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Atmos. Chem. Phys., 11, 12887–12900, 2011
www.atmos-chem-phys.net/11/12887/2011/
doi:10.5194/acp-11-12887-2011
© Author(s) 2011. CC Attribution 3.0 License.
Atmospheric
Chemistry
and Physics
Resolving both entrainment-mixing and number of activated CCN
in deep convective clouds
E. Freud1, D. Rosenfeld1, and J. R. Kulkarni2
1The Department of Atmospheric Sciences, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
2Institute of Tropical Meteorology, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
Received: 24 February 2011 – Published in Atmos. Chem. Phys. Discuss.: 22 March 2011
Revised: 27 November 2011 – Accepted: 1 December 2011 – Published: 20 December 2011
Abstract. The number concentration of activated CCN (Na)
is the most fundamental microphysical property of a con-
vective cloud. It determines the rate of droplet growth with
cloud depth and conversion into precipitation-sized particles
and affects the radiative properties of the clouds. However,
measuring Nais not always possible, even in the cores of
the convective clouds, because entrainment of sub-saturated
ambient air deeper into the cloud lowers the concentrations
by dilution and may cause partial or total droplet evapora-
tion, depending on whether the mixing is homogeneous or
extreme inhomogeneous, respectively.
Here we describe a methodology to derive Nabased on the
rate of cloud droplet effective radius (Re) growth with cloud
depth and with respect to the cloud mixing with the entrained
ambient air. We use the slope of the tight linear relationship
between the adiabatic liquid water mixing ratio and R3
e(or
R3
v) to derive an upper limit for Naassuming extreme in-
homogeneous mixing. Then we tune Nadown to find the
theoretical relative humidity that the entrained ambient air
would have for each horizontal cloud penetration, in case of
homogeneous mixing. This allows us to evaluate both the
entrainment and mixing process in the vertical dimension in
addition to getting a better estimation for Na.
We found that the derived Nafrom the entire profile data is
highly correlated with the independent CCN measurements
from below cloud base. Moreover, it was found that mix-
ing of sub-saturated ambient air into the cloud at scales of
∼100m and above is inclined towards the extreme inho-
mogeneous limit, i.e. that the time scale of droplet evapo-
ration is significantly smaller than that for turbulent mix-
ing. This means that ambient air that entrains the cloud is
pre-moistened by total evaporation of cloud droplets before
it mixes deeper into the clouds where it can hardly change
Correspondence to: E. Freud
(eyal.freud@mail.huji.ac.il)
the droplet size distribution, hence Reremains close to its
adiabatic value at any given cloud depth. However, the ten-
dency towards the extreme inhomogeneous mixing appeared
to slightly decrease with altitude, possibly due to enhanced
turbulence and larger cloud drops aloft.
Quantifying these effects, based on more examples from
other projects and high resolution cloud models is essential
for improving our understanding of the interactions between
the cloud and its environment. These interactions may play
an important role in cloud dynamics and microphysics, by
affecting cloud depth and droplet size spectra, for example,
and may therefore influence the cloud precipitation forma-
tion processes.
1 Introduction
Clouds are responsible for two thirds of the planetary albedo
and hence play a dominant role in determining the Earth
energy budget and the global temperature. Aerosols affect
cloud albedo by nucleating larger number of smaller droplets
that enhance the light scattering for a given amount of cloud
water (Twomey, 1974). According to the IPCC (2007) re-
port, the uncertainty in the aerosol cloud albedo effect, par-
ticularly in the anthropogenic aerosol component, dominates
the uncertainty of the climate radiative forcing. Aerosols
can also alter the cloud coverage and lifetime of both cool-
ing (Albrecht, 1989) and warming (Koren et al., 2010), and
significantly affect the precipitation processes and hence the
redistribution of heat and energy in the atmosphere (Rosen-
feld et al., 2008a). This occurs through the aerosol impacts
on precipitation forming processes and the following mod-
ification of cloud dynamics. These processes are at least
as important and even less understood than the albedo ef-
fect which was highlighted as the main source of uncertainty
(IPCC, 2007).
Published by Copernicus Publications on behalf of the European Geosciences Union.
12888 E. Freud et al.: Entrainment and activated CCN in convective clouds
Aerosols and clouds are microphysically related through
the number of the activated aerosols that serve as cloud con-
densation nuclei (CCN) and produce cloud droplets. This de-
pends on the sizes, concentrations and chemical properties of
the aerosols as well as on the super-saturation that they were
exposed to. As long as the droplet concentrations and their
surface areas are too small to balance the super-saturation
produced by the cooling of the rising saturated air, more CCN
will activate into cloud droplets. Stronger updrafts will re-
sult in higher droplet concentrations. Even relating the much
more common retrievals of aerosol optical depths (AOD) to
CCN concentrations at a given super-saturation can be prob-
lematic, because the same retrieved AOD can be the result of
significantly (orders of magnitude) different CCN concentra-
tions (Andreae, 2009).
The number of activated CCN (henceforth: Na) into cloud
droplets is the most fundamental microphysical property of
a convective cloud. It determines the rate of the droplets’
growth with cloud depth and in turn their conversion into
precipitation-sized particles. It also affects the radiative
properties of the clouds as higher concentrations will reduce
the droplet sizes for a given amount of cloud water (Twomey,
1974). Naembodies not only the CCN activation spectra, but
also the actual super-saturation that these CCN were exposed
to. However, direct measurement of Nais usually not possi-
ble because entrainment of sub-saturated ambient air into the
cloud decreases the cloud droplet concentrations by evapora-
tion and dilution. Even the cores of deep convective clouds,
where measurements are normally avoided due to the strong
vertical motions and icing hazards, are prone to entrainment.
This is mainly because of their fairly small horizontal extent
and the strong turbulence in and near the convective clouds.
Indirect measurements of Naby satellite and lidar retrievals
were previously applied to shallow marine stratiform clouds,
with the main assumption that the clouds are composed of
nearly adiabatic elements (Bennartz, 2007; Brenguier et al.,
2000; Sch¨
uller et al., 2003; Snider et al., 2010). These re-
trievals had large uncertainties and were not always validated
with direct measurements. Furthermore, that methodology is
not applicable to convective clouds due to a large departure
from the assumption that they are close to adiabatic, and also
due to the variable cloud top heights and depths at scales
smaller than the typical satellite sensor resolution.
Here we introduce a methodology for deriving Naof con-
vective clouds in a wide range of aerosol and cloud droplet
concentrations, and even for diluted clouds. This methodol-
ogy, presented in Sect. 3, is based on in-situ measurements of
the cloud droplet spectra at different levels in clouds. But first
we discuss the entrainment-mixing process of sub-saturated
ambient air into the cloud in Sect. 2.
2 Entrainment-mixing processes
Typically, as soon as a convective cloud is formed in a super-
saturated rising bubble of air, it continues to grow upwards
into a layer of sub-saturated air. As long as the cloud is not
precipitating and without significant dilution by entrained air,
its liquid water content (LWC) is expected to be close to the
adiabatic water content (LWCa1). Nearly adiabatic values
of LWC are often measured in Stratus (St) and Stratucumu-
lus (Sc) clouds because of their relatively wide extent so that
much of their cloud volume does not come into contact with
the surrounding sub-saturated air. Convective clouds, how-
ever, have a much smaller horizontal dimension and are more
turbulent, so that the entrained sub-saturated air from the sur-
roundings of the clouds has a high chance of quickly pene-
trating deeper into the cloud and reaching its core while low-
ering LWC by dilution. Barahona and Nenes (2007) devel-
oped a parameterization based on the assumption that mixing
occurs already at the cloud formation level, which results in
a reduction in the number of activated CCN in convective
clouds. This is because the entrainment at cloud base lowers
the maximum super-saturation that is reached. Morales et al.
(2011) showed that this parameterization yields a mean cloud
droplet number concentration that is comparable with the
numbers measured in convective clouds. The cloud droplets
that are exposed to that sub-saturated air will partially or
completely evaporate and increase the water vapor partial
pressure in the entrained air. The fate of the droplets is de-
termined by the mixing proportions of the cloudy and am-
bient air, its relative humidity (RH) and the sizes and con-
centrations of the droplets. Without mixing, precipitation,
secondary droplet nucleation and droplet coalescence, the
droplet mean volume radius, henceforth Rv, is expected to
be equal to Rvin an adiabatic parcel (Rva), which only de-
pends on Naand LWCa(Eq. 1). Again, model and airborne
studies reveal that in Sc clouds, Rvand Rvaare quite similar,
except for close to the cloud edges, and especially near the
top of the cloud where most mixing occurs (e.g. Pawlowska
et al., 2000). How exactly mixing and entrainment affect the
droplet size distribution (DSD) and Rvis an issue that has
been studied for more than three decades and there is still
no satisfying answer, specifically in convective clouds. This
is because mixing starts with eddies with a length scale of
hundreds or even thousands of meters that gradually break
into smaller filaments down to the Kolmogorov microscale
(∼1 mm in normal atmospheric conditions), where variations
in temperature and water vapor fields are homogenized by
molecular diffusion. Such scales cannot be explicitly re-
solved by today’s cloud models and standard airborne cloud
microphysics instrumentation (Baker et al., 1984; Brenguier,
1993; Lehmann et al., 2009).
1The subscript “a” added to LWC, Rvand Rein this paper stands
for “adiabatic” to denote the values of these parameters in an adia-
batic air-parcel
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E. Freud et al.: Entrainment and activated CCN in convective clouds 12889
Until the late 1970s the research of the entrainment-mixing
process was based on the idea that the cloud droplets at
any given level are equally exposed to the entrained sub-
saturated air, regardless of their specific location in the cloud,
and as a result evaporate partially or completely together –
what was later described as homogeneous mixing by Baker
et al. (1980). In a laboratory study, Latham and Reed (1977)
found that concentrations of small droplets become very in-
homogeneous after admixture with sub-saturated air, because
some of the droplets totally evaporate while others remain
unchanged. This finding helped explain some of the discrep-
ancies between earlier calculations and modeling results, and
observations in clouds. In their published studies, Baker et al.
(1980) and Blyth et al. (1980) prepared the ground for the
current research on the effect of mixing and entrainment on
cloud droplet spectra. They defined the range of the mixing
effect on cloud droplet spectra based on the time scales of
droplet evaporation (τevap) vs. turbulent mixing (τmix). In the
case that τevapτmix the droplets that border the entrained air
bubble or filament will quickly evaporate until the entrained
air becomes saturated, so further mixing will decrease the
cloud droplet concentration by dilution and will leave the
shape of the droplet spectra unchanged. This is referred to as
the extreme inhomogeneous case. The other extreme is the
homogeneous mixing. It fulfills the condition: τevapτmix.
That means that the sub-saturated air will be first fully mixed
in the cloud volume, so all droplets will be exposed to the
same sub-saturation, and then will partly evaporate until the
air becomes saturated again. This will cause the droplet size
spectra to shift towards the smaller sizes but the number of
droplets will remain the same unless some of the smallest
droplets would fully evaporate. In reality though, the ratio
between τmix and τevap, also called the Damk¨
ohler ratio (Di-
motakis, 2005), is typically not much smaller or larger than
unity. It depends on the mixing scales, which are hard to de-
fine, the turbulence, the ambient RH, the droplets’ sizes and
concentrations etc. (Lehmann et al., 2009).
Figure 1 demonstrates the fundamental differences be-
tween the fully homogeneous and extreme inhomogeneous
mixing scenarios, as described above. It shows an example of
the theoretical relationship between the droplet mean volume
radius (Rv) and the adiabatic fraction (AF), which is the ratio
between LWC and LWCa, for the two mixing scenarios. We
use typical values for the parameters that affect this relation-
ship to get typical values of Rv. We assume isobaric mixing
of cloudy and ambient air that have the same temperature.
This figure resembles the mixing diagram shown in Burnet
and Brenguier (2007) and the parameters are calculated in
the same way, but here we plot AF on the abscissa rather than
the normalized number of droplets, because it represents bet-
ter the amount of entrained air that the adiabatic parcel has
been mixed with. How much the droplets will reduce in size
in relation to Rvawhen exposed to sub-saturated air is de-
termined by the initial water vapor content of the entrained
air: the drier it is the smaller the droplets will become upon
Fig. 1. Mixing diagram: the relationship between the droplet mean
volume radius (Rv) and the adiabatic fraction (AF) for fully ho-
mogeneous and extreme inhomogeneous mixing events between
an adiabatic cloud parcel and entrained non-cloudy air with vary-
ing relative humidity (RH) at the mixing level of ∼2200m above
cloud base, where the temperature of the cloudy and entrained air
is ∼10◦C and the adiabatic liquid water mixing ratio is 5 g kg−1.
The cloud base is at 850hPa and 20 ◦C. The concentration of the
activated CCN (Na) is 500mg−1. It can be seen that entrained air
with higher RH results in a smaller dependence of Rvon AF, espe-
cially for AF>0.2. When entrained air is saturated (RH =100 %),
or when mixing is extremely inhomogeneous, Rvremains constant.
mixing and saturation of the entrained air, until their mass is
not sufficient to saturate the mixed air and they completely
evaporate. Mixing with air that is already saturated, or in
case of extreme inhomogeneous mixing, Rvwill be equal to
Rvafor all adiabatic fractions. Figure 1 clearly shows that
the Rvvs. AF curve strongly depends on the RH of the en-
trained air, but this dependence is highly non-linear: at low
RH this relationship is almost independent of RH, whereas
in high RH this relationship has a strong sensitivity to RH. If
the RH of the entrained air is known then the deviation from
the homogeneous mixing curve for that RH with respect to
the extreme inhomogeneous mixing horizontal line in Fig. 1
can give an indication of the extent of the mixing inhomo-
geneity. For example, if the ambient RH is 30 %, but the data
points plotted on a mixing diagram like Fig. 1 align around
the RH=95% curve, then this would be a strong indication
of mixing tendency towards the inhomogeneous limit.
Generally, it appears in the literature that the observa-
tional studies find a clear tendency towards the extreme in-
homogeneous mixing (Hill and Choularton, 1985; Paluch,
1986; Bower and Choularton, 1988; Pawlowska et al., 2000;
Gerber, 2006) or intermediate features between the homo-
geneous and inhomogeneous mixing scenarios (Jensen and
Baker, 1989; Paluch and Baumgardner, 1989; Morales et al.,
2011), although parts of this tendency may be explained by
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12890 E. Freud et al.: Entrainment and activated CCN in convective clouds
instrumental artifacts (Burnet and Brenguier, 2007). In an
earlier study of ours that analyzed many convective cloud
droplet spectra in the Amazon basin (Freud et al., 2008),
we also concluded that the mixing process tends towards the
extreme inhomogeneous limit, as the droplet effective radii
(Re) did not show a significant dependence on the extent of
droplet exposure to entrained air. Our analysis here, looks
deeper into the mixing process in a quantitative way, so we
are able to use the deviations from the extreme inhomoge-
neous mixing assumptions to derive a better estimation for
Na, which is the main objective in this study.
3 Methods
The number of activated CCN, Na, which we aim to derive,
is a macro-physical cloud property similar to the precipita-
tion initiation height. It represents a whole cloud or even a
cloud domain where aerosol and thermodynamic features do
not vary considerably. Therefore it cannot be based on an in-
dividual measurement at the cloud droplet probe spatial reso-
lution (typically ∼100 m), such as the maximum droplet con-
centration. This is because a single measurement may have
a large uncertainty, be sensitive to processes on a scale too
small to represent the entire cloud (e.g. local strong updraft
near cloud base) and be affected by the extent of dilution that
the measured cloud volume had experienced. Instead, basing
the estimation of Naon many measurements throughout the
cloud and at different levels, and using a more robust micro-
physical property such as Reor Rv, is expected to be more
representative and less prone to the uncertainties of the indi-
vidual measurements. This is the approach we use here.
The methodology we use to derive Nais first stated here
briefly as a process that would be easy to follow. This list
is followed by a more detailed description of each step with
further explanations for clarification. The methodology is
applied to the data of the research flight of 25 August 2009
over central India (for further information and description of
instrumentation see Kulkarni et al., 2009) as an example. Ad-
ditional examples can be found in the supplementary material
online.
1. Assume extreme inhomogeneous mixing. Derive a first
estimation for Na(Nainit) from the slope of LWCato R3
v
for AF larger than e.g. 0.25 (Fig. 2 and Eq. 1)
2. Use Nainit to calculate the relative humidity that the en-
trained air would have had if it was homogeneously
mixed into the cloud (henceforth RHbest) for each hor-
izontal cloud penetration. Figure 3a shows an example
of how the results typically look.
3. Use the mean RHbest for all penetrations that were de-
rived in step 2 to evaluate the effect of inhomogeneous
vs. homogeneous mixing on Na. Then reduce Nainit ac-
cording to this effect (Fig. 4).
Fig. 2. The droplet mean volume radius (Rv) vs. the adiabatic liquid
water mixing ratio (LWCa) for different threshold adiabatic frac-
tions. The 1 Hz measurements were taken during the CAIPEEX-1
(Cloud-Aerosol Interaction and Precipitation Enhancement Exper-
iment, phase 1; Kulkarni et al., 2009) program over central India
on 25 August 2009 (flight 20090825) at elevations between 500 and
5000m.a.s.l. The green, red, blue and cyan colors denote thresh-
old adiabatic fractions of 0, 0.1, 0.25 and 0.5, respectively. The Rv
and AF data are based on the Droplet Measurement Technologies
(DMT) Cloud Droplet Probe (CDP) measurements while the num-
ber of activated CCN (Na) is derived from the slope of the linear
best fit (Eq. 1). It can be seen that the AF filter selected does not
affect the derived Naremarkably. Using Na0.25 as Nainit looks like a
reasonable compromise between having enough data points to rep-
resent the entire profile, and having a large LWCarange for deriving
a representative Nainit for the entire profile.
4. Calculate RHbest for each penetration again, this time
based on the corrected Nafrom step 3, similar to what
is done in step 2 (Fig. 3). Then calculate the mean pen-
etration residual (MPR).
5. Slightly reduce the last derived Na(e.g. by 5%) and
repeat steps 4 and 5 until MPR reaches its minimum
value (see example in Fig. 3b). The number of iterations
for each dataset depends on the amount of Nareduction
chosen for this step.
3.1 Step 1: calculating Nainit by assuming extreme
inhomogeneous mixing
The liquid water content of a cloud parcel is the sum of
masses of all droplets or the product of the droplet number
concentration and the mass of a droplet with an average vol-
ume, i.e droplet whose radius is Rv. Since all small cloud
droplets are spherical Nacan be calculated in the following
way:
Na=1
ρw·3
4π·LWCa
R3
va
(1)
Atmos. Chem. Phys., 11, 12887–12900, 2011 www.atmos-chem-phys.net/11/12887/2011/
E. Freud et al.: Entrainment and activated CCN in convective clouds 12891
(a)
(b)
Fig. 3. (a) A mixing diagram for different horizontal cloud passes
at various altitudes within the same cloud. Each data point is based
on the CDP 1Hz measurement from flight 20090825 (the same
as in Fig. 2) and each color denotes the same cloud pass. The
dashed lines denote the Rvto AF theoretical relations for the de-
rived RHbest (see text for description) that best fits the data points
(with AF>0.1) for each cloud pass separately. Nainit, which is used
in the derivation of the RHbest values for each penetration (shown
in the legend), as well as the mean penetration residual (MPR; see
Sect. 3.4) calculated for all fits, are shown at the top of the panel.
(b) Same as (a), but with the final derived Na(see Sect. 3.4) and
the minimal MRP that showed best overall fit to the same dataset
as in panel (a). The legend shows that there is a small decrease in
the RHbest values in this panel. This is due to the higher Rvavalues
here in comparison to (a).
where ρwis the water density, which is nearly constant at
1gcm−3. Because we deal with rising air and change of al-
titude, all concentration units are per unit mass instead of the
more standard volume units. We use [mg−1] and [kg−1] to
replace [cm−3] and [m−3] respectively, by multiplying by the
air density. The profile of LWCais determined by the cloud
base pressure and temperature and it indicates the amount of
water vapor that turned into cloud water in an adiabatic par-
cel. Nacan represent the number of activated CCN for the
(N = 906 mg )
ainit -1
Fig. 4. Rv(blue circles) and Rva(red circles) vs. the adiabatic liquid
water mixing ratio (LWCa). The red data points denote the calcu-
lated Rvabased on the inferred LWCaprofile of flight 20090825
over central India, and Nainit (= 906mg−1) that was derived by
Eq. (1) for the data points with AF>0.25 (Fig. 2). The blue data
points show the theoretical values of Rvbased on the actual 1Hz
AF data (>0.25) and Nainit, assuming homogeneous mixing with
entrained air whose RHbest is the mean of the RHbest values in
Fig. 3a. The ratio of the slopes of the blue and red linear best fits ap-
proximates the effect of the homogeneous vs. inhomogeneous mix-
ing assumptions on Na, and is therefore used as a first correction for
Nainit.
entire profile as long as there is no significant droplet coales-
cence, as it reduces the droplet number concentration. Be-
cause the vast majority of measurements inside a deep con-
vective cloud do not even come near the adiabatic fraction
of unity, the challenge is to get a good representation of Rva
based on the measurements of Rv2, as Rvastrongly affects
Na(Eq. 1).
Freud et al. (2008) showed that Reis not very sensitive
to the degree of mixing in deep convective clouds sampled
in the Amazon basin. They concluded therefore that mix-
ing tends towards the inhomogeneous extreme. If this is the
case then Reand Rvanywhere in the cloud are expected to
be close to their corresponding adiabatic values, regardless
the history of the entrainment and mixing processes in the
cloud. Therefore, as a first approximation, we can assume
inhomogeneous mixing by using the calculated Rvinstead
of the theoretical Rvain Eq. (1). Since ρwis nearly constant,
Nacan be derived from the mean ratio of LWCato R3
va(Eq. 1
and Fig. 2).
Figure 2 presents the relationships between R3
vand LWCa
for different but overlapping subsets of the 1Hz data from
CAIPEEX-1 (Cloud-Aerosol Interaction and Precipitation
2Normally Reis measured and used rather than Rv. For sim-
plicity and consistency of the description of the methodology we
use Rvin the examples. However, in Sect. 3.5 we show how to use
Rewith the proposed methodology
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12892 E. Freud et al.: Entrainment and activated CCN in convective clouds
Enhancement Experiment, phase 1; Kulkarni et al., 2009)
flight 20090825 over central India. Each subset has a dif-
ferent minimum adiabatic fraction threshold, so the datasets
become smaller as the threshold increases. The slope of the
best fit line of each dataset is used to calculate Na, which
we will henceforth refer to as Nainit to point out that this is
the first and initial Naestimation based on the assumption
of extreme inhomogeneous mixing. For deriving Nainit with
Eq. (1), the best fit line has to be forced through the axes-
origin. One can see that only few data points have AF>0.5
(the cyan data points), which means that most parts of the
cloud are far from adiabatic. There is still a fairly wide range
of adiabatic fractions which represents the varying propor-
tions of cloudy and ambient air mixtures. Using various adi-
abatic fractions as filters (the different colors in Fig. 2) yields
slightly different values for the derived Nainit, depending on
the specific dataset. If mixing was indeed extremely inho-
mogeneous, Nainit would not have been dependent on the AF
filter whatsoever. However this is clearly not the case and
we do see a small decrease in Rvat the smaller adiabatic
fractions (green and red markers in Fig. 2), which seemingly
affects the derived Nainit to some extent. Because we do not
have adiabatic samples throughout the vertical profile and we
do not know the actual Na, the adiabatic slope in Fig. 2 is
not known. We can though still expect Nato be lower than
906mg−1, which is the minimal Nainit in the presented case.
Another added value of using AF as a filter is for excluding
data points from adjacent clouds with higher bases that occa-
sionally exist and can not always be evaded when collecting
data. These clouds would have smaller Rvin relation to the
convective clouds of our interest at the same altitude, so we
desire to exclude them from our analysis. The trade off of us-
ing a too high AF threshold may be that too many data points
will not pass the filter and that the remaining data points may
be concentrated at the lower part of the profile, so the de-
rived Nainit would be too sensitive to small errors in Rvand
LWCa. Using AF>0.25 as the threshold for calculating Nainit
(the blue data points and slope in Fig. 2) would be a good
compromise. It is important to mention though that the final
derivation of Nais not sensitive to the AF threshold chosen
here.
In theory and as shown in Eq. (1), the derived Nadepends
on the inferred LWCa, therefore it is very important to doc-
ument the cloud base properties (altitude, pressure and tem-
perature) correctly. In fact, if the cloud bases cannot be doc-
umented because of e.g. air traffic control limitations or high
terrain, the maximum integrated LWC values can assist in
estimating the highest possible cloud base altitude, because
they cannot exceed the inferred LWCavalues. However, if
the cloud base properties are well documented the same con-
dition can be applied to make sure that there is no overes-
timation of droplet concentration and/or oversizing of the
droplets by the cloud droplet probe. Such cases would re-
quire corrections of the dataset as they affect the derived Na
(see Sect. 3.6).
3.2 Step 2: using Nainit to calculate RHbest
Nainit derivation is based on the assumption of extreme inho-
mogeneous mixing. In order to improve the first estimation
of Na, the degree of actual mixing inhomogeneity must be
taken into account. This can be done by examining the de-
pendence of Rvon AF (as shown in the theoretical example
in Fig. 1) for each horizontal penetration independently. This
is not only because Rvis altitude-dependent, but due to the
fact that the degree of mixing inhomogeneity may vary with
altitude because droplets grow and turbulence changes. The
theoretical relative humidity that best fits each penetration-
data, RHbest, can be found by assuming homogeneous mix-
ing and using the Rvto AF relationship as well as the val-
ues of LWCaand Nainit. RHbest represents the theoretical RH
of the entrained air if it were homogeneously mixed with an
adiabatic cloud at a specific level (and the number of droplets
was conserved). The closer RHbest is to the real ambient RH,
the stronger the tendency of the mixing towards the homo-
geneous limit. Figure 3 shows examples of such RHbest fits,
calculated for horizontal penetrations at varying altitudes as
represented by the different colors, for the 20090825 case
study. Focusing on the left panel (Fig. 3a); the RHbest cal-
culation in this panel uses Nainit as input, which determines
Rvafor each penetration or level. The mean RHbest, as can
be derived from the individual RHbest values presented in the
legend, is smaller than 100% because Rvis not independent
of AF. This is another indication that the mixing is not ex-
tremely inhomogeneous.
The mixing diagram (Fig. 1) is based on the assumption
that the droplet number remains constant throughout the mix-
ing process (until all droplets evaporate at once), and that no
coalescence changes the drop concentration during the pro-
cess. Significant coalescence does not occur below about Re
of 13µm (Freud and Rosenfeld, 2011). Therefore samples
with Re>13µm were excluded from this and the following
steps. Using this filter, however, typically does not affect the
derived Nabecause the vast majority of measurements have
Re<13µm
3.3 Step 3: correcting Nainit by assuming homogeneous
mixing
Although Nainit is based on the extreme inhomogeneous as-
sumption, still some of the RHbest values that were derived
in the previous step are smaller than 100% (Fig. 3a). This
implies that mixing is not extremely inhomogeneous and it
allows to derive a more realistic Nathan Nainit. This is done
by deriving Nafrom the relationship between LWCaand R3
va,
in a quite similar way to what is shown in Fig. 2, but without
assuming extreme inhomogeneous mixing.
The red data points in Fig. 4 denote the Rvavalues cal-
culated from Nainit and the inferred LWCaprofile. How-
ever, since RHbest values were already derived in the pre-
vious step, we can use their mean value in order to
Atmos. Chem. Phys., 11, 12887–12900, 2011 www.atmos-chem-phys.net/11/12887/2011/
E. Freud et al.: Entrainment and activated CCN in convective clouds 12893
calculate the theoretical Rvvalues for the actual AF data
(with the same AF filter as used in Fig. 2, i.e. 0.25) with-
out assuming extreme inhomogeneous mixing. This is done
by assuming homogeneous mixing with pre-moistened en-
trained air (with RH=RHbest), which appears to be a better
representation of reality than assuming extreme inhomoge-
neous mixing (Burnet and Brenguier, 2007). The blue cir-
cles in Fig. 4 denote the derived theoretical Rvvalues for the
actual AF values. The ratio between the blue and red lin-
ear best-fit slopes indicates by which factor Nachanges due
the assumption of fully homogeneous vs. extreme inhomoge-
neous mixing, respectively. Nainit can therefore be divided by
this factor as a first correction towards finding Nathat best fits
the dataset. In the example shown in Fig. 4 this factor equals
0.963 while in other cases it can be as low as ∼0.8, depend-
ing on RHbest. However, this is still not the final and best
estimation of Na, because RHbest was based on Nainit, which
was known a-priori to be an overestimation of the real Na,
but nonetheless this step makes the described methodology
more efficient by reducing the number of iterations required
in the following steps.
3.4 Steps 4–5: iterations for finding minimal residuals
Because RHbest and the estimated Nadepend on each other,
Naderived in step 3 is not necessarily the final one. In order
to quantify the quality of the RHbest fits, which were derived
by prescribing Na, the mean penetration residual (henceforth
MPR) can be calculated for the entire profile. This is done
by averaging the squared vertical distance of all data points
from the best fit curve in each penetration separately, and
then averaging all penetrations, so that each penetration gets
the same weight in the averaging regardless of the length of
the cloud pass. The lower the MPR the better the overall
RHbest fits (see MPR values in both panels in Fig. 3 and in
the online supporting material).
The aim of the iterations is to find the Nafor which the
MPR is minimal. Steps 1–3 brought Nato a good starting
point for the iterations, which can be considered as fine tun-
ing of Na.Nashould be tuned downwards, because assuming
extreme inhomogeneous mixing and hence small Rva, results
in higher Na(Eq. 1) than without this assumption. A reason-
able step for each iteration would be to lower Naby incre-
ments of a few percents, depending on how much we trust
the cloud droplet measurements and how certain we are in
the cloud base altitude (see Sect. 3.6 for discussion on un-
certainties). MRP is computed in each iteration, based on
the recalculated RHbest fits, until the minimal MPR is found.
Smaller increments will result in more iterations. The cor-
responding Nato the minimal MPR is the Nathat best fits
the entire profile data. This still allows the degree of mix-
ing inhomogeneity to vary with altitude and by penetration.
The RHbest values for penetrations at different cloud depths
has an added value because they can be used to assess the
change in the effects of the nature of the entrainment and
0
5
10
15
20
0 5 10 15 20
India
Israel
Texas
y = 1.08x R= 0.991 (n=2192)
y = 1.08x R= 0.993 (n=1625)
y = 1.08x R= 0.995 (n=1880)
Effective Radius [µm]
Mean Volume Radius [µm]
Fig. 5. The cloud droplet effective radius, Re, versus the droplet
mean volume radius, Rv, for over 5800 1Hz-averaged droplet size
distributions mainly in convective clouds. The color-coding rep-
resents different field campaigns and location data: purple for the
Israeli rain enhancement program; blue for CAIPEEX-1 in India;
and green for SPECTRA (The Southern Plains Experiment in Cloud
seeding of Thunderstorms for Rainfall Augmentation; Axisa et al.,
2005). The number of measurements that were used to calculate the
linear best-fit for each location is denoted by “n” in the lower-right
part of the figure. Notice that Reis larger than Rvon average by
8 % regardless of the location, and that the linear correlation coeffi-
cient is greater than 0.99. This means that for practical uses Remay
be used instead of Rvfor the derivation of Na(see Eq. 4).
mixing with altitude, which has rarely been done in the past.
But in order to do that there is a need for a more complex
mixing model that simulates the changes in the shape of the
DSD as well as reliable and accurate profiles of RH outside
the clouds and near the cloud edges, which we currently do
not possess.
3.5 Replacing Rvwith Re
The methodology described above uses Rvto derive Na.
However, in remote sensing and in-situ applications nor-
mally Reis measured and used rather than Rv.Reis always
larger than Rv, except for the theoretical case of a mono-
dispersed cloud-droplet population. The ratio between Re
and Rvdepends on the specific droplet spectrum, but typi-
cally is around ∼1.1 and exhibits little variance because the
two variables are highly correlative (Fig. 5).
In order to replace Rvwith Rea new parameter needs to
be defined:
α=Re·N
LWC1
3(2)
here Nand LWC are the measured droplet concentration and
liquid water content, respectively. The physical units of αare
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12894 E. Freud et al.: Entrainment and activated CCN in convective clouds
(a)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
-200 -150 -100 -50 0
20090814 India
20090814 India cut
20090825 India
20090825 India cut
20100226 Golan
20100226 Golan cut
20100226 Sea
20100226 Sea cut
Relative Change in Na
Cloud Base Error [m]
(b)
1
1.2
1.4
1.6
1.8
2
0.8 0.85 0.9 0.95 1
20090814 Central India; N
a=911 mg-1
20090825 Central India; N
a=817 mg-1
20100226 Israel Sea; N
a=464 mg-1
20100226 Israel Inland; N
a=433 mg-1
y = 1.00 * x-2.70
y = 1.01 * x-2.54
y = 0.99 * x-2.61
y = 1.00 * x-2.48
Relative Change in Na
Relative Sizing Error
Fig. 6. Sensitivity tests: (a) The relative change in Nadue to un-
certainties in cloud base altitude for four different cases (flights
20090814 and 20090825 over central India and two profiles from
flight 20010226 over Israel, one over the sea and one ∼70km in-
land). The change in cloud base altitude causes changes in the
cloud base pressure and temperature, and hence modifies the pro-
file of LWCa. This affects Rvaand AF and eventually Na. The
filled circles and solid linear best fit curves mark that Naderivation
was based on the full profile, while the filled triangles and dashed
lines mark that the data from the first kilometer above cloud base
were filtered out before Nawas derived. This suggests that when
there is no data available from the lower part of the profile, Nacan
be derived with the same confidence as when all data is available.
(b) The relative change in Nadue to uncertainties in the sizing of the
cloud droplets by the cloud droplet spectrometer. The same cases
as in (a) are presented with the derived (original) Navalues for each
case in the legend, before the errors were introduced. The dashed
lines denote the best power fit for each case and show fairly high
sensitivity of the derived Nato sizing errors.
[mkg−1
3], however, if the units of [mg−1], [µm] and [g kg−1]
are used for N,Reand LWC respectively, αgets the units of
[µm g−1
3]. Combining Eq. (1) for non-adiabatic values with
Eq. (2) and using the latter above-mentioned units yields:
α=62.03·Re
Rv(3)
The parameter αcan be calculated for each single droplet
spectrum. Sometimes the parameter kis used instead of α
for relating Reand Rv(e.g. Martin et al., 1994)3. Eq. (3)
also applies for adiabatic parcels, therefore Eq. (1) can be
approximated by using a mean α(possibly based on the mea-
surements with the highest AF) this way:
Na=α3·LWCa
R3
ea
(4)
Now with Eq. (4), Nacan be derived from the vertical pro-
file of Rearather than Rvaand the knowledge of the cloud
base properties and the mean α. The accuracy of the mea-
surement of Reby remote sensing of convective clouds, is
better than 1µm according to Zinner et al. (2008). On the
other hand, the small scatter of the data points in Fig. 5 as
well as the calculated standard error values for each dataset,
indicate that the uncertainty in αis much smaller than 1%.
Therefore the error due to inaccuracies in αare negligible
with respect to the instrumental sizing errors.
3.6 Susceptibility of methodology to uncertainties
The methodology discussed here to estimate Nauses the
information regarding the inferred LWCaprofile and the
droplet sizes as measured by a research aircraft. The cal-
culation of a representative LWCaprofile depends on proper
documentation of the cloud base properties, such as height,
temperature and pressure. These may slightly vary in a field
of growing convective clouds but the effect of this variability
is minimized when analyzing cloud elements higher above
the average cloud base. This is one of the main benefits when
sampling and analyzing deep profiles. Sometimes there are
circumstances which do not allow cloud base measurements,
such as air traffic control limitations or high terrain. In those
cases the cloud base parameters need to be guessed wisely,
by e.g. making sure that the measured LWC do not exceed
the inferred LWCavalues. Uncertainties in LWCanot only
affect Nainit by changing the slope in Fig. 2, it also affects the
values of AF and hence RHbest and MPR, and eventually the
value of the final Na. Figure 6a shows the sensitivity of the
final derived Nato changes in cloud base height (and a cor-
responding change in cloud base pressure and temperature
according to a standard atmosphere). It shows that lowering
the cloud base by 100 m translates into a decrease of ∼5% in
Na. It also shows that if we exclude all data from the lowest
kilometer of the cloud profile, Nashows the same sensitivity
3kand αare related by: k=(62.03
α)3
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E. Freud et al.: Entrainment and activated CCN in convective clouds 12895
to uncertainties in cloud base altitude. This is reassuring and
indicates that even without proper documentation of cloud
base, Nacan still be estimated with a high certainty, at least
as long as there is good documentation of the rest of the pro-
file.
Some dynamical variability that leads to varying cloud
base updrafts (w) is common in a field of convective clouds.
The varying cloud base updrafts between clouds and within
a single cloud as well, may nucleate a different number of
cloud droplets, even if the aerosol properties are the same.
However, as the cloud develops, the turbulent mixing of the
air inside the cloud reduces the variability (when disregard-
ing entrainment). In addition, the very weak updrafts do not
contribute much to the vertical buildup of the clouds. There-
fore, the mean updrafts weighted by their contribution to the
cloud volume are what that counts for Na, as defined here.
Our sampling strategy naturally favors the deeper clouds for
obtaining profiles of deep convective clouds and hence re-
duce the variability of the mean cloud base updrafts. More-
over, even if the kexponent is assumed to equal unity in the
CCN spectra equation:
Na=c·Sk(5)
where Sis the super-saturation and cis the number of acti-
vated CCN at a super-saturation of 1%, then Nachanges only
according to w0.5(Rogers and Yau, 1989). Therefore, for the
typically smaller kvalues, the sensitivity of Nato wis even
smaller. This is why Rvthat is measured aloft is not nearly
as sensitive to variations in cloud base updrafts as it is to Na.
Other sources of uncertainty are related to the cloud
droplet probe that measures the sizes and concentrations of
the cloud droplets (Lance et al., 2010). If the sizing of the
droplets is trustworthy then correcting for errors in droplet
concentration is straight-forward (see Sect. 4). Any left un-
certainties in the droplet concentration would be translated
into uncertainties in Naby a factor of ∼0.9 (not shown here).
However, any sizing errors of the cloud droplets would be
amplified when deriving Nabecause of their non-linear rela-
tions (Eq. 1). Figure 6b shows that the average changes in Na
due to sizing errors by 1, 2, 5, 10 and 20% are ∼3, 6, 15, 30
and 78%, respectively. This yields a sensitivity of Nato the
sizing error to the power of ∼−2.6, which is slightly smaller
than the exponent of Rvin Eq. (1). It is therefore important
to test the sizing calibration of the cloud droplet probe as of-
ten as possible during field campaigns in order to minimize
the effect of sizing errors on the derived Na.
It is also important to point out that the final derived Na
does not depend on Nainit, so using a minimum AF for deriv-
ing Nainit (in Fig. 2) other than 0.25, may only have an effect
on the number of iterations needed before reaching the opti-
mal Na. Using a too small minimum AF and including data
from clouds with higher bases, may result in a mean RHbest
of 100% in step 2, which will make step 3 redundant and
increase the number of iterations. On the other hand, using a
too high AF filter may lead to a too low and unreliable Nainit
value in case it is based on too few data points from the lower
part of the cloud, which could be smaller than the actual Na.
Therefore it is advisable to plot the data as shown in Fig. 2
and choose a proper minimum AF to base Nainit on.
Changes in Naalso induce changes in RHbest. The exam-
ple in Fig. 3 shows that in the same dataset when prescribing
a smaller Nathe resulting RHbest values tend to decrease.
This is because Rvabecomes larger. A sensitivity test based
on the same four examples as in Fig. 6 (not shown here) re-
veals that the relative change in the mean RHbest is approx-
imately half of the relative change in Na. That means that
RHbest is even less sensitive to errors in droplet sizing and
cloud base estimation than Na.
Another important point to emphasize is that the method-
ology described here is valid as long as the droplet num-
ber concentration per unit mass of air in an adiabatic par-
cel remains nearly constant, i.e. droplets grow mainly by
condensation with little coalescence that leads to reduction
of droplet concentration, and there is no nucleation of new
cloud droplets that would increase it. Nucleation of new
droplets by entrained CCN (or those that were not activated
near cloud base) can occur in case there is a combination of
low droplet concentration and accelerating updrafts. In real
clouds it is more likely to occur in highly diluted parts of
the clouds, so defining a threshold AF as a filter (e.g. 0.1)
can be useful to exclude these cases, as well as those cases
with data contamination by clouds with higher bases than
the clouds of our interest. In addition, droplet concentration
is lowered when droplet coalescence is significant and dur-
ing rainout, so the mixing diagram may not be valid in these
cases, which are advised to be excluded from the analysis.
Adding an error bar to the derived Naat the end of the
routine described in Sect. 3 is not an easy task. This is be-
cause it mainly depends on the calibration and performance
of the specific cloud droplet probe. An advantage is that
the routine relies more on the sizing accuracy of the probe
rather than on the concentration measurements. Testing the
sizing calibration with a spinning disc or by releasing glass
beads across the probe laser beam is something that is nor-
mally done quite often during a field campaign. The accu-
racy of a properly calibrated cloud droplet probe is typically
higher than the resolution of the probe, i.e. approximately
±1µm. Our experience shows that drift in the concentration
calibration is more common, therefore it is important to cor-
rect this drift in the data analysis phase by e.g. comparing the
cloud droplet probe integrated LWC with the Hot Wire LWC,
which is usually more reliable as the measurement is quite
straight forward in comparison with the cloud droplet probe.
Then the droplet concentration could be multiplied by the
calculated correction factor, which may change even during
flight, while leaving the shape of the droplet size distribution
unchanged. Another key point for minimizing uncertainty in
Naestimation, is to avoid mixing clouds with bases at differ-
ent altitudes or with varying aerosol or thermodynamic prop-
erties in the same analysis. Such cases would cause a fairly
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12896 E. Freud et al.: Entrainment and activated CCN in convective clouds
large variation in Rv(or Re) for given LWCavalues, which
are calculated for the main cloud base. In order to exclude
data from penetrations to clouds with elevated bases, a filter
based on a minimum adiabatic fraction could be used (like in
the example shown in Fig. 2). Furthermore, penetrations with
well developed warm rain or ice formation should also be ex-
cluded from the analysis as large fraction of the drops are lost
to hydrometeors and the spectra of the remaining drops are
altered, hence changing Re,Rvand AF and consequently the
derived Na. This can be done by e.g. excluding measure-
ments with Re>13µm, which normally indicates effective
coalescence (Freud and Rosenfeld, 2011), and/or by using
the precipitation probe measurements. But because the vast
majority of the measurements in each profile have smaller Re
values than 13 µm, the derived Nais typically not sensitive to
whether this filter was applied or not. Some coalescence may
also take place at smaller Revalues but the limited time and
the partial droplet evaporation due to ongoing mixing help to
constrain the variations in Re.
If these requirements are satisfied, and the steps described
in Sect. 3 are followed, the derived Nais expected to repre-
sent quite well the number of activated CCN near the cloud
base or even the bases of a field of microphysically similar
clouds.
4 Results and discussion
We applied the methodology described in the previous sec-
tion to data collected in deep convective clouds over Israel,
India, the Amazon, Texas and California, under a variety
of meteorological conditions and aerosol characteristics. Na
was derived for each cloud profile (the profiling was not La-
grangian, but rather penetrating tops of consecutively grow-
ing convective clouds in a cloud cluster) and it ranged be-
tween 100 to 2500 per milligram of air, which occupies a
volume of approximately 1cm3at a typical cloud base alti-
tude of 1.5kma.s.l.
In the previous section we stated that coalescence becomes
active and drizzle particles start to form when Rereaches
∼13µm. This does not mean that no droplet coalescence
takes place at smaller Revalues, but the time is expected to
be a limiting factor to droplet growth in convective clouds at
small Revalues (Freud and Rosenfeld, 2011). Suppose that
we have two clouds with the same Na. One cloud grows very
fast (strong updrafts) and the other grows at a much slower
rate. Both eventually reach Re= 13µm. If time would play a
major role in the advancement of coalescence in clouds with
Re<13µm, the cloud that grows more slowly would have
reached 13µm at much lower altitude. This is not observed
to happen, because Reshows little variation at a given height
(e.g. Fig. 5 in Freud and Rosenfeld (2011) and Fig. 3 here),
which is explained mainly by the inhomogeneity of the mix-
ing. In addition, a closer look at Fig. 5 shows that the ratio
between Rvand Rebecomes more variable when Reexceeds
Fig. 7. Each data point represents RHbest that was calculated for one
cloud pass (and based on the derived Naof each profile) vs. LWCa,
which relates to the vertical dimension. The same color-coding
as in Fig. 5 is used with the addition of data from the Large-
Scale Biosphere-Atmosphere Experiment in Amazonia – Smoke,
Aerosols, Clouds, Rainfall, and Climate (SMOCC; Andreae et al.,
2004) in cyan. It appears like the highest RHbest values are found
near cloud base, indicating strong tendency towards extreme inho-
mogeneous mixing, maybe due to the small droplets and fairly weak
turbulence there.
13µm. This indicates that at Re<13µm droplets mainly
grow by condensation which maintains the shape of the DSD.
Only when droplet coalescence becomes sufficiently active
(at Re>13µm) the shape of the DSD may change by form-
ing a tail of larger droplets, depending on the droplet concen-
trations and the available time for droplet coalescence. This
would make the Rvto Reratio somewhat sensitive to the up-
drafts.
In addition, the coalescence rate increases linearly with the
cloud drop concentration for a given Re. Therefore, greater
AF is expected to cause precipitation initiation at smaller Re.
But we see no obvious evidence for that. We hypothesize
that this is because the higher adiabatic fractions are associ-
ated with stronger updrafts, leaving less time for coalescence
to advance with respect to samples with weaker updrafts and
smaller AF. This might serve as a compensating mechanism
for the effect of AF on rain initiation, leading to the robust-
ness of the dependence of Reon cloud depth. It would be in-
teresting look into this hypothesis with a multi-dimensional
cloud model that explicitly resolves DSD and entrainment-
mixing.
At the end of Sect. 2 we mentioned that the RH of the am-
bient air together with what we defined in Sect. 3 as RHbest,
can be used to assess the degree of mixing inhomogeneity.
Unfortunately we do not have accurate and reliable RH data,
but analyzing the derived RHbest values for many penetra-
tions can still be informative. Figure 7 shows the derived
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E. Freud et al.: Entrainment and activated CCN in convective clouds 12897
RHbest values of more than 500 penetrations in convective
clouds over Israel, India, the Amazon and Texas, versus
the adiabatic liquid water mixing ratio for each penetration,
which is a representation of the vertical dimension. There is
a fair amount of scatter in the data, but the median RHbest
is 95.25%. This value is definitely higher than the typical
RH aloft between the convective clouds, and therefore an in-
dication that in the vast majority of cases, the entrainment-
mixing process is far from fully homogeneous. A closer look
on RHbest in the vertical dimension may give the impression
that there is a weak tendency towards smaller RHbest values
at larger cloud depths or at least that the highest RHbest oc-
currences are concentrated near cloud base. This may be in-
terpreted as a weak tendency towards homogeneous mixing
at greater altitudes, as Small and Chuang (2010) reported in
their study based on few cases, but by using slightly different
methods. A possible explanation for this trend is that turbu-
lence aloft is more pronounced due to stronger updrafts aloft,
so τmix decreases. In addition the droplets are larger aloft so
τevap increases for a given RH. This results in a decrease in
the Damk¨
ohler ratio and hence a tendency towards homoge-
neous mixing aloft. Since we do not have accurate profiles of
ambient RH in the cloud-free air, our dataset does not enable
us to rule out that all apparent RHbest decrease aloft can be
explained by lower ambient RH at greater altitudes, which
is not uncommon in an unstable atmosphere with convective
clouds. But even if there were such RH measurements, most
entrained air comes from the direct vicinity of the clouds.
This air may be more humid due to the evaporated cloud
droplets and may produce humidity halos around the clouds
(e.g. Lu et al., 2003; Heus and Jonker, 2008). However, mea-
suring accurately the small changes in RH by a fast moving
aircraft is very challenging.
Moreover, in the simple model results shown in Fig. 1,
as in earlier publications, the mixing of entrained air is as-
sumed to occur with an adiabatic parcel at a constant level.
This is of course not necessarily true, as different parcels in
the clouds may have been exposed earlier to entrained air
at other altitudes. In convective clouds, the air can move
vertically quite rapidly, so if a mixing event at a low alti-
tude already caused a small reduction in Rv, and another
mixing event higher up caused an additional small reduc-
tion in Rv, the combined effect will result in a smaller de-
rived RHbest than when we assume exclusive one-level mix-
ing. This is because in one-level mixing the maximal Rvis
always Rvawhile in secondary mixing even if it is extremely
inhomogeneous, Rvwould be smaller than Rvaand RHbest
would be under-estimated. This might cause a false interpre-
tation of a trend towards homogeneous mixing aloft and may
partly contribute to the tendency seen in Fig. 7. In addition,
the preferential evaporation of the smaller droplets, which is
not accounted for in the simple homogeneous mixing model,
adds complexity and uncertainty, and requires a deeper anal-
ysis with detailed simulations. Therefore we cannot say that
we found proof for clear tendency towards less inhomoge-
neous mixing higher in the cloud, but clearly mixing has a
general tendency towards the inhomogeneous limit at all lev-
els as indicated by the high RHbest values.
Our interpretation of the high RHbest values is that the
entrained drier air quickly causes a total evaporation of the
cloud droplets that border the entrained parcel, so the en-
trained air gets more moist but cannot be considered as a
cloud at that point. As it approaches saturation, the molecu-
lar diffusion of vapor from the droplets to the sub-saturated
air slows down, increasing the time scale of the droplet evap-
oration, so further turbulent mixing with the cloud tends to
be more homogeneous. It appears that the entrained air is
pre-moistened (this term has been used by Burnet and Bren-
guier, 2007) in a nearly extreme inhomogeneous manner and
then is mixed more homogeneously as it approaches satura-
tion. Small and Chuang (2010) compared edges and cores of
clouds and found a similar tendency. At smaller scales than
that is measured with a 1Hz probe on an aircraft (∼100m),
mixing may have an increased tendency toward the homo-
geneous mixing type (Lehmann et al., 2009), but variations
in such scales cannot be resolved with our current dataset.
However, for applications requiring spatial resolutions of
∼100m and above, the mixing can be considered as highly
inhomogeneous.
As discussed in Sect. 3, taking into account the mixing in-
homogeneity is important for obtaining a better estimation
for Na. The example in Fig. 3 shows that using the final Na
(panel b), as compared to Nainit (panel a) that is based on the
extreme inhomogeneous mixing assumption, results in im-
proved overall fits of the RHbest curves to the data points.
This example is not unique, we find similar improvements in
all analyzed profiles (see more examples in the supplemen-
tary online material). The difference between Naand Nainit is
on average ∼30%, as Fig. 8 shows, regardless of location.
This means that it is important to account for the relative
inhomogeneity of the mixing at all levels despite the high
median RHbest (95.25%), which clearly indicates a strong
tendency towards the extreme inhomogeneous mixing limit.
What is also evident in Fig. 8 is that all data points fall above
the 1:1 dashed line. This is because the inhomogeneous mix-
ing assumption, which is made to derive Nainit, marks the up-
per limit of the Naestimation. If the actual mixing is more
inhomogeneous, then the difference between Naand Nainit
would be less pronounced.
Na, being an estimation of the number of activated CCN
near the cloud base, can be compared against the CCN con-
centrations at a given super-saturation that were measured
below cloud base. This may reveal some information about
the CCN activation process and/or instrument performance.
Such a comparison is shown Fig. 9. This plot displays data
from different locations, instruments and super-saturations,
as indicated in the figure legend. A perfect fit between the
CCN concentration at a given super-saturation and Nashould
not be expected because Naencapsulates the information
about cloud base updrafts, which the CCN concentration is
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12898 E. Freud et al.: Entrainment and activated CCN in convective clouds
0
1000
2000
3000
4000
5000
050010001500200025003000
ISRAEL
INDIA
AMAZON
TEXAS
NW EUROPE
CALIFORNIA
y = 1.3x R= 0.96
Activated CCN (Inhomogeneous) [mg-1]
Activated CC N [mg-1]
Fig. 8. Comparison of Nainit , which is based on extreme inho-
mogeneous mixing assumption, with the final derived Na, that as-
sumes homogeneous mixing with pre-moistened air. The color-
coding is the same as in Fig. 7, with added data from flights within
the projects of EUCAARI (European Integrated project on Aerosol
Cloud Climate and Air Quality interactions; Kulmala et al., 2009)
over the Netherlands and the North Sea (in orange) and SUPRECIP
(Suppression of Precipitation Experiment; Rosenfeld et al., 2008b)
over California (in red). Each data point here represents one pro-
file. The black linear best-fit and equation show that, on average,
Nais smaller than Nainit by ∼30 %. It does not appear like there are
significant differences between the different locations, as they fall
within the same range of slopes, although the Amazon and Texas
data stand out for having generally high and maybe slightly unrea-
sonable values of Na, which may be an indication of droplet under-
sizing by the cloud droplet probes (see Sect. 3.6).
independent of. Despite that, the linear fit for each loca-
tion separately, shown in Fig. 9, is fairly good (R>0.87), but
the different locations exhibit significantly different slopes.
This is probably due to the different instrumentation and cal-
ibrations used in each location and optionally different cloud
base updrafts. Taking into account the characteristic cloud
base updraft speed (Morales and Nenes, 2010) may help ex-
plaining some of the differences between the locations. How-
ever the relatively small variability around the fit within a
location indicates that the variability in updrafts cannot ex-
plain the very different slopes. This would be mainly caused
by the cloud drop spectrometer sizing and counting errors,
as well as the different calibrations of the CCN counters. If
the cloud droplet probe is calibrated properly and performs
well, the Nato CCN relationship can be used to roughly esti-
mate the characteristic cloud base updraft, providing that the
CCN spectra is known. That would be one example of an
applicable use of Na.
Another interesting finding which may be applicable, is
that Nawas not very sensitive to small variations in cloud
base altitude and did not differ significantly when the lower
part of the cloud profile was not considered. This is because
Fig. 9. CCN concentration vs. Na. Each data point denote a full
vertical profile in a deep convective cloud. The CCN concentra-
tions were measured below cloud base (with DMT CCN counters)
at different super-saturations as indicated in the legend. The color-
coding is similar to Figs. 7 and 8 and represents the different field
campaigns. Notice the fairly strong linear relationship in each field
campaign separately. The different slopes cannot be fully explained
by differing updrafts and super-saturations, but rather by the differ-
ent instruments and calibrations used.
the Naderivation utilizes information from different levels,
and the error in fractional adiabatic water becomes smaller
at greater cloud depths. This renders this methodology es-
pecially suitable for remote-sensing derivations, which nor-
mally do not “see” the lowest parts of the convective clouds.
5 Summary and conclusions
The study presented here aims at deriving the number of ac-
tivated CCN into cloud droplets near cloud base in deep con-
vective clouds. These clouds are prone to significant mixing
with entrained dry air, due to their relatively small horizontal
extent, strong turbulence and the fact that they tend to grow
into sub-saturated layers of air. Here we present a methodol-
ogy for deriving Nafrom data of substantially sub-adiabatic
clouds, by first assuming that the entrainment and mixing of
air into the cloud is extremely inhomogeneous. This yields
the upper limit for Na, which we refer to as Nainit and that
serves as a starting point for the fine tuning of the final Na
derivation as well as to obtain information regarding the na-
ture of the mixing process between the cloudy and the en-
trained sub-saturated ambient air.
The Naderivation methodology regards the cloud, or set
of clouds, as a unity, so Nais more like a macro-physical
property of the cloud or the cloudy domain, as long as the
aerosol properties and thermodynamics are fairly homoge-
neous. Narepresents the typical number concentration of
CCN that are activated into cloud droplets near the bases of
Atmos. Chem. Phys., 11, 12887–12900, 2011 www.atmos-chem-phys.net/11/12887/2011/
E. Freud et al.: Entrainment and activated CCN in convective clouds 12899
the measured cloud or cloud cluster. It is initially based on
the entire profile data and then tuned based on data of indi-
vidual cloud penetrations. Nais independent of the actual
amount of entrainment aloft, which can vary significantly
between clouds. In order to apply this methodology it is
necessary to penetrate convective clouds at different levels.
Preferably in horizontal penetrations from cloud base to the
level where significant precipitation is formed (i.e. not pre-
cipitation falling from above). Significant precipitation for
that matter means that more than a few percent of the cloud
water, as measured by a precipitation probe, has been con-
verted into hydro-meteors (e.g. Freud and Rosenfeld, 2011).
The described methodology may also be applied to shallow
convective clouds, but the confidence in the derived Namay
be slightly reduced due to potential increase in Nasensitivity
to sizing errors of the cloud droplet probe and small varia-
tions/errors in cloud base properties (Sect. 3.6). Applying
the methodology to stratiform clouds is typically not as ad-
vantageous compared to the methods that have been used al-
ready for such clouds (e.g. Bennartz, 2007) because nearly
adiabatic cloud parcels, in which droplet concentrations are
essentially Na, are very common.
After applying the methodology described in Sect. 3 to
a large set of data collected in Israel, India, the Amazon,
Northwestern Europe, Texas and California, we conclude the
following:
–R3
v(and R3
e) grows nearly linearly with the adiabatic
water mixing ratio in deep convective clouds before sig-
nificant droplet coalescence takes place, at a rate that
primarily depends on Na.
–Nais closely related to the CCN concentrations. Char-
acteristic updrafts and cloud base super-saturations may
be derived from this relationship and the measured CCN
activation spectra.
–Mixing of sub-saturated air into the cloud according to
our dataset and spatial resolution appears to be strongly
inhomogeneous, but does not reach the extreme inho-
mogeneous limit. The results presented here support the
thesis that the entrained air is pre-moistened by quickly
evaporating cloud droplets at first and then mixes more
homogeneously as it approaches saturation.
–It appears like mixing may be less inhomogeneous
higher in the cloud due to the larger cloud droplets and
stronger turbulence there. Drier air aloft and the history
of mixing at lower levels of the cloud may also con-
tribute the this observed trend.
Supplement related to this article is available online at:
http://www.atmos-chem-phys.net/11/12887/2011/
acp-11-12887-2011-supplement.pdf.
Acknowledgements. Some of the examples presented in this paper
rely in parts on data obtained from the Cloud Aerosol Interaction
and Precipitation Enhancement Experiment (CAIPEEX) of the
Indian Institute of Tropical Meteorology (IITM), with J. R. Kulka-
rni as a program manager and B. N. Goswami as the director.
Additional examples are based on data from Texas, with D. Axisa
having taken the lead on the instrumented aircraft, data collection
and quality control. Some additional aircraft data are taken from
the European Integrated Project on Aerosol Cloud Climate Air
Quality Interactions (EUCAARI) in northwestern Europe, and
from the Smoke Aerosols, Clouds, Rainfall and Climate (SMOCC)
aircraft campaign in the Amazon. Both EUCAARI and SMOCC
were funded by the European Commission. Data are used also from
the research flights of the Israeli rain enhancement program funded
by the Israeli Water Authority, and from the SUPRECIP campaign
in California, funded by the California Energy Commission.
The authors would like to express their gratitude to all sponsors,
partners and collaborators for their efforts in collecting these
valuable and extensive datasets.
Edited by: A. Nenes
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