model MISTRA have been performed. The sensitivity studies consist of five different model runs. In each of the model runs, all initial data are the same with the only
exception that the number concentration and the chemical composition of the aerosol particles differ in each model run. In Section 2, a short summary of the governing model
equations of MISTRA will be given. In Section 3, the numerical results of the five model studies are presented while Section 4 summarizes the findings of the sensitivity
studies.
2. Description of MISTRA
Since a detailed model description of MISTRA is already presented in Bott et al. Ž
. Ž .
1996 henceforth abbreviated as BTZ , only a short summary of the governing model
equations will be given here. The model is one-dimensional and consists of a set of prognostic equations for the ensemble mean values of the components u and Õ of the
horizontal wind, of the specific humidity q and the potential temperature u. In these equations, the most important processes being considered are vertical advection, turbu-
lent mixing, radiative heating, condensationrevaporation and the collisionrcoalescence of cloud droplets.
In the microphysical part of the model, aerosol particles and cloud droplets are Ž
. treated in a joint two-dimensional particle spectrum f a, r . The size distribution of the
dry aerosol particles with radius a is subdivided into 30 classes with 0.01 F a F 10 mm. In each of the 30 aerosol classes, the particles may grow due to the uptake of water
Ž .
vapor, thus, forming humidified aerosol particles or in case of their activation cloud droplets with total radius r. Along the r-coordinate, the particle spectrum is subdivided
into 100 water classes with a F r F 50 mm yielding altogether a spectral distribution of Ž
. Ž
. 3000 particles f a , r
with different combinations of a , r
i s 1, . . . ,30, j s
i j
i j
Ž .
1, . . . ,100. Thus, a set of 3000 prognostic equations for f a , r describes the time
i j
evolution of the aerosol particles and cloud droplets. In addition to the processes mentioned above, gravitational settling of the particles and the collisionrcoalescence of
droplets are also accounted for in these equations. The activation of aerosol particles to form cloud droplets, as well as their diffusional growth, are explicitly calculated by
solving at all relative humidities 30 coupled droplet growth equations according to the subdivision of the particle distribution into 30 aerosol classes. Radiative effects are also
included in the droplet growth equation. For more details about this treatment, see Bott
Ž .
et al. 1990 . In general, aerosol particles consist of different fractions of water-soluble and water
unsoluble material. Important water-soluble substances are sodium chloride, ammonium nitrate and ammonium sulfate. Water unsoluble substances are mineral dust, organic
materials, etc. The chemical composition of an aerosol particle largely depends on the mechanisms of its formation. For instance, in the remote marine environment, aerosol
particles mainly consisting of ammonium sulfate or ammonium bisulfate originate from
Ž .
the oxidation of dimethyl sulfide which is emitted from the oceans Bigg et al., 1984 . Over the continents, airborne clays and other disrupted soil particles are important
components of the aerosol particles. Apart from their chemical composition, the total aerosol number concentration is also largely varying depending on their origin. From
Ž .
measurements of aerosol size distributions over the Atlantic Ocean, Hoppel et al. 1990 clearly identified a transition from continental to marine type aerosol particles whereby
the total number concentrations were strongly decreasing with increasing distance from the continent.
In order to investigate the importance of the physico-chemical properties of aerosol particles on the evolution of stratiform clouds, in Section 2 the numerical results of five
model runs with MISTRA will be presented. In each model run, the initial meteorologi- cal conditions are the same with the only exception that the aerosol size distribution will
be different. Each of the utilized aerosol spectra is given by the sum of three log–normal
Ž .
size distributions Bott, 1997 :
2
3
d n n
log arR
Ž .
a a , i
i
s exp y
2
Ž .
Ý
2
dlog a
ž
2p log s 2 log s
Ž .
i
is1
i
In model run 1, a typical maritime aerosol spectrum will be used. For this case, the Ž .
coefficients appearing in Eq. 2 have been determined in such a way that they fit with Ž
. measurements of marine aerosol size distributions by Hoppel and Frick 1990 . These
coefficients are given by: n
s 100 R s 0.027
log s s 0.25
a ,1 1
1
n s 120
R s 0.105 log s s 0.11
3
Ž .
a ,2 2
2
n s 6
R s 0.120 log s s 0.45
a ,3 3
3
The marine aerosols are assumed to consist of pure ammonium sulfate, i.e., they are Ž .
Ž . completely water-soluble. The aerosol spectrum resulting from Eqs. 2 and 3 is
depicted as curve 1 in Fig 1. For the chosen size range between 0.01 and 10 mm, the total number concentration is 181 particles cm
y3
. In model run 5, a typical rural aerosol size distribution will be utilized. The
Ž . Ž
. corresponding coefficients in Eq. 2 are Jaenicke, 1988 :
n s 6650
R s 0.0074 log s s 0.225
a ,1 1
1
n s 147
R s 0.0269 log s s 0.557
4
Ž .
a ,2 2
2
n s 1990
R s 0.0419 log s s 0.266
a ,3 3
3
The chemical composition of the rural aerosols is assumed to be a mixture of ammonium sulfate and mineral dust whereby the water-soluble fraction is linearly
decreasing from 90 for the smallest to 50 for the largest aerosol particles. This size-dependent partitioning of the water-soluble and unsoluble mass fraction is based on
Ž .
measurements by Winkler 1974 . The resulting rural aerosol spectrum has a total number concentration of 3842 particles cm
y3
and is given by curve 5 of Fig. 1. Model runs 2, 3 and 4 are considered to simulate the transition from the remote marine to the
continental environment. In these model runs, the aerosol spectrum is assumed to consist
Fig. 1. Aerosol size distributions of the five model runs.
Ž of a mixture of the rural and the maritime size distribution with model run 2 75
. Ž
. maritime and 25 rural , model run 3 50 maritime and 50 rural and model run 4
Ž .
25 maritime and 75 rural aerosols. The resulting total number concentrations are 1097, 2012 and 2927 particles cm
y3
, respectively. The particle spectra are given as curves 2, 3 and 4 in Fig. 1.
In BTZ, it has already been mentioned that the activation of aerosol particles to form cloud droplets depends on their size and chemical composition as expressed by the
Kohler equation:
¨
e a, r A
B
Ž .
S a, r s s exp
y 5
Ž .
Ž .
3 3
ž
e r
r y a
s
Ž .
Here, e a, r is the equilibrium water vapor pressure at the particle’s surface and e is
s
the saturation vapor pressure over a plane water surface. Arr is the so-called curvature Ž
. term describing the increase of e a, r due to the curvature of the particle’s surface
Ž .
Ž
3 3
. Kelvin effect , while Br r y a
is the solution term yielding a reduction of the water Ž
. vapor pressure due to dissolved salts within the particle Raoult’s law . The constants A
Ž .
and B are taken from Pruppacher and Klett 1997 .
3. Numerical results
