Directory UMM :Data Elmu:jurnal:A:Atmospheric Research:Vol55.Issue1.Sept2000:

Atmospheric Research 55 Ž2000. 15–33
www.elsevier.comrlocateratmos

Microphysical properties of stratocumulus clouds
Hanna Pawlowska a , J.L. Brenguier b,) , Frederic Burnet b
b

a
Institute of Geophysics, UniÕersity of Warsaw, Warsaw, Poland
Centre National de Recherches Meteorologiques,
GMEIr MNP, 42 aÕ. Coriolis,
´´
31057 Toulouse Cedex 01, France

Received 11 December 1998; accepted 1 March 2000

Abstract
Data collected in situ with the Meteo-France Merlin-IV instrumented aircraft during the
EUCREX mission 206 are analyzed to document cloud properties that are relevant to the
calculation of cloud radiative properties. Ascents and descents through the cloud layer reveal that
most of the vertical profiles of liquid water content ŽLWC. and droplet sizes are close to adiabatic

profiles. Analysis of horizontal legs shows that sub-adiabatic regions are characterized by reduced
droplet concentrations, while droplet sizes remain close to their adiabatic values at that level.
Statistics of LWC, droplet concentration and droplet mean volume radius normalized by their
adiabatic values are presented for four distinct regions of the cloud layer. This information is
provided for tests of a parameterization of optical thickness based on the adiabatic model. q 2000
Elsevier Science B.V. All rights reserved.
Keywords: Cloud microphysics; Stratocumulus

1. Introduction
The radiative properties of warm clouds result from scattering of light by cloud
droplets. They are thus modulated by the spatial and size distributions of the droplets,
which are extremely variable. The challenge in the development of parameterizations of
cloud radiative properties for general circulation models ŽGCM. is to express this
variability by a few parameters predictable at the GCM scale Žthe typical grid of a GCM
is presently of the order 100–200 km..
)

Corresponding author. Tel.: q33-5-61-07-93-21; fax: q33-5-61-07-96-27.
E-mail address: jlb@meteo.fr ŽJ.L. Brenguier..

0169-8095r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 8 0 9 5 Ž 0 0 . 0 0 0 5 4 - 5

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

Hansen and Travis Ž1974. have shown that the optical properties of a homogeneous
cloud volume are expressed as functions of two microphysical variables: the liquid water
content ŽLWC. and the droplet effective radius. In order to calculate the radiative
transfer through a cloud, it is thus necessary to assume some spatial distribution of these
parameters. An attractive simplification is to assume that the cloud is a horizontally
infinite homogeneous layer of geometrical thickness H. This is referred to hereafter as
the vertically uniform plane parallel model ŽVUPPM.. The two-stream approximation
ŽCoakley and Chylek,
1975; Stephens, 1978; Slingo, 1989. or the doubling–adding
´
matrix method ŽTwomey et al., 1966. for radiative transfer calculations are based on this
hypothesis. A vertically stratified cloud can then be modeled as a stack of VUPPMs
ŽSlingo and Schrecker, 1982..

Microphysical measurements in stratocumulus have revealed a significant variability
of LWC and effective radius in the horizontal as well as in the vertical ŽSlingo et al.,
1982; Nicholls, 1984; Stephens and Platt, 1987; Martin et al., 1994.. The radiative
transfer calculation is an integral over the cloud thickness and the vertical variability of
the microphysics affects this integral in a strongly non-linear way ŽLi et al., 1994.. The
horizontal variability is also important because in a GCM, the radiative properties are
meaningful only at the scale of a cloud system. Here again, the effects are not linear
ŽBarker, 1992, 1996; Davis et al., 1996; Duda et al., 1996.. These numerous studies
have shown: Ži. that the area-averaged albedo of an inhomogeneous cloud field is lower
than that of a uniform cloud with the same liquid water path ŽLWP.; Žii. that the albedo
bias is more sensitive to the variance of LWC than it is to the mean; Žiii. that the LWC
variance becomes increasingly important as the cloud fraction increases. Other results
ŽHignett and Taylor, 1996. suggest that for a GCM, the parameterization of the LWC
fraction within a grid box is not sufficient and that the spatial distribution of LWC
within the grid box is also a prerequisite for the determination of the radiative properties
of the cloud system. Coley and Jonas Ž1997. combined the cloud fields from a
Large-Eddy Simulation ŽLES. with a Monte Carlo radiative transfer model to demonstrate the importance of the spatial distribution of LWC within a cloud field. They
showed that irregular cloud fields are more sensitive to changes in the droplet concentration than a PPM with the same LWP and the same mean profile of LWC. All these
results confirm that the spatial distributions of LWC and effective radius are of crucial
importance for parameterization of cloud radiative properties.

The microphysical properties of clouds are governed by processes at scales smaller
than the cloud depth. The interactions between dynamics, thermodynamics and microphysics are so complex, that it has not yet been possible to relate directly the mean
dynamical fields to the mean microphysical or radiative properties at the meso and large
scales. However, at the scale of an updraft, the coupling between dynamics and
microphysics is better understood, so that it seems more feasible to parameterize the
coupling at this scale and then extend the result to larger scales by parameterizing the
statistics of the local radiative properties. This is the strategy adopted during the
EUCREX experiment. Instrumented aircraft have been deployed in order to document
the relationships between cloud microphysics measured in situ and cloud radiative
properties measured remotely. The contribution of this paper to the EUCREX mission
206 case study ŽBrenguier and Fouquart, 2000. is to document both horizontal and

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

17

vertical distributions of the microphysics, which will be used in the conclusion paper
ŽPawlowska et al., 2000. to estimate cloud optical thickness and albedo from the scale of
a cloud cell to the scale of the cloud system. The sampling strategy for in-situ
measurements with the Merlin-IV ŽM-IV. was thus designed as series of ascents and

descents through the cloud layer to document vertical profiles of the microphysics, and
constant level legs to document its horizontal variability.

2. The data set
2.1. Fast-forward scattering spectrometer probe (Fast-FSSP) data
The microphysical measurements analyzed here have been collected on board the
M-IV with the Fast-FSSP ŽBrenguier et al., 1998., an improved version of the FSSP.2
The Fast-FSSP provides droplet spectra with a better accuracy and a better size
resolution than the standard probe Ž256 size classes instead of 15 in the standard probe..
During the experiment the instrument was set to measure droplets in the diameter range
2–28 mm. In addition, the Fast-FSSP provides precise timing Ž1r16 ms. for the arrival
time of each particle in the detection beam. This information allows optimal estimation
of the time variation of the droplet concentration, i.e. its spatial variation along the
aircraft trajectory ŽPawlowska et al., 1997.. Fig. 1 shows an example of the variations of
LWC in Ža. and of the droplet spectrum in Žb. during an ascent through the stratocumulus layer.
Current processing of Fast-FSSP data provides significant estimations of the droplet
number concentration at 1 Hz Ž100 m spatial resolution.. At higher frequencies or if
droplets are sorted by size for producing a spectrum as in Fig. 1b, the number of counted
particles per sample is too small for a significant estimation of their concentration, and
optimal estimation is needed. Most of the droplet spectra are characterized by a mode

and the relative concentration in the modal size class is much larger than the relative
concentration in classes far from the modal value. It follows that the statistical
significance of the concentration estimate is satisfactory at the mode but very poor on
the sides. The estimation of LWC from the spectrum is thus strongly affected by the
uncertainty in the estimation of the relative concentration of the biggest droplets when
they are not numerous. It is, therefore, necessary to group some of the 256 Fast-FSSP
size classes in order to increase the statistical significance of the measurements. The
complete series of arrival times has thus been split into 16 series according to the droplet
sizes. The 16 new size classes have been defined by grouping some of the 256 original
classes of the instrument, in such way that the number of particles counted in each class
along the selected sample are similar. The relative concentration densities Žcmy3 mmy1 .
in the 16 size classes have then been calculated with the optimal estimator to form a
spectrum. Fig. 1b is a contour plot of the variation of that spectrum along an ascent
through the cloud layer.
2

The FSSP is manufactured by Particle Measuring Systems, Boulder, CO, USA.

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

Fig. 1. Time variation of LWC Ža. and the droplet spectrum Žb. along an ascent through the cloud layer with
the M-IV. In Žb., the droplet spectrum is represented by the isocontours of droplet concentration density per
droplet radius. The upper scale indicates the corresponding aircraft altitude.

2.2. Sampling strategy
Fig. 2 shows the M-IV aircraft altitude as a function of time in mission 206. It
illustrates the sampling strategy for in-situ measurements. The M-IV was flying in the
cloud layer, back and forth between point M in the Southeast and point A in the
Northwest, with the ARAT-F27 and the DLR-F20 flying along the same track, 2–5 km
ŽTable 1 in Brenguier and Fouquart, 2000., above the cloud layer, for remote sensing of
the cloud radiative properties. The first leg Žfrom 09:30 to 09:50 UTC. is at a constant
low level inside the cloud layer, from M to A. On its way back to M Ž09:50–10:20., the

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

19

Fig. 2. Altitude vs. time for the M-IV Žin-situ measurements., the ARAT-F27 and the DLR-F20 Žfor remote

sensing., flying back and forth between points M and A that mark the end of the sampling leg ŽBrenguier and
Fouquart, 2000..

M-IV performed series of ascents and descents, extended 100 m below cloud base and
100 m above cloud top in order to document the thermodynamics outside of the cloud
layer. The third Ž10:20–10:45. and fourth Ž10:45–11:10. legs were flown at a series of
horizontal steps. The cloud top was slightly lower in the North ŽA. than in the South
ŽM.. During the third leg ŽM–A., the flight level was maintained just below cloud top
and the level was lowered each time the aircraft was exiting the cloud layer. This is the
reason for the descending steps in Fig. 2. On the way back to M, it was not possible to
evaluate the altitude of the cloud top from inside the aircraft within the cloud layer.
Therefore, the changes in flight altitude were decided on the basis of marks noted during
the previous leg Žthe highest level during this leg is clearly lower inside the cloud than
the highest level during the previous one.. The fifth leg Ž11:10–11:30. is similar to the
second one. The last leg Ž11:30–11:50. is also of the zigzag type but the duration of the
ascents and descents was shortened in order to increase their number Ž11 profiles instead
of six and eight during legs 2 and 5, respectively..

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

Fig. 1 illustrates the limitations of the zigzag procedure. Vertical sampling is of
course not feasible with an aircraft. With its rate of climbing, the M-IV is traveling
about 5–10 km while it crosses the cloud thickness of about 400 m during a profile. This
is larger than the typical scale of the cloud cells Ža few kilometers., as shown in the
POLDER images ŽPawlowska et al., 2000.. Therefore, the variations of LWC and of the
droplet spectrum in Fig. 1 do not characterize a single cell. It is clear in this example
that the M-IV entered at least three cells during its ascent. Nevertheless, the cloud base
altitude being about the same for all cells, their microphysical characteristics at a given
level are comparable and the composite of the three cells sampled in Fig. 1 at different
levels form a significant trend for LWC and the spectrum. The zigzag legs will be used
in Section 3.2 to document the vertical profiles of the cloud parameters and it must be
remembered that sharp changes seen in these profiles do not correspond to vertical
transitions within a single cell but rather to transitions between adjacent convective cells,
which are sampled successively along an aircraft ascent or descent.

3. Description of the cloud structure
3.1. General features
The cloud system sampled during mission 206 has two interesting features related to

its spatial and temporal variations. Fig. 3a shows flight sections where LWC was
detected. Each point is an average over 100 m of flight. The aircraft trajectory is
reported with altitude as a function of the aircraft position along the leg M–A, with the
distance measured from point M. The cloud base is located at about 750 m and slightly
descending northward. The cloud top exhibits a stronger trend, descending from 1100 m
at the southern edge to 900 m at the northern edge. The same features can be noted in
the POLDER images with a decrease of the optical thickness from South to North
ŽPawlowska et al., 2000.. Close to point A, the layer was broken with isolated
convective cells. Fig. 3b–d shows vertical profiles of the thermodynamics at the
southern edge, with a strong and sharp inversion at the cloud top, a well-mixed
boundary layer with constant potential temperature and a uniform profile of wind speed
and direction. The wind direction was perpendicular to the aircraft trajectory. Fig. 3e–g
shows the same parameters measured at the vicinity of point A. The inversion is broader
than at the South and there is a significant wind shear through the inversion layer.
Fig. 4 summarizes both spatial and temporal variations. It represents the altitude of
the base of the inversion as derived from temperature measurements for three-time
periods covering, respectively, legs 2 and 3 Ž10:00–10:40., legs 4 and 5 Ž10:40–11:30.,
and leg 6 Ž11:30–12:00.. At the beginning, two regions can be identified. Up to a
distance of 60 km from M, the inversion was almost reaching 1100 m, with convective
cells ascending up to that level and the vertical soundings are similar to the sounding

shown in Fig. 3b–d Žsharp inversion and no wind shear.. From 60 km to the end of the
leg, the inversion was slightly descending from 950 m down to 850 m at point A, with
soundings similar to the one shown in Fig. 3e–g. During the second period, the
transition in the sounding is observed at only 40 km from M and the sharp inversion

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

21

Fig. 3. Ža. Trajectory of the M-IV Žaltitude vs. distance from point M. restricted to 10 m samples where LWC
is measured; Žb and e. vertical profiles of the potential temperature within the two regions marked on Ža.; Žc
and f. same as Žb and e. for the water vapor mixing ratio and LWC; Žd and g. same as Žb and e. for the wind
speed and direction.

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

Fig. 4. Altitude of the base of the inversion layer estimated from temperature measurements during ascents or
descents. The symbols correspond to three successive periods indicated in the upper right corner.

between M and that point is lower, at about 1000 m. During the last period, the
inversion was broader all over the leg Žsimilar to Fig. 3e. and its altitude was lower on
both ends, with a maximum at almost 1000 m in the middle. This observed time
evolution mainly reflects advection of large-scale structures across the sampling leg
M–A. Such structures can be identified in the AVHRR satellite image at 08:25 UTC
ŽFouilloux et al., 2000..
3.2. Vertical Õariability
The vertical profiles of microphysics are documented with 22 M-IV ascents or
descents through the cloud layer. However, as already mentioned, the sampling during
an ascent or descent does not represent precisely a vertical profile in a single convective
cell but rather in a series of adjacent cells. In addition, it is possible to select the top of a
convective cell when starting from above cloud a descent with the aircraft, but it is
difficult from inside the cloud layer to end an ascent right at the top of a convective cell.
In fact, the aircraft trajectory shows that ascents and descents are regularly spaced along
the legs. Despite these two limitations, impact of horizontal variability on the vertical
sampling and spatial randomness of the sampling, the microphysical characteristics
exhibit a remarkable trend with the vertical.
Fig. 5 presents three examples of vertical profiles of Fast-FSSP data processed with
optimal estimation at 10 Hz ŽPawlowska et al., 1997.. Three parameters are displayed:
the droplet number concentration in the 2–28 mm range Ža, d, g., LWC with the
predicted adiabatic value indicated by a solid line Žb, e, h., and the effective radius
Ž re s r v3rrs2 . Žc, f, i., where r v and rs are the mean volume and mean surface radii of

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33
23

Fig. 5. Three examples of vertical profiles of concentration, LWC and effective radius. Each dot corresponds to a 10-Hz Žabout 10 m. value calculated with optimal
estimation. The solid line in the LWC figure is the adiabatic profile.

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

the droplet size distribution, respectively. The concentration is almost constant with
altitude, the lower values at the cloud base being due to the detection threshold of the
Fast-FSSP at r s 2, mm. Fig. 5a–c and g–i show examples of nearly adiabatic profiles
of LWC, while Fig. 5d–f show evidence of dilution. As drizzle was not observed within
the cloud layer, this feature can be attributed to entrainment and mixing of dry air from
above the inversion. However, it can be noted that the decrease in LWC is mainly due to
a decrease in number concentration while the effective radius is only slightly affected by
mixing. This feature will be discussed in Section 3.3. The important point here is that
the microphysics in the cloud layer is obviously varying regularly with altitude. The
adiabatic model of droplet growth, with a constant droplet number concentration and
LWC increasing as predicted by the solid lines in Fig. 5, represents therefore a more
realistic model than a VUPPM with constant values of the microphysical parameters
along the vertical.
The adiabatic model has been largely used for parameterization of the condensation
process in convective clouds ŽMason and Chien, 1962; Mason and Jonas, 1974; Lee and
Pruppacher, 1977; Brenguier, 1991., but only occasionally for the parameterization of
their radiative properties ŽBoers and Mitchell, 1994.. In fact, radiative transfer calculations with a VUPPM have been tested vs. vertically stratified models by considering a
cloud composed of a stack of homogeneous layers whose microphysical characteristics
were specified using measured vertical profiles ŽSlingo and Schecker, 1982; Platnick and
Valero, 1995.. The same procedure can be applied by deriving the microphysical
properties from the adiabatic model of droplet growth. However, a stratiform cloud layer
is not fully adiabatic because of mixing between the cloud and the overlying dry air or
drizzle scavenging. The statistical distribution of sub-adiabaticity in the cloud layer is
also an important factor to consider in a GCM parameterization scheme. This is
discussed in Section 3.3.
3.3. Horizontal Õariability
The radiative properties of a cloud are mainly determined by its microphysical
characteristics close to the cloud top. However, it is difficult to precisely document those
characteristics, especially when the cloud top is rather inhomogeneous due to cumulus
cloud turrets that overpass the mean cloud top level. In addition the cloud top is the
region of highest variability in the microphysical parameters: droplet sizes are progressively increasing from the cloud base up to a maximum value below cloud top, above
which they rapidly decrease in the narrow mixing region that separates the cloud core
from the overlying dry air ŽFig. 5.. It is therefore impossible with an aircraft to locate
precisely the region of maximum droplet sizes.
In EUCREX mission 206, the mean cloud top altitude was decreasing progressively
from South to North and the horizontal sampling consisted of a series of horizontal
sections flown a few tens of meters below the mean cloud top Žsee Fig. 2, legs MA:
10:20–10:45 and AM: 10:45–11:10.. Schematics of this sampling strategy, with the
flight altitudes and times, are illustrated in Fig. 6. The first leg was flown from South to
North and the aircraft was descending to a lower level each time the cloud depth above
seemed to be too thin. While flowing the second leg from North to South inside the

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25

Fig. 6. Schematics of the horizontal sampling at the top of the cloud layer. For each section, the mean altitude
and the start and end times of the leg are indicated.

cloud layer the plane ascended step by step at the same distance points as before, except
for the last level because the cloud top height was slightly lower than during the
previous leg. Two series of cloud samples are thus available at two different levels in the
upper part of the cloud.
It is impossible to compare directly the results of in-situ measurements with remote
sensing, because the in situ and the remote sensing aircraft were not synchronized, so
there are no simultaneous measurements of the same cloud spot. In addition, the
radiances measured remotely reflect integrals of the local radiative cloud properties over
the whole cloud depth, while horizontal in situ sampling provides information at only
one level. There is however much to learn from the horizontal statistics of the
microphysical parameters. Fig. 7 summarizes the results from the first horizontal leg Žthe
four highest sections in Fig. 6 at 1072, 1028, 855, and 788 m, respectively.. On the left
column, the data are represented in a normalized coordinate system. The x-axis
corresponds to the measured concentration normalized by its adiabatic value. The
adiabatic concentration Ž Nad . used here as a reference is calculated as the average of the
maximum values measured during each cloud traverse, within the corresponding cloud
section. Its value for each section is indicated in the x label between parenthesis. The
y-axis represents the mean droplet volume normalized by its adiabatic value, derived
from the formula:
4
3
r vad
s
pr w Nad ,
Ž 1.
3
where r w is the liquid water density, and wad is the adiabatic LWC. The adiabatic LWC
is calculated from the aircraft altitude above cloud base Ž h s z y z base ., with the cloud
base altitude Ž z base . estimated from Fig. 3, as indicated on top of each graph:

ž

wad s c w h,

/

Ž 2.

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

27

where c w is the rate of condensation, that depends only upon pressure and temperature
at the cloud base ŽBrenguier, 1991.. In such a normalized system the product of the
coordinates is proportional to wrwad Žwhere w is the measured value.. The solid isolines
represent percentages of this ratio Žfrom 10% to 100%.. The data have been processed
with optimal estimation at 10 Hz, that is a horizontal distance of about 10 m.
Most of the data are distributed in the area of LWC values greater than 40% of the
adiabatic value. There is a significant dispersion of the measured concentrations, but the
normalized mean volume radius remains within 80% of its adiabatic value Žright hand
scale in the figure.. This feature is well illustrated in the cumulative probability
distributions of the normalized values of LWC, mean volume radius and number
concentration Žright column in Fig. 7.. The statistics of the mean volume radius for the
four sections are very similar with nearly no samples with a mean volume radius smaller
than 80% of the adiabatic value. On the contrary, the droplet concentration is more
uniformly distributed between 40% and 100% of the reference value. Such a feature is
typical of an inhomogeneous mixing process between the cloud and the dry air from the
inversion layer above. During such a process, some droplets are completely evaporated
and the concentration is reduced both by dilution and loss of droplets. The remaining
droplets are then exposed to saturated air and their size is slightly affected ŽBaker and
Latham, 1979..
The distribution of wrwad evolves from a steep distribution in the southern part of
the leg to a linear distribution to the North. Close to point M, the cloud layer is
continuous and thick Žthickness: more than 450 m.. The proportion of clear air samples
is about 10% of the total and about 80% of the measured values are characterized by
w ) 0.6wad . In the northern part of the leg, the cloud thickness is reduced to less than
200 m and the cloud layer is broken. The proportion of clear air samples has increased
to 35% and w ) 0.6wad in only 20% of the samples. It is also interesting to compare
these distributions with those measured slightly lower in the cloud layer at the same
place. Fig. 8 shows these distributions for both the upper and lower levels reported in
Fig. 6. Except for the second section, the proportion of clear air samples is slightly
reduced at the lower level. Otherwise, the distributions are quite similar indicating that
the mixing, which originates from the cloud top, affects the cloud layer at a depth of
more than 50 m from the cloud top.
These overall features are crucial for the parameterization of the microphysics in a
GCM radiation scheme. In Section 3.2, it has been shown that a vertical stratification of
the microphysics is more realistic than a vertically uniform profile, and that this
stratification approaches the adiabatic model. The sampling along horizontal legs
provides crucial information about the distribution of sub-adiabaticity. The distribution

Fig. 7. Left column: statistics of mean volume radius vs. droplet concentration along four of the flight sections
shown in Fig. 6. Each dot corresponds to a 10-Hz sample. The droplet concentration is normalized by a
reference value indicated in the x label. The mean volume radius is normalized by its adiabatic value at that
3
level Ž r v3 r r vad
in the left axis, r v r r vad in the right axis.. Solid isolines represent the various percentages of
wr wad . The sampling altitude z and the estimated cloud base altitude z base are indicated on top of each graph.
Right column: Cumulative frequency distributions of wr wad , r v r r vad and Nr Nad along the same flight
sections as in the left column.

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

Fig. 8. Statistics of wr wad along the eight flight sections shown in Fig. 6. The indicated altitude refers to the
mean altitude of the section as in Fig. 6.

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

29

of wrwad varies from a steep distribution in regions of homogeneous cloud deck, with
most of the cloud volumes filled with almost adiabatic LWC, to a nearly linear
distribution in regions of thin and broken stratocumulus. Since the in cloud light
extinction is proportional to the total droplet surface, the knowledge of LWC is not
sufficient for its parameterization. Information about droplet sizes is also required. The
statistics of the mean volume radius as a function of droplet concentration shown in Fig.
7 suggests that a simple yet realistic hypothesis is to consider that variations of LWC
with respect to the adiabatic value are due to fluctuations of the droplet concentration,
while the droplet sizes remain equal to their adiabatic value at this level: N s Nad wrwad
and r v s r vad .

4. Estimation of the adiabatic cloud optical thickness
An important parameter in the radiative transfer calculations in cloud is the cloud
optical thickness which is defined as the integral of the extinction coefficient Ž sext . over
the whole cloud depth Ž H ., i.e.

ts

H

H0

sext d h s

H

H0

`

Qext

H0 p r

2

H 2

H0

n Ž r . d r dh s Qextp N

rs d h

Ž 3.

where Qext is the mean Mie extinction factor, nŽ r . is the droplet size distribution, N is
the droplet number concentration, and h is the altitude above the cloud base.
In the VUPPM approximation where the microphysical parameters are uniform along
the vertical, the above equation reduces to:

ts

3 Qext W
4 r w re

Ž 4.

,

where W s wH s 4r3pr w Nr v3 H is the LWP. Although very useful in a GCM parameterization, such a formula fails in describing the dependence of optical thickness as a
function of cloud geometrical thickness. The cloud geometrical thickness is related to
cloud dynamics and the droplet concentration reflects the level of pollution of the air
mass. With the additional hypothesis of adiabaticity for the vertical profile of the
microphysics, it is possible to explicitly calculate Eq. Ž3. as a function of these two
parameters. In the adiabatic hypothesis, the cloud droplet concentration N is constant.
Since the droplet size distributions are not monodisperse, it is necessary to express a
relationship between r v and re . From droplet distributions observed in stratiform clouds,
Martin et al. Ž1994. reported values of k s r v3rre3 , from 0.67 in continental air masses to
0.8 in marine ones. The adiabatic cloud optical thickness is thus derived from Eq. Ž3. as:

ž /

3
3c w
t s Qext
5
4pr w

2r3

Ž kN .

1r3

H 5r3

Ž 5.

Such formula expresses that the cloud optical thickness is proportional to N 1r3 as
suggested by Twomey Ž1977. but also that it is proportional to H 5r3 and not proportional to H as in the VUPPM approximation. It also attests that the parameter k can be

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H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

implicitly taken into account by replacing the droplet concentration N by a ‘‘scaled’’
droplet concentration kN. It follows that a high accuracy in k is not crucial, since the
aerosol indirect effect involves changes of N by a factor of up to 50 Žfrom 20 cmy3 in
pure marine air, to 1000 cmy3 in polluted air..
The values of H and N measured in situ during ascents or descents will be used in
Pawlowska et al. Ž2000. to estimate the adiabatic optical thickness with Eq. Ž5.. The H
and N values corresponding to the 22 cloud traverses are reported in Fig. 9. N is
selected as the maximum value of concentration measured during the traverse. The
continuous isolines represent the adiabatic cloud optical thickness derived from Eq. Ž5.
with Qext s 2.2, c w s 1.5 = 10y3 grm4 , r w s 10 6 grm3, and k s 0.8. The dashed
isolines correspond to the values of the effective radius at the cloud top that can be
derived from the above mentioned relations Žsee also Eq. Ž11. in Martin et al., 1994.:

ž

re Ž H . s r v Ž H . rk 1r3 s wad Ž H . r

ž

4
3

pr w kN

//

1r3

.

Ž 6.

This figure reveals that the adiabatic optical thickness varies from 8 to more than 35,
the largest values corresponding to the thickest cloud layer at the southern part of the
leg. The corresponding values of effective radius at the cloud top range from 6 to less
than 8 mm.

Fig. 9. Values of cloud geometrical thickness H and droplet concentration N for each of the 22 ascents and
descents performed between points M and A. The solid isolines correspond to the adiabatic optical thickness as
derived from Eq. Ž5.. The dotted isolines correspond to the effective radius at the cloud top as derived from
Eq. Ž6..

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31

5. Discussion
For the numerical study of the aerosol indirect effect, parameterizations of the
interaction between cloud microphysics and cloud radiative properties are needed. The
primary effect of aerosol changes on cloud microphysics is to modify the droplet
concentration. Therefore, empirical parameterizations are not suited if they cannot
capture the basis of the relationship between the droplet concentration and cloud
radiative properties. At the scale of a cloud system, the large variability of the droplet
concentration that results from variability of the cloud nuclei activation process, from
mixing processes between the cloud and the overlying dry air, and from drizzle
scavenging prevents the observation of such relationships. However, within a convective
core, the droplet concentration is almost constant and the vertical evolution of the
microphysics follows simple laws.
The objectives in EUCREX were to document precisely this vertical evolution in
order to support the use of the adiabatic microphysical model for parameterization of the
optical thickness at the scale of a cloud cell. The second step is to document the
horizontal variability of the cloud microphysics with respect to the adiabatic reference.
The vertical evolution has been observed via series of short ascents and descents
through the cloud layer. They confirm previous observations in similar clouds, namely
that LWC is close to its adiabatic value, that the droplet concentration is almost constant
and that the droplet sizes are increasing according to the adiabatic model. The model has
then been used to estimate the maximum values Ži.e., adiabatic. of optical thickness at
different locations within the cloud system. These estimates are compared in the
conclusion paper of values derived from radiometric measurements from above the
cloud layer.
The effects of the mixing and of the resulting variability of the microphysical field on
the radiation field are more difficult to characterize and parameterize. We believe that
cloud-resolving simulations of 3D cloud fields will be necessary, with detailed radiative
transfer calculations. Such models can be used to simulate various levels of variability
and, after integration over the whole domain of simulation, to establish parameterizations between the mean dynamical properties of a cloud system and its mean radiative
properties. However, most of the cloud resolving models are predicting only LWC and
even models with detailed microphysics cannot simulate explicitly the effects of mixing
on droplets because this process proceeds at very small scales, down to a few
centimeters, that is scales smaller than the model grid. For validation of the numerical
simulations, it is thus crucial to document the statistics of the microphysics, including
the effects of mixing processes on droplet sizes.
Series of horizontal legs have been performed close to cloud top to document this
second aspect of the problem. They reveal that the variability in LWC is more important
in thin cloud layers than in thicker clouds where a large percentage of the values remain
within 60–100% of the adiabatic value. In addition, it appears that the variability in
LWC is mainly due to a variability in the droplet concentration while the droplet sizes
remain close to their adiabatic values at the corresponding level. Such a feature can be
simply implemented in a cloud-resolving model. Once w is known in a grid box, the
radiative transfer can thus be calculated by assuming that N s Nad wrwad Ž h. and

32

H. Pawlowska et al.r Atmospheric Research 55 (2000) 15–33

re s r vad Ž h.rk 1r3. The results of the statistical analysis on the distributions of LWC, N
and r v are summarized in a series of cumulative distributions over horizontal cloud
sections sampled during the EUCREX mission 206.
The cloud system described in this study is typical of a polluted air mass Ž N f 400
cmy3 .. In particular, there was no production of drizzle in the EUCREX mission 206
cloud system, while drizzle scavenging is also likely to play an important role in the
spatial variability of the microphysics and the life time of the cloud system ŽVali et al.,
1998.. Additional measurements of the same type are thus necessary in pure marine and
slightly polluted air masses in order to demonstrate the indirect effect of aerosols on
climate and provide complementary observations for validation of the numerical models.
The ACE-2 ŽAerosol Characterization Experiment. is a good opportunity for such
measurements.

Acknowledgements
The authors are grateful to the Meteo-France Merlin-IV teams for their efficient
contribution to the data collection and to the GMEIrMMA for data processing. This
work has been supported by INSU-PATOM under grant 94r08 and by the European
Union Environment and Climate Division, under grant ENV4-CT95-0117.

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