TRRNSMISSION
7.5 Calculation of LIDAR extinction coeffi- cients
computed atmospheric transmission profiles at four SAGE II wavelengths:
1.0psix, 0.6 psi», 0.45 /-Lm and 0.385 ps»,
50
40
20
A. l.0 /lm
.B. 0.6/1m c. 0.45 /lm n. O. 3il5JJffi
where each term has been defined previously in section (2.8) of Chapter 2.
In equation (6.1) the extinction term is written as an integral over the two-way path from the LIDAR to the scattering volume.
In analysing the LIDAR data it is often convenient to use the backscatter ratio R(z) (Russell et al. 1979) which is defined as the ratio of the total backscatter coefficient to the molecular backscatter coefficient:
(7.6)
where f3a(z) and f3m(z) are the aerosol and molecular backscattering coeffi- cients respectively.
The Klett inversion method (Klett 1981; Klett 1985) has been used to solve the LIDAR equation to obtain the total volume extinction coefficient cr(z). The method reduces the LIDAR equat ion to a Bernoulli differential equation which is convergent for z :::; zre! where zre! is a reference alti- tude chosen above the aerosol layer where the particle content is negligible.
The determination of the total volume extinction coefficient f3(z) from equa- tion (6.1) requires quantitative knowledge of a relationship between cr(z) and j3(z) usually expressed as a ratio called the backscatter phase function w(z)
= ~~~~.
This ratio represents contribution from Rayleigh scattering by moleculesW m and scattering by aerosols W a :(7.7)
( )_ f3a(Z)
Wa Z - ( ) a« Z
(7.8)
whereW m is the Rayleigh baekscatt er phase functionfor molecularscattering and is equal to
~ ~
0.119 sr-1 (Chazetteet
al. 1995) andwa(z)
is the87f
aerosol baekscatter phase function which depends on the size distribution and refractive index of the aerosols, and can therefore vary with altitude.
The backscatter phase function for aerosols may lie in the range 0.013 sr-1 to 0.030 sr-1. This interval has been deduced from SAGE II data (Ackerman
et
al. 1989) and Mie scatteringtheory. Table (7.2)shows a comparison of the values of the aerosol backscatter phase functions following the El Chichon and Mount Pinatubo eruptions calculated by several workers using LIDAR (Thomas et al. 1987; Jager and Hofmann 1991; Chazette et al. 1995), SAGE II satellitedata (Ackermanet
al. 1989) and radiosonde measurements (Deshler et al. 1993). As shown in table (7.2), the values of the aerosol backscatter phase function are largefollowing major volcanic eruptions. This increase in the aerosol backscatter phase function is due to large injection of dust and sulphur ous gases such as sulphur dioxide in the stratosphere.Year 1983 1984/1985 1991 to 1993 Chazette et aL (1995) 0.025 sr -1 0.016 sr 1 0.025 sr 1
using LIDAR
Jager and 0.017 sr Ito 0.024 sr 1 Hofmann (1991) using LIDAR 0.045sr 1
Ackerman et aL (1989) 0.013 sr Ito
using SAGE II 0.025sr 1
Deshler et aL (1993) 0.015 sr lat 17 km
using balloo n measurement s 0.026 sr lat 19km
0.015 sr lat 23km
Table 7.2: Values of the aerosol backscat t er phase functi on following the El Chichon and Mount Pinatubo er uptions obt ained using LIDAR, SAGE II and balloon measurements.
Wm has been computed using the Cl RA-1986 model. The determina-
tion of the backscatter phase function due to aerosols to.; from the LIDAR measurements requires several assumptions. First ,W a is assumed to remain constant wit h alt itude. This assumption has been shown by Chazet te et al.(1995) to be representative of the alt itude range where the backscatter coefficient ismaximum and the values ofWa obtained are in agreement wit h other in situ and LIDAR measurement s. Second ly, it is assumed that the scattering rati o R(z) (equ ati on (7.6)) remains close to 1.00 at and above the reference alt it ude, zre/'
The valu e of W a in the stratosphere following maj or volcanic eru ption is large but decreases during the post-volcanic perio d. For example, during the period following the El Chichon eruption in 1983, rep orted average valu e of
q;a
using LIDAR dat a at Observatoire de Haute-Provencs in Sout hern France (Ch azet t e et al. 1995) is 0.023±
0.003 sr-1 but decreases to 0.016±
0.004 sr-1 during the years 1984 to 1985. For background aerosols which are
located around 20km (Junge 1961)W a has an estimated value of 0.018 sr-I. Due to biomass and large scale sugar-cane burning which occurs from June to October over the Kwazulu-Natal coast and also the large concentra- tion of chemical industries in the south of Durban, we consider the strato- sphere above Durban to be loaded in aerosol. For the present study, we estimate that a value of Wa = 0.020 sr-1 will be suitable for the altitude range of the L1DAR measurement (20 km ~ Z ~ 60 km). In the Klett in- version method, zref is chosen to be 40 km as we assume there will be no aerosol present at and above this height. We also assume that the scattering at and above 40 km is only due to air molecules and R(z) ~ l.
The uncertainties in the determination of the total volume backscatter coefficient (3(z) arise from the following causes:
(1) statistical fluctuations of the measured L1DAR signal which are asso- ciated with random detection processes,
(2) the presence of aerosol particles at and above the reference altitude
zref and the subsequent uncertainty in the value of R(zref),
(3) the uncertainty in the phase function Wa and its altitude dependence.
The first uncertainty in the statistical fluctuations of the measured L1- DAR signal can be reduced by averaging all the L1DAR raw data during the acquisition period which is 4 to 5 hours. This leads to a statistical uncer- tainty of less than 2.5
%
(Chazette et al. 1995). The next two uncertainties are reduced when zref is approached in the Klett inversion algorithm. zrefis chosen as high as possible so as to minimise the uncertainty due to low aerosol loading at higher altitude. The total uncertainty associated with all the three causes is less than 7
%
when the signal-to-noise ratio is significantabove 40 km (Chazette et al. 1995).