Oct 20, 1991 - Structure of Ozone and Aerosol Distribution in the Atmosphere. From the Salyut 7 ... neities in the form of thin, different colored bâ¢nds are noticeable in the ..... oerosol extinction ot 550 nm (10 -3 km -1 ). Fig. 5. Modeling of the ...
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. D10, PAGES 18,647-18,653, OCTOBER20, 1991
The Ozone and Aerosol Fine StructureExperiment:Observingthe Fine Structure of Ozone and Aerosol Distribution in the Atmosphere
FromtheSalyut7 Orbiter 1. Introduction and the Occultation Experiment ß
G. M. GRECHKO, N. F. ELANSKY,M. E. PLOTKIN,AND O. V. POSTYLYAKOV Institute of AtmosphericPhysics, Moscow
The OzoneandAerosolFine Structure(OZAFS)experiment, conducted on the SovietSalyut7 orbitingstationin September 1985,wasintended to studyozoneandaerosolfinestructure in the atmosphere. The experimental technique wasto combin6 the observations of the distribution of species fromtheattenuation of radiation on tangent routeswithphotographic observations of the
Earth'stwilight •limb.The photographic method Usedfor measuring the verticaldistribution of
attenuating al;mospheric components fromspacecraft d6esnotcallfor sophisticated instrumentation. An absorption methodwasusedfor the experiment, anda •0mpletemathematical modelof this
method was• constructed. Themodelassociated directlymeasured values Withatmospheric charac-
teristicsof interest.An algorithmof themeasured dataprocessing wasusedto obtainminimalerrors of the ozor•6and aerosolretrievalon the basisof the completemodelof the experiment,which
9ontains measuring errors. Thismethod makes it possible toreconstruct ozone profiles andaerosol
extinction profilesin the•tratosphere with1ow• errors(5 ,to10%),_and highspatialresolution (about1 km).
1.
INTRODUCTION
Various methods have been used for observing atmo-
50 km for ozone and from !0 to 20 km for aerosol extinction [Chu et al., 1989]. The Ozone and Aerosol Fine Structure (OZAFS) experi-
sphericozoneand aerosol.Primarily,thesehaveconsisted ment conductedon the Soviet Salyut 7 orbiting station in of direct measurements obtained by means of sensors on September 1985wasdesigned to expandthe possibilities of balloonsand planesand remoteground-based and satellite- observationsof the distributionof speciesfrom the weakenbasedmeasurements. Globalmonitoringof the distribution ing of radiationon tangentroutesby combiningthemwith of atmospheric specieswascarriedout usingsatelliteinstru- photographic observations of the Earth'stwilightlimb. As ments,includingSBUV (solar backscattered ultraviolet wasprovedby experiments carriedout in 1978-1979on the spectrometer),LIMS (limb infraredmonitorof the strato- Salyut6 orbitingstation,[Grechkoet al., 1983],inhomogesphere),SAM (stratospheric aerosolmeasurement instru- neities in the form of thin, different colored b•nds are ment),andSAGE(stratospheric aerosolandgasexpe.riment) noticeablein the coloringof the twilight limb at its large [World Meteorological Organization, 1986]. In general,
high-resolution resultshavenotbeenrequired fromthese
extentalongthe horizon(+-60ø and morealongthe azimuth
t or sunrise). Suchbandlike devices.However, recent events, suchas the eruptionof the fromthe placeof the sunse structureof the limb, accordingto numericalcalculations,is E1Chich6n, theappearance ofanozone holeabove Aniarc- formed under the effect of enhanced ozone and aerosol
tica,considerable localinhomogenei.ties in theozonedistri- concentrationlayerswhich are verticallythin bu.textensive butionin theArctic,andthedetection of polarstratosphericin the horizontaldirection.Aerosoland ozonelayersdisplay
clouds,have compelledresearchersto focustheir attention differentcolorsin the limb. In the stratospheric regionof the on methodsfor observingthe fine structureof the distribulimb, the aforementioned bandlikestructureis causedjointly tion of admixtures above individual regions. Moreover, the by ozoneandaerosollayers.In the tropospheric regionit is study of heterogeneousaerosol and ozone processesrecausedonly by aerosollayers.(Detailednumericalanalysis quiressimultaneousmeasurements of at least two of these of the formation of the color and radiance of the Earth's admixtures. twilightlimb is describedby Elanskyet al. [thisissue,(a)].) At present, this missionhas been partly fulfilled by the Sincethe positionof layersvarieslittle with respectto the SAGE II, whichcontinuesthe seriesof experimentsstarted depthof the Sun'sdipbehindthe horizon,limb observations with SAM and SAGE [Russelland MCCormick,1989].The ,.
SAGE II device is a seven-channelphotometerwhich measuresthe transparencyof the atmosphereon tangentroutes,
madealongthestation's orbitmakeit possible to obtaina
numberof vertical crosssectionsof the twilight atmosphere
and to plot the distributions of the structureof ozoneand in the visibleandnear-IRregionof the spectrum.The device aerosollayersabovelargeregions.Consistentobservations makesit possibleto obtain30 verticalprofilesof ozoneand of the Sun'sdisk and the Earth's twilight limb duringa single aerosolextinctionper day abovevariouspointsof the globe sunset(or a singlesunrise)make it possibleto use vertical with discretenessat a heightof 1 km. Profilesare retrieved with 10% accuracyat an altitude interval rangingfrom 10 tO Copyright1991by the AmericanGeophysical Union. Paper number 91JD01395. 0148-0227/91/91JD-01395505.00
profiles ofozone andaerosol extinction, retrieved fror•the fittenuation of the Sun's radiation, to enhance the accuracy
of spatial characteristicsfrom scatteredsolar radiation. Ozone and aerosol fields reconstructed in this way can be
usedfor studyingthe influenceof mesoscaledynamicpro18,647
18,648
GRECHKOET AL.' OZONE-AEROSOL FINE STRUCTUREEXPERIMENT,1
2
•
4
o
6
?
Fig. 1. The spectrophotographicassembly. Numbered parts are as follows' 1 and 5, clamping rings; 2, neutral
attenuator;3, interferencefilter; 4, filter casing;6, tetrahedralprisw; 7, body.
ces•ses(including internal gravitational waves) and the intera•tion of these species.
This method of altitudinal fixing is highly accurate (see Figure 2) and doesnot require complex ballistic calculations.
•in thispaperwe describe a photographic experimentCorrectionfor radiationweakeningtowardsthe edgeof the performed in 1985 at the Salyut 7 station. We also examine the algorithmfor retrieving the vertical profilesof ozone and aerosol extinction (which is more accurate than the previous one used in similar experiments [Grechko et al., 1988]) from data on the attenuation of direct solar radiation by the atmosphere on tangent routes. A detailed analysis of the results of the OZAFS experiment at the Salyut 7 station is provided by Elansky et al. [this issue, (b)] in which vertical profiles are provided for ozone and aerosol extinction, obtained from the algorithm of retrieval described in this paper. Fine structuresfrom data of panoramic observations
solar disk [Allen., 1963] and the averagingof data in the overlapping region of the LSPH of the neighboringframes were carried out to obtain a single dependence of the blackening on the LSPH. 3.
THE MATHEMATICAL
MODEL
In the spectralrange A = 520-660 nm the optical thickness of the atmospherer x(H) of the beam with perigeeheightH is a sum of partial optical thicknessesof ozone r•Z(H),
aerosol v•(H) andmolecular scattering v•nø•(H)'
are also treated. 2.
OF THE EXPERIMENT
a THE OCCULTATION
EXPERIMENT
Let Bx[ ] denotethe integral operator with the kernel Bx(H, h)=0
The setting and rising Sun was photographed on black-
and-white film by a Hasselbladcamera with an objectiveof 8/500mm on which a speciallydesignedspectrophotographic Bx(H, h)= assembly was installed (Figure 1). The spectrophotgraphic assembly consistedof a prism (a tetrahedral pyramid) whose axis coincided with the optical axis of the objective. Four interferencelight filters (,• = 522 nm, ,•2 = 574 nm, •-3 = 602 nm, ,•4 = 665 nm) with half widths zX•0.5= 10 nm and a set of neutral light filters for aligningthe fluxes of radiation were located in front of the prism, opposite each face. Four images of the solar disk about 5 mm in diameter, with a distance of 13 mm between the centers of neighboring images, were formed on the photographic film. The light filters were chosenso that two of their wavelengths(•2, •3) coincided with the absorption maximum in the Chappuis band. The wavelengthsof the other two (,•l, &) were located on its wings with close values of absorption coefficients of
h-•H
(1)
2n :t(h)(R + h)
[(nx(h)(R+ h))2- (nx(H)(R+ H))2]1/2 h>H
where nx(h) is the refraction index of air and R is Earth radius. In the approximation of the spherically symmetrical
air density variation (•) o
I
2
I
3
I
$
4
I
5
I
2
20 - • 'i
ozone. The interval between frames was 4-6 s, which
ensured the overlapping of atmospheric sectionsprobed in the region of the perigee of the sightingbeam. Sensitometric wedges were printed on the photographic film used in the experiment. On the basis of these wedges (after development), characteristiccurves were derived. The
•Ol(H)
E v
-• 15-
photometryof solarimpages was carriedout on the AMD-I microphotometer. Photbmetrywas made of the vertical cross section passing through the center of the solar disk
iI
witha stepof 30/am,whichcorresponds to theshiftof the heightof theperigee•f thesighting !ine(line-of-sight perigee height, LSPH) by 150 m. The size of the horizontal hole of the device was 1 mm by 30 tam. The altitudinal fixing of the blackeningfor each frame was carried out on the basis of
I
lO
o.o
o.'•
o.'•
0/3
o.•
o.'•
o.•
height fixing error (kin)
Fig. 2. Altitude-fixing errors based on the method of solar disk compressionby refraction (solid line), and mean air density varia-
refractlop compression of thesolardisk[Sokolovslcy, 1981]. tions(dashedline).
•
.
GRECHKO ETAL.' OZONE-AEROSOL FINESTRUCTURE EXPERIMENT, 1
18,649
atmosphere the opticalthickness r•(H) is connected with the profilesof concentrations of ozoneNo,•(h) and air Nmol(h ) andaerosol extinction K(h) onthewavelength A0=
G servesas an operatoracting from the spaceof real numbers to the spaceof functions.Thisoperatoris suchthat oz moln ra(H) = rraBa[Noz(h)] + rra t}•[Nmol(h)] + kaBa[K(h)] •b(h)= Ga is a functionequalto the numbera with any valueof the argumenth. The kernelof the operatorB• is
550 nm by the equation
or in the explicit form
givenby(1).Thusthescheme oftheindirectmeasurement of thevectorf containing profilesof the concentration of ozone
rx(H)=
f5 , xNoz(h )+rr B2t(Hh)(rrøz
•aølNmol(h )
No,•(h)andaerosolextinction K(h) canbe writtenin the form
d = A lf 1 + A2f2 + v
+ k•K(h)) dh
(6)
whererr•z andrr•ølarecross-sections of ozoneabsorptionwhere the randomvector v = (VAI(H)VAI(H)VAI(H)VAI(H))* andRayleighscattering andk• is the spectralvariationof
simulatesnoiseof densitometry.The mathematicalprocess-
describedby the Angstromlaw k• = (A/A0)-" with the
sol extinction K(h).
(equation(6)) consistsof aerosolextinctionwith respectto the wavelengthA0 = 550 ing of indirectmeasurements retrieving profiles of ozone concentration Noz(h) andaeronm. In thispaperwe suppose that this spectralvariationis Angstromcoefficienta = 1.5.
Theexposure of photographic film,HA(h), at thepointof 4. THE TECHNIQUEFOR RETRIEVINGOZONE AND the imageof the Suncorresponding to the LSPH h is equal AEROSOL to the productof exposuret, the atmospheric attenuation coefficient exp (-r•(h)), and the illumination of the film, In creatingthe algorithmfor retrievingprofilesof attenuE•, in the absenceof atmospheric attenuation, atingatmospheric components, we usedthe "experimental H•(H) = tE• exp (-r•(H))
(2)
data reduction" method [Pytyev, 1983]. This method was chosen because it allows for the construction of the algo-
In the linear section of the characteristic curve the depen- rithm ensuringthe retrieval of profiles with the fewest denceof the blackeningD•(H) on the exposureH•(H) can possible errors. be representedin the form In accordancewith section 3, the scheme of measuring verticalprofilescan be written,
D•(H) = y logH•(H) + • + •(H),
(3)
d = (AiA2)f + v wherey is the contrastof the photographic film, • is an unknownconstantdependingon contrastand sensitivity, OperatorsA1, A2 and the vector and•(H) is randommeasuring noise.From(2) and(3) we obtainthe expression linkingtheblackening andthe optical
(7)
f= f2
thickness of the atmosphere,
are determined by (4) and (5). The statisticalprocessing of the data on ozoneprofiles,air density,and extinctionof in whicha• = • + y log(tE•) is anunknown constant and aerosolmakesit possibleto find the averagevalueEll = f0 b = -y loge is determined fromthecharacteristic curveof of the vector of profiles fl and its covariation operator the film. E(fl - f0)(fl - f0)* = F. Noiseaccompanying measurements Let us denoted = (D•i(H)D•2(H)D•3(H)D•4(H))* as have an averageof Eu = 0, and the covariationoperator the vector of blackeningsrecordedby the four-channel Euu* is equalto T. There is no informationon the vector D•(H) = a• + br•(H) + •(H)
device,
f2 = (a•la •2ax3a•4)*, whichdepends ontheillumination of
f• = (Noz(h)K(h)Nmol(h))* f2=(a•a•2a•3a•4) *
(4)
as the vector of values influencingthe directly recorded
scheme of measuring (7).
reductionmethodconsistsof transformingthem with the aid
oz b• •iB•i oz b•2B•2
bk, 1B A1 b• A1n A1 bk•2B•2 b• •2 møln •2
b•B•3 bk•3B•3 b•3•3 oz bk møln b••4B•4 •4B•4b• •4 •4 G
A2=
us saythat the model[A1, f0, F, A2, T] is givenfor the
The principleof processing experimental data in the
blackening d, and
A1
the film whenthere is no atmosphericattenuation.Thus let
(5)
of a computer to a formtypicalof the measurement of the atmospheric parameters understudyin theexperiment, with prescribed characteristics described by anoperator U. Thus the experiment in whichthe ozoneprofileis measured is describedby the operatorUo• = [(IOO)O], sinceUo•f =
0 G
(IOO)f1= noz(h),andthe experiment in measuring the profileof aerosolextinctionis described by the operator Ua = [(OIO)O]sinceUaf-- (OIO)fl = K(h). The operator
0
Usp plotted correspondingly prescribes theexperiment. This
0
0
0
0
resultsin the spatialspectrum Uspfof attenuating compofl- The result of the reduction asoperators describing the dependence of blackenings d on nentsof the atmosphere the vector
R(d)= Uf + (R(d)- Uf) canberegarded astheresultUf of
18,650
GRECHKOET AL ' OZONE-AEROSOL FINE STRUCTUREEXPERIMENT,1 2
3
(o) •o
ic
E 25
•' :5
•. 2o
5
lO o
20
lO
30
•
40
5'0
60
0
0
10
20
30
40
50
60
oerosol retrievolerrors
ozone retrievolerrors
Fig. 3. Height dependenceof ozone and aerosolretrieval error types due to various causes' 1, densitometricnoise' 2, height attachmenterror; 3, 3'error; 4, exposurescatter;5, accuracyof molecular scatteringevaluation' 6, Angstrom coefficient
scatter of 1.0-2.0.
measuringthe vector f in the experiment U which is distorted
causes: (1), densitometry noise in images of the Sun, (2)
bythenoiseof theminimum possible powerE R(d)- UI•I2. error in determining the contrast coefficient of photographic The formal mathematics of the reduction method in the
model correspondingto the experiment under consideration is described in more detail in the appendix. The reduction R(d), which minimizes the error in retrieving profiles of attenuatingcomponentsf•, is given by
R(d) = • = Qd + (I - QA1)f0
(8)
using the operators
film, (3) errors in accounting for Rayleigh optical thickness causedby the difference of real profiles of the density of air
fromthemodelprofileusedduringtheretrieval,(4)errorof altitudinal fixing of the Sun's images, (5) random deviations of exposuresfrom the nominal in the series of frames used, and (6) the difference between the spectral variation of aerosol extinction and the Angstrom law (with a = 1.5). The
main fact,or influencing retrieval errors is densitometry
Q -- FA•[P2(A1FA• + T)P2]-,
P2- I - A2A•-
(9)
The error of the retrieval of profiles has the value
noise, whose amplitude (in the value of blackening) was derived, according,toour estimates, as/iD • 0.02. Figures 5 and 6 show the root-mean-squareretrieval error causedby this factor.
E i1 - fl 2 = tr (I - QA1)F.
(10)
It should be noted that the estimate of the profiles (8) and the
The error/iT .indeterminingthe contrastcoefficientof the
photographic film, 7, leadsto the changein the profile'of
retrieved values by k = 1 + /57/7 times at all heights.Thus error (10) are stablewith respectto smallchangesof operators A1, F, and T and the vector f0, while the operator P2 an error of this type results in an error in determining the overall ozone and aerosol content but does not distort the dependson the exactly known operatorA2 and is calculated vertical structure of values which are retrieved. The value of
analytically.
In general,thereductionR(d) to the experimentU(U10) in determiningthe characteristicsof the atmosphereU lfl - Uf
isgiven'by theformulaR(d)= Ul[1, witherrortermEIIR(d) - uf1t 2 - tr ul(I - QA1)FU•,anddoesnotdepend onthe value of the vector f2- This vector dependson the unknown illumination of the film in the absenceof atmosphericattenuation.
In the SAGE retrieval technique the measurements of unattenuated solar radiation are used to calculate tangential
this error is determined by the accuracy of densitometry and can be brought to 2-3%. In the experiment it comprised5 to 10%, mainly owing to the considerabletime interval between imprinting sensitometricwedges and photographingof the Sun.
The average errors of retrieval caused by the remaining factors 3-6 were evaluated in the numerical experiment under the following conditions.The error in Rayleigh opti.cal thickness
was calculated
from
data on variations
in air
opticaldepths.The OZAFS retrievaltechniquedoesnot use density above the territory of the USSR in the moderate the photography of the unattenuate.dSun. Our retrieval technique allows retrieval of the air density
profile, but ,to reduce calculationtime:,this was not done. Variations in air density during the retrieval of profiles were assumed to be zero. The retrieval error caused by this assumptionis studied below. 5.
ERROR ANALYSIS
In the method described above, errors in retrieving ozone concentration and aerosol extinction are due to the following
latitudinal belt in September[Gidrometeoizdat, 1980], which correspondsto the conditions of our experiment. The accu-
racyofaltitude fixingbased onthevalueofthecompressibn of the Sun'simagedepending on'i•heLSPH of the centerQf
thesolardiskisestimated by Gurvichand•okolm)sky [1989]
andisgivenin Figure2 alongwithvariations of thedensity of air.Thedispersion of exposures duringphotography .was assumedto be equal to 7% from the nominal. The Angstrom coefficient a varied in the numerical experiment within the limits of 1.0-2.0.according to the data qf the SAGE experi-
GRECHKOET AL.' OZONE-AEROSOLFINE STRUCTUREEXPERIMENT, 1
18,651
,35-
30-
Z2o-
1,5-
100
Fig. 4.
Ozone and aerosolmodel used for the retrieval algorithm: averageprofiles (solid lines) and root-mean-square variations (dashed line).
ment [Brogniez and Lenoble, 1987], and during the retrieval we assumed
a = 1.5.
The height dependenciesof different types of errors of the retrieval of ozone and aerosol which correspond to the conditionsof the experiment of 1985 are given in Figure 3. At heights below 30 km the main contribution to the retrieval error is made by densitometry noise. For this reason the retrieval algorithm was optimized to minimize only errors of this type. Above 30 km, errors associatedwith the spreadof exposuresbecome critical. Thus in retrieving ozone at high altitudes, one should construct an algorithm that minimizes the sum of these two types of errors. In the photographic experiment conducted in 1985 at the Salyut 7, station accuracywas not optimal. Accordingto our estimates, the accuracy of the retrieval could be at least doubled if the following procedures are followed during the stagingof future experimentsand subsequentprocessing:(1) reduce the noise of densitometry to /SD • 0.005 using a more advanced microphotometer, (2) eliminate the error in the altitudinal fixing of the Sun's images due to the exact fixation of time intervals between frames, (3) take into account in the retrieval algorithm the real spread of exposures,which makesup not lessthan 5% for any photographic shutter, and (4) bring the accuracy of determining the
contrast coefficient y to 2% (this is important only for determining the integral characteristics of retrieved values). In these conditions the errors of retrieving ozone will comprise about 5% at a height of 20-30 km and about 10% at a height of 15-20 km with errors of the retrieval of aerosol extinction comprising about 7% at a height of 12-22 km. 6.
THE NUMERICAL
EXPERIMENT
Let us next illustrate the measuring scheme and the method of retrieval in the closed numerical experiment. Let us consider the results of the retrieval of two types of profiles: the profile with large variations of ozone and aerosol by altitude, and the smooth profile which differs greatly from the average value. The average values and root-mean-square variations of ozone and aerosol extinction profiles in the model of the atmosphereused in the retrieval algorithm are given in Figure 4. The average values and variations of ozone are taken from Zuyev and Komarov, [1986], and the average aerosol extinction is taken from Lenoble and Brogniez, 1984] with the root-mean-square variation equal to 60% of the average. The simulation results for the retrieval of profiles with fine structure are given in Figure 5. The initial ozone profile was
3O
(
25-
•_.•z_•'_• •1.......
_
lO
ozonenumberdensity(10•8 rn-'• )
0 oerosolextinctionot 550 nm (10-3 km-1 )
Fig. 5. Modeling of the fine structure profile retrieval for (a) ozone and (b) aerosol: 1, exact profile' 2, retrieved profile for densitometricnoise equal to 0.005; 3, retrieved profile for densitometricnoise equal to 0.02; 4, retrieval error for densitometric noise of 0.005' 5, retrieval error for densitometric noise of 0.02.
18,652
GRECH•:OET AL ' OZONE-AEROSOL FINE STRUCTURE EXPERIMENT,1 35
(b) 30-
•'25 -
• 20-
15-
o ozonenumberdensity(10'sm-3 ) Fig. 6.
2
oerosolexbnction at 550 nm (10-3 krn -1 )
Same as Figure 5, but for ozone hole type profile retrieval.
obtained by adding the sinusoid with 2.5-km period to the this method a complete model of the photographic experiaverage profile (see Figure 4). The amplitude of the sinusoid ment is constructed that associatesdirectly measured values was equal to the root-mean-square variations. The initial with atmospheric characteristicsof interest. The algorithm profile of aerosol was obtained by adding the sinusoid with of the mathematicalprocessingof measuredvalues is opti1.5-km period to the average profile. The amplitude of the mized to obtain minimum errors of retrieval on the basis of sinusoidwas equal to 50% of the averagevalue. The retrieval the complete model of the experiment which possesses of the profiles was carried out from the profiles of the concrete measuring errors. The suggestedmethod makes it blackening of the solar disk image obtained in the numerical possibleto reconstructozoneprofilesand aerosolextinction experiment and distorted by the accidental noise with the profiles in the stratospherewith low errors (5 to 10%), and root-mean-square error &D = 0.02 and &D = 0.005 (such high spatial resolution (about 1 km). blackening errors correspond to errors of measuring the optical thickness &r = 0.04 and &r = 0.01, the typical value APPENDIX: THE REDUCTION METHOD of the contrast of the photographic film being y = 1.1). The first error (&D = 0.02) corresponds to the conditions of the The retrieval of profiles of attenuating componentsof the 1985 experiment. The second error (&D - 0.005) may be atmosphere was conducted by the reduction method. The achieved if such experiment is performed optimally. In model [A i, fo, F, A2, T] of the linear measuringscheme experiments measuring the intensity of radiation attenuated by the atmosphere, the relative measurementerrors 4% and 1% correspond to these accuracies, respectively. In Figure 6 the initial ozone profile simulates an ozone "hole," while the initial aerosol profile corresponds to the corresponds to the absorption photographic experiment. average value. In addition, Figures 5 and 6 show absolute This meansthat operatorsA• and A 2 are known, noisev has errors in the retrieval of profiles with two possibleaccuracies a zero average, and covariation operator T is equal to Evv*. of measurements of the thickness (&r =0.04 and &r =0.01). We also know the average fo = Ef• and the covariation These examples of the retrieval of profiles of ozone and operatorF = E(f• - fo)(f• - fo)* of the componentf] of the aerosol with fine structure (Figure 5) show that the method vector used makes it possible to reconstruct sufficiently well layered distributions with characteristic layer thickness Ah • 1 km with reasonable accuracy of optical thickness measure-
d (A]A2) f2
ment.
The example of the retrieval of the ozone profile typical of the ozone hole (Figure 6) shows that even in the case when the true profile greatly differs from the average statistical profile of ozone put into the inversion algorithm (i.e., the difference considerably exceeds model root-mean-square variations), errors of the retrieval continue to be small. 7.
CONCLUSIONS
The method of measuringthe vertical distribution of ozone and aerosol in the atmospherefrom spacecraftdoes not call for sophisticated instrumentation. Within the framework of
which influences the results of the experiment. We shall considercharacteristicsU•f• of the vector f• which denotes profilesof attenuatingatmosphericcomponents.The task of the reduction
is to minimize
errors
Ella(d)- u,fll 2-- min{gila'(d)- u,f,ll2la' The vector R(d) = U•f] + (R(d) - U•f•) is regardedas a result U•f• of the experiment U], which is distorted by
interference R(d)- U•f• withlowerpowerElla(d)- u•f•ll2 -
