relationships exist between the altitude above cloud base and droplet concentration on the one hand, and the droplet effective radius and the extinction coefficient on the other
hand. Such profiles can then be used for deriving the optical properties of the cloud cell as functions of its geometrical thickness and droplet concentration, both parameters
which characterize the morphology of the cloud and the level of pollution of the airmass. The second step then consists in the characterization of the horizontal inhomogeneity of
the cloud layer for the determination of the mean cloud albedo.
Ž .
The EUropean Cloud Radiation EXperiment EUCREX-94 has been designed to test such an approach. The experimental strategy was based on coordinated flights with three
aircraft, one flying in cloud for measurements of the microphysical parameters, the two others flying 2 to 5 km above cloud top for remote sensing measurements of the cloud
Ž .
radiative properties with multidirectional radiometers POLDER , a multi-wavelength Ž
. Ž
. radiometer OVID and a lidar LEANDRE . Additional information about the cloud
radiative properties at a larger scale have been obtained from the space-borne AVHRR radiometer. The case study presented here is mission 206, which was conducted on April
18, 1994. The aerosol background in the boundary layer was significantly affected by pollution from north-western Europe and the droplet number concentration observed in
the stratocumulus was reaching values higher than 400 cm
y3
, quite higher than the values currently measured in pure marine boundary layer clouds. In this introductory
paper, the experimental approach will be discussed in relation to existing theories and parameterization schemes. The instrumental setup will be described and the meteorologi-
cal situation during mission 206 will be presented. The various measurements performed
Ž .
during this case study are presented in separate papers, by Pawlowska et al. 2000a for Ž
. Ž
. in situ measurements, by Schuller et al. 2000 for OVID, by Pelon et al. 2000 for
¨
Ž .
LEANDRE, and by Fouilloux et al. 2000 for AVHRR measurements. Finally, these various observations are summarized and compared in the conclusion paper by
Ž .
Pawlowska et al. 2000b .
2. Parameterization of the cloud microphysicsr r
r r
r radiation interaction
Ž .
The complex interaction between cloud droplets and radiation in the short-wave SW range can be reduced to a set of three parameters: the extinction coefficient s , the
ext
single scattering albedo v, and the asymmetry factor g. Extinction is expressed as
`
Ž .
2
Ž . Ž .
s s H Q x p r n r d r, where r is the droplet radius and n r their size distribu-
ext ext
Ž . tion, l is the radiation wavelength and x s 2p rrl is the size parameter. Q
x is the
ext
Ž .
Mie efficiency factor van de Hulst, 1957 , that is generally replaced by its mean value over the range of x values corresponding to cloud droplets and short wave radiation, a
value close to 2. The above formula is thus simplified as:
s s 2p r
2
N, 1
Ž .
ext s
`
Ž . where N s
H n r d r is the total droplet concentration and r is the mean surface radius
s
of the droplet size distribution.
Theoretical calculations have shown that the single scattering albedo and the asym- metry factor can be parameterized as linear functions of the effective radius of the
droplet size distribution, r s r
3
rr
2
, where r is the mean volume radius of the
e v
s v
Ž .
distribution Hansen and Travis, 1974; Twomey and Cocks, 1989 . With this definition of the effective radius, the above expression for the extinction becomes:
3 w
s s ,
2
Ž .
ext
2 r r
w e
4p
3
with w s r Nr ,
3
Ž .
w v
3 where r
is the liquid water density.
w
Therefore, the first step for parameterizing radiative properties of inhomogeneous clouds consists in the definition of the spatial distribution of w and r . The emissivity of
e
Ž .
a cloud in the long-wave IR range is proportional to the vertical integral of w, also referred to as the liquid water path W. The conservation of W in any parameterization is
thus a constraint in the choice of the vertical profile of w. The simplest solution is to assume that w and r are constant both in the horizontal and in the vertical, with
e
Ž .
w s WrH where H is the cloud geometrical thickness VUPPM . More sophisticated parameterizations have been proposed to study the effects of horizontal inhomogeneity
and vertical stratification of cloud microphysics on the radiative properties. Our method- Ž
ology relies upon the independent pixel approximation Cahalan et al., 1994a; Davis et .
al., 1997a,b , which states that the radiative properties of a cloud column are fully determined by its microphysical properties and are independent from properties of
adjacent columns, as long as the size of the cloud column is larger than the geometrical cloud thickness.
2.1. Vertical stratification Ž
. Ž
. Ž
Stephens 1978a,b and Stephens et al. 1978 present, in a series of three papers PI, .
PII, and PIII, respectively , an extensive study of the radiative properties of extended water clouds. In PI, theoretical calculations are performed with various types of clouds
in order to derive their SW heating rate and IR cooling rate. In PII, analytical approximations are validated against the detailed calculations, and in PIII, predictions
are compared to in situ measurements. The clouds are supposed to be horizontally homogeneous and various assumptions are tested for the vertical profiles of w and r :
e
constant w and r , constant r with w increasing with height above cloud base, and
e e
finally, both w and r increasing with height. The conclusions are particularly relevant
e
to our discussion. The general conclusion is that, in operational models, the maximum predictable information about the optically active cloud constituents will be restricted to
such things as the grid average LWC or total liquid water path. However, it is also stated that the predicted SW heating and IR cooling vary significantly with the different LWC
profiles tested while the changes related to different size distributions are entirely masked by large variations of the cloud LWC structure. Therefore, accurate modelling
of the SW heating and IR cooling in extended water clouds requires that the vertical
profile of w is included. In PI, Sec. 4d, it is also stated that whereas the absorption is relatively insensitive to changes of cloud microstructure, the cloud albedo is more
strongly dependent on drop-size distribution. This series of papers thus suggest that it is crucial for the study of the aerosol indirect effect to consider in radiative transfer
calculations the vertical profiles of w and r , and the relationship between N and r .
e e
Detailed measurements of the thermodynamics, cloud physics, and radiation fields Ž
. performed during the Joint Air–Sea Interaction experiment JASIN are reported by
Ž .
Slingo et al. 1982 who precisely document the difference between the horizontal and the vertical variabilities of the microphysics in stratocumulus. The observed vertical
profiles of LWC are close to the adiabatic reference while the total droplet concentration is almost constant with altitude. Therefore, the observed droplet spectra show an
Ž . increase of the mean volume radius with altitude above cloud base according to Eq. 3 .
In contrast, the horizontal variability, mainly close to the cloud top, is related to entrainment of dry air and mixing that results in diluted droplet concentrations while the
droplet radii remain close to their adiabatic values at that level.
These observations and data from previous experiments are used in Slingo and Ž
. Schrecker
1982 for validating the following parameterizations of bulk radiative
properties as functions of w and r .
e
s s w a q brr 4
Ž .
Ž .
ext e
1 y v s c q d r 5
Ž .
e
g s e q fr , 6
Ž .
e
where a, b, c, d, e, and f are wavelength dependent. Simulations with constant w and r
are performed to test the minimum number of spectral bands needed for the
e
calculation of realistic profiles of the heating rate. The second series of simulations is made with a fixed r and w increasing according to the adiabatic profile. Typical values
e
Ž .
of r , reported in the literature between 4.21 and 16.6 mm , are selected to test the
e
dependence of cloud SW properties on drop size distribution. They are considered as representative of the whole cloud depth. For LWC profiles, three typical types of clouds
are selected with w values at cloud top from 0.41 to 1.11 g m
y3
. The predicted variations of the cloud absorption and cloud albedo as functions of the effective radius
provide information about the indirect effect. However, the assumption of constant Ž .
effective radius throughout the cloud depth with no explicit reference to Eq. 3 leads to unrealistic results. For example, the assumption of an effective radius of 4.21 mm for a
sub-tropical type cloud with a LWC value at the top of 1.11 g m
y3
, corresponds to an unrealistic total droplet concentration larger than 3500 cm
y3
. The third set of simula- tions is performed with various vertical profiles of w and r . They show that the heating
e
rate profiles mainly depend on the vertical distribution of LWC while the assumption on r does not seem to be crucial. However, the indirect effect refers specifically to the
e
increase of the droplet concentration that could result from changes in the properties of Ž .
the CCN. The effective radius is related to the droplet concentration through Eq. 3 but its mean or maximum values are also determined by the liquid water path or, for
adiabatic profiles, by the cloud geometrical depth. Therefore, studies of the indirect effect should be based on sets of w and r actually observed in clouds as in Slingo
e
Ž .
Ž . 1989 or restricted through Eq. 3 to realistic values of the droplet concentration as in
Ž .
Ž .
Slingo 1990 and in Jones et al. 1994 . 2.2. Horizontal inhomogeneity
The various approaches described in the previous section have considered simple idealized models. Actual clouds are more complicated because of the spatial variability
of the microphysical fields. The adiabatic model provides a simple and unique descrip- tion of the vertical profiles but it is actually restricted to the convective cores in a cloud
layer. The effects of entrainment and mixing with dry air and of the precipitations lead to an infinite variety of spatial distributions of the LWC and droplet sizes, that is of the
in-cloud extinction. The optical properties of a cloud layer are dependent upon the statistical distributions of these parameters but also upon the scale of the inhomo-
geneities, especially at scales comparable to the mean free path of the photons in the cloud layer.
Two steps are particularly crucial for the study of the effects of inhomogeneities on cloud radiative properties. The first is to develop numerical models able to simulate the
radiative transfer in an inhomogeneous medium. The second is to generate for such models cloud simulations with realistic distributions of the internal properties. Monte
Ž .
Carlo techniques Cashwell and Everett, 1959 have provided an efficient solution to the first step, but the second, namely, the characterization of the microphysical variability in
actual clouds, is still a puzzle. Ž
. Cahalan et al. 1994a,b have shown that a mosaic of plane parallel clouds with
various values of optical thickness has a lower albedo than the homogeneous plane
Table 1 Description of the legs flown by the three aircraft, between points M and A, during mission 206
Ž . Aircraft
Time Height m
Comments Merlin
9:30–9:51 850
M–A horizontal 9:57–10:18
400–1200 A–M zigzag
10:21–10:41 700–1100
M–A horizontal near cloud top 10:46–11:06
700–1000 A–M horizontal near cloud top
11:10–11:29 500–1200
M–A zigzag 11:34–11:55
600–1000 A–M zigzag
ARAT 9:58–10:07
4500 A–M
10:11–10:30 4500
M–A 10:34–10:54
4500 A–M
10:57–11:17 4500
M–A 11:20–11:39
4500 A–M
11:42–12:03 4500
M–A 12:06–12:18
4500 A–M
Falcon 10:06–10:21
3000 M–A
10:26–10:41 3000
A–M 10:46–11:00
4600 M–A
11:04–11:20 6000
A–M 11:25–11:42
6000 M–A
parallel cloud with the same liquid water path. It has been also demonstrated that the shape of the cloud cells in the layer is as important as the horizontal distribution of
Ž .
optical thickness Welch and Zdunkowski, 1981 . Various techniques have been devel- oped for generating inhomogeneous clouds, such as the Bounded Cascade Model
Ž .
Marshak et al., 1994 . However, the generating procedure is rather artificial since it is derived from remotely observed statistical properties of the clouds. It is thus not evident
that the parameters used for describing the inhomogeneity of the internal structure are the most relevant for describing the radiative properties of the layer. Therefore,
additional information is needed about the relationship between the internal cloud structure and the resulting radiative properties.
Our first objective in the EUCREX project is to test the radiative transfer models and the remote sensing retrieval techniques at the scale of the cloud cells. At such a scale, in
situ measurements provide an accurate description of the microphysical properties within the column. The second objective is to expand the analysis to larger scales via a
precise description of the horizontal statistics of the internal cloud structure.
3. The instrumental setup
