1. Ratish Menon CAPITA Group Seminar August 2, 2010
Inversion of Particle Size Distribution from Spectral Extinction Coefficient Measurements
Ratish Menon
CAPITA Group Seminar
August 2, 2010

2. Background
Size distributions provide an insight into the sources and composition of the atmospheric aerosols
Spectral extinction is a function of particle size distribution

4. Inversion Tool
Aerosol size distribution,displayed as a volume distribution function (dV/dlogDp), is expressed as the set of 11 narrow size distributions covering the size range 0.1 to 10 μm
Each volume distribution has same integral of aerosol volume
Shape of the extinction curve depends on the characteristic diameter
Magnitude of the extinction curve depends on the aerosol cross section available in the considered aerosol volume

5. Extinction Calculations
All calculations were carried out using MieTab 7.24
Refractive index of the particles was assumed to be i
The Probability distribution functions (PDFs) were calculated using the equation
F(R) = EXP(-((LOG(R)-LOG(RBAR))**2)/(2(LOG(SIGMA))**2),
where f(r)dr is the relative number of particles with radii between r and r+dr.
Rbar is the mean diameter.
The distribution is normalized so that the integral of f(r)dr over all r yields 1.0.
Note that log(sigma) plays the role of the standard deviation in this model.
Sigma used in the current calculations=1.325
Narrow size distributions were selected such that their volume mean diameters are at 60% increment on the semi-log scale.
Volume distributions were derived by multiplying the total volume of the distribution with the PDF.
Number mean diameter was calculated from the volume mean diameter for each size distribution using the equation
Dn= Exp( (Dv-3*(lnσ )2))*0.5 where, Dn =Number mean dia; Dv=Volume mean dia; σ = Std.Deviation
Number density was calculated by dividing Integral aerosol volume of the distribution with the volume of a single particle having a diameter equal to number mean diameter
The major parameters provided as input to Mie program include number mean dia, number density, and geometric standard deviation

6. CASE 1- Kanpur AERONET Data on 2006-02-14 (Winter)
Wavelength
AOT
0.34
0.4882
0.38
0.469
0.44
0.4087
0.5
0.675
0.2637
0.87
0.2079
1.02
0.1757

7. CASE 2- Kanpur AERONET Data on 2006-06-14 (Summer)
Wavelength
AOT
0.34
0.38
0.44
0.5
0.675
0.87
1.02

8. CASE 3- Kanpur AERONET Data on 2006-11-14 (Agricultural burning over IGP)
Wavelength
AOT
0.34
0.38
0.44
0.5
0.675
0.87
1.02

9. Non-Uniqueness in Solution
An alternative set of volume distribution can provide identical quality of fit

10. Discussion
The method to be extended for spectral reflectance measurements for satellite data to be useful?
Would use of spectral extinction measurements (from AERONET) together with spectral reflectance measurements (from satellite sensors) be a good approach to arrive at a unique solution?

11. Thank you