A method of measuring atmospheric ozone absorption coefficients

Journalof Atmospheric andTerrestrial Physics,1966,Vol. 28, pp. 667-672.Pergamon PressLtd. Printedin Northern Ireland

SHORT PAPER

A method of measuring atmospheric ozone absorption coefficients R. A.

HAMILTON

The Observatory, Lerwick

and J. M.

WALKER*

College of Advanced Technology, Birmingham

(Received 29 December 1965) Ah&&--A method is described of determining the ozone absorption coefficients in the wavebands normally used when measurements are made of the amount of atmospheric ozone by a Dobson spectrophotometer. The ratio of absorption coefficients in different wavebands is obtained from the calculated amounts of ozone when simultaneous measurements are made with different wavebands. Values obtained from observations at Oxford and at Lerwick show good agreement: the values differ appreciably from those of V&roux and other workers.

1. INTRODUCTION

International Ozone Commission adopted in 1957 the ozone absorption coefficients determined in the laboratory by VI~ROUX (1953) for calculation of the amount of atmospheric ozone from measurements by Dobson spectrophotometers of the relative intensity of wavebands in the ultra-violet. DOBSON and NORMAND (1962) from atmospheric observations concluded that the Vigroux coefficients were considerably in error. Later DOBSON (1963) made laboratory measurements of the ratios of absorption coefficients of different wavebands and obtained values which differed considerably from those of Vigroux but were in quite good agreement with atmospheric observations at Oxford and at Edmonton. The Oxford atmospheric absorption coefficients were derived from the observations made with the object of determining the extra-terrestrial constant L, of Dobson spectrophotometer No. 1 in 1957. Dobson states that Oxford has a most unsuitable atmosphere for this work, and estimates the errors in L,, as about fO.010 or less. As will be shown in this paper, errors in L, cause errors in the ratios of the absorption coefficients. In this paper a method is described of measuring the ratio of absorption coe& cients which is not invalidated by errors in the extra-terrestrial constants. In addition the method indicates whether there are errors in the extra-terrestrial constants, though there are not enough equations to enable these errors to be determined uniquely. THE

2. THEORY

OF METHOD

The Dobson spectrophotometer measures the relative intensities of two wavebands in the solar spectrum. The instrument and the method of its operation is

* Present address: Imperial College, London. 667

described in the 1.G.V. Instruction &fANUAL (1955), which defines in greater detail the conventional symbols used below, and lists also the wavelengths of the pairs of wavelengths A, B, G and D which are used. Most. observations are made on A and D wavelengths, and are knclwl as _dn observations, as the effect of aerosol is thus eliminated. Let 1,Z’ be the intensities of the two wavebands measured by the spectrophotometer after the radiation has passed through the atmosphere, and let I,, I,’ be the corresponding intensities which would be measured by the spectrophotometer if taken outside the atmosphere. Then log 111’ =z log I&” where

u,cC fl,fl’ 6,tY z 2 m ,u

.- ( x -

cc’) px -

(13 -

fY)mn -- (6 -

6’) set 2

(1)

are the ozone absorption coefficients for the two wavebands. are the molecular scattering coefficients. are the aerosol scattering coefficients. is the vertical thickness (in cm at N.T.P.) of oxone. is the Sun’s zenith distance. is the equivalent path-length of sunlight through the atmosphere. is the relative path-length of sunlight through the ozone layer.

In this discussion only observations were considered when the atmosphere was clear so that (6 - 8) is negligibly small and the last term of (1) is henceforth omitted. The quantity log 1J1, is the extra-terrestrial constant L,; it is a quantity which is a characteristic both of the individual spectrophotometer-the sensitivity of the photomultiplier, size of slits etc.-and of the solar spectrum, which may vary during the solar cycle. Writing N = L, equation

log I/I’

(1) becomes

N = (CC-

cr’) /.&Z+ (/3 -

/Y)m

(2)

Let dN, be the error in the assumed extra-terrestrial constant of the spectrophotometer for A-wavelengths, and let xd be the amount of ozone calculated when the V&roux coefficient (tl - a’),A is used. Then from (2) X -+ dN,

= ,~ux,(cr -

CX&, + m(,!? -

j3’)

But writing

x4( cc -- Q’)~~ = x (a-Similarly

so

a’),

dNA 1 + g * x (a - CC’)~

(

1

A method of measuring atmospheric ozone absorption ooefficients

069

Thus if a number of observations are made simultaneously on different wavelengths at varying solar zenith distances and the value of the ratio of the computed ozone amounts x,/x~, is plotted against q/x the points should lie on a straight line which cuts the q = 0 axis at a value (xA/XA& given by _@ - Cc& (a -

a')AD =

xA _. ( xAD 1 0

(a -

a')OA (4

(a -

")OAD

From such equations the values of (a - a')A, (a - a')B . . . can be determined in terms of (a - a’)gg. It is to be noted that (4) does not include the errors dNA . . . thus by extrapolating to q = 0 errors arising from errors in Lo are eliminated. 3. COMPUTATION OF THE ABSORPTION COEFFICIENTS

The data used in this investigation consists of the observations made during the 1957 determinations of Lo at Oxford, which Dr. Dobson has kindly put at our disposal, and a similar series of observations made on very clear days at Lerwick in 1963 when Lo was determined in the same way. Although these observations consist primarily of sets of observations made during one day at varying solar zenith distances, it must be stressed that this is not necessary: any observations made in clear conditions can be used, provided they cover a sufficient range of q. Altogether about 130 sets of simultaneous observations at Oxford, and 100 at Lerwick have been considered. The Oxford observations were mainly made near noon and when p = 2 and ~1= 3 approximately. The Values of XA/XAn. . . were calculated for each observation and were plotted on graphs with q as abscissa: the scatter of the points was such that roughly 50 per cent lay within O-01 of the mean. At Lerwick a larger number of observations were made per day, on fewer days : the scatter was only about one half of that of the Oxford observations. It is more convenient to use as abscissa the dimensionless quantity q’ = 0.35 q/x (the mean value of x is about 0.35). Mean values of xA/xAD . . . and q' were calculated for three groups for the Oxford observations, and for five groups, q = 0*30.4, 0.4-05 etc. for the Lerwick observations. These are plotted for wavelengths A, B and C in Fig. 1, in which the regression lines have been drawn. In the case of the A-wavelengths it can be seen that the two lines are close and parallel, and give values of I.014 and 1.011 for (xA/xAD)O. In the case of the B-wavelengths the lines cross and give values of 0.966 and 0.962 for

(xS/xAD)O.

In the case of the C-wavelengths the values differ considerably for high values of q', but converge and give values of 0.956 and O-961 for (xo/~AD)o. From the values (XA/X_,& etc. in Fig. 1 the absorption coefficients for wavebands A, B, C and D can be calculated, assuming l-388 for that of waveband AD (see below). These values computed from the Oxford and the Lerwick observations are given in Table 1 together with V&roux’s values, and the Oxford laboratory values given by DOBSON(1964). Ratios XA~/XADwere also evaluated, as the effect of haze is thus eliminated, and plotted against q', but the scatter of points was rather large. The best lines gave values of (a - a'),J( a - a')AD of 1.210 for Oxford, and 1.204 for Lerwick compared with values of 1.223 and 1,214 derived from the values in Table 1.

T?. A. HAMILTON and .I. 31. WALKER

A7 0

Lerwck Orford

/ L.96

_r-x-

,-*-Y

XC m

xc

xAD

82 CJ5

cJ94i

0

~

02

n?;

0.4

0 5

06

0.7

0.8

o-9

qN

Fig. I. Table 1. Ozone absorption coefficients assuming that (rx - cr’)~~ = 1.388 11 Vigroux Oxford Lerwick Oxford Labodory

1.762 1.786 1.781 1.742

Wwelengths R 1.223 1.182 1.176 1.142

G

0.865 0.827 0.831 0.808

L) 0.374 0.398 0.393 0.354

The advantage of t,he atmospheric method of measuring absorption coefficients over the laboratory method is that the measurements are made on the ozone at the low temperature, about -4O"C,at which it exists in the atmosphere, and over the same bandwidths as those used in making routine observations. Vigroux measured absorption coefficients of narrow bandwidths and these showed wide variations over a range of a few Angstroms both in the absolute values at room temperature and in the temperature coefficients of the absorption coefficients. Errors will occur when mean values of absorption coefficients over a waveband of about 11 h for the shorter wave slit are computed. Moreover there are clearly technical difficulties in making laboratory experiments at -4O"C,and there seems to be little doubt but that the Vigroux coefficients are in error-those of B and C wavepairs by about 4 per cent. In Dobson’s laboratory experiments he used a Dobson spectrophotometer, and thus averaged the absorption coefficients over the required bandwidths. However he was only able to measure the ratio of the absorption coefficients for the different wavebands at 60°C and at room temperature, and he was obliged to usevigroux’s temperature coefficients to compute the values at - 40%. In the case of D-wavelengths,

A method of measuring atmospheric ozone absorption coefficients

871

the absorption is small and the absolute values and their temperature coefficients vary rapidly with wavelengths, and it seems likely that the rather larger temperature correction used for D-wavelengths than for the other wavelengths is excessive, and consequently that the D-wavelength absorption coefficient obtained by Dobson is too low. V&roux’s absorption coefficient I.388 for AD-wavelength is now accepted, even though it may be slightly in error, so as to avoid a discontinuity in the published values of ozone amounts, the majority of which have been made on AD-wavelengths. Stations at higher latitudes, however, must use B- or C-wavelengths during the winter and it is important for them that correct values of absorption coefficients for B and C, relative to AD, shall be used so that there shall be no discontinuity in ozone amounts at the time of year when the change of wavelength is necessary. It seems preferable to use absorption coefficients obtained at the station with the spectrophotometer in use by the method described above rather than values measured in the laboratory. Probably most stations have available measurements made in clear conditions over a range of ,u from 3.0 to midsummer noon values and can thus determine the absorption coefficients. 4. CORRECTIONSTO THE EXTRA-TERRESTRIAL CONSTANTS

From (3) it is seen that the gradients of the lines in Fig. 1 are given by

The gradients are measured, and all the quantities dN,, . . . and thus three equations of the form 0.6 dN,

-

0.7 dN,,

=

in (5) are known except dN,,

-3

are obtained. These three equations are insufficient to determine the four unknowns, but the fact that the gradients of,the lines are not zero indicates that dN, . . . are not all zero. These values dN, . . . arise from random and systematic errors in the determination of L, : systematic errors arising from diurnal variation of ozone amount cannot be detected for this leads to errors such that

However it is possible to minimize the random errors by accepting a least squares solution. In the case of Oxford the least squares solutions are dN, = -0.004, dN, = 0.005, dN, = -0.002, dN, = -0.005 and dN,, = O*OOl. For Lerwick the values are dhT, = -0.004, dNB = 0.006, dN, = 0.002 and dND = -0.004, dN,, = 0. These values are of little general interest, but they indicate the probable magnitude of the error in L,,. If these corrections are made to the wedge calibration tables consistent values of ozone amount will be obtained on all wavelengths for all values of p. 9

672

1X.A. HAMILTON

and J. M.

CI'ALKER

5. C~NOLUSI~NS

The ozone absorption coefficients for the wavebands used by the Dobson spectrophotometer can be determined by making simultaneous observations on different wavebands over as wide a range of ,u as is practicable. The values obtained from series of observations made at Oxford and a,t .Lerwick show good agreement: the values differ by up to 5 per cent from the values determined by Vigroux. Acknowledgement+--We wish to thank Dr. G. $1. B. DOBSON for his advice and encouragement, Mr. L. S. LESLIE and Mr. J. R. M. GEORGESONwho have carried out many tedious calculations, and the Director-General of the Meteorological Office for permission to publish this paper. REFERENCES DOBSON G. M. B. and NORMAND CHARLES DOBSON G. M. B. 1. G. P. Instruction Manuel VIUROUX E.

SIR

1962

Ann. Int. Geophys. Yr. Vol. XVI, p. 161.

1963 1967

Q. Jl R. Met. Sot. 89, 409.

1953

Ann. Int. Geophys. Yr. Vol. V, p. 46. .!lnn. f’hys. 12, h’o. 8, 1.