SECTION II

VERTICAL DISTRIBUTION OF OZONE

2.1 The prob1em of distribution of ozone with height

in the earth's atmosphere

The ozone content o£ the atmosphere in different parts

of the earth, is found to vary between 0.15 to 0.40 em at

N.T.P. Because o£ the very high absorption coefficient of

ozone in the ultra-violet, this small amount of ozone present

in the atmosphere has important effects (1) by causing a rise

of temperature with height above 30 Km in the stratosphere

and (2) protecting plant and animal life on the surface of

the earth against photochemically active radiation. The study

of total ozone amount and its distribution with height, is

also of importance on account of its variability associated

with day-to-day changes in weather. The work done by different

workers on different aspects of atmospheric ozone studies has

been reviewed by Fabry (1950) in "L' Ozone Atmospherique", by

Gotz (1951) in the "Compendium of Meteorology" and by Prof.

K.R.Ramanathan (1954) in his Presidential Address to the

meeting of the International Meteorological Association.

Laboratory experiments have established several

absorption bands of ozone out of which the following ones are

important for the study of atmospheric ozone.

0 0

1 • Hartley Band : Between 2000 A and 3200 A with maximum 0

at 2553 A. This is a.very strong absorption band and

is independent of temperature.

2. Huggins Band : Weak absorption bands in the region

3200 A to 3690 l. The absorption maxima are influenced

by temperature.

- II.2 -

3. Chappius Band : Weak absorption bands in the region

4500 A to 7500 A. Maximum bet~een 5500 A to 6200 A. The Chappius bands are not suitable for study of

atmospheric ozone because of vapour bands in the

solar spectrum in this region. Taking various factors

into consideration, it is found that the region • •

3000 A to 3400 A is most suitable for the studies o!

atmospheric ozone.

Ozone distribution with height has been studied by

sending spectrographs with stratospheric balloons by Regener

(1934) and recently in V-2 rocket explorations by Johnson,

Purcell and Tousey (1951). These direct methods give a good

picture of the variation of ozone concentration with height.

However, it is practically impossible at present to adopt

these methods for routine measurement of vertical distribution

of ozone and one has to rely mostly on the indirect methods

such as the inversion-effect of the zenith scattered light,

discovered by GOtz (1931).

With the help of Dobson Spectrophotometer, it is

possible to measure the logarithm of the ratio of zenith

scattered intensity (I) or lights or two different wave-leQgths, jl say A • 3112 A and X • 3323 A. (L • Log (I/I') + Const.). I The first one is more strongly absorbed by ozone than the

other. With the increase or solar zenith distance (Z),

because of rise in the effective height of scattering for

wave-length ]\ , the ratio Log (I/I') decreases. Once the

effective height of scattering for A , goes above the region

- II.) •

of maximum ozone, its intensity (I) decreases at a rate

smaller than that of I'. This leads to an inversion in

L - z4 curve which is known as Gotz umkehr curve. . Chapman

(1934-35) theoretically derived a number of umkehr curves

for different assumed ozone distributions and taking into

consideration only primary scattering.

Gotz, Meetham and Dobson (1934) put forward two

different methods of deter~ng vertical distribution of ozone

from the observed umkehr curve. In the analytical method

referred to as ~~thod A, the atmosphere is divided in the

following layers :

Altitude Ozone amount

Above 50 Km o, but scattering not zero

50 - 35 Km x1

35 - 20 Km x2

20 - SKm x- (x1 + ~ + u)

5 - OKm u

x is the total oz:> ne amount obtained from direct sun

measurements and u is taken as a fixed percentage of x from

the knowledge of ozone content in the surface layers. The

equation of Log (I/I') can be obtained on the basis of primary

scattering for diffe;ent values of Z such as 0°, 80° and 90°

in terms of x1 and ~· The solution is obtained graphically

by plotting x2 as a function of x1 and determining the

intersection of the curves for Z c 80° and 90°.

The synthetic method or the Method B consists of

starting with an assumed vertical ozone distribution and

- II.Z.. -

varying it till the calculated and measured umkehr curves are

in tolerably good agreement at several points. In the original

method, the atmosphere was divided into a number of horizontal

sections such that the mass of air in any section was 1/ J10 that of the section below it. The whole of the air and ozone

in any section were supposed to be concentrated in a very thin

layer at a suitable height above the bottom of the section.

This means that in any section, ozone decreases exponentially

with height. The Method B was modified by Karandikar and

Ramanathan ( 1949). They divided the atmosphere into 9 Km

layers and the center of mass of a layer was assumed to be

situated at a height of 3 Km above the base of the layer. It

was assumed that no ozone is present above 54 Km and there is

uniform ozone distribution within the layer.

The effect of secondary scattering was considered on

the experimental basis by Ramanathan, Moorthy and Kulkarni

( 19 52) and on the theoretical grounds by \'Val ton ( 195 3) • They

showed that the e.ffect of applying correction was tc:> bring

down some ozone to the lower part of the atmosphere. Walton

(1955) has extended the theory so as to include tertiary

scattering.

2.2 "The ca1cu1ation of vertica1 distribution of ozone by

the GOtz umkehr effect (Method B)" by K.R.Ramanathan

and J.V.Dave. Communicated to the International Ozone

Commission for publication and regular use during the

International Geophysical Year.

l~OTB -I I . .

The valuez of 0( ,o<. c:.nci f3, {~ ~Jven in 'I'o.ble 3 have

been chanc;ed by tz1e int:;<::rr.c.;_ t,ion-::..1 0'3one Go .. :mission Circular No.

0.4 d&ted 5~h July, 1957 21-:.d ti1e ve.luE:s o~ «.,d..' fourid by

V"i~:ro1..1.x ( 1953) ~1ave been &dopted. It _has teen de:cid~d that all

ozone statio11.s s:O:ould adopt these new ·v£.lues simultaneously from I

·ch e 1st July 1957. 'I'he ·new vc:.lues of ( «- nl... ) are approximately

1. 36 tii:1es lmver t:_an those .ldopted previously. Because of the

fact that_what we measure oy the Dobson upectrophotometer is

( ol..- t:J/..1

)x, the effect of c.dop·cini~ the new values of ( o<.-~ ~} is

to increase the totc:.l ozone oy about 36 5~. · ' .

It is recomr.1encied tnat · the present t::,bles for

calculatin.; vertical distribution cm1tinue to be used, but if I

the tot.o.l ozone amounts are ca.lculat;ed \'ij.tb. th~ new ( ot..- a( )

values as given in the abo-;e Circuls..r, the calculated ozone

amount should first be divided by 1 .36 before using the tables.

At the end of the c~lculation, all the ozone values, both total

as well as the 2mount in each layer, should be multiplied by

1.36.

. .

THB CALCULATION OF TH~ Vi!.lLTICAL DISTRIBUTION

OF OZONE 2Y THE GOTZ UMI~HR-E?Fi2;CT (METHOD B).

By

K .1~ .!L-il•L-d'J.i-i ·rHAN & J. V. D AV l.

Physical Research Laboratory, Ahmedabad 9. India.

The present note sives the details of Method B for

calculating the vertical chstri but ion of ozone in the atmosphere

from observations on the umkehr-effect. The method was

oris,inally due to Gotz, Nleetham and Dobson ( 1 ).

nlthough the method is not free from objection, it

gives information of value about the changes in the vertical

distribution of ozone associated with day-to-day changes in

weather; it is also comparatively easy to use in clear weather

at all stations equipped with a Dobson Spectrophotometer.

The measurements recuired are the ratios of the

intensities of light of tvlO wave-lengths from the clear zenith

sky, one of which is much more absorbed by ozone than the other,

for zenith distdnces Z of the sun varying from 40° or 6o0 to 90°. n

Considering for example, the li~ht of two wave-lengths 3112 A ,, .

and 3323 A (for which the decimal absorption coefficients of

ozone are 1.23 and 0.08 respectively), it is found that the

raU_o I.= Lag.[ I()112)/I( 3323)J in the light from the zenith

2 •••

2

sky decreases as l increases until a value of about 86°.5 is

reached, and then increases as Z increases to 90°.

Instead of L, one can plot N = 100(10 - L) \V"here 10

is the value of 1 extrapolated for a point outside the

atmosphere. It is the general practice to plot 1 or N against

z4 so as to give an open scale v1hen the sun is near the horizon.

Sample curves of N against z4 for >... _}., 3112/3323 and

}. A 3054/3253 are shown in Fig. 1. (Curves C and A respectively).

The light reaching the observer from the sky in any

direction is sunlight scattered by the whole column of atmosphere

in that direction. It includes primary as well as multiple

scattered light. If only primary scattered light from molecules

is considered, it is easy to obtain an expression for the light

of any wave-length reaching the observer from the zenith.

In Part I, the method is described of calculating the

vertical distribution of ozone, first on the assumption that the

light from the zenith sky is only primary scattered light. A

short section is added explaining the effect of secondary

scattereQ light and a method of correcting for it. A fully

worked out example follovlS.

In Part II, supplementary tables applicable to s~ations

at or near two higher le¥els, 912 mb and 810 mb are provided.

3 •••.

' ,, .... ~. -···- '. ___ __. ...................... o~~· ,: ......... -. t.J.J..• '. :· .

• •

• ..

. / • • • • •

• •

• •

•

•

. ...... ,. · . • • :· c . , l • •

FIG.I. UMK£HR CURVES WITH

DOBSON SP£CTROPHOTOME TER.

\ .v,· ........ ·.- • .r;·.~o.: " .......... , ... .'7:·;~.,w ,.,.. .... , .. , :~

4

38

24

9.-------tr-----

FIG.2. DIVISION OF THE

ATMOSPHERE.

... . '

FtG.3. 01/..GRAM EXPLAINING ~S ANO ~h.

~ .. ~- . . . ' ' ' f.,_ ....... ,., . ._ ... ~.,. .~ .... .. .,.

. . ... · ... ' ... ~-- ---~--------~- ---· ~-_ ..... .............___ ~·. ·--~·' • .,, .-1 .' -~ ...... -~-~-~·

3

I. Calculation of primary scatterec light received from th~

zenith sky at the ;:;round.

For ce;.lculating the light ·scattered vertically

dovmward, the Citmosphere is divided into layers{2). 'fhe first

layer is from t:1e g;round (1013mb level) to 6 km, The second

lc..yer is from 6km to 12 km. . The. other layers are each 6 km

thick up to 54 km., above 54 km the whole atmosphere is treated

as one

Po

p

I n (!. j::i, ,.,

lc.:.yer.

,o.

- 1013 mb.

- ?ressure.at height h taken from rocket panel

data. (Table 1.)

- £•lass of air in the nth .layer expressed as a

fraction of the total mass of air in a standard

atmosphere \lvhich exerts a pressure of 1013 mb at

its base. The air in each 6 krn layer is supposed

to be concentrated at a height of 2 km above the

base of t~1e layer. 'i'hese assumptions are not

free from objection, but are simple and reasonably

accurate.

Decimal scattering coefficients for light of

wave-lengths .A , A.1

by a standard atmosphere.

- Decimal absorption coefficients of ozone for

.A 1

).' (per em of ozone at S. ·1'. P. ) (Table 3) •

4 •••

... . .. ' . . . . . . . •• . •• . r

4

The table includes data for all the four pairs of

wave-lengths norn~lly used for ·ozone deteroination

\."lith the Ozone .Spectrophotometer.

- Integrated air-path from the top of the atmosphere

to h (expressed as multiple of air-mass in one

st.:.":l..nd~rd atmosphere) , and f~om h vertically

dmmward to the observer, ( Te_ble . 4}. For an

observer at pressure-level Po = 1013 mb,

Fh = 1-r _P_ ( Ch(Z) Po

1] where Ch(Z) is the

Chapman !unction for a spherical atmosphere for

zenith ru~gle Z with the vertical through the

observer.· The. values of Ch ( Z) have been

tabulated by N.V.Wilkes{3)• ~~hile considering

air-mass in the slant path above a particular

height h, it is to be noted that the temperature

of the air in-the first few kilometers above h

exerts a domina~t influence. The mean temperatures

in the atmosphere as shown by rocket ascents have

been taken as a guide in preparing Table 1 A.

If the observer is located at· a pressure­

level kp0 instead of at p0 , the values of Fh in

5 •••

5 -

all rovrs in 'I'able 4 except the first row

(corresponding to 2 ~u) should be changed to

·­··-k + _E._ [ Ch ( Z) - 1] • Jup~:>lementary Table 4X

Po has been prep&red for k = 0.9 and 0.8 corresponding

to pressure levels 912 and 810 mb respectively.

These will hold for stations at 1 km and 2 km

. _respectively &bove sea level. For the lowest

layer, in Tc.~ble 4X, h has been taken to be.~3 km

above 1013 mb lGvel. This is sufficiently

accurate.

Total geometrical slant path of light in each

layer.

- Corresponding vertical path in the layer.

- have be0n tabulated in Table 6 for all those

layers in \'Thich there is a slant path. A

constant value of the radius a = 6370 ·km has

been used. Q 7• 3 uee ~~g. • For layers in which

there is only a vertical path, 6 s - h. h = 0.

Y1, Y2, y3

etc. upto y9 are the ozone amounts in

1o-3cm/km in successive layers as we go up; it is assumed that

the ozone amount above 54 km is ne6ligible so that the total

6 •••

- 6 -

ozone amount x = 6y1 + 6( Y2 +- y3 + ir '' 'i+ y9). The factor 6 in

the first terrn on the ri~ht ird.ll require a sms.ll adjustment if

the station is above the 1013mb level.

The tot&l ozone Y in the path of the light when the

.zenith dist&nce of the sun is Z and th6 light is scattered from

the nth l~yer i.::. given by the sum of the ozone amounts in the

sl<:mt path an.d in the vertical path. In the nth layer, part of

the path is vertical and part slant.

1\.

.L Yr 6hr

6hr)+ t.YrD~

'l'ables 6 provide the values ·Of fl S O.h for

calculating Yn for the light scattered from each layer and for

. different zenith dist.::mces of the sun r~nging from 37° to 90°.

An example of the calculation of Y is given in Table 8.

The intensities of the primary sca,ttered li,sht of

wave-length )\ for the r.th layer at the ground is given by

1 0- l3 ? - &(. y h K . . . !J In = K. (3. - /j, rr:n x ' w ere l.S a constant depending

on the value of Z. and I the tot&l intensity from ail the layers

is given by

7 ••.•.

7

.o I =~ f'·I =y J'"'i t-. - n "~ ." • L The ratio of the· intensities of the primary scattered

lig,ht of two wav~-lengths ). and .A fro~ the zenith sky is

given by 10

I f~ [' :!:: I -- t 1' (3'

I

.-· 10- {3 F o( yJ I .!j D\1 X -L-.

r !linn X 10- .~· F - e~..' YJ • -6 II1n - f3 F for different layers

a...'1.d Z ·required in the computation of Log( I 1 /I) are given in

Tables 5A, B, G and D corresponding to different pairs of

;i'he values of Lo~ 0

111ave-lengths.

Forms I, II and III are for computing Log(I 1 /I) for

.;.ny assumed ozone distribution and for makin.:::-; changes • in it

corresponding to small chan7es in the distribution. These are

given at the end.

By the method of successive ap~roximation, the ozone

amounts in the different layers are so adjusted that the

calculated values of Log(I 1 /I) agree with the calculated values

at four or five points of the umkehr curve within the limits of

experimental error.' In practice, a constant is added to the

calculated value of Log(I'/1) so that the calculated and the

observed values coincide at some fixed zenith distance like 60°,

B •••

where tl:.G intensity is detern1ined nainly by the total amount of

ozone and.not by its distril:Jution. 70°, 75°, 80°, 84°, 86~5,

88° and 90° are convenient points to choose for fitting the

.curves.

Correct~on for Jecondary Jcattering

In the above, account is taken only of the primary

sc,::..t"l:,ered. light from the molecules of the atmosphere. But the

air is illuminated not only by direct sunlight but also by light

scattered once or more by- the rest of the atmosphere and by the

ground. Neglect of thb illumination of the air colunm by

diffused light would be justifisd if the ratio of the intensities

of light of tl'io different \"lave-lengths (which is the quantity

actually measured) 6ave with sufficient accuracy the ratio of

the primary scattered li:;ht only of the same two radiations for

different zenith dist&.nces of the sun •

.ii little considerc..tion shows that this assumption is

not jus-cified. Of the lig,ht of t-v:o wave-lenths under compar.i.son.,

one is much more absorbed by .ozone than ·che other, and

cOJ;lsequently 1 the contributions from the different layers of

the atmosphere to the total primary-scattered light from the··

zenith are different, and v::J.ry differently with the zenith

9 •••

9 -

distance of the sun. _The multiple scattering which is dependent

on the distribution in height of the primary scattered light

will na.turally differ for the two wave-lengths.

Let P, P 1 be the intensities of primary scattered • "\t

light of ti1e. two vlave-len·:;ths _A , /\. from the zenith, and f-1,

:iYl' the intensities of the multiple sea ttered light.

t~hat 1"le measure with the spectrophotometer is Log I/I'

for different solar zenith distances.

Now I I'

= P + IVI

P' + M'

p 1 + MLP =----~----~------

?' 1 + 1>1' /P' ) We could correct the I/I' curve to give the P/P' curve if we

knew the valuas,of M/P and M'/P' for different zenith distances

of the: sun.

G. F. v.Jalton ( 4) has calculat~d th~ intensities· of primary

(P) and secondary (S) scattered light from the zenith sky for

different a.Jtitudes of the sun. .rlfter evaluating S/P for

appropriate valu<.:s of ti( and t3 for a few simple distributions of

ozone with total ozone amounts of 0.30 and 0.18 em, he has

calculated the corrections to be applied to th8 observed

intensity-ratios to convert them to what they would be if there

were only primary scattering. He found that the corrections

10 •••

10

varied with the zenith dist.=nce of the sun, but were nearly

const.mt \'lhen sec Z was bt:tween 5 and 20. The effect of

correcting for thb secondary scattering was to lower the C.G.

Of th~ OZOn8 by 2 to 3 km.

Hamanathan !•1oorty a.."'1.d !~ulkarni ( 5) obtained similar . '

results by deriving umkehr curves for I(}112)/I(3075) from the

observed un~ehr curves of I(3112)/I(J323) and I{J075)/I(J278).

'The objec·t. of using the C:.erived curve was to compare thG

intensities of ti'lO wave-h,n:;ths both of which are pretty strongly

absorb;;:d by ozone; in that case, the assumption I/I' = P/P' would

be more nearly correct. They came to the same conclusion as

~~alton viz., that the eff.::ct of taking multiple scattering into

account was to increase the ozone amount in the layers belov1 the

maximum of ozone and to reduce it at higher levels.

Although there are still a few unsolved questions

about the correction required for multiple scatterin;~, it is

believed that Table 7 provides for different solar zenith

distances, reasonable corrections when the ozone amount is

b2tween 0.18 and O.JO em.

11 •••

- 11

Table 1

Pressure at different hei<:~hts above sea-level ·~

(?rom rocket-panel data)

Height Ian Pressure mb Height km Pressure mb -----------------------------------~----------------

0 1013·. 44 1.90

2 803.5 48 . 1.15

6 487~5 50 0.902

8 372.4 54 0.547

12 . 206.5 56 0.426

14 150.7 60 0.254

18 78.5 62 0.194

20 56.9 66 0.111

24 30.5 6S 0.082

26 22.5 72 0.045

30 12.5 74 0.033

32 9.31 78 0.017

36 5.32 80 0.012

38 4.07 84 0.007

42 2.43

-------------------------------------~--------------

12 •••

•. -...

_... \...V • • •

fable 1 A

Values of Ch(Z) a.dopted for different values of h(km) and of Z(degrees). 'i'he rocket temperatures at h to h· + 10 (km) have been taken into consideration in tabula_ting these.

~---;---:~~-----::-----~:-----~:-----::-----::~---::~:----::-----::-----h .. ,,

--------~-------~----------~----------------------------------~--~-----------2,3 I 1 • 251 1. 993 2.90 3.80 - 5. 55 8.73 1,3.3 1 8. 7 35.5

8 11 it ll .3. 81 5. 58 8.84 13.6 19.5 38.7

14,20 I It iY ti 3. 81 5.59 8.87 13.7 19.7 39.7

26,32 i n i1 ti 3. 81 5.57 8. 81 13.5 19.2 37.6 J

38,44,50 ii ii if 3.80 5. 55 8.73 13.3 1 8. 7 35.5

56 II n i1 3.80 5.56 8.77 13.4 1 9. 0 36.6

62 li \1 t1 3.81 5.57 s. 81 13.5 19.2 ')7.6

6'8 l1 il n 3. 81 5.59 8.87 13.7 19.7 39.7

--------1-----------------------------------------------------------~--------

_., l\.)

13

Table 2

Lo::;arithm of the mass of air in different layers expressed as fraction of the mass in a vertical colunm of the std. atmosphere.

--------------------------------------------~-------------------Layer Layer ----------------------------------------------------------------

0-6 1. 715 42-48 3.100

6-12 1.443 48-54 4.778

12-18 1,101 54-60 4.461

18-24 2.676 60-66 4.149.

24-30 2.250 66-72 5.?20

30-36 3.848 72-78 5.431

36-42 3.455 78-84 5.ooo -----------------------------------------------------------~----

'fable 3 Decir11al absorption .coef'ficisnts of ozone and scattering coefficients of u.tmosphere for light of different pairs of ViaVe-len c;·ths • ·-o . .

-· --------).j-~r---- -0(------~·;-----~~]------ ft-,- ----~ ~(/f/ 73')------------------------------------------------------------------

A 3054/3253 B 3085/3291 c 3112/3323 D 3175/3399

2.58 1.77 1.23 0.54

0.16 . 0.12 0.08 0.02

0.503 0.481 6.464 0.425

0.384 0.365 0.350 0.318

0.1173 0,1198 0.1224

. 0.1260 -----------------------------------------------------------------..

' . ~ n' o( , t< refer to 1 em of ozone at ..:>. T. P. and ;:~ , 1 -;~ to an

atmosphere which exe:-ts a pressure ·of 1013 mb at· its base.

14 ...

..... Vl • • •

'rable 4

Values of.Fh- Integrated air path (expressed as multiple of orie·standard atmosphere) from the top of the. atmosphere to the level of primary scattering and from that level to the observer at p = 1013 inb.

. . . 0

-~-z---;~:----:::----~::----~~ :---~ ~::----::: ----~:;~-----:::-----~::----------~---------------------------------·------------------------------------

2

8

14

20

26

32

38

44 50

56

62

68

74

1.199 1.788 2.505 3.221 4.6:10 7.1.33 10.748 15.032 28.342

1.092 1.365 1.699 2.033 . 2.684 . 3.882 5.635 7.786 14.859

1.037 1.1.481.283 1.418 1_.683 2.1.71 2.887 3.778 6.751

1.014 1.056· 1.1.07 1.1.58 1.258 1.4,41 1.713 2.049 3.172

1.006 1.022" 1 •. 042 '1.-062. 1.101. 1.173. 1.278 1.404 1.813 . ' ' . . . 1.002 1.009 1.017 1.026 1.Q42 1.072 1.115 1.167 1.337 . . . .

1 .001 1 .004 1 .008 1 .011 1 .01 g 1 .031 1 .049 1 .071 1 .139

1.000 1.002 1.004 1.005 1.009 1.015. 1.023 1.033 1.065 . . . .

1.000 1.001 1.002 1.002 1.004 1.007 1.011 . 1.016 1.031 . '

1 .ooo 1 .ooo 1 .001 1 .001 . 1 .002 1 .003 1 .005 ' 1 .00$ 1 .015

1.000 1 .ooo 1 .ooo 1 .001. 1 .001 1 .001 1.002 1 .003 1 .007

1 .ooo 1.000 1.000 1.000 1.000 1.001 1.001 1.001 1.003

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.001 1.001

80 t 1 • 000 1 • 000 1 • 000 1 • 000 . 1 • 000 1 • 000 1 • 000 1 • 000 1 • 000 -------t----------------------~------------------·-----------------------------

F h .= 1 +. _L [ Ch ( Z) - 1} Po

..... ~

Table .. 5A

Log b~ ..;. j'.1 F [3 (3054) == o.soJ -~---~---·-----~---·----·-·..;·--·--·-----·-;;.,;-.....;_;.;.·;,;·----·-----·---- .... ·------------------------

1 2 3 4 s· 6 7 s 9 1 o --- ---------------------------~~--..;.----~~-~--~----~---~-------------------

37 1.112 2.894 2 .. 579 2.166 3.744 3.-344 1;.-. 951 4.-597 - 4' •. 228 4 •. 275

60 2.316 2.756 2.524 2.145 ...... ,

3. 31~0 - 4 • .596 4.274 4 .. 228 .3.7.3o 4.950

70 2.455 2.588 2.456 2.119 3.726 3 • .))6 4 .. 948 lh595 4.274 4.22~l ....... Vl

75 2.095 2.420 2.)$$ 2. 094 3.716 3.332 4<~946 4·.594 4.274 4.228

$0 3.3S6 2. 09.3 2.254 2.04.3 .3 .696 3 • .324 - 4.592 4.273 4.228 4.·943

84 4.127 3.4-90 2.009 3. 951 3.660 3 • .309 4fl936 4.589 4.271 4.225

S6.o5 b.J09 4.609 J.-649 3. 814 3.607 J.-287 4.927 4.-585 4.269 4.225

83 a. 1 54 5.527 3 .. 201 3.645 3.544 3- •. 261 4.916 4.580 4.267 4.225

90 15.459 9.969 5.705 ]".080 3.338 3.175 4.B82 4.564 4.259 4.223 --~--~-----------------------------~-------------------·--------------------

....... a-• • •

_.. -..J • • •

Table 5A {contd) I

1 ... 1-, ,_,, og ,.. · m - , r -· n r~ rl (3253} = 0.384

-~~----~------:------~------:------~------:------~------:------;------~~--2 \

----~-----------------------------------------------------------------------

37 1.255 1.024 2.703 2.287 3.864 3.463 3.071 4.716 4.394 4.346

60

70

75

1.028 2.919 2.660 2.270 3.858 3.461 3.069 4.715 4.394 4.346

2.753 2.791 2.608 2.25'1 3.850 3.457 3.068 4.714 4.393 4.346

2.478 2.662 2.556 2.231 3.842 3.454 3.067 4.714 4.393 4.346

80 3.945 2.412 2.455 2.193 3.827 3.448 3.064 4.713 4.392 4.346

84 4.976 3.952 2.26.7 2.123. 3.800 3.436' 3.059 /+.710 4.391 4.346

86.5 5.588 3.279 3.992 2.01.8 3.759 3.420 3.052 4.70'i 4.390 4.346

88 7. 943 4.453 3.650 3. 889 3. 711 3.400 '3 .044 . 4. 703 4.383 4.346

90 12.832 7.737 4.509 3.458 3.554· 3.33.5 3.018 4.691· 4.382 4.344

------------------------------------------------------------·----------------

~

"'

Table 2B • Log 6m - BF . n , [3 (3085) = o. 481

-~~~---~-------;-----~-------:---~--;------:------;-----~------;-----~-;-2 \. .. . . .

----~-----------------~~~------~--------------------------------------------

37 T.138 2.918 2.6oz 2.188 3.766 3.366 4.974 4.619 4. 297 . 4. 255 .. ...

60 2.855 2.786 2~549 -~.168 !.758 3.363 4~972 4.618 4.297 4.255

70 2.510 .·2.626 2. 4 84 . 2 • 1 44 3.749 3.359 4.970 '4.617 4.296 4.255 ...... -J

75 .. 2.166 2.465 2.419 2.119 '3.739 3.354 4.969' 4.617 4.296 7;.255

80 3.498. 2.152 2. 2 91 . 2 • 071 }.720 J.347 4.965 l+. 61 5 4.295 4.253

84 4.284 '3. 576 2.057 3. 983 3.686 3 .332, . 4. 959. 4.61 2 . 4.294 4.253

86.5 b. 545 4.733'3.712 3. 852 3.635 3.312 4.950 4.608 4.292 4.250

88 8.485 5.698' 3.284 3.690 3.57_5 . 3. 287 4.940 4.603 4.289 . 4.250

90.: ... "1'4 •. 9.~2 "8.296. 5.854 3.150.J.37S 3.205 4.907 I;.". 5S8 4. 282' 4. 248 ..... . ~. . . . .. . 00. ~---------------------------------------------~------------------------------.. • • •

-' \.0 • • •

Table ~a 'contd.) I t

Log d m - {j F /3 ( 3 2 91 ) = 0 • 3 6 5 n

~--------------------------------------------------------------------~--------\ \n 1 2 3 4 5 6 7 8 9 10 z \

-----------------------------------------------------------------------------37 1.277 1.044 2.722 2.306 3.883 3.48.} 3.09·0 4. 735 4.413 4.369

60 1.062 2.945 2". 632 2.291 3.877 3.480 3.089 4.734 4.413 4.369

70 2.301 2.323 2.633 2.272 3.870 3.477 ).087 /+. 734 4.412 4.369 _.. co.

75 2.539 2. 701 2. 583 2.253 3. 862 3.474 3.086 4.733 4.412 4.369

80 2.032 2.463 2.487 2.217 3.848 3.468 3.083 4.732 4.412 4.369

84 3. 1 1 i 2.026 -~L309 2.150 3.822 3.457 3.079 4.730 4.410 z .. 369

~,:6 r-'-• . _.,) :5.'19~ 7~- 3 '~

~. 00 2".047 2.051 J.7J4 3 .41+ 1 3.072 4.727 4.409 4.367

F.~ r; ) '· ~ 6.228 4.601 3. 722 3. 928 3. 738 3 .42~2 ).064 4 .• 723 4.407 4.367

90 IT .370 6.019 .4.637 3.518 3.588 3.360 3.039 4.711 L1-. 402 4.362

--------------------------~·--------------------------------------------------

Table 5C

Log ~ mn - (1'i (3 (3112} = 0.464

-:'\-----~------:------;------:----~-~------~------;------~------~------~~--

--------------------------------------------------------------------~---~----

37 1.159" 2.936' 2.620. 2.206 3.783 3.383 4.991. 4.636· 4.314 .. 4.267,,

60 2.885' 2.810· 2.568. 2.186 3.776 3.380 4.989" 4 .. 635.·4.314. 4.267

70

75

8o

84

86.5

88

90

2.553" 2.655 2.56& 2.162 . 3.767 3.376 4.987 4.634 t.31j. ~.267 .. . . : . . ..

2.220 2.500 2.443 2.139 3.757 3.372 4.986 4.634 t.31"i . t.267 .. :. . .. 3.576 2.198 ~.320 2.092 -3.739 3.36~ 4.983. 4.632 4.3f2 .· 4.267

4.405 3.642 2.094 2.007 3.706_ 3.351 4.977 4.629 4.311 4.267

6.72'8 4.828 3.761 3.8~1 3.657. 3.331 4.968 4.625 4.309 4.267

8.740 5.8}0 3.348 3.725 3.599 3.307 4.958 4.621 4.307 4.265

14.564 8.548 5.969 3.204 3.409 3.228 4.927 4.606. 4.3oo 4.2~5

N ~-~----------------------------------------------------------~----------~-~--0 • • •

..... '-0

I\) ~

• • •

Table SC 'contd.) I . . .I .

Log .6mn - (3 F (3 (33.23) = o·.350

~------------------------------------------------------------------------. . n ........ ··· .. 1 2 3 4 5.. . 6 . 7· 8 9 10

- -----------~~-----~~----------------------------------------------------

37 1.295 1.061 2. '738 2.321 3.898 3.497 3.105 4.750 4.428 4.382

60 1.089 2.965 2.699 2.306 3.892 3.495 3.104 4.749 4.428 4.382

70 2.838 2 •. 848 2.652 2.289 3.8$5 3.492: 3.102 4 •. 749 4'.427 4.382 1\.)

75 2.58$ 2 .• 731 2 •. 605 2.271 3.878 3.489 3 •. 1 01 4 •. 748 4.427 4.382 0

$0 2.101 2.504 2.512 2.'236 3.865 3.483 3.099 4.747 4.427 4.382

84 3.218 2~084 2~341 2.172 3~839 3.473 3.094 4.745 4.426 4.382

$6.5 5.953 -· 3.471 2~091 2~076 3.803 3.458 3.088 4.742 4.424 4.382

$$ "b.454 4. 718 3~779 3.959 3~759 3.440 3.o8o· 4.738 4.422 4.380 ....

90 11.795 'b.242 4. 738 3.566 3.615 3.380 3.056 4.7-27· 4.417 4.378

-----------------------------------------------------------------------------

'!'able 5 ~

Log 4'1m ... r3F n '

. J3 ( 3 1 7 5 ) = 0. 42 5

~~~~---------~~~-------------~~---------~~-----~--------~~---~-~~-----~---n . ... . . . , . ..

1 . 2 3 4 5 6 7 8 9 10 z

~~~-~--w--~---•~-~----------~----~---~~--~--~-~---~----~-~--~--------~~~--~--

37 1~205 2~979 2.660 2.245 3.822 3.422 ].030 4.675 4.353 ,4.312

60

70

75

2~955 2~863 2.613 2.227 3.816 3.419 ].02$ 4.674 4.353 4.312

2.650 2.721 2.'556 2~206 3.807 3.416 3.027 4.673 4.352 4.312

2.346 2.579 2.498 2 .. 184 3.799 3.412 ).025 4.673 lt.352 4.312

so 1.756 ~.)02 ~.386 2.141 3.782 3.405. 3.022 4.671 4.351 4.310

84 4.6jJ 3.79.3 2".178 2.064 3.751 3.392 3.·017 . 4.669 4.350 4.310

86.5 5.147 3.048 3.S74 3.948 3.707 3.375 j.oo9 4.665 4.348 4.310 '

S8 7.J26 4.134 J.495 3.~os 3.653 3.l52 .r.ooo 4.661 4.346 ~.310

90 ··0.676. ?.12s 4.232 3.328 3.479 3.2so 4.971 4.647 4.34o 4.3os

~ -~·~~~-~--------------- --~----------~-~---~------~--~~~---------~~~-~---·--~ N • . •

•

N

"""' •

N \..V

• •

I Log [)rnn - [3 F

Table 5D (contd,) t f3 (3399) = 0.318

~. ----.--. ------------------""-----------------~-------.-------------------------n . ·. .

1 2 3 4 5 6 7 8 9 10 .

-- - ----------------------~-~--------------------------------------~--------

37 1.334 1.096 2.771 2.354 3.930 3.529 3.137 4.782 4.460 4.417

60 . 1.146 1.009 ~-736·· ~-340' 3.925 3.527 3.136 4. 781 4.460 4.417

70 2. 918 2.903. 2.693 2.324' J. 919 3.525. 3.134 4. 781 . 4.459 4.417 ..

75 2.691 2.797 2.650 2.308 3.912 3.522 · 3.134 · 4.7BC· 4.459 . 4.417 ..

80 2.249 2.589 2.566 2.276 3.900 . 3.517 3.131 . 4.779. 4.459 4.417

84 3 .1,.47 2.209 2.411 2.218 3.877 .3.507 3.127 4.777 '4.~58 ·4.417

86.5 T;. 297 3.651 2.183 2.131 3.844 3.493 J~ 121 4.775 '4.457 4.415

88 b".935 4.967 3.900 2.024 3.804 3.477 ·3.114 ·4.772 '4.455 ·4.415

90 TO. 102 b. 718 4.954 3.667 .3 .673 3.423 3.093 ·4~ 761 4.450 ·4.412

-------~---------------------------------------------------------------~-----

..

N N

- 23 -

.::·able 6

1\ ' " . , __ . s. -- ;_\ h for different Z and h

z = 37°

----;------------------~----------------------------------;--i~-10=3

1 2 ·3 · 4· 5 6 7 8 9 n

54-4tl.:

48-42 42-:36 36-3.0 30-2.4' 24-~ 8· 18-12 12-- .6

6- 0

cm/km ----~·--~---~-~~------------- ---------------------~---------1·, 4-' 1• 4· .. 1_. ~:

1~4 1 • 5 1 ~ 5·, ,,5 1 ~ 5 1 • 5. 1·. 5: 1j5 1.5

~.5 1 -.5: 1 5· . .

a .s 1' 5· . . .. 1·, 5. 1 ', .5: . 1 • 5 1.0 ·. :1·. 5 .. 1,0 ;1·.0

1 .5 1 • 5 1 • 5 , .• 5. 1.5 1.5 1 .5 1 • 5 1.5

1.5 1.5 1.0 1 .5 .1.0 1. 0 -

1 • 5 1 a 5

1 • 5 1 .o 1.0 -

1. 0 v = J9 Y3 = Y7 = y6 = y = 5 y4 :. y3 = y2 : yl :

------ ~-----------..... !'-...~~---- --~-;--------------------~--------.. z = 60° .

------ --------------------------------------------------- --------:

54-48 5.7 5 •. 7 5.'] 5·.8 5 •. 8 5.9 5.9 5.9 4,0 y9 : ·.--

48-42 ;5 •. 7· 5.7 5 •. 8 .. 5.8 5.9 5.9 5.9 ·4.0 Ye = 42-36 5 • .7: 5.8 5.$ 5.9 5.9 5.9 4.0 y7 --"'- 30 r: 8 5 ~e. 5 • .9 5.5) r:; 9 4.0 ··v- . :) ··~ . .; •.- y6 0::.

30-24 ;5 .8. 5 • .9 5.9 5 •. 9 4.0 - - ' y5 :.

,... ' l8 :5 .•. 9 5·.9 5 • .9 4 •. 0 y4 '~ l-4-- :

18-1.2 ·-5· •. 9 . 5 • .9 4.0 - y3 ::.

12-.6 :5.-9 4.0 y2 :.

6- 0 '4 .. 0 y1 :.

--------------------------------------------------------------------

24 •.•

- 24 -

Table 6 (contd.)

z :: 70°

~::~--~-----;-----;-----~-----;-----~-----;-----~---~-~--¥:~;:~10=3

·--------------------------------------------------------------------54-48 10.5 10,6 10 • .7 10.9 11 • 0 11 • 1 11 • 3 11 • 4 7.6 y9 = 48-42 10.6 10.7 10.9 11 • 0 11 • 1 11.3 11.4 7.6 y8 = 42-36 10.7 10.9 11 .o 11 • 1 11 • 3 11 • 4 7.6 - y7 = 36-30 10.9 11 • 0 11 • 1 11 • 3 11 • 4 7.6 y6 = 30-24 11 • 0 11 • 1. 11 • 3 11 • 4 7.6 y5 = 24-Hl 11 ~ 1 11 • 3 11.4 7.6 y = H~-12 ! 11 .3

4 11 • 4 7.6 y3 =

12~ 6111.4 7.6 y2 = 6- 0 l 7.6 y1 :.

------~--------------------------------------------~-~-----~--------

54-48 14.9 15.2 15.4. 4-8-42 15.2 15~4 15~6

42-36 : 15.4 15~6 16~0

36-30 . 15.6 16.0 16.2

30-24 16 .. o 16.2 16;5 24-H! 16.'2 16.5 16.8 18-12 16.5 16.8 11 • 4 12- 6 16.8 11 • 4

6- 0 11 • 4

15.6 16.0 16.2 16.0 16.2 16.5 16.2 16.5 . 16.8 16,:5 16.8 11.4

16.8 11 0 4 11 • 4

16.5 16.8 16.8 11.4

"11. 4

11 • y9 :. Yg :. y7 :.

y6 =

y5 = y -4 -y3 = y2 = y1 =

----------------------------------------------------------- --------

25 •••

- 25 -

Table 6 ~ contd ~)

z = so? -.. -\.~ ~--- ~-----:.-----:-----:-----:-----:-----~-----:----:-;:-~.:- ~ ;= 3-L : 1:6_ _ _ . . . · ·· ~/Ian ; :=ze- ;;~~-.-;;:;--;;~.~--;~:;--;~:;--;;:6-.-;6:;--;;:;--~;: $ ~-;;-=-~-4~-42 22.7 · 23.4. 24.0. ·24•8. 25.6. 26.5 27.j 1$.$ Yg ~

4'~-36 23.4. 24.0 24.8 25.6 26.5 '27.3 18.$ y7 =. 3·;-30 24.0 ·24,8 25.6 26.5 ·27.3 18.$ - - -Y6 = 3r·-24 24.8 '25.6 26.5 27.3 1a.s Y5 = 21!.-1$ 25~6 ·26.5 ·27.3 18.8 -: .Y

4-

1C-12 26 • .5 27.3 ·18.8 ·Yj = 12- 6 27.3 1$.8 y2 =

6- 0 . 1 8. 8 y 1 = ' .

------------------------------------------------~---------- --------

.'->4' 8 ~; 8-i 2

':.2-; 6

)o-:o 30-; 4 2h-~8

~8-12

:2- 6 6- 0

------------------------------------~-----~-----~---~--------31 .o 32.4 . 34.0

32.4 34.0 35.8 34.0 35 .. 8 37.8 35.8 37.8 '40.2 37.8 40.2 43.0 40.2 43.0 46.4 43.0 46.4 33.2 46.4 33.2 3).2

)5.8 .37 .8 40.2 37.8 40.2 43.0 40.2 43.0 46.4 43.0 46.4 33.2 46.4 33.2 33.2

43.0 46.4 .33.2 46.4 33.2

33.2

y9 ::.

Yg_= y7 :. Y6 :. y5 = y -4 -y3 ~

y2 = y =

1

----------------------------------------------------------- --------

26 •••

- 26 -

I' able 6 ( contd ~)

z = 86°.5

.. :

-:~-~-~~----~-----;-----:-----~-----~-----;-----~-----;-::~::-~~=3--~!~~-------~----------------------------------------- -----------54-4S 37 40 42 46 50 55 62 72 5 48-42 40 . 42 46 50 55 62 72 57 42-36 42. A6 50 55 62 72 57 36-30 46 50 55 62 72 57 30-24 . 50 55 62 72 57 24-18 55 '62 72 57

y9 :::. Yg = y7 = y6 = y 5 "' y = 4

18-12 62 72 57 - - - - - - y =

~~=-~-t~~----~:----=-----=-----=-----=----~=-----=-----=-----~~-=---------r----------7----------------------------------~---------------l)/~-48 41 44 . 47 51 57 65 77 98 91 y9 :. !,.8-42 44 47 51 57 65 77 98 91 Yg = \2-36 47 51 57 65 77 98 91 y7 ... 36-30 51. 57 65 77 9$ 91 y6 '::.

30-24 57 65 77 98 91 Y5 ':.

24-18 65 77 9S 91 y4 :::. ~ 8-12 . 77 98 91 y3 = 12- 6· 08 91 Y2 :

"' 6- 0 91 y1 = ------~-------------------------------------------------- -----~----

27 •••

- 27 -

~able 6 (contd.l

z = 90°

---------------------------------------------~----~------~---7---10··:, n y 1n

1 2 3 4 5 · 6 7 8 9 n Lay · · · cm/km ------~--------------------------------------------------- ---------54-43 42 46 50 55 62 72 89 125 22 y9 =

.. 48-42 46 50 55 62 72 89 125 222 Y8 = 42-36 50 55 62 72 89 125 222 y7 =, 36-30 55 62 72 89 125 222 y6 =

30-24 62 72 89 125 222 y5 = 24-18 72 89 125 222 y4 = 18-12 89 125 222 y3 = -

12- 6 125 222 y2 = 6- 0 222 y1 =

-----·----------------------------------------------------~---------

28 •••

L

l\) '-0 • • •

Table 7

Correction for second:.-.17 scattering (Provisional). Amount to be

subtracted from values of N(Z) - N(60°) when observations are made I

with C )... A•

-------------------------------------------------------~--------------

z

Jubtract to correct for se condar·y scattering.

60

o.o

70 75

1.0 2.0

so 'g4' '86.5 88 . '90

4.5 6.0 6.0 6.0 6.0

------------------------------------------------------------------------- .

l\) ro

29

.Gxample

Jm eAample showing th6 calculation of Log{I'/I) is

given below: It r~l~tes to an umkbhr curve obtained at Ahmedabad

on 16-10-56 with C pair of wave-lengths. The total ozone amount

vms 0.192 em. The values of N observed on light scattered from

the clear zenith sky are given in 'l'able 9B.

A trial distribution was assumed to start with; this

Nas based on a gen~ral knowledge _of average distribution

corresponding to 0,.192 em. The values of y (in 10-3cm/km)

assumed to exist in layers 1 to 9, were

o, _0.5, 0.5, 5.5, 12.0, 8.0, 3.8, 1.4, 0.).

In Table 8, is shown an example of calculating

Y = Yn +' x, the total ozone in the path of the light when the

zenith distance of the sun was 86~5.

Using these values of Y and Form I, the values of

Log( It /I}= - 1 were cor.1puted for different values of z. 1-m

example is shown for Z = 86?5. As we are interested only in the

l~clativE: valut:s of L, or of }; which is equal to 100{10

- L) when

Z chan6es, the computed value of 100 Log(I 1 /I) at 60° has a

correction added to it so that it becomes idl.ntical v~i th the

observed vw.lues of Nat 60°. The same correction term is added

30 ••.•

L

\.>..) _, . • •

Table 8

Example showing calculation of ozone path Y for : = 86~5; x = 0.192 em • . ~. ----------------------------------------------------- -----------------------·~

'l'rial y1 Y2-- y Y· . y .. y ',; y8: ... Y9 .. ····· ....... - ... ozone 3, . .. It . . .... 5 ... - . . 6 .. . . . ~- 7 . distn. o.o 0.5 0.5 5.5 12.0 8.0 .· 3.8 1 .4' 0.3

-------------~------------------------------------------~------·------------­. Layer .1 2 .3 -4 .. 5 6 ' . . '7 .. 8 ,.·9 . 10 . -----.~~:.~---~--------~.-.~--------------------·-----~------·----------------· ... ----------

9

8

7

6

5

4

3

2

.0111 .0120 .0126 .01.3.8 .... 0150 .• 0165 .• 01-(~6- .0216 • 1 '171 ·.0000

.0~~~ .~;~~ .• 8644 .0700 .077Q .086& .1008 .0798 JOO .0000

.1596 .1748 .1900 .2090 .2356 .2736 .• 2166 .0000 .• · )00 .oooo

.3680 .4000 .4400 .. 4960 .5760 .4560 .0000 .oooo .l )00 .oooo

.6000 .6600 .• 7440 .• 8640 .684'0 .0000, .oooo .• oooo .• 0000 .0000

.3025 .3410 .3960 .3135 ..• 0000 .• 0000 ..• 0000 .0000 .• OOt.O. ,0000·

.0310 .0360 .0285

.0360 .0285 .• 0000

.oooo .oooo .oooo .• oooo .oooo .oo~o .• oooo

• 0000 • 0000 • 0000 ' • 0000 . • 0000 .. • 000 :) . • 0000 .

1 • 0000 • 0000 • 0000 • 0000 • 0000 ..• 0000 ' • 0000 • 0000 ' • oouo . • 0000 .

--~----------------------------------------------------------· --------------Yn 1.56421.7111 1.87551.9663 1.5876·0.8329·0.3360 0.101· ·o.0171·o.oooo

i=i:.;~t-1~756---~~~;;-~;:c;67-~;~;.5s--~~7$0--.~~c;;;-~;~;;$-~;~;9~ ~0~;c;9--c;-:·~~;-- ----- ----------------·--·-·---· .... ._ .... -..·-·-·-- _..;.·..;..-....;.· .. :.~ :..:.p.:,;~· .. : .. .:..·-~ ..:. __ :.:.·.:....:.._ __ ·_...:·_..:.:,·__ -~ ------------

Similar calculatiOnb oP t and y are to be m3de for other vcll. UGS oi z • n ...

\.V 0

31

'£able 9 .:. . •

tr-ial distribution and changes in trial distribution. ·rhe . y' s are in urli t s of 1 o-3 cm/km. ----------~--------------~---------------------------------~--------

Layer 1 3 4 6 9

?rial ~istn. 0.0 0.5 0.5 5.5 12.o e.o 3.8 1.4 0.3

-----------------------------------------~--------------------------

L: .. );(a) -0.1 0.1

6 y(b) · .. 0.5 0.5 ·2.0 . -2.0 -1 .o -0.1 0,1

b y( c) 0.5 1.5 1.0 -2.0 -1.~0 -0.1 0,1 .. . . • I

--------------------~-----------------------------------------------l;inal distn. 0.5

. , . .:,. 2.0 1.5 3.5 11.0 1. 4 o. 4 --------...---_ ... ______________ ....,. ______________________________________ _

..

. . . . ... . . . ·::able 9 B. .. .. Observed and calculated values of N for different. values of Z and for various ozone distributions~ ----------~---~----~-------~-------------~-~----~~~--~---~-~----~~(de.~_:r·ees) . 60 ?O ·-75 ·· · ao .,.}4. . ~ .. 86.5 88. 90 . --------------------------~-~-----~~-----------------------------~~~ .

z4 x 1o-7· 1~:30 2,4o·· .3~16 · ·4.10 ·4~98 5.6o 6.oo 6.56 -----~--------------------~----------~------------------------------Observed N 32.0 51.0 67 •. 5 92.2 119,3 126~3 124~5 113;0 --------------------~-----------------------------------------------N accord-in6 to 32,0 52.7 70.4 96.5 120,6 127.0 123,2 108, '9 trial distn.

b. y(a) )2,0 120,7 127. 2· 123.8 110.J

'\ y{b) 32.0 · · 51-•'8 ··69~0 93.9. ....

118.3 127.0 124.9 112,2 l.-·

~ y(c) 32.0 51.8 68.6 93.5 117.9 126.9 124.7 112.4 -~-~--~~~--~-----~~--~-~~~-~---~~~~~~--~---~--------

3~ •••

:

j

--- -------- -------

- 32

Table 9 C

Lxample showing correction due to secondary scattering and its effect.

----~~-------------~-----------~------------~-------------------------L&yer

Yn,

1

2.0 2 3

2.0 3.0 5 6

10.0 .7.0 7

3.2 8

0.9 9

0.2

------~----~------------------------------------~~-----------------~-~ z 6o 70 75 so 84 86.5 88 90

-------------.------~---~---·----·------.-.~- ......... ~------~~----..,.. .... -_________ .. ____ ._ Observed N corrected 32.0 50.0 65.5 87.7 113.3 120.3 .. 118.5 . 107~0 for :.:icc • .Jcat.tering

Calculated N 32.0. 51 .o 66.5 89.0 111.6 120.5 .. 119.2 106.5

----------------------------------------------------------------------

33 •••

VJ .{:'-

• •

.a. v• 1u. .... ""- V.L .""v-.L.I.L.t"'\,A,""""-.L.I.Q -'-"o'- , ... , .__ ... 0 ..... v'"'"'"' ""LJ'-' ..... - \,A. ..... ...,"" ....... ..,"""'..., .... _. ......

=~~~~~=1~:l~=~~~=~~~~~~~~=~~~~~~~~==~=~=~~~~===~L=~~~=~===~=~=l~~~=~~~~=~~2~==~=~=~~l2~~~~~=== n ' 1 ' 2· ' 3 ' 4 ' 5 ' 6 ' 7 ' 8 ' 9 ' 10 -------~-------~~------~-------~-------~-------~-------l-------l-------~~-~----~~------~--------

=======~g======r=~~~=====~~~=====~~~=====~~~=====~~~~====~~~=====~~~=====~~~=====~~~======:===== y f . • •

n . ---------------~-----------------------------~------------------------~--~----------------------X . . . . -------------------------------------------------------------------~---------~-~-----------~----y = Yn +X :1.756 1.90.3 2.067 2.158 1.780 1.025 0.528 0.293 0.209 0.192 =====================================~==========================================================

' Log~ mn - (3F ~'5.728 4.828. ·3. 761 ·. 3.881 3.657 3 . .331 4.968 4"625 4.309 4.267 ---------------~------------~---------------------~-~-------------------------~-~---------------~ y :2.160 2.341 2.543 2.654 2.189 1.261 0.649 0 • .360 . 0.257 0.236 ==========~====t================:=======:===;===:=======:=======:~======:=======:=======:=======

. D ~~.568 '5.487 5.217 5~22" . 5.468 4-070 4.319 4.265 4.052 4.031 --------------~~------------------------------~--~----------------------------------------------Antilog D :.03000 .03003 .03016 .• 0.3017 .0.3029 ".03118 .03208 .03184 • 03113 • 0.31 07 ====;=========================================================================================== D = Log ~ mn - f; F - ~ Y. I= L .6In = K11L.1mtilog D = 0.03795 Kf~. =============r=7=======~========================================================================

Log~ r~- 0 F!5.953 3.471 2.091 2.076 3.803 3.458 3.088 4.742 4.424 4.382 -----,--------~~----~---------------------------------------------------------------------------

ol... y !0.140 0.152 0.165 0.173 0.142 0.082 0.042 0.023 0.017. 0.015 ===============~================================================================================ l .

D' i~.813 · 3.319 ~.926 3.903 r.661 · ~-376 3.046 4.719 4.407 4.367 ---------------4------------------~---------------------------~----------~-----------~----------f~ntilog D' j-02007 .02208 .02843 ;0

2800 .0

2458 .02238 .02111 ..• 02052 .02026 .02023

===========================================================;===========================;======== - I I

D ' = Log 6. mn · ... (~ F - d... Y. ' ~J . o' I,'= 1-.~I~ = Kj~ L Anti~og D' = 0.0277 K n. ---------------------------~--------------------------~-----------------------------------------

Log

Log

I= 4.900 +Log Kl"1.

' (I' /I) = 1 • 543 - Log · ( (3 / J1 ). =

Log I 1 . = 2.44.3 + Log K f.. 1•

1 .421 1 00 Log (I r /I) = 142.1

\.A) \.A)

\;.)

\Jl • •

Form II for computing Log(I'/I) for a changed initial diotribution

Station: Ahmedabad Z = 86~5 A/ ~ = C o(. = 1 .23 _ ===================~======================================~=================~=====================

Date: 16-10-56 i

~= 0.08 x = 0.192 em.

n r 1 ' 2 . ' 3 ' 4 . ' 5 ' 6 ' 7 ' 8 ' 9 .' 10 ----------------~--------------------------------------------------------------·------------------:

Change in Yn t - - .- - - - -0.1 - +0.1 ===================~==================;=====~==========================·===========================

. +0.004 +0.004 +0.005 +0.005 +Q~006 +0.006 +0.007 +0.006 0.000 •

6,y r-----------~-------------------------------~------------------------------~---. -0.005 -0.005 -0.006' -0.006 -0.007 -0.006 ~---------------------~--------------------------------------------------------; -0.001 -0.001 ~0.001 -0.001 -0.001 o.ooo +0.007 +0.006 o.ooo

===================~==============~==;============================================================

D (from Form I) ' . o.4S7 5.217 5.227 5.468 4.070 4.319 4.265 -4.052 4.031 ----------------~--~-------------------~----------------------------------------------------------eo{ ~ Y , -0.001 -0.001 -0.001 -0.001 -0.001 Q.OOO +0.009 +0.007 0.000 ===================~==============================================================================

D - ,J.. ~ y f "b.4S8 5.21S 5.22S 5.469 4.071 4.319 4.256 4.045 4.031 I -------------------r--------------------------------------------------.----------------------------Antilog(D- ·~ ~Y) :.0

3000 0.

3003 .0

3017 .0

3017 .0

3029 .0

311S .0

3208 .0

3180 .03111 .03107

~===============================================================;=~=======================~======~

I = L . . 0 In = K f3 L Antilog (D - ·::< h Y) = 0.03790 K f'. Log I = 4.898 + Log K \1 • ======================================================~==================•======•=================

D' (from Form I) f · . . 4.719 .

-------------------1------------------------------------------------------------------------------~~ L\ Y ! 0.000 0.000 0.000 0.000 0.000 0.000 +0.001 0.000 0.000 ===================r==============================================================================

'h D' - ol... u Y ? . . 4. 718 . --------------------~---------------------~--~---~--~--------------------------------------------~ I ;

Antilog {D '- .,..;.., 6.. Y): • 02052 ============================================================================================;=====

I' r {\I' = L w n , t

= K {1 L Antilog (D' - o( ~ Y) I

= 0.0277 K 0. Log I 1 - . I

= 2.443 + Log K 0 . -~----------~-----------------~------------------------------~--------~---------------------------

- 100 Log(I'/I) = 142.3

\..0 +-

35

to the computed values for all otht;r an.~les also. We thus get

a computed ( c()nstant-1) or N curve which can be_ compared with

the observed curve. .a sa.mple co.lculation is shown io ·· T(\bles 9A

and 9B and Forms I and II.

The values of N calculated according to the trial

distribution and adjusted so that the observed and calculated

values coincide at 6o0, are entered in row 4 of Table 9B. It

\vill be noticed that the computed values are significantly lo'iler

at 90° and significantly higher at 75° and 80°. The first defect

can be remedied by adding a sraall amount of ozone at the top.

To remedy the second defect, some ozone has to be brought down

from the middle layers to the bottom layers. These changes in

distribution are made in successive approximation. lorm II is

used for computing changed Log(I'/I).

Considering the scatter of values in the observed

umkehr curve, it was considered that the v&lues in the last row

of Table 9B were sufficiently sat-isfactory and that the

distribution given in the last row of Table 9A accepted as the

distribution, provided the zenith skylight was assumed to be

due only to primary scattering.

The· observed values given in row 3 of ·rable 9B were

corrected for secondary scattering according to Table 7. The

36 ••• ·'

new distribution to fit the corr8cted observed curve and the

corresponding calculated values of N are given in Table 9C.

The followin~ hints n~y be of some help in making

the chanbes in distribution.

( 1 ) ~iith an assumed trial distribution, ca.lculate Log( I' /I)

at Z = 60°. Add an ap:_)ropri::t te constant to this so as -t,o n1a.ke

it e~ual to the observed valu~ of N/100 at 60°.

(2) Galculate Log(I'/I) for 90° and 88°, and apply the

same correction. If the calculated value is too high, remove a

little ozone from thG top layer to layer 6 or 7. If it is too

low, add some ozone to the top. A small change at the top vlill

make a large difference in N ( 90°) and N( 88°) . Get agreement

at 88° and 90° to within 2 units of N.

) I 0 0 0 (3 Calculate Log(I' I) for 86.5, 84 and 75 and add

ths same correction to each. Adjust ozone in the middle and

lower layers so as to get satisf2ctory agreement at all the

points.

37 •••

37

II Supplemt:ntary Tables for use at stations situate·d at about

912-mb level and at 810-mb level.

The m2.in modifications in the tables for a station at

0.9 p0

( = 912 mb) and at 0.8 p0

( = 810mb}. are given below.

It is assumt:d tl"lat the values of h in both these cases may be

taken to be 3 km instead of 2 km. This is sufficiently ~ccurate

for the present purpose. · The ai:r mass in the first layer (ground

to 6 km) should be changed as ~iven in Table 2X.

If the pressure at the station-level is kp0 ,· the value

of }i.., is given by

F = k+__E_ 1b

The first row of Table 4 for Fh corresponding to the lowast

layer is changed as shown in Table 4X. The values of Fh in all

the other rows are decreased by 0.100 when the station is at or

near 912 mb, and by 0.200 when it is at or near 810 mb.

For stations at or near 912 mb· and 810 mb respectively,

the values of Log ~ mu ~ F in the second columns of tables

5A to 5D (corresponding to th~ lowest layer) require the changes

given in T2bles 5A (X) to 5D (X}. For stations upto a height

of 2. 5 km, the tables for the m:arest pressure-level may be

used v:ithout appri::::ciablG error.

38 •••

For thu succeeding layers 2, 3, 4 &tc., the values of

Log u m - f3F tabulated in Tables 5A to 5D should be increased n

by (1 - kJJ~ for a station at pressure level kp0

• Thus, for a

station at 912 mb level, all tht: values in th,;: third column of

Table 5A should be incruasu·d by 0.1 00. f?) , and for a station at

the 81 0 mb levt: l' by 0. 200 r~ . An exarnplG is given in Table

5A (X) for the second and .third laye:rs,

: Tho values of 6 s -- D. h in the S~.;; cond column of

Table 6 corresponding to th-..: first laye:r roquircs a small and

ratht:;r insignificant che.nge, duG to tht; raising of the ct3ntre

of the layer from 2 to 3 km. 'I'hese changes for each value of

Z are tabulated in Table 6X.

It is r&cornmended that each station should modify

tablt:s for r0gular us~ at the station.

39 •••

39

Table 2X

-------------------------------Log 6 lib

-------------------------------1013 mb 1.715

912 mb 1,622

S10 mb 1.503

-------------------------~-----

'i.'he A m1 s in the, other layers remain the s..:tme as in Table 2.

40 •••

·rable 4X

~~----~"---------------------~-·--------~--------------·-------------------~~ l\~ .. · P mb I 37° 60° . 70° · 75'? · eoo 84 o 86~5· 88° 90° 0 . . . . .

h . . . . . .

------~----- --~----------~-------------------~-----~--~----~--~-~----~--~---1~13 ; il' 2 /1.199 1~788' 2.505. 3.221' ·4.610 7.133 10.~48 15.032 28.342, I . 912 I

I ..

b 3 11.076 1.597 2.232 2.8~6 4.0~5 6.329 . ·9.529 13.320 25.101

810 ' 3 !0,976 1.497 2.132 2.766 .3.995 6.229 9.429 1.3.220 '25.001 ' ~ \

______ J _____ l-------------------·-~-------------------------~----------------

~ ~

• • •

- 41

. . Table 5A{X} Log 6rlb_ ~- f3f ~or. th§ _lowest layer

-----~------~---x-;-3054~--------~---=---------)!~;~3253 _________ _ z I -.----------:----------------- ________________ ;... ________ ..., ___ _ _ _ __ -r-~2! ~-_ ~~ ___ ~1 ~ -_~1~ __ -~! 2 _ ~~ _ _ __ ! 212 _ ~~ ___ 21 ~ ~ :?~ ___ ~! 9 _ ~~ __

37 I 1.112 1,081 1.01~ 1.255 1,209 1,128 ;

60. ~.816 ~.8~9 ~.750 1.028: T_oo9 2-928

70 2.455 ~.499 2.431 2, 753 ~.765 2.684

75 ~.095 2.180 . 2".112. 2.478 2, 521 2.441

80 3~396 3.562 3.494 3.945 ~.o5o' 3.969

84 I 4,127 4.439 4.370_ I 4.976· 3.·192 },111

s6.5 1 o.3G9. "5'.829 'b.76o ~- 5.588 ·5.963-· 5.882 l i s8 -i · 8. 1 54 8. 9 2 2 . s. s 53 _ I 7. 9 43 · '6. •. so7 ; • 42 7

90 l 15.459 · --14.996 14.927 l 12.832 · TI .. 983 TI-.903 - ----~-----~---·:-------·------------.-'-~-------·----- ... ---~-~-----------

Table ,2B(X) Log ll.IDu - (iF fC?r the lowest la~r--· · · -· · _ ---~------------~-;-30~5~-------~------------->r~--3291 __________ _

z ----~---~-----~-~--------~- -------------------------------:1013mb .912mb 810mb 1013mb.; 912mb· 810mb· ----- --------------------------- ----------------~-----------~--

37 ; 1.138 1,104 . "f.034 1.277 1.229 1.147

60 . 2.855 2.854 2. 783 . . 1.062 1.039 2.957

70 ~.510 2.548 -· 2.478 : 2.S01 -2.807 2.725 , .

. . 75 ·~.166 2.243 2.173 2.539 2,576 2.493

80 3.49$ 3.652 3.581 2,0)2 ~.127 --2.045

84 1;,284 4.578 4.507 3.111 3.312 3._229

86.5 "6.-545. 5.039 -- o.96s l 5.792 4.144 4.061

88 1 8~485 7.215 7.144 0,228 '5.760 '0.678 L.-- .

90 1 14.082 . 13.548 . 1J,4ig I 11.370 10.460 10.378 ----~--------~--------~-------~~-~-~-~-----~----~~-----~~~--~--

-------------------------

- 42 -

Table 5C(X) Log .6.llb.- !3F for the lowest layer -----~--------~x-:-3112 __________ --------~-x-:-3323----------~

z ---------------------------- --------------------------~~-~-1 OJJ mb 912 mb 810 mb · 1013 mb · 912 mb 810 mb ----- ---------------------------- --------------~---------------

37 1.159

60· .2.8.85

70 2.553

75 2.220

80 3.576

84 4.405

86.5 b".728

88 8.740

1.123

2.881_

. 2.586

. 2.292

3._722

4.685

5.201

7•442

1.050

2.808

2.514

2.220

3.649

4.613

5.128

7~_369.

1.295 1.245 1.161 .

'f.0$9 ·'f. 063 2.'979 ~

2.838 2.$41 2.757

2.588 . 2.6_19 2.535 ..

2.101 . 2,189 ,. 2.105

3 •. 21 8 3.407 3.323

5.953 .. 4.287 . 4.203

6.454 6.960 .· "6.876

90 14.564 13.975 13.903- 11.795 . 10.837 -15.753 -----~-~T~bi;-5n(i1-~~-il-~-=-;1-;·--i~;-~h;-i~~~;t-i~;~--------~-------------------------------~ ... ----,..,_-------~-- ... ~-- ... ..;.-------------~

: i .. A = 3175 . · · · · )!. ~ 3399 z j ---------------------------- ----------~-------------------

-----L _ !~!~ ~~1~~- _ 2! ~-~~ ___ ~~ ~-~~- · · __ !~! ~~-~~---2~~-~~---~! ~-~~ ----! . 37

1~ T. 205 T. 1 65- 1. o88

60 l 2.955 2.943 2.~67'

10 1 2.650 2.673 2.597

75 I ~.346 2,404 ~.327

80 ! 3.156 3.882 3.805 .

84 1

86.5

88

4.683 4.932 4-~56

5.147

7.326

5. 572 .

7.961

5.496

7.8_84

90 . l 13.670 12.954 12.878 ----------~~--------------------

1.334

1-.146

2. 691

2.249

3.447

4.297

"6.935

10.702

1.280

1.114

2.912

2. 711

1.193

1.027

2.825

2.623

2.320•. 2.233 .. 3. 609 J. 522

4. 592·

5.386·

9.b40

4.505

5.299

9.553 ____ ..,._ __ ..._.,_..., ____ .. ________ .,.,

43 •••

-· 43 -

T3.ble _5A(Y)

-~og /.li-r~n·- {3F f;or second a~d hij;her,layers for a station at.810 mb. --------------------------------------------------------------------.. j f

A= 3054 0,200 f3 = o";101 X;_ 3.~53 0.200 (11

= 0.077 ----------~--------~------- ~------------------~------------

2 3 etc·! .. .. 2 3 etc •• z

-~-~------·-~------------ ~-~--~--~---~---~-------------. ..

37 ~.995· 2.680 1 .. 101 2.780

6o 2.857 2.625 2.996 2.737

70 .2.689 2.557 2 .• 868 2.685

75 2.521 2.4S9 4.739 2.633

so 2.194:: 2.355 2.489 2.532 .. ..

84 3.591 2.110 2,029 2.344

86.5 z;. 710 . J-o750 3.356 2.069

38 5.628 3.302 4.530 3.727

90 8 .. 070 5.~06 -7.814 4.586 . . l

--------------------------~---------------------------------------

44 •••

j

----------------------------

- 44 -

?able 6X

~s - tJh for. the first layer when the centre is at 3 km.

-~----------------_______ ....,. __ ------------------------------------\ z 37 60 70 . 75 80 84 $6.5 . 88 .. 90

Laye~ · ------------------------~--·----~~-~----------~-------~-----------

54-48 1.4 5.7

48-42 1.4 5.7

42-36 . 144 5.8

36-30

30-24

24-18

18-12

12- 6

6- 0

1.4 5.8

1.5 5.8

1.5 5.9

1.5 5.9

1..5 5.9

0.8 3.0

10.5 : ·14. 9

10.6 15.2

. 22.1

22.7

23.4 ..

.. 1'0,7 15.4

10.9

11,0

11 • 1

11 • 3

11 • 5

15.7 24.2

16.0 24.9

16.3 25.8

16.5 26,6

16.9 27.5

8.5 '14.1

·. 31 • 1

. 32.6

34.2

36.1

38.2

40.6

43.6

47.0

25.1

37

40

43

46

51

56

63

75

43

42

45

48

52

58

67

79

103

71

43

47

51

56

63

74

93

137

193

----- ~~------------------------~~~----~----------~-------~----

45 •••

45

I~ZFElt.GNCBS

1. Gotz, F.K.P., Mt:etham, A.PL. and Dobson; G.Il'l.B.,

Proc. Roy. Soc., A, 1934; ill, p. 416.

· 2 • Karandikar, H.. V. and l~am;~na than, . K .H. ,

Proc •. Ind. Ac2.d. Sci·., A, 1949,- ~' p. 330.

3. Wilkes 1 N.V.,

Proc. Phys. "' \:)OC • I B, 1954, ~' p. 304~

4~ \ialton, G.F.,

I.U.G.G •. Genoral Assembly, Bruxelles.- 1953·,

Proc-as-Ver~aux IAN, p. 316.

5. Ramanathan,- J(.H •. , I-1oorty, Bh.V.R. and Kulkarni, R.N.,

C~~uart. Journ. Roy. Met. Soc., 1952, ~' p. 625.

oooGOOOOOooo

- II.; -

2.) Importapce of modified Method B in studying the

vertical distribution of ozone in the lower atmgsphere

While working out a few vertical distributions or

ozone by Method B as described~in article 2.2, it was observed

that the ozone content or the first four or five layers could

be fixed within o.; unit (one unit = 10-) cm/km) and that or

the upper layers within 0.1 to 0.2 of a unit. Again, it was

found necessary to put a smaller ozone amount in 12 - 18 Km

layer than in 6 - 12 Km in order to have a tolerable fit at

70°, 75° and sao. Hence it was considered worthwhile to study

this minimum in ~reater detail for a few instances.

Before taking the vertical distribution obtained by

Method B as granted, it is necessary to keep the following

points in mind :-

1. A complete observation of the umkehr curve is spread

over a period of three to four hours and neither the

total ozone nor its vertical distribution can be

expected to remain unchanged.

2. The effect of forward scattering by large particles

of dust and haze is likely to be more pronounced for

solar zenith angles up tQ 60° or 70°, specially for

low level stations and ftazy skies.

3. The assumptions involved in Method B.

4. Neglect of the effect of higher orders of scattering

and scattering by large particles of dust and haze.

- II.6 -

Hence it is desirable to have the vertical distribution

of ozone obtained by this indirect method tested by direct

measurements in a few instances. ·

Two sets of observations were selected.and analysed to

study the variation in the vertical distribution of ozone.

(1) during different parts of the year and (2) during the

period when there were large changes in total ozone amount.

The first set was selected from the observations taken

by Mr. R.N.Kulkarni, M.Sc., during the year 1952. Since Mr.

Kulkarni selected 70° as the starting point for analysis, the

observed umkehr curves were extrapolated to 60° in some cases.

The second set was selected from the observations taken by

Mr. S.S.Degaonkar, M.Sc., during the period 1954-55. All the

observations were taken at Mt. Abu with Dobson Spectrophotometer

No. 39.

The vertical distributions of ozone for four different

months during 1952 as obtained by Mr. Kulkarni using the old

9 Km method, are presented in Table 10 A and those obtained by

the modified method are given in Table 10 B. Only the primary

scattered radiation is taken into consideration·in both the

cases.

From Table 10 A, it can be seen that there is no

appreciable change in the ozone content of the layers between

0 and 18 Km, and 27 and 54 Km. Any change in the ozone content

is due to the changes in the layer 18 - 27 Km. On the other

hand, the results given in Table 10 B bring forward the following

points :-

- II.7-

Table 10

Vertical distribution of ozone in different months during

1952 (A) as analysed by Mr. Kulkarni - 9 Km steps. (M.Sc.

thesis submitted by him to Gujarat University in 1953) and

(B) by the modified method B (6 Km steps). Observations by

Mr. Kulkarni.

~ L m

54-45 Km

45-36 Km 36-27 Km

27-16 Km 16- 9 Km

9- 0 Km

54-48 Km 48-42 Km 42-36 Km

36-30 Km 30-24 Km 24-18 Km

1 S-12 Km 12- 6 Km 6- 1 Km

13-4-52 i i

25-3-52 24-9-52 5-11..;52 i I

0.173 0.163 0.162 0.156 I I '

(A) 9 Km steps

I

o.4J : .. ·· o.2~ 1 o.4) 0.017 i 0.015 1. 5 ; 1. 5 1.4

0.3) 0.016 0.015 1.4

7.2J : 7.21 7.4} 0.147: 0.158 9.1 10.3 7.S

. 7.2} 0.137 0~134

7.7 1.0) 1.0} I 1.0} o.oo9 o.oo9 1 o.o o.o 1 o.o

'

1.o) I 0.009 0.009 ' o.o 1

{B) 6 Km steps . . I

o.2J I o.2} o.21

o.8 0.0221 1.0 0.023 0.8 0.019 2.1 1 2.6 2.2

6.31 ' 5.2} 6.3} 9.5 0.128 14.2 0.160 9.2 0.129 5.5 7.3 6.0

0.1) . o.s 0.019 2.3

6.0} 8.5 0.116 4.8

2.0} 1.0 0.0231 1.0

I

o.o} o. 51 o.o) I o.o o.ooo 1.0 0.014 2.1 0.023 o.o

11.0

12.1 1

- II.t-

1. The ozone content between 36 - 54 Km is slightly

higher in the summer months of March and April than

that for the months of September and November.

2. The ozone content between 18 - 36 Km and specifically

between 24 - 30 Km sho~ an increase with increase in

total ozone amount. This is in confirmi ty of the

results given in Table 10 A.

3. Unlike the results seen in Table 10 A, the ozone

amount from the ground to 18 Km, shows large

variations from day-to-day. The ozone content of the

surface layer ( 1 to 6 Km) is minimum in April and

maximum in November. Again the height distribution

of ozone below 18 Km is found to vary considerably.

This would be expected if there is occasional transfer

of stratospheric ozone into the troposphere followed

by turbulent diffusion.

A sudden increase in total ozone amount was observed

at Mt. Abu, Ahmedabad and New Delhi on 2nd March 1955. At

Mt. Abu, it shot up from 0.180 em on the 1st to 0.210 em on

2nd March. Afterwards, it showed a gradual fall and attained

a value of 0.175 em on the 6th March. The umkehr observations

at Abu during this period as analysed by Mr. Degaonkar using

the old 9 Krn method are given in Table 11 A. The distribution

as obtained from the modified method, is presented in Table 11 B.

The secondary scattering corrections have been applied in both

the cases (Walton, Table 7, Section II).

J

- II.9 -

Table 11

Vertical distribution of ozone at Mt. Abu during the period

2 to 6th March 1955. {A) analysed by Mr. Degaonkar with 9 Km

steps. (M.Sc. thesis submitted by him to the Gujarat University

in 1955) and (B) by the modified method {6 Km steps).

Observations by Mr. Degaonkar.

' $ • I o ... 2.;. .3-55 . ... .3-.3-55 4-.3-55 6-.3-55 i

L~ .. • . . ... ... , . .. ... 0 I 0 0

0.210 0.194 0.184 0.175 I I

·(A) 9 Km steps .......... , .......... 1. • l

54-45 Km 0.21 : 0.41 0.2} . i 0.2} 0.011 i 0.01.3 . 0.012 \ 0.011

45-.36 Km 1.0 I 1.0 1.1 1.0

.36-27 Km 5.7} '6.41 6.0} 6.2} 0.1.36 0.1.37 0.128 I 0.128

21-18 Km 9.4 8.8 8.2 8.o

18- 9.Km .3.5} .3.0} .3.5J 12.5] 0.06.3 l! 0.045 0.045 i 0.0.361

9- o Km .3.5 ,2.0 I 1.5 l 1.5

54-48 Km 48-42 Km 42-.36·Km

.36-.30 Km

.30-24 Km 24-18 Km

18-12 Km 12- 6 Km 6- 1 Km

. . ,

(B) 6 Km steps

I 0. 1} . . 0 ~ 2 J 0 • .3 }' . ; 0. 2J I o. 8 0.018 o. 7 0.019 0.6 0.017 : o. 7 0.016 2.1 2.2 1.9 : 1.7

I '

4.1l 6.11 4.4} \ 4.9} 9.5j o.124 8.5 o.126 1o.o 0.122j9.6 0.126 7.0 6.5 6.0 I 6.5

1

5.o] ) .3. 5} 2.0] } 1 .o} .3.5 0.069 .3.0 0~049 .).0 0.045 2.0 0.0.3.3 .3.5 2.0 .3.0 .3.0

- II.10 -

The results of computation presented in Tables 11 A

and B are in good agreement for heights above 18 Km. The

sudden increase of the total ozone amount on 2nd March, can

be attributed to a large influx of ozone into the troposphere.

The gradual decrease observed on the following days, is

presumably due to destruction of ozone at ground and downward

transport from upper troposphere. A gradual decrease of ozone

in 12 - 18 Km layer can be seen clearly from Table 11 B. A

gradual increase in the afternoon surface ozone at Ahmedabad

was observed during this period (Please see Section III).

2.4 Secondary and mu1tiple scattered light corrections

to the observed umkebr curve

Secondary scattering corrections to be applied to the

observed umkehr curve given in Table 7 (Section II) were

calculated by Walton for a plane-parallel infinite atmosphere

of finite optical thickness and on the assumption that ozone

is concentrated in one or two thin layers. Since a good part

of the umkehr curve is related to very low altitudes of the

sun, it was considered desirable to study the effect of the

curvature of the atmosphere and of the actual distribution of

ozone, on the ratio R2/R1 of secondary and primary scattered

radiations. •

2.41 Effect of the curyature of the atmosphere

The method of computing secondary scattered radiation

for a curved atmosphere has been described in article 1.2 while

treating the problem of the intensity and polarisation of the

sky during twilight. For computing the secondary scatte·red

- II.11 -

radiation R2 (i.e. R2n + R2t> received by an observer at the

ground, it is necessary to compute the secondary emission

E2 (i.e. E2n + E2t) at different points in the direction of

observation. Neglecting the anisotropy of the molecules, the

equation of E2 can be written down from Eqs. 10 to 18

(article 1.2) as follows :-

• ,!~ ff-f Cca' X.,..,• +<~ \ .,.. ) + .,.,~m'i'' [<:JD~ 'X_ r.t• __ + ._.,• X u.J]

for a given solar zenith angle Z0 and the height (bn) of the

point Q above the observer for which E2 is to be calculated.

For the curved earth, the variation of R1n' with Cos~1

(shown in Fig. 5, article 1.2) will be much more pronounced

and non-linear for shorter wave-lengths and in the presence of

a strong absorbing layer. On the other hand, for a plane-parallel

atmosphere, R1n' is constant and its value may be taken as that

for qb' = 90° (piane perpendicular to the principal plane through

the sun) • The integral

t, [.c t.o'x.,-.~--.~~t~l) __ + --~ t' _ _c_~~~tl . ~t yJ_ .'x. t -t.l)} . JZ ''"' ·- t!-_1'.~.-- ---·--· 0

was calculated {A) by taking into consideration the vari~tion

of R1n' with ¢ 1 , corresponding to the case of the actual earth

and (B)' taking R1 n, as constant over ¢' and taking its value as - I

that for ~ = 90° which corresponds to the case of a

plane-parallel earth. The method of computation used was

similar to that adopted for twilight work, but in this case

the atmosphere was divided into 9 Km layers and the centre

of gravity of the layer taken at a height of 3 Km above the

j

--------------------------------------

- II.12 -

base of the layer.

The results of computation by both the methods are

presented in Table 12, for A. 3112 A and Zo =sao. The

effect of a thin layer of ozone containing 0.180 em of ozone

at N.T.P. and situated at a height of 27 Km above sea-level,

was also considered. Proper allowances were made for reduction

in intensity whenever the direct or the scattered light

travelled through the ozone layer. The decimal scattering

coefficient ( f-' ) or the atmosphere was taken as 0.455 and

the decimal absorption coefficient ( ~ ) of one em of ozone

at N.T.P. was taken as 1.23.

From Table 12, it can be seen that when the point of

secondary emission Q, is situated at the ground, no appreciable

error is introduced even if variation of R1nr with p' is

neglected. This is because in this case, most of the

contribution to the integral comes from a cone having a

semi-angle less than 75°.

On the qther hand, if the point is situated at 18 Km,

there is a little over estimation. But as can be seen from

Table 13, most of the secondary scattered radiation is obtained

from the first 9 Km and hence no appreciable error is introduced

even if a plane-parallel earth is assumed.

(?."'11 f ( ~~,_x..,,.w

0

). • 3112 A

9' in degrees

- II,13-

Table 12

;. e;c., X.-t~~-:t __ ~l \f'• ( CQ'lX~tl ,_:t __ ~ __ :X._tttJ J--K~ . .D. 'l>~----z0 = 88° ~ • 0.455 oJ.. = 1.23

For Q situated at 0 Km

No ozone 0,18 em of o3 at 27 Km

A B A B

30 · 1,38 X 10-2 1,39 X 10-2 2.91 X 10-3 2,92 X 10-3

60 0.75 0.77 1.07 1.03

75 0,18 0.18 0,07 0,07

80 0,04 0.04 o.oo o.oo 85 0,00 o.oo o.oo o.oo

~ " .. .. ... ... ... . ~ .. ·' ..

For Q situated at 18 Km

• • 0 ,. • .0 ,. ~ o I • • ..

30,150 4,04 X 10-2 4,07 X 10-2 0,89 X 10-2 0,89 X 10-2

60,120 4.88 s.oo 0,68 0.70

75,105 6~57 6.80 0.35 0,36

80,100 8,09 8.38 0,18 0.18

85, 95 11.12 11.52 0.02" 0,03

90 5.00 5.56 o.oo 0,00

•

J

- II.14 -

Table 13

Distribution of secondary scattered light in the atmosphere

Ioe = 1,

Layer

0- 9 Km

9-18 Km

18-27 Km

27-36 Km

36-45 Km

45-54 Km

0

).= 3112 A Zo = ggo

No ozone

0.52 X 10-3

0.24

0.09

0.03

0.01

o.oo

~ D 0.455 ~- 1.23

0.18 em of o3 at 27 Km

0.77 X 10-4

0.27

0.09

0.07

0.02

0.01

2.42 Effect of distributing tota1 ozone content of the

atmosphere into three thin layers

In the previous sub-section, 0.18.cm of ~zone was

assumed to. be concentrated in one thin layer situated at a

height of 27 Km. However, ozone is actually distributed from

the ground to 54 Km·, the maximum being at about 25 Km. The

distribution of secondary scattered radiation as shown by

Table 13 (Section II) for Z0 = 88° suggests that if ozone

amount be divided in more than one thin layer, keeping in

mind its vertical distribution, the ratio ~/R1 is likely to

be ·affected. For this purpose, computations were carried out

by assuming total ozone content of the atmosphere distributed

in three thin layers:

(A)

(B)

and (C)

- II.15-

0.02 em at 9 Km

0.05 em at 18 Km.

0.11 em at 27 Km.

The calculations were carried out for two different

wave-lengths 3112 A and 3323 A having o(.. 1.23 and 0.07,

and ~ = 0.462 and 0.350 respectively. The following changes

were made in the method described in article 1.2.

1. Keeping in mind the results of article 2.41, variation

of R1n' with¢' was neglected. R1n' was assumed to be

constant over¢' and its value taken·'as that for ¢' = ~0 •

2. Wilkes tables were used to compute equivalent air-paths

for different Z and S' corresponding to H = 7 Km and

the radius of the earth 6400 Km.

3. The atmosphere was divided into 3 Km layers and the

centre of a layer was taken at a height of 1 Km above

the base 0 f the 1 ayer.

4. Actual air-mass in a layer was taken instead of the term

p'• ~h where p' is the density at the centre of the

layer.

5. Proper allowances were made for the reduction in

intensity whenever the direct or the scattered light

crossed any one of the ozone layers.

The ratio R2/R1 for different values of Z and two

different distributions of ozone is given in .Table 14 along

with Walton's results for an ozone amount of 0.18 em situated

- II.16-

at 24 Km. It can be seen that the effect of distributing

ozone in three thin layers is to reduce R2/R1 by a small

amount in the range 0° to 75° and to increase by a small

amount in the range 75° to 90°. The ratios obtained by Walton

are slightly higher than ours.

Table 14 . '0

R2/R1 for 3112 and 3323 A for different values of Z

Z in \No

0.18 em 0.18 em Walton degrees ozone at 24 Km in three 0.18 em at

I layers 24Km . ,. ... - . ' . 0

3112 A

0 0.49 0.47 0.46 0~52

60 0.59 0.56 0.54 0.59

75 0.66 0.59 0.57 o.6o

80 0.70 0.52 0.54 0.52 -.

90 0.67 0.44 0.44 0.45 . ·' 3323 A

0 I- 0.43 0.42 0.42 0.48 '

60 I

0.50 0.50 0.50 0.54

75 0.56 0.56 0.55 o.61 I 80 0.58 0.58 0.57 o.63

90 0.58 0.54 0.55 0.60 ... . ,. ~ .. . -· . . ....... • ..

The secondary scattering corrections to be applied to

the observed umkehr curve are given in Table 15. It can be

seen that there is no appreciable difference in corrections

obtained by different methods.

j

- 11.17 -

Table 15

Secondary scatt.ering corrections to be applied to the observed

Z in degrees

0

60

75

80

90

umkehr curye

o. H~ em at 24 Km

o.oo o.oo 0.01

0.03

o.os

0.18 em in three layers

o.oo o.oo 0.01

0.02

o.os

2.43 Effect of multiple scattering

Walton 0.18 em at 24 Km

o.oo o.oo 0.02

0.04

o.o6

The problem of scattering of light by the atmosphere

taking into account all the orders of scattering was solved - . . .

by Chandrasekhar. The functions necessary for calculating

the intensity and polarisation of any part of the sunlit sky - . . .

have been tabulated by Chandrasekhar and Elbert for a number

of values _of lr1• (For details, please refer to Section IV).

The theory is still to be extended to the case when one or

more absorbing layers are present.

A general idea about the effect of multiple scattered

light on the observed urnkehr curve can be obtained in the

following manner. In column 3 of Table 16, are given the ratios

of multiple scattered light (M) to the primary scattered light

(P) for 't 1 .. 1.0 for different values of f 0

c: Cos Z calculated

from the tables supplied by Chandrasekhar and Elbert. These

j

-·II.18-

are the ratios when no absorption layer is present. For

obtaining the ratio M/P when an absorbing layer is present,

we shall make the following assumptions which may be considered

as correct to the first approximation.

1. The ratios given in column 3 stand for 3323 when ozone

is present and for 3112 when it is absent. The ratios

R2fR1 (or M/P) for 3112 and 3323 without ozone differ

by a small amount as can be seen from Table 14, column 2.

However, this difference can be neglected because while

calculating the corrections to the observed umkehr curve,

it becomes trivial.

2. Since most of the secondary scattered radiation is

obtai ned from the space below the ozone 1 ayer, it has

not to travel through the ozone layer while giving rise

to third and higher orders of scattering. It can be . expected that the ratios M/P or S/P are affected by

the same amount by ozone.

The ratio S/P without and with 0.18 em of ozone at

24 Km as obtained by Walton, are given in columns 4 and 5

respectively (Table 16). The amounts by which the ratio S/P

decreases due to ozone are given in column 6. The column 7

gives M/P for 3112 as expected from the assumptions stated above.

The corrections given by

- Log

are shown in column a.

1 + (M/P)3112 1 + (M/P) 3323 ·

It can be seen that the correction is

appreciably affected when all the orders of scattering are taken

into consideration.

- II.19-

Table 16

Corrections to be applied to the obseryed umkehr curve when

multiple scattering is taken into consideration

z · · I (S/P) {S/P) Effect ~ !

(M/P) 3323 without with- of 03 (M/P) tcorrection

11.5

48.7

60.0

71.3

76.1

79.6

81.9

84.2

0.98

0.66

0.50

0.32

0.24

0.18

0.14

0.10

1.24

1.49

1.65

1.86

1.95

2.04

2.03

86.5 o.o6 2.09

87.7 0.04 1.95

2.5 Conclusion

ozone 0.18 em on S/P 3112t at 24 Km ;

0.56

0.60

0.652

0.710

0.734

0.745

0.749

0.748

0.55

0.571

0.591

0.608

0.573

0.522

0.488

0.466

0.982

0.952

0.906

0.856

0.781

0.701

0.652

0.615

1.22

1.42

1.49

1.59

1.52

1.41

1.33

1.25

0.733 0.455 0.621 1.30

0.715 0.455 ,0.6)6 I 1o24

' i i o.oo ~ l 0.01 ~

, o.o3 0.04

i 0.07 i ' 1 o.1o ;

I 0.12

0.13

0.13

1 0.12

The method B for calculating the vertical distribution

of ozone as used in India uptil now is modified in the following

manner :- {1) Division of the atmosphere into 6 Km layers instead

of 9 Km ones and {2) fitting of the curve at ei&ht different

places. With the help of this modified metqod, it has become

posable to follow the day-to-day changes in distribution of

ozone with height in the entire atmosphere.

It has been shown that the effects of the curvature of

the earth and of the actual distribution of ozone, on the

I

- II.20 -

secondary scattering corrections, are quite negligible. On

the other hand, the effect of higher orders of scattering on

the observed umkehr curve is quite considerable. ~more

satisfactory theory and calculations are essential to obtain

an idea of the proper corrections to be applied to the observed

umkehr curve, when all the orders of scattering are taken into

consideration. It would be sufficient to treat the problem

for a plane-parallel atmosphere having only one absorption

layer of ozone at a proper height.

2.6 References

1 Chapman,s.

2 Fabry,c.

3 Gotz:,F.W.P.

4 Gotz,F.W.P.,

Meetham,A.R. &

Dobson,G.M.B.

5 Gotz,F • W.P.

1934-35 Phil. Trans. Roy. Soc. London

lJ1t A, P. 205

1950 "L'ozone Atmospherique" National

Centre of Scientific Research,.

Paris.

1931 Gerl. Beitr • .l1 P. 119

1934 Proc. Roy. Soc. A~ P. 416

1951 "Ozone in the Atmosphere" -

Compendium of Meteorology,

Amer. Met. Soc. Boston, Mass.

P. 275

- II.21 -

6 Johnson,F.s.,

Purcell,J.D. &

Tousey,R.

1951

7 Karandik ar, R. V. & 194 9

Ramanathan,K.R.

8 Ramanathan,K.R. 1954

9 Ramanathan,K.R., 1952

Moorthy,Bh.V.R. &

Kulkarni,R.N.

10 Regener,E. &

Regener,V.H.

11 Walton, G.F.

1 2 Walton, G.F.

V .sh 13 Wilkes,M\

1934

1953

1955

1954

Journ. Geophys. Res. 2Q

P. 583

Proc. Ind. Acad. Sci. Z2 Sec. A, P. 330

Presidential Address, Rome

Assembly of the International

Association of Meteorology,

Sept. 1954. Butterworths

Scientific Publications,London.

Quart. Journ. Roy. Met. Soc.

1§, P. 625

Phys. z. ll, P. 788

I.U.G.G. General Assembly,

Bruxelle·s, Proces-Verbaux,

I.A.M., P. 316

Phil. Mag. ~~ P. 281

Proc. Ph~ Soc. Ql, B, P. 304