_---------_
0 ,_ ...._ I ..._.._..X _:-_
, , l
245 250 255
I I I
230 235 240
T(°K)
Figure 4. Same as Fig. 3, except for the FIR-E-measurements. Each data
point is from the mid-altitude of a loop during a Lagrangian spiral descent.
w produces less than linear increases in IWC, because
the ascent times required to reach equilibrium between
settling and condensation are less at higher values of w.
Individual IWC from the EDP and FIRE data sets
are partitioned into vertical velocity intervals bounding
those from the parameterization and plotted against
temperature in Figs. 3--4. The curves from Fig. 3 are
reproduced in Fig. 4. In general, the parameterization
has reasonably captured the variation of IWC with tem-
perature and vertical velocity. The FIRE data at low w
does not compare as favorably with the parameterization
as the other methods; this might possibly be due to
the small horizontal distances over which this data was
averaged.
4. CONCLUSIONS
A simple pararneterization for atmospheric ice water
content can account reasonably well for ice water contents
observed by aircraft in numerous synoptic contexts in
mid-latitude and tropical areas. The physical processes
are idealized condensation and crystal settling. Starr
and Cox (1985) constructed a model in which many
of the processes contributing to ice-cloud formation, as
well as the circulation in which the cloud formed, were
calculated explicitly over the development history of the
cloud; phase changes, crystal settling, and radiative
processes were the key elements in their model. The
parameterization developed here is intended for use in
large-scale models in which atmospheric ice distribution
is sought diagnostically as a function of an instantaneous
atmospheric state, so some of the details of the Starr and
Cox model cannot be included. Atmospheric ice water
content in large-scale models will, of course, interact
with the radiative field, so feedbacks, which are likely
to be significant, will develop between the cloud field
and atmospheric dynamics and thermodynamics. This
parameterization is essentially a simplification for the
solution of large-scale equations for atmospheric ice,
analogous to those for water vapor, which could added
to large-scale models as a more explicit means of treating
ice clouds (or atmospheric liquid water in general).
Since the history of atmospheric ice which would be
contained in such large-scale equations is absent, the
parameterization has adopted assumptions to permit
diagnostic solution.
ACKNOWLEDGMENTS
This analysis was partially supported by NASA
under contracts L98100B (AJH) and NAG5-1056 (LJD).
REFERENCES
Cox, S. K., D. S. McDougal, D. Randall, and R.
Schiffer, 1987: FIRE-- The First ISCCP Regional
Experiment. Bull. Amer. Meteor. Soc., fiT, 114-
118.
Griffith, K. T., S. K. Cox and R. G. KnoUenberg, 1980:
Infrared radiative properties of tropical cirrus clouds
inferred from aircraft measurements. J. Atmos. Sci,
37, 1077-1087.
Hahn, C. 3., S. Warren, J. London, B. Chervin, and R.
Jenne, 1984: Atlas of simultaneous occurrence of
different cloud types over land. National Center ]or
Atmospheric Research Technical Note, 241+STR,
209 p.
Heymsfield, A. J., 1977: Precipitation development
in stratiform ice clouds: A microphysical and
dynamical study. J. Atmos. Sci., 34,367-381.
Ramanthan, V., E. J. Pitcher, R. C. Malone, and M.
L. Blackmon, 1983: The response of a spectra
general circulation model to refinements in radiative
processes. J. Atmos. Sci., 40,605-630.
Starr, D. O'C., and S. K. Cox, 1985: Cirrus clouds. Part
I: A cirrus cloud model. J. Atmos. Sci., 42, 2663-
2681.
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A scheme for parameterizing cirrus cloud ice water content in general circulation models

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