derivation of total ozone abundance and cloud effects from spectral irradiance measurements

Derivation of total ozone abundance and cloud effects fromspectral irradiance measurements

Knut Stamnes, James Slusser, and Melissa Bowen

We describe a method to infer total ozone abundance and effective cloud transmission from global (diffuseplus direct) spectral irradiance measurements taken at the Earth's surface. The derivation of total ozoneabundance relies on the comparison of measured irradiance ratios at two wavelengths in the UV part of thespectrum with a synthetic chart of this ratio computed for a variety of ozone abundances. One of thesewavelengths should be appreciably absorbed by ozone (e.g., 305 nm) compared with the other one (e.g., 340nm). This synthetic ratio (and therefore also the inferred total ozone abundance) is insensitive to the value ofthe surface albedo used in the model computations. Comparison with independent in situ and remote (fromground and space) determinations of total ozone abundance shows that measurements of global irradiancesprovide a reliable means of inferring the total column ozone amount for clear as well as cloudy sky conditions.Computer simulations are used to demonstrate that the ozone abundance inferred from global irradiancemeasurements is quite insensitive to cloud effects, whereas the use of the scattered irradiance only or thezenith sky intensity (measured routinely in the Dobson network on overcast days) requires substantialcorrections for cloud effects. Effective cloud transmission is estimated from the data by comparing themeasured irradiance at a wavelength where ozone absorption is minimal (e.g., 350 nm) to the clear-sky value.Irradiances generated by a plane-parallel radiation model as a function of cloud optical thickness are used toestimate an equivalent stratified cloud optical depth. These estimates of cloud transmission and opticaldepth are sensitive to ground reflection, implying that the accurate determination of cloud attenuationrequires precise knowledge of the surface albedo.

Introduction

Since the discovery of the Antarctic ozone hole' andreports indicating declining levels of ozone abundanceon a global scale,2 3 there has been renewed scientificinterest as well as considerable public concern aboutthe possible impact of ozone depletions on the UVradiation reaching the biosphere. While a long-termglobal data set on total ozone abundance exists fromthe Dobson network dating back more than 30 years,relatively few measurements are available of the bio-logically effective UV radiation reaching the ground.

The penetration of UV solar radiation through theatmosphere depends not only on solar elevation andozone abundance but also on the following geophysicalparameters: (1) stratospheric temperature; (2) alti-tude distribution of ozone; (3) surface albedo; (4) cloud

The authors are with the Geophysical Institute and Departmentof Physics, University of Alaska Fairbanks, Fairbanks, Alaska99775-0800.

Received 11 September 1990.0003-6935/91/304418-09$05.00/0.C 1991 Optical Society of America.

height, optical depth, and morphology. Besides thetotal ozone content, temporal and spatial variation incloud cover may be the most important parameteraffecting UV penetration, and possible systematicchanges in cloudiness might jeopardize attempts toassess trends in ozone abundance.4 Thus, in view ofthe sparsity of measurements providing a direct linkbetween the UV radiation received by the biosphereand the total ozone abundance, one needs to accountfor possible trends in cloud cover as it affects UVpenetration to assess trends in the UV radiation envi-ronment.

The purpose of this paper is to document and discussa procedure for deriving total ozone abundance andeffective cloud transmission from global spectral irra-diance measurements. This allows us to determinethe link between the biological UV dose, ozoneamount, and cloud attenuation from spectral measure-ments of the UV radiation calibrated in absolute units.Such measurements are currently emerging,5-8 andthey are urgently needed to establish this missing linkand thereby enable us to monitor the time evolution ofthe UV radiation environment. This time history is ofgreat interest to biologists concerned with the impactof potential ozone depletions on living organisms (see,

4418 APPLIED OPTICS / Vol. 30, No. 30 / 20 October 1991

for example, Ref. 9). Application of the techniquesdocumented here to analyze UV radiation measure-ments in Antarctia is reported elsewhere.8

Method of Analysis

Our analysis is based on the assumption that observedspectral irradiances in the UV region between say 280and 350 nm are available with appropriate resolution(a few nanometers are adequate for our purposes).Such measurements are now available through theU.S. National Science Foundation UV monitoring pro-gram in Antarctica where scanning spectrometers areused to measure the global downward irradiance with aspectral resolution of about 0.5 nm. Our aim here is todemonstrate that spectral measurements such as thesecan be used to make reliable simultaneous assessmentsof biological UV dose, ozone abundance, and effectivecloud transmission.

The global irradiance (i.e., the sum of the diffuse anddirect irradiance rather than the individual compo-nents) is required to assess the biological effects of UVradiation. It is easier to measure only the global irra-diance, because the separation into diffuse and directcomponents requires tracking of the sun. Moreover,measurement of the direct component is complicatedbecause it requires a correction for scattered lightcaused by forward scattering of atmospheric particu-late matter into the instrument field of view, which isusually considerably larger than the solar disk. In theDobson method (which relies on direct Sun measure-ments whenever the Sun is not obscured by clouds),this forward-scattering problem is dealt with by utiliz-ing the difference between two wavelength pairs for apartial correction of the effects of particulate matter,including the wavelength dependence of aerosol scat-tering. These considerations provide a strong motiva-tion for using global irradiance measurements to infertotal ozone abundance and cloud attenuation as well asa biological UV dose.

The simultaneous determination of total ozoneabundance and biologically effective UV radiation ispossible by taking ground-based spectral measure-ments (calibrated in absolute units) of both the diffuseand direct components.5 One may then infer the totalozone amount by utilizing the directly attenuated solarirradiance at two different wavelengths in the UV re-gion, one that is appreciably absorbed by ozone (forexample, 305 nm), the other that is not (for example,340 nm). The Dobson method relies essentially onthis principle.' 0 If, however, only the global irradi-ance is measured (which is the quantity of interest forUV dose determination), the scattered radiation mustbe taken into account. To infer column ozone abun-dance and effective cloud transmission from the globalirradiance measurements, we have utilized a UV radia-tion model that includes multiple scattering andground reflection. Global spectral irradiance mea-surements described elsewhere8 will be used to test andverify the procedures presented here for the inferenceof total ozone abundance. These measurements are

part of the National Science Foundation UV monitor-ing program in Antarctica.

UV Radiation Model

The basic model is described in detail elsewhere."Only a brief outline is provided here. The tempera-ture-dependent ozone absorption cross sections aretaken from Ref. 12. We used the values given for 226K; this is close to the 229 K temperature adopted in theinference of ozone abundance from the Dobson net-work. To account for molecular scattering, atmo-spheric density profiles are needed. In this work weutilized the McClatchey et al.1

3 atmospheric densityprofiles for the sub-Arctic summer. The inferredozone abundance and cloud optical depth are, howev-er, quite insensitive to the choice of a clear sky atmo-spheric density profile.

To solve the radiative transfer equation we used thediscrete ordinate method described in Ref. 14. Thissolution pertains to slab geometry. To account for thelarge solar zenith angles encountered at McMurdo, weadopted a newly developed spherical radiative transfermodel.15 This spherical model takes into account theearth's curvature by converting the spherical radiativetransfer problem into a series of plane-parallel ones.For solar zenith angles of less than 900, it is sufficientto treat the multiple scattering in slab geometry as longas the single-scattering driving term is correctly com-puted using spherical geometry.15

To illustrate how effective cloud transmission can,in principle, be determined from the irradiance data,we show a comparison in Fig. 1 of the computed clearsky irradiance and the observed irradiance at 349 nmwhere ozone absorption is minimal. Computed clearsky irradiances are shown for three values of surfacealbedo (0.70, 0.75, 0.80) presumed to bracket the valueappropriate for the partially snow-covered surface atArrival Heights, McMurdo, in January. Unfortunate-ly, no measurements of surface albedo at McMurdo are(to our knowledge) available for the period of observa-tions. The measurements shown in Fig. 1 were takendaily in 1989 at 0.00 GMT, which is close to local noonat McMurdo Station. A more detailed description ofthe measurements is provided in Ref. 8. Assumingthat the surface albedo was 0.75, we notice that on twodays there is close agreement between observed andmodel-predicted irradiance. We may therefore for thesake of argument assume that the sky was clear onthese two days and that discrepancies between theobserved irradiance and the predicted clear sky valueon other days are due to cloud effects. Thus, we mayuse this discrepancy to define cloud transmission andan equivalent stratified cloud optical depth as ex-plained below. Possible aerosol effects (expected tobe small in the pristine Antarctic atmosphere) are thusincluded in our definition of cloud. Here we shouldstress that our inferred cloud optical depth is depen-dent on our choice of surface albedo, which shouldhave been determined by a measurement. The lack ofsuch a measurement implies that the effect we ascribe

20 October 1991 / Vol. 30, No. 30 / APPLIED OPTICS 4419

E

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Fig. 1. Comparison of computed global irradiance at 349 nm forclear sky conditions (solid curves) and observed irradiance (dashedcurve). The computed curves pertain to the surface albedo of 0.7(lower curve), 0.75 (middle curve), and 0.8 (top curve).

to clouds could partially be due to the incorrect choiceof surface albedo, as illustrated in more detail below.

Estimation of Cloud Transmission and Equivalent OpticalDepth

It may be inferred from Fig. 1 that clouds have a stronginfluence on UV attenuation. Thus, changes in tropo-spheric cloud cover can significantly affect UV pene-tration, although variations in cloudiness are expectedto influence UV-B (280-320-nm) and UV-A (320-400-nm) radiation in much the same way because the wave-length dependence of the cloud effect is very weak inthe UV spectral range.'r- 8 The effect of clouds on UVpenetration will, in general, depend on cloud type,height, and morphology. If such information is notavailable from observations, one may nevertheless at-tempt to quantify the influence of clouds on the irradi-ance reaching the biosphere by comparing the mea-sured irradiance to the anticipated clear sky value at awavelength where ozone absorption is minimal. Ourmodel allows the insertion of stratified cloud layers.'9Thus, we may compute the downward irradiance at thesurface as a function of cloud optical depth. Compari-son of model-predicted and observed irradiance willthen allow us to infer the equivalent stratified cloudoptical depth, which makes the computed irradianceagree with the observed value. In Fig. 2 we show anexample of model-predicted irradiance (normalized tothe clear sky value) as a function of optical depth forseveral solar zenith angles.

Since the real cloud cover may consist of brokenrather than idealized stratified clouds, the inferredoptical depth is to be interpreted as the equivalentstratified cloud optical depth consistent with the ob-servations and the assumed surface albedo in the sensedefined above. In spite of this limitation we believethat the equivalent optical depth inferred from theobservations in this manner may provide a usefulquantitative measure of the influence of clouds on the

00

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Fig. 2. Computed global irradiances as a function of the cloudoptical depth normalized to the clear sky value. The solid curves arefor the surface albedo of 0.4, and the dotted curves are for 0.8.Ratios are shown for several solar zenith angles from top to bottom:10, 30, 50, and 70°.

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Fig. 3. Schematic illustration of the synthetic chart used to deter-mine ozone abundance. The computed ratios of irradiance at 340-305 nm are shown as solid curves as a function of the day number(zenith angle) for several values of total ozone abundance. Thesmooth curves are 20 DU apart. The solid curve with squares marksthe corresponding observed irradiance ratios.

penetration of UV radiation. However, since thecloud optical depth inferred in this manner may bemodel dependent, it may be preferable to describe thecloud effect instead by an effective cloud transmission,which is just the ratio of the true global irradiance atthe ground to the clear-sky value. Accurate knowl-edge of the surface albedo would significantly enhanceour capability to retrieve a meaningful value of cloudtransmission or optical depth.

Determination of Column Ozone Abundance

To infer column ozone content from the observed glob-al irradiances we proceed as follows. The radiativetransfer model is used to generate a synthetic chart ofthe ratio of global irradiances at 340 and 305 nm. This


chart was produced for a variety of column ozoneamounts (by scaling the standard profile from themodel atmosphere) and for the actual solar zenithangles occurring throughout the season. The columnozone amount was then derived by matching the ob-served irradiance ratio on any particular day to theappropriate curve in the synthetic chart. This proce-dure is illustrated in Fig. 3. A similar procedure forinferring column ozone amounts from global irradi-ance data is described in Ref. 17.

Uncertainties in Cloud and Ozone Derivation

Influence of Surface Albedo on Cloud Estimation

The downward irradiance at the surface depends onthe reflection by the underlying surface as illustratedin Fig. 1. In general, the downward irradiance re-ceived at the surface is expected to increase with thesurface albedo for specified atmospheric and illumina-tion conditions. This implies that the surface albedomust be known to estimate effective cloud transmis-sion or optical depth by the method outlined above.Consequently, the surface albedo for the particularmeasuring site is a quantity of some importance in thisconnection. We show that our attempts to determinecloud transmission or optical depth may be seriouslyjeopardized if measurements of the surface albedo arenot available unless this quantity can be reliably esti-mated by other means.

To illustrate the uncertainty in the cloud attenua-tion estimation resulting from inadequate knowledgeof the surface albedo, in Fig. 4 we show a plot of thecomputed irradiance (normalized to the clear sky valuefor an albedo of 0.75) as a function of the cloud opticaldepth for several surface albedo values (assuming thesurface to be a Lambertian reflector). A solar zenithangle of 60° was used in this calculation. Clearly thisratio is quite sensitive to changes in the surface albedo.This implies that the cloud optical depth, inferredfrom irradiance measurements by comparison to sucha synthetic curve, would have great uncertainties at-tached to it unless the surface albedo is accuratelyknown. For example, we estimate from Fig. 4 that anuncertainty in surface albedo of 10% would imply anuncertainty in inferred cloud optical depth of about30-40% for this particular solar zenith angle.

Uncertainties in Ozone Derivation from Cloud Effects

As mentioned, the wavelength dependence of cloudscattering in the UV region of interest is very weak andmay be neglected. Because a ratio of attenuated di-rect solar irradiance at two nearby wavelengths is usedin ozone derivation from direct Sun measurements, thecloud attenuation will exactly cancel if it is assumed tobe wavelength independent. This implies that theinference of total ozone abundance from direct Sunmeasurements will be essentially unaffected by cloudscattering. However, ozone inference from the globalor scattered irradiance and from the zenith sky intensi-ty, in particular, will be affected by cloud scattering.To illustrate the influence of cloud scattering on ozone

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Fig. 4. Computed global irradiance (normalized to the clear skyirradiance for a surface albedo of 0.75) as a function of the cloudoptical depth for several surface albedo values ranging from 0.65(bottom curve) to 0.85 (top curve) in steps of 0.02.

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Fig. 5. Ratio of scattered to global (scattered plus direct) irradi-ance as a function of cloud optical depth for 305 nm (dotted curves)and 340 nm (solid curves). Three values of the secant of the solarzenith angle were used: 3.0 (top curves), 2.0 (middle curves), and 1.0(bottom curves).

retrieval we show in Fig. 5 the ratio of diffuse to globalirradiance as a function of cloud optical depth for thetwo wavelengths adopted for ozone determination inthis work. As expected, this ratio approaches unityasymptotically with increasing cloud optical depth butdoes so differently for the two wavelengths. Thus,when global irradiance is used (in lieu of the directcomponent) to determine total ozone abundance, theeffect of cloud scattering will not exactly cancel be-cause the cloud optical depth will affect the two wave-lengths differently (although assumed wavelength in-dependent). This occurs because the relativeimportance of clear-sky scattering and absorption isvery different for the two wavelengths as a conse-quence of the strong wavelength dependence of bothozone absorption and molecular scattering.


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3.0 dotted curve, r = 0.3; chain-dashed curve, = 3.0; dashed curve, =

30.0. (b) Same as (a) but for scattered irradiance only. (c) Same as(a) but for zenith sky intensity.

2.5

To investigate the influence of clouds on the deriva-tion of total ozone abundance from irradiance (or thezenith sky intensity) data, we simulated the measure-ment procedure by computing the ratio of irradiances(or intensities) at 340 and 305 as a function of the solarzenith angle for clear and cloudy sky conditions. Wethen define aso-calledNvalue as follows: N = log(F1/F2), where F1 and F2 are the computed irradiances (orintensities, whichever are appropriate) at wavelengthsof 340 and 305 nm, respectively. The clear sky calcula-tions were done for total ozone column values of 340,350 (standard case), and 360 Dobson units (DU). Forthe cloudy sky simulations reported in Figs. 6 and 7,the total ozone content was taken to be 350 DU. InFigs. 6 and 7 we plotted the deviation in the N valuewith respect to the clear sky case with 350 DU of totalozone as a reference. Thus, the three dotted curvespertain to clear sky conditions for total ozone abun-dances 10 DU apart; the bottom curve is for 340 DU,the middle curve (zero reference line) is for 350 DU,and the top curve is for 360 DU.

The three other curves in Fig. 6 show the effects ofadding a cloud of optical depth () of 0.3, 3.0, and 30.0.Figure 6(a) shows a simulation pertaining to the use ofglobal irradiances, while Fig. 6(b) pertains to the use of

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the scattered irradiance only and Fig. 6(c) to the zenithsky intensity. Focusing first on Fig. 6(a), we noticethat for solar zenith angles of less than 60° the thin ( =0.3) and the medium ( = 3.0) clouds have a minoreffect on ozone determination, while an optically thick


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cloud ( = 30.0) tends to overestimate the ozoneamount by as much as 10 DU for high Sun. For solarzenith angles larger than 600, however, the effect ofcloud scattering results in an uncertainty of less than 5DU in ozone determination for any cloud opticaldepths of less than 30. Comparing these results withthose displayed in Figs. 6(b) and 6(c), we see that use ofglobal irradiances will lead to uncertainties in ozonederivation caused by cloud scattering, which are con-siderably less than those resulting from the use ofscattered irradiances [Fig. 6(b)] or zenith sky intensi-ties [Fig. 6(c)].

Finally, the influence of cloud height is illustrated inFig. 7 showing the uncertainty resulting from a cloud ofoptical thickness of 3.0 placed at low (2.75-3.0-km),medium (0.5-0.75-km), and high (6-8-km) altitudes.The effect of cloud height appears to be a relativelybenign complication in ozone inference from globalirradiance measurements; only the high cloud underhigh Sun illumination leads to appreciable uncertainty(about 10 DU).

Validation of Method

We have applied the method presented here for deter-mining ozone abundance and cloud attenuation to theglobal irradiance measurements taken at McMurdoStation, Antarctica, during the 1988/1989 season.The time series of ozone abundance as well as cloudtransmission and equivalent optical depth between 15Sept. 1988 and 15 Apr. 1989 are presented and dis-cussed elsewhere.8 For demonstration purposes wefocus here on Oct. 1988 because additional ozone dataare available from satellite observations (TOMS) andballoon soundings20 allowing us to assess the merit ofour method. Thus in Fig. 8 we show a comparison offour different total ozone determinations: (1) fromour analysis of UV spectrometer measurements (solidcurve), (2) from satellite data (TOMS, long-dashedcurve), (3) from Dobson measurements (ArrivalHeights, McMurdo, dotted curve), and (4) from in situballoon soundings2 0 (short-dashed curve). These var-ious methods give similar but not identical results.The difference between the results is, however, notlarger than one might expect considering that the coin-cidence in time and space between the various observa-tions was not perfect. Thus, the TOMS data repre-sent a daily average over an area of 22,500 km2, whilethe balloon soundings are 1-h averages of readingstaken within a 50-km radius of McMurdo.20 The Dob-son readings taken at Arrival Heights were obtainedwithin 4 h of local noon. We note that, whereas ourresults seem to agree well with the Dobson and balloonresults, the TOMS data seem to yield consistentlylower values than the other three methods before day281 (7 Oct.).

To check the consistency of the ozone abundanceand the equivalent cloud optical depth derived fromthe data as described above, we computed the annualvariation in the irradiance integrated over the ob-served spectral range (280-350 nm) using the inferredozone amount and cloud optical depth as input. Thusin Fig. 9 we show a comparison of the observed down-

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Fig. 9. Comparison of observed (dashed curve) and model-predict-ed (solid curve) temporal evolution of global irradiance integratedover the 280-350-nm wavelength range. The observed irradiancesare daily noontime values obtained at McMurdo Station betweenSept. 1988 and Apr. 1989. The total ozone amounts and effectiveoptical depths inferred from the spectral irradiance measurements,taken during this time period, were used in the computations.

ward irradiance (daily values from 15 Sept. 1988 until15 Apr. 1989) and the theoretical value computed byusing the inferred ozone amount and cloud opticaldepth. The observed and predicted irradiance com-pare well throughout the year.

DiscussionWe have used a surface albedo of 0.75 in all calcula-tions reported in this paper. Albedo measurements inAntarctica have been reported in Refs. 21-24. Themeasurements by Warren et al.24 at the South PoleStation agree well with theoretical predictions25 andindicate a snow albedo of about 0.96 in the UV regionaround 350 nm. This albedo was relatively insensitiveto grain size (in the UV-visible) and snow impurities.


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Fig. 10. Chart of the irradiance ratio of 340/305 nm for inferring the ozone abundance for a variety of solar zenith angles (SZA's) and totalozone abundances. The lines are 10 DU apart; the top curve corresponds to 500 DU, the bottom curve to 200 DU: (a) 020' SZA; (b) 20-401SZA; (c) 40-60O SZA; (d) 60-80O SZA. Note that the ordinate scale changes from panel to panel.

The surface albedo at Arrival Heights, McMurdo, isexpected to change throughout the season. ArrivalHeights is located near a glacier that is snow coveredyear round, and the albedo of the surrounding areasthat are not snow-covered in summer might be about0.20. This implies that the average summertime albe-do for the Arrival Heights area (which is largely snowcovered even in summer) is probably higher than 70%[S. Warren, Department of Atmospheric Science, Uni-versity of Washington, Seattle, Washington 98195(personal communication 1990)]. Thus, the value of0.75 adopted here for demonstration purposes may beappropriate for solstice conditions.

The inference of ozone abundance is based on com-paring the ratios of observed irradiance values at twowavelengths in the near UV (305 and 340 nm) withcorresponding computed ratios. The computed ratiosare insensitive to the value of ground albedo adopted inthe calculation. The use of 0.4 for the ground albedoyielded ozone amounts within 1% of the values ob-tained by adopting 0.75. In Fig. 10 we provide a com-plete chart that could be used by others in possession

of global irradiance measurements at these two wave-lengths to infer total ozone abundance. This chart isconstructed to cover ozone abundances between 200and 500 DU in steps of 10 DU and solar zenith anglesbetween 0 and 800.

The estimation of cloud optical depth is based on thecomparison of the ratio of observed to computed clearsky irradiance at 349 nim with the same synthetic ratiocomputed as a function of cloud optical depth. Asalready mentioned this estimation is sensitive to thesurface albedo assumed in the computations, and ac-curate retrieval of cloud transmission or optical depthwould require precise knowledge of the surface albedo.Preferably,. the albedo should be measured simulta-neously with the downward global irradiance. Thenthe procedure outlined here would provide a reliablemeans of quantifying the effect of clouds on the UVradiation environment. Even without precise knowl-edge of the surface albedo, this procedure still hassome merit because it provides an estimate of thecombined effect of clouds and surface reflection on UVirradiance received by the biosphere. This is also


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Conclusions

We have described a method for inferring total ozoneabundance and effective cloud attenuation from globalspectral irradiance measurements. This procedure al-lows us to establish the missing link between the totalozone abundance, the cloud transmission (or opticaldepth), and the biological UV dose from such measure-ments calibrated in absolute units.

Total ozone abundance is derived by comparing themeasured ratios of global irradiance at two wave-lengths in the UV region with synthetic ratios generat-ed from a comprehensive radiation model for a varietyof ozone abundances. One of these wavelengthsshould be appreciably absorbed by ozone (e.g., 305 nm)compared with the other one (e.g., 340 nm). Thesynthetic ratios and hence the inferred ozone abun-dances are insensitive to the value of the surface albedoassumed in computing these ratios. The derivedozone abundances agree as well as expected with thoseinferred by other techniques, including ground-basedDobson spectrometer measurements, in situ balloonsoundings, and satellite (TOMS) retrievals. The un-certainties in the derived ozone abundances fromcloud effects are discussed. Computer simulations areused to demonstrate that for cloudy sky conditions theinference of ozone abundance from the global irradi-ance is generally superior to using only the scatteredirradiance or the zenith sky intensity used routinely inthe Dobson network when the sun is obscured byclouds.

Cloud transmission and optical depth are estimatedfrom the global irradiance at a wavelength where ozoneabsorption is minimal (e.g., 350 nm) by comparing it tocomputed values obtained from a comprehensive radi-ation model valid for stratified atmospheres. An ac-curate estimate of cloud transmission and opticaldepth requires precise knowledge of the surface albe-do. In the absence of such knowledge, information onthe combined effect of surface albedo and cloud atten-uation is obtained instead. This is also useful infor-mation, although it does not allow us to separate theinfluence of surface reflection from the cloud effect. Itdoes, however, permit us to study the impact ofchanges in cloudiness on the UV radiation environ-ment over time scales that are short enough (say hoursor days) that the surface albedo stays constant.

This study was supported by the National ScienceFoundation through grant DPP-88-16298 to the Uni-versity of Alaska. We thank Sylvia Nichol of the NewZealand Meteorological Service for providing the Dob-son data taken at Arrival Heights. We thank D. J.Hofmann for providing a preprint of his paper describ-ing the balloon observations over McMurdo. We also

thank Jim Closs of NASA's Climate Data System forproviding TOMS data.

References1. J. C. Farman, B. G. Gardiner, and J. D. Shanklin, "Large losses

of total ozone in Antarctica reveal seasonal ClO,/NO, interac-tion," Nature (London) 315, 207-210 (1985).

2. R. T. Watson and Ozone Trends Panel, M. J. Prather and AdHoc Theory Panel, and M. J. Kurylo and NASA Panel for DataEvaluation, "Present state of knowledge of the upper atmo-sphere 1988: an assessment report," NASA-RP-1208 (1988).

3. World Meteorological Organization, Scientific Assessment ofStratospheric Ozone, 1989, Global Research and MonitoringProject, Geneva (1989).

4. K. Stamnes, S. Pegau, and J. Frederick, "Uncertainties in totalozone amounts inferred from zenith sky observations: implica-tions for ozone trend analyses," J. Geophys. Res. D10, 16,523-16,528 (1990).

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derivation of total ozone abundance and cloud effects from spectral irradiance measurements

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