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A New Hypothesis for the Vertical Distribution of Atmospheric Aerosols
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: [email protected]
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.
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.
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
where W and w are respectively the r.m.s (root mean square) circulation speeds of the large and turbulent eddies and R and r are their respective radii.
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:
where w* is the increase in vertical velocity per second of the turbulent eddy due to MFC process and dW is the corresponding increase in vertical velocity of large eddy.
The fractional volume dilution rate k is equal to 0.4 for a scale ratio ( z ) i.e., R/r =10 . Identifiable large eddies can exist in the atmosphere only for scale ratios more than 10 since, for smaller scale ratios the fractional volume dilution rate k becomes more than half. Thus atmospheric eddies of various scales i.e., convective, meso-, synoptic and planetary scale eddies are generated by successive decadic scale range eddy mixing process starting from the basic turbulence scale (ref.2).
From Eq.(2) the following logarithmic wind profile relationship for the ABL is obtained (ref. 1).
The steady state fractional upward mass flux f of surface air at any height z can be derived using Eq.(3) and is given by the following expression (ref. 1).
where f represents the steady state fractional volume of surface air at any level z . Since atmospheric aerosols originate from surface, the vertical profile of mass and number concentration of aerosols follow the f distribution.
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 f to be established at the normalised height z is equal to the time taken for the large eddy to grow to the height z and is computed using the following relation.
where li is the logarithm integral.
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 T (Eqs. 4 and 5).
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
The aerosols are held in suspension by the eddy vertical velocity perturbations. Thus the suspended aerosol mass concentration m at any level z will be directly related to the vertical velocity perturbation W at z i.e., W=mg where g is the acceleration due to gravity. Eq.6 can be expressed as follows:
where m* is the suspended aerosol mass concentration in the surface layer. Let r and N represent the mean radius and number concentration of aerosols at level z . The variables r* and N* relate to corresponding parameters at the surface levels.
Substituting for the average mass concentration in terms of mean radius and number concentration
The number concentration of aerosol decreases with height according to the f distribution which can be expressed as follows:
N = N* f
From Eq.(8) it follows that
r = r*z1/3
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 f distribution. The variable f can be expressed in terms of the incremental growth dW of the large eddy across unit crosssection on its surface as follows. Let dN denote the number concentration of aerosols in the ascending volume dW of the large eddy.
dN = N* f dW
i.e., f = (1/ N* )( dN/ dW)
From the logarithmic wind profile relationship (Eq.3) it follows that
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 f 2 distribution. With the aeosol source at the surface the aerosol size spectrum in the steady state atmospheric conditions can be expressed as follows:
A graph of ln(f2/ln3) ) versus lnr is shown in Fig.2. The computed aerosol size spectrum is identical to the Junge aerosol size spectrum. The aerosol number concentration initially increases with size for small sizes and for further size increase, the aerosol number concentration decreases steeply. The slope of the spectrum ranges from -2 to -4.8, in the decreasing number concentration size range.
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 3 and sometimes shifts to the peak region of the spectrum for the visible light scattering particles size range. This results in anomalous turbidities with whitish sky colour.
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.
1. A.Mary Selvam, A.S.R.Murty and Bh.V.Ramana Murty, A new hypothesis for vertical mixing in clouds. Preprint volume, 9th 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, 9th International Cloud Physics Conference, Tallinn, USSR, (1984).
3. E.C.Junge, Air chemistry and radioactivity, Academic Press, London, 1963, pp.382.
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