A.Mary Selvam, A.S.Ramachandra Murty and Bh.V. Ramanamurty

Indian Institute of Tropical Meteorology, Pune 411 008, India

*Proc.of the XI Int. Conf. on Atmospheric Aerosols,
Condensation and Ice Nuclei, 2-7 Sept.1984, Budapest, Hungary, 77-81.*

(Retired) email: selvam@ip.eth.net

Website: http://www.geocities.com/CapeCanaveral/Lab/5833

**Abstract**

A simple model which can explain the observed vertical
distribution and size spectrum of atmospheric aerosol has been proposed.
The model is based on a new physical hypothesis for the vertical mass exchange
between the troposphere and the stratosphere. The vertical mass excange
takes place through a gravity wave feedback mechanism. There is a close
agreement between the model predicted aerosol distribution and size spectrum
and the observed distributions.

**Introduction**

Information on the distribution of atmospheric aerosol
is important for the understanding of the physical processes relating to
the studies in weather, climate, atmospheric electricity, air pollution
and aerosol physics. Based on certain physical and dynamical processes
taking place in the *atmospheric boundary layer* (ABL), a simple model
which can explain the observed vertical distribution of atmospheric aerosols
has been proposed in the following. It is shown that the observed aerosol
distribution is due to vertical mass exchange between the troposphere and
the stratosphere. The physical basis and the theory relating to the model
are discussed below.

**Physical Mechanism**

A gravity wave feedback mechanism for the vertical
mass exchange between the troposphere and the stratosphere has been proposed.
The vertical mass exchange takes place through a chain of eddy systems.
The ABL contains large eddies (vortex rolls) which carry on their envelopes
turbulent eddies of surface frictional origin (ref.1). It is shown that
the buoyant production of energy by *microscale-fractional-condensation*
(MFC) in turbulent eddies is responsible for the sustenance and growth
of large eddies(ref. 2). The buoyant production of turbulent energy by
the MFC process is maximum at the crest of the large eddies and results
in the warming of the large eddy volume. The turbulent eddies at the crest
of the large eddies are identifiable by a *microscale-capping-inversion*
(MCI) layer which rises upwards with the convective growth of the large
eddy in the course of the day. The MCI layer is a region of enhanced aerosol
concentrations. As the parcel of air corresponding to the large eddy rises
in the stable environment of the MCI *Brunt Vaisala* oscillations
are generated (ref.2). The growth of the large eddy is associated with
generation of a continuous spectrum of gravity (buoyancy) waves in the
atmosphere. The atmosphere contains a stack of large eddies. Vertical mixing
of overlying environmental air into the large eddy volume occurs by turbulent
eddy fluctuations (ref.1). The circulation speed of the large eddy is related
to that of the turbulent eddy according to the following expression

(1)

where ** W** and

The total fractional volume dilution rate of the large eddy by vertical mixing across unit cross-section is derived from Eq.(1) (ref.1) and is given as follows:

(2)

where *w***_{*
}**is the increase in vertical velocity
per second of the turbulent eddy due to MFC process and

The fractional volume dilution rate ** k**
is equal to

From Eq.(2) the following logarithmic wind profile relationship for the ABL is obtained (ref. 1).

(3)

The steady state fractional upward mass flux ** f**
of surface air at any height

(4)

where ** f** represents the steady state
fractional volume of surface air at any level

The model predicted aerosol vertical distribution
are computed using Eq.(4) and are shown in Fig. 1. The model predicted
profiles closely resemble the observed profiles reported by other investigators
(ref. 3). The peaks in the aerosol concentration at 1 km (*lifting condensation
level*) and at about 10-15 km (*stratosphere*) identify the MCI
at the crests of the convective and meso-scale eddies respectively. Earlier
it was shown that the scale ratios for the convective and meso-scale eddies
are respectively 10 and 100 with respect to the turbulence scale. Thus
for the turbulent eddy of radius 100m, the MCI's for the convective and
meso-scale eddies occur at 1 km and 10 km respectively.

The vertical mass exchange mechanism predicts the
** f** distribution for the steady state vertical transport of
aerosols at higher levels. Thus aerosol injection into the stratosphere
by volcanic eruptions gives rise to the enhanced peaks in the regions of
MCI in the stratosphere and other higher levels determined by the radius
of the dominant turbulent eddy at that level.

The time ** T** taken for the steady state
aerosol concentration

(5)

The vertical dispersion rate of of aerosols/pollutants
from known sources (e.g., volcanic eruptions, industrial emissions ) can
be computed using the relation for ** f** and

**Atmospheric Aerosol Size Spectrum**

The atmospheric eddies hold in suspension the aerosols and thus the size spectrum of the atmospheric aerosols is dependent on the vertical velocity spectrum of the atmospheric eddies as shown below.

From the logarithmic wind profile relationship ** W**
can be expressed as

(6)

The aerosols are held in suspension by the eddy vertical
velocity perturbations. Thus the suspended aerosol mass concentration ** m**
at any level

(7)

where *m***_{*
}**is the suspended aerosol mass concentration
in the surface layer. Let

Substituting for the average mass concentration in terms of mean radius and number concentration

(8)

The number concentration of aerosol decreases with
height according to the ** f** distribution which can be expressed
as follows:

*N = N _{*}
f*

(9)

*r = r _{*}z^{1/3}*

(10)

The mean aeosol size increases with height according
to the cube root of ** z** . As the large edy grows in the vertical,
the aerosol size spectrum extends towards larger sizes while the total
number concentration decreases with height according to the

*dN = N _{*}
f dW*

i.e., *f = (1/ N*_{*}
)( dN/ dW)

From the logarithmic wind profile relationship (Eq.3) it follows that

Therefore

(11)

In steady state atmospheric conditions the aerosol
number concentration at any level is determind by the upward and downward
transports each of which follow the ** f** distribution. Hence
the total number concentration of aerosols follow the

A graph of ** ln(f^{2/ln3)}** )
versus

The particles which scatter visible light occur normally
in the size interval where the spectral slope is -3. This gives rise to
the normal blue colour of the sky. However in the regions of high humidity
or in the presence of volcanic dust clouds, the minimum particulate size
*r***_{*}**(Eq.10)
increases and thus the spectral slope become less than

**Conclusion**

There is a close agreement between the model predicted and the observed aerosol distributions. The physical hypothesis relating to the dynamics of the atmospheric eddy systems proposed in the present paper can be extended to other planetary, solar and stellar atmospheres. The dust/particle rings observed around the major planets, and the sun and some galaxies may be explained based on the above physical hypothesis. It is probable that a steady state particle flux between various galaxies in the universe takes place through cosmic eddy systems by the same mechanism.

**References**

1. A.Mary Selvam, A.S.R.Murty and Bh.V.Ramana Murty,
A new hypothesis for vertical mixing in clouds. Preprint volume, 9^{th}
International Cloud Physics Conference, Tallinn, USSR, (1984).

2. A.Mary Selvam, A.S.R.Murty and Bh.V.Ramana Murty,
Role of frictional turbulence in the evolution of cloud systems, Preprint
volume, 9^{th} International Cloud Physics Conference, Tallinn,
USSR, (1984).

3. E.C.Junge, Air chemistry and radioactivity, Academic Press, London, 1963, pp.382.