3. Numerical results
Ž The model runs to be presented in this section start at midnight local time 00.00 h in
. the model simulations . With each aerosol size distribution, a 24-h run is performed. The
initial vertical temperature profile at 00.00 h is given by a dry adiabatic stratified atmosphere in the lowest 700 m with the temperature at the first grid point equal to the
sea surface temperature of 288.4 K. At 700 m, a strong temperature inversion of 8 K is applied. Above this inversion level, the lapse rate is set constant to y0.006 K m
y1
. In Ž
.
y1
the lowest 700 m, the initial specific humidity is q s min q , 0.0085 kg kg . Above
s
the inversion level, q s 0.004 kg kg
y1
. At the sea surface, the saturation specific humidity q is utilized. In all layers, the initial horizontal wind speed is set equal to the
s
Ž .
Ž .
y1
geostrophic wind of u , Õ s 6.0, 0.0 m s . The large-scale subsidence is held fixed
g g
at y0.006 m s
y1
.The numerical discretization in space and time as well as the integration techniques are the same as in BTZ and are, therefore, not repeated here.
Fig. 2 shows for the first model run vertical profiles of the effective radius at the times indicated in the figure. The layers where the liquid water content exceeds 0.05 g
m
y3
define the cloudy region. In these layers r 0. It is seen that during the model
e
simulation, cloud top remains constant at 690 m. In contrast to this, the base of the cloud
Fig. 2. Vertical profiles of the effective radius at the times indicated at the top of the figure. Model run 1.
is gradually decreasing, until the cloud touches the ground at midnight. This is due to the formation of drizzle, which at this time has already reached the ground. From the
figure, it is also seen that r is increasing with decreasing height within the cloud. This
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is explained by the fact that the concentration of the larger drizzle drops is increasing in lower cloud layers. Near the cloud base, the main liquid water content is mainly found
in the large drops with radii exceeding 50 mm. Model run 1 was the only case study where the drizzle reached the ground. The
reason for this is that in the remote maritime situation, the total number concentration of cloud condensation nuclei is very low, yielding only few but relatively big cloud
droplets. This favors the formation of drizzle by the collision process, which becomes very effective in the case where large cloud droplets are produced.
Fig. 3 shows the vertical profiles of r at the same times as Fig. 2 but now for model
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run 2, i.e., the mixture of 75 maritime and 25 rural aerosol. By comparing this figure with Fig. 2, it becomes apparent that the effective radius is now distinctly lower than in
model run 1. Note the different scale of the abscissa in both figures. Apart from the 24.00 h curve, the values of r are always lower than 12 mm in contrast to model run 1
e
with r 15 mm. At 24.00 h, drizzle formation is again observed at cloud base.
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However, the drizzle is now much weaker than in the first model run and, therefore,
Fig. 3. Same as Fig. 2 but for model run 2.
does not reach the ground. It is also seen that cloud top increases with time. This is due to the different microstructure of the cloud with many but relatively small cloud droplets
as compared to model run 1. As a consequence of this, the reflectivity of the cloud is larger in run 2 than in run 1, now yielding an efficient backscattering of the incoming
Ž .
solar radiation. For more details on this process, the reader is referred to Bott 1997 . Ž
. In model runs 3–5, this trend is continued see Figs. 4–6 . With increasing fraction
of the rural aerosol component the effective radius becomes smaller whereby at the same time drizzle formation is more and more inhibited. From Figs. 5 and 6, it is seen that in
all cloud layers and at all times, the effective radius is smaller than 10 mm. Furthermore, the values remain much more constant throughout the entire cloud because now drizzle
formation is almost no more observed.
Figs. 2–6 have shown that due to the fine resolution with vertical grid distances of D z s 10 m, in MISTRA it is possible to obtain very detailed information about the
vertical variation of r within the cloud. Thus, it could be seen that in case of drizzle
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formation at some locations within the cloud, the effective radius might reach values exceeding 50 mm, see e.g., the 24.00 h curve of Fig. 2. On the other hand, in large-scale
models, the vertical resolution is much coarser so that usually, only an average value of the effective radius is used for the determination of the radiative properties of the cloud.
Fig. 4. Same as Fig. 2 but for model run 3.
Fig. 5. Same as Fig. 2 but for model run 4.
In order to obtain this value for the five model runs of the present investigation, it seems appropriate to introduce a weighted average of the effective radius r whereby
e
the liquid water content is taken as the weighing function. Hence, r is defined by:
e
z
1
r z m
z d z
Ž . Ž .
H
e w
z
r s 6
Ž .
e
z
1
m z d z
Ž .
H
w
z
with z and z
are the cloud base and top, respectively, and m is the cloud water
1 w
content at height z. Fig. 7 shows for the five model runs the time evolution of r . As was to be expected,
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r is largest in model run 1 with pure maritime aerosol particles. Furthermore, a strong
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time variation of r can be observed with values ranging between 15 and 30 mm. The
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largest values are observed during the night when drizzle is formed in the lower region of the cloud. During the day, the solar irradiation tends to partially evaporate the cloud
yielding minimum values of r at this time.
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In contrast to model run 1 with pure maritime aerosols in the other four model runs, the effective radius is distinctly smaller with much less pronounced variation in time.
Fig. 6. Same as Fig. 2 but for model run 5.
Even though the fraction of the rural aerosol component is linearly increasing from 25 in model run 2 to 100 in model run 5, this linear behavior is not observed in the values
of r . It is concluded from these findings that a small fraction of rural aerosol
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components in the total aerosol spectrum has a strong impact on the value of the effective radius. In other words, as long as there is any influence of continental air
masses at a particular location over the ocean, it seems to be appropriate to use the lower continental values of the effective radius in comparison to pure maritime situations.
From the results of the present investigation, it can be seen that in all case studies the effective radius is relatively constant with height with an additional peak in lower cloud
layers, which is due to drizzle formation. These findings are in contrast to corresponding Ž
. observations see, e.g., Nicholls, 1984 . While the peak of r at cloud base as caused by
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drizzle seems to be realistic, the field measurements indicate that usually r increases
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with height in an almost linear way. The reasons for the discrepancy between the numerical calculations and observations is explained by the fact that MISTRA is a
one-dimensional model of the cloud-topped planetary boundary layer which is based on the assumption of horizontal homogeneity of all variables. Hence, only average values
of all thermodynamic quantities can be calculated. As a consequence of this, the activation of cloud droplets in the model does not take place at cloud base where the
Fig. 7. Time evolution of the mean effective radius r for the five model runs.
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relative humidity is below 100 because it is an average over up- and downdraft regions of the cloud. However, according to the field observations, the activation of
cloud droplets takes place in the updraft regions at cloud base where the supersaturation is largest. A detailed discussion of this problem of one-dimensional cloud models may
Ž .
Ž .
be found in Bott et al. 1997 and Brown 1997 . Nevertheless, the main conclusion of the present investigation, that is the influence of the physico-chemical properties of
aerosols on the size of the mean effective radius, is barely affected by this model artifact. The reason for this is that in all cloud layers, the values of r change in the
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same way as a function of the particular choice of an aerosol spectrum. At present, we are working on an improvement of MISTRA by including the effect of updraft and
downdraft regions on the microphysical evolution of the particle spectrum.
4. Summary and conclusions
Kategori