Effect of volcanic aerosols on stratospheric radiance atwavelengths between 8 and 13 ,yrm
B. Halperin and David G. Murcray
A set of stratospheric aerosol optical models is employed in a radiative-transfer computation to study theeffects of postvolcanic particle size distributions and compositions on the spectral radiance in the 8-13-umwindow region. The models are based on direct measurements of post El Chichon aerosol size distributionsand vertical profiles. They represent various maturity states of aerosols composed of sulfuric acid aqueoussolutions, formed and evolved in the stratosphere following a massive volcanic eruption. Comparisons aremade with concurrent radiance observations obtained on balloon flights 6 months after the eruption and 1 yrlater. Most of the calculations are done using the LOWTRAN-6 code (either alone or combined with a multiplescattering calculation), revised so as to include the appropriate aerosol optical models. A better quantitativeagreement is found between the calculated and observed spectral radiances when the aerosol loading isrelatively high, indicating that additional minor radiance sources of a yet unresolved nature should beincorporated in the present version of the calculation.
1. Introduction
The ability to predict the performance of passive IRsurveillance systems requires a comprehensive knowl-edge of the radiometric properties of the atmosphere.This should include an extensive experimental database of spectral radiances covering a diverse set ofatmospheric conditions, as well as theoretical model-ing capabilities which enable one to extend knownparameters to other, possibly more adverse, condi-tions.
A significant variable perturbation to the IR signa-ture of the atmosphere is caused by the layer of strato-spheric aerosols, a vast amount of which has beenformed following the major eruption of the El Chichonvolcano in Mexico in Apr. 1982.1 To study the poten-tial optical and radiative effects of such an event, sev-eral coordinated measurement programs have beencarried out, particularly toward the end of 1982, whenthe concentration of volcanic aerosol particles in thestratosphere reached its maximum value at mid-lati-tudes. These measurements included active and pas-sive remote sensing of the stratosphere from a varietyof platforms 2-4 as well as in situ measurements of
The authors are with University of Denver, Physics Department,Denver, Colorado 80208.
particle composition and size distribution as functionsof altitude and latitude.5-7 It was confirmed that a fewmonths after the eruption the stratospheric aerosolparticles were composed of H2SO4 liquid aqueous solu-tion with an acid weight percentage ranging between60 and 80%,6 being compatible with prevailing strato-spheric temperatures and humidities.8
At the same time, and independent of the above-mentioned measurements, spectral radiance measure-ments in the atmospheric window region between 8and 13 gm have been obtained on balloon flights, most-ly over southern Texas. This has been part of a long-term study made by the University of Denver Atmo-spheric Spectroscopy and Radiance group beginningin the early 1970s and extending to these days.9 10 Itcould be readily recognized that in the spectral regionsof the window between the main absorption bands of03 and C02, the average radiance levels after the ElChichon eruption were several times higher than thoseof the preeruption spectra. This result follows fromthe relatively high emissivity of sulfuric acid aerosolscompared with the emissivity of the gaseous compo-nents of the stratosphere at the far wings of theirabsorption bands. Solar transmission measurementsmade by Witteborn et al.11 in Dec. 1982 revealed ab-sorption features due to H2SO4 aerosols, centered at8.5 and 11 Am, in agreement with the radiance observa-tions.
The fact that independent in situ measurements ofthe physical properties of the volcanic aerosols andtheir spatial distribution has been carried out at aboutthe same time and geographical region (30'N) as
those of the radiance observations stimulates one toattempt a theoretical simulation of the observed spec-tral radiance, where the parameters of the optical mod-el should be consistent with the measured physicalproperties of the aerosols. A success of such a simula-tion would demonstrate the consistency between dif-ferent observational methods and provide greater con-fidence in our understanding of the optical propertiesof the volcanic aerosol system. Thus the purpose ofthe present work is twofold. First, we study the com-bined radiative effects of sulfuric-acid aerosols plusthe main gaseous components in the stratosphere onthe observed 8-13-Aum radiance spectra and its tempo-ral evolution during a volcanically perturbed period.Then, once the H2SO4 aerosol contribution to the ob-served radiance is established, a more profound discus-sion of radiance contributions to this window regionoriginating from other sources (e.g., minor gaseousspecies) is facilitated.
In Sec. II we present results of Mie scattering calcu-lations for a diverse set of stratospheric aerosol modelscorresponding to progressive states of aerosol maturi-ty. The optical properties resulting from these calcu-lations are then employed in radiative-transfer com-putations, and the simulated 8 -13-,gm radiancespectra are compared with observed spectra obtainedon balloon flights (Sec. III). Possible effects due tomultiple scattering, especially in the presence of freshvolcanic aerosols, are discussed in Sec. IV.
II. Optical Properties of Sulfuric-Acid Aerosols
A. Particle Size Distributions
Specification of the composition, shape, and sizedistribution of the stratospheric aerosol particles is aprerequisite for performing optical model calculationsof the radiative characteristics, such as absorption,emission, and scattering coefficients. Owing to theirliquid phase (supercooled aqueous solution of H2SO4,where the equilibrium acidity percentage is deter-mined by the stratospheric water-vapor mixing ratioand temperature, and may vary between 60 and 80% byweight8), the stratospheric aerosol particles are spheri-cal (droplets) with the sphere radii behaving accordingto some time-dependent particle-size-distributionfunction n(r). The temporal changes in n(r) occur on arelatively short time scale (days or weeks) in the coupleof months following the eruption and on a time scale ofseveral months about one year later. They reflectprogressive maturity states following a volcanic erup-tion and are the net result of several kinetic processesin which different mechanisms take part.51 2 Relatedto the time dependence of n(r) are altitude and lati-tude dependencies.
Several functional forms based on theoretical mod-els as well as on direct or indirect aerosol measure-ments have been recommended in the past for differ-ent stratospheric aerosol size distributions. 3"14
Flexible parametric dependencies have been assumedto enable one to describe background stratospheric aswell as fresh and aged volcanic aerosols by the same
type of function. In the present work we follow a morepractical approach, and instead of representing thetemporal behavior of the relative size distribution bymeans of a continuous, sometimes artificial, variationof a single parameter, we employ results of direct mea-surements made in consecutive months during the firstyear after the El Chichon eruption. To avoid possiblebiases introduced by a particular experimental meth-od, we make use of published results obtained inde-pendently by two research groups relying on two dif-ferent physical methods. The first method is that ofHofmann and Rosen (HR) who used optical particlecounters based on calibrated light scattering within aballoon-borne chamber.5 The second experimentalmethod is that of Oberbeck et al. (OB), who used wireimpactors to collect particle samples, which then werephotographed using a scanning electron microscope.7Both groups have formulated their results in terms of amultimode lognormal distribution function of theform
Ni In l(r/ri)n(r) = rvexp~-2r 1i r [ t1(1
Here n(r)dr is the number of particles per unit volumehaving a radius between r and r + dr, is the number ofobserved modes, ri is the ith modal radius, Ni is thetotal number concentration of the ith mode, and ai is ameasure of the ith modal width. The values of theabove parameters, corresponding to measured size dis-tributions from May through Dec. 19825,7 at a latituderange between -30 and 40°N, are presented in Table I.We labeled the distributions according to the first twoletters of the investigators names, month (in 1982),and day of measurement. Thus HRMAY19 stands for
Table I. Parameters Characterizing the Multimode Lognormal SizeDistributions [Eq. (1)] (for meaning of labeling see text)
a This mode contained a relatively significant amount of silicateparticles which have been completely depleted by sedimentationonly toward the end of 1982.
b The second mode of HRLNSP2 is a general estimate obtainedfrom the shape of the spline curve relative to the lognormal part ofthe curve. The other two parameters are meaningless here, becauseit is not a lognormal function.
Hofmann and Rosen, 19 May 1982. Also shown inTable I are values corresponding to the preeruptiondistribution5 (HRPREER) as measured from Feb. toApr. 1982. The last distribution shown in the table,HRLNSP2, is a combination of a lognormal functionand a spline curve, recently suggested by Rosen andHofmann15 as the best fit to their measurements per-formed on 12 Feb. 1983. (This is the second of twoLNSP models presented by them, the first one corre-sponding to measurements made in July 1981, whichfor future reference is labeled HRLNSP1.)
Figure 1 displays the particle volume distributions,(4 7r/3)r3 n(r), corresponding to the size distributionfunctions of Table I. The reason for plotting particlevolume distributions, rather than n(r) itself, is relatedto the wavelength region ( > 8 gm) dealt with in thiswork. As will become evident later, at these wave-lengths the optics is sensitive to the volume of theparticles (Rayleigh regime).
Experimental evidence6 indicates that the relativesize distribution is highly variable with altitude.However, for the purpose of optical modeling, a givenaltitude range can effectively be characterized by theaverage relative size distribution n(r) within that range(see the discussion in Sec. III. B). It should be notedthat while the HR distribution corresponds to an aver-age altitude of -25 km, the parameters Ni of the OBdistributions were originally adjusted to a referencealtitude of -21 km. However, in Fig. 1 we plotted theparticle volume distribution functions normalized sothat the number of particles with r > 0.15 Am is N(O.15)= 1 for all the distributions. Here N(r) is the integralsize distribution function
N(r) = I n(r')dr. (2)
This normalization procedure turns out to be of someconvenience when verticle profiles (number concen-tration as function of altitude) are considered, becauseit is the altitude dependence of N(r) which is usuallypresented in the literature. Thus, for the purpose ofoptical modeling, the (absolute) effective size distribu-tions as functions of altitude are obtained by multiply-ing the normalized values of n(r) by the altitude-de-pendent values of N(O.15).
From the plotted curves shown in Fig. 1 it can beseen that the eruption resulted in a drastic change inthe particle size distribution. Unlike the preeruptiondistribution, which is limited to a range of submicronparticles, a significantly large proportion of particleswith radii of several microns appears -1.5 monthsafter the eruption. A few months later (Sept. 1982)the largest radii are only '-'im, with a gradual increaseby a factor of <2 during the following 5 months. (Notethat the HROCT23 distribution exhibits a somewhatirregular behavior compared to the general temporaltrend and compared to the OBNOV05 distribution,which for reasons of graphic clarity is not shown in thefigure. This may well be a result of the double-valuedresponse and a bias of the optical particle counter atthe 1-Mm size region, as suggested in Ref. 15.) Re-
:E
E
E
:1.
0.01 0.1 1.0 10! ~~~~~~~~~~rm)Fig. 1. Particle volume distributions corresponding to measure-ments before and during 1 yr after the El Chichon eruption. Thedistributions are normalized so as to yield the same number ofparticles with r > 0.15 m, N(0.15) = 1 (for labeling, see Table I).
maining constant for the first few months of 1983, thenumber concentration began to decrease exponential-ly with time with a somewhat faster decay of the largerparticles (not shown in Fig. 1). The exp(-1) decaytimes of N(O.15) and N(O.25) above 15 km were ob-served to be 8.5 and 7.6 months, respectively,12 result-ing in a gradual decrease of the average particle radiusduring the period of Apr.-Sept. 1983.
B. Spectral Extinction and Absorption Coefficients
To carry out a Mie scattering computation to deter-mine the extinction, absorption, and single scatteringalbedo of the aerosol particles as functions of wave-length, a complete data set of the real and imaginaryparts of the index of refraction is needed. Detailedresults of measurements made by Palmer and Wil-liams16 for several concentrations of H2SO4 aqueoussolutions, and presented in convenient tabular form,are particularly apt for such a computation. A seem-ing problem arises, however, since the Palmer andWilliams measurements were performed at a tempera-ture of 300 K, whereas stratospheric temperatures maybe much lower, typically -215 K just above the mid-latitude tropopause. Pinkley and Williams17 extend-ed the measurements down to 250 K and show that inspectral regions far from strong absorption bands, thevalues of the refractive indices agree with values calcu-lated by means of the Lorentz-Lorenz correction ap-plied to the values at 300 K. In the spectral regionbetween 8 and 13,Mm, the difference was typically near5% and always <10%. Since the temperature effectintroduces only small modifications to the refractiveindices, and the Pinkley and Williams17 results arerestricted to a relatively narrow concentration rangeand are presented in a less accurate and less conve-nient form compared with those of Palmer and Wil-liams,'6 we preferred to rely on the latter ones as thebasic data set for our computations. The implicationsof this choice are discussed further at the end of thissection.
In the acidity range between 50 and 75% (acid weightconcentration) the real and imaginary parts of the
Fig. 2. Relative extinction coefficients as functions of wavelength for three particle size distributions and two acidity percentages.The extinctions are scaled so that their values are equal to unity at
-= 0.55,um.
ID
- . HRLNSP2 75%
O 10 X \ O OBDEC3 75%
J i \ -0BDECI3 62%
OBSEP23 75%
HRPREER 75%
4 ' '' 5 i' 0 15 20 25X(m)
Fig. 3. Single scattering albedo eo(X) as a function of wavelength Afor different particle size distributions and an acidity percentage of75%. For the OBDEC13 distribution, results corresponding to 62%
acidity also are shown.
1-3
refractive indices of H2SO4 aqueous solutions varymonotonically with the concentration, and a linearinterpolation seems justified. Using such an interpo-lation scheme we performed standard Mie scatteringcomputations for several acid concentrations and eachof the particle size distributions of Table I. Volumeextinction and absorption coefficients, kext and kabs,and the single scattering albedo wo as functions ofwavelength have been calculated. In Fig. 2 we presentrelative extinction curves calculated for three of theabove distributions and two acidities. The curves arescaled so that their values at the smallest wavelengthin the calculation (X = 0.55 Mm) are equal to unity in allcases. In this way one can see how the ratio of IR tovisible extinction varies with aerosol size distribution.Computed spectral curves of the single scattering albe-do wo are shown in Fig. 3. (Following Pollack et al.18
for wavelengths shorter than 2 Mm we employed awavelength-independent value of 1.5 X 10-3 for theimaginary index of refraction, dominated by absorp-tion due to impurities.) It can be seen that in thespectral region between 8 and 13Mm the single scatter-ing albedo is usually limited to values smaller than 0.1,except for the HRMAY19 distribution, where w0 risesto values near 50%. This phenomenon stems from theabundance of particles with radii larger than 1 Am inthis distribution. Its effect on multiple scattering ra-diative calculations and predictions are discussed inSec. IV. Thus, for the preeruption as well as for themore mature distributions of the Sept.-Dec. period of1982, the volume absorption coefficients kabs, whichcan be written as
EI-z
UJLL1U-
0Z0 104
I-a.
0:m
-J0
hiT5
5 10 15 20 25
Fig. 4. Volume absorption coefficients, kab2(A), as functions ofwavelength for the (normalized) HRLNSP2 distribution and three
different acidities: 50, 62, and 75% H2 S04.
kabs(X) = [1 - wO(X)Ikext(X) (3)
follow spectral curves which for X > 8 Am are similar tothose of kex6 (A) in Fig. 2.
The volume absorption coefficients calculated forthe HRLNSP2 distribution in the wavelength region 5Am > X > 25 Mm are shown in Fig. 4 for three differentacidities: 50,62, and 75% H2SO4. Here a normalizeddistribution [N(0.15) = 1] was assumed.
A comparison between the scaled extinction curvescorresponding to different distributions shown in Fig.
2 (including those of the other post El Chichon distri-butions which are not shown in the figure for reasons ofgraphic clarity) reveals that for X > 5 gm the spectralvariation of the curves for a given acidity is very simi-lar, excluding the HRMAY19 distribution. Changingthe acidity percentage results in some band-shapevariation including crossover points (e.g., at X = 11.5um). The somewhat puzzling invariance of the spec-tral shape for different distributions follows from thefact that the radii of the particles are small comparedto the IR wavelengths under study. This is just theRayleigh limit of the Mie theory, where the spectralabsorption and extinction coefficients can be approxi-mated by19,2 0
kabs(X) -"extX)
36ir m'm2 f 1 r n(r)dr. (4)X ('- + 2)2 + 4(m'm") 3
Here m'(X), m"(X) are the real and imaginary parts ofthe refractive index of the aerosol particles. The inte-gral in Eq. (4) gives the total volume of the aerosolparticles per unit volume of air, which is, therefore,proportional to the aerosol mass mixing ratio. Thefactor which multiplies the integral depends on boththe composition and wavelength but does not dependon the particle size distribution. This factorization ofkabs(X) and kext(X) explains the similar spectral shapesof the preeruption and Sept.-Dec. curves in Fig. 2 for X> 5 m. On the other hand, for the HRMAY19 distri-bution n(r) begins to rapidly fall off only for values of rlarger than several microns. In that case, additionalterms appear in Eq. (4) where wavelength-dependentcoefficients multiply higher moments of the distribu-tion function.
Finally, we should discuss the effect of stratospherictemperatures on the spectral extinction and absorp-tion coefficients. We used the Lorentz-Lorenz rela-tion in the form
m2 -1 -1
m22 P - a lt° (5)
where m is the complex refractive index of the H2SO4solution, p is its mass density, and a0 is its specificpolarizability (i.e., per unit mass). Assuming that aoistemperature independent, its real and imaginary partsas functions of wavelength were determined by substi-tuting known room temperature values for m', m", andp. (Note that the assumption is valid far from absorp-tion bands but not necessarily near them, becausevariations in a0 may occur due to thermal excitationsinto higher lying rovibrational levels.) Then, employ-ing extrapolated low-temperature values of p(T) fromtables in Ref. 21, we solved the equation for m' and m"at 215 K. The result was a typical increase of 2-3% inm' and 8-10% in m" compared to their 300 K values.The resulting effect on the volume absorption coeffi-cient throughout the 8-13-,m region was a homoge-neous increase by -5%. Hence the error involved inusing room temperature extinction and absorption co-efficients in the radiance calculations is limited to onlya few percent.
Ill. Calculated and Observed Radiance
A. Vertical Profiles
An aerosol optical model for atmospheric radiative-transfer calculations should specify the single-scatter-ing properties (kext, kabs and the angular phase func-tions) as functions of altitude (vertical profiles). Thealtitude dependence results from variations in boththe particle-size distribution and the index of refrac-tion. The main factors which determine the varia-tions of n(r) with altitude are particle-growth mecha-nisms and sedimentation, the former begin closelyrelated to the initial concentration and net lifetime ofH2SO4 vapors.'2 The temperature profile and water-vapor mixing ratios affect the altitude dependence ofthe aerosol refractive index through composition(acidity) and density variations.8
Results of vertical-profile measurements made byHofmann and Rosen are available in the literature interms of integral size distributions N(r) for May, Aug.,and Oct. 19826 and in terms of N(0.15) mixing ratios forDec. 1982.' The August and especially the Octoberprofiles which were measured in southern Texas exhib-it a deep minimum at an altitude of -21 km. Thisseparates two distinct aerosol layers peaked at -19 and22 km with the higher lying layer characterized by alarger average particle radius and a higher acidity(-75%) compared to the lower lying layer (60-65%).6On the other hand, the minimum in the Decemberprofile, measured over Laramie, WY, is far less obvi-ous.
Consistent with the two-layer characteristics of thestratospheric aerosols over Texas during Aug.-Oct.1982, the optical model that we adopted to simulatemeasured radiances at that period and location as-sumes two different size distributions, above and be-low 21 km, with acidities of 75 and 62.5% H2SO 4 , re-spectively. The size distribution function for theupper layer is taken as HROCT23 (for details, seeTable I), while for the lower layer it is assumed to beapproximated by OBSEP23. This choice is supportedby several arguments: (1) The HROCT23 distribu-tion actually represents average results of measure-ments made between 21.5 and 24.5 km,5 whereas theOBSEP23 distribution is based on sampling madefrom U-2 flights below 21 km.2 The HROCT23 distri-bution represents a more mature state of the aerosolparticles compared with OBSEP23, and, therefore, theaverage particle radius is larger.3 The calculatedchannel ratio N(0.15)/N(0.25) of the OBSEP23 distri-bution is 4.2 and found to be in reasonable agreementwith the average value of channel ratios below 21 km,6which span a range between 3.5 and 6. The channelratio of the HROCT23 distribution is 1.6, which istypical of the measured channel ratios between 21 and30 km, spanning a rnge between 1.2 and 36 Note,however, that in this optical model we disregard thepresence of silicate particles included in the thirdmode of the OBSEP23 distribution.
The altitude dependence within each layer for theOct. 1982 profile was assumed to follow the vertical
Fig. 5. Volume extinction coefficients as functions of altitude cor-responding to measurements over Laramie, WY 2 yr apart: (a)Calculated scaling factors, ket(\ = 0.55,um), corresponding to mea-sured profiles of N(0.15) on 9 Dec. 1982 and assuming a singlenormalized distribution given by OBDEC13. (b) kext ( =0.525 gm)
obtained from dustsonde measurements on 30 Nov. 1984.
profile of N(0.15) measured on 23 Oct. 1982, as dis-played in Ref. 6. Thus the absolute particle size distri-butions as functions of altitude above and below 21 kmwere obtained by multiplying the normalized distribu-tions HROCT23 and OBSEP23 by the vertical profileof N(0.15). Obviously, more subtle optical modelscould have been constructed by allowing for a differentvertical profile of the number concentration Ni of eachmode and thus introducing an altitude dependence ofthe shape of the distribution function within eachstratospheric sublayer. However, owing to the lowspectral sensitivity of the extinction curves in the 8-13-,um region to the details of the particle-size distri-bution (as discussed in Sec. II), we felt that such aprocedure might be superfluous for our present pur-poses. For similar reasons, further simplificationshave been introduced by us in the optical models corre-sponding to later periods when vertical mixing due tovarious dynamical processes tends to diffuse the dis-tinction between the aerosol sublayers. For example,in simulating the spectral radiances measured at theend of 1983, we employ a single normalized size-distri-bution function, where only the mixing ratio varies as afunction of altitude by the same proportion for eachmode.
Most of our radiative transfer computations havebeen carried out by means of the LOWTRAN-6 code,22
where the aerosol subroutines have been replaced byour own Mie scattering calculated spectral data set.Complying with the LOWTRAN procedure, we found itconvenient to express the vertical profiles of the spec-tral extinction and absorption coefficients within eachstratospheric sublayer in terms of scaling factors,which are equal to the values of kext(z) at X = 0.55,gm,and are specified for increments of 1 km of the altitudez. Since within each stratospheric sublayer the shapeof the size-distribution function is assumed to remaininvariant, the extinction and absorption coefficients atother wavelengths bear the same altitude dependenceas that of the scaling factor and can be expressed assimple products of scaled wavelength-dependent
150 I
[.,XN I
'E
I'100 4co,
0 ~~~~HNO3
a:50 AOSL ARS
AEROSOL
9 10 11 12 13M(pm)
Fig.6. Observed spectral limb radiance obtained on a balloon flightover Palestine, TX (320 N) on 22 Sept. 1982. The observationaltitude and zenith angle are 40 km and 95.4°. The spectral resolu-tion is -0.1%, and the spatial resolution (vertical field of view) is<1°. Also shown are blackbody radiances calculated at 210 and
220 K.
quantities (see Fig. 2) multiplied by the altitude-de-pendent scaling factor.
Results of calculated scaling factors corresponding,for example, to the aerosol vertical profile measured on9 Dec. 1982 over Laramie, WY,1 are shown by curve a inFig. 5. In the absence of published distribution func-tions referring to the Dec. 9 vertical profile, we calcu-lated these scaling factors assuming a single normal-ized size-distribution function specified by theparameters of OBDEC13 in Table I. We are aware ofprobable differences between the details of the as-sumed distribution which was measured at a latitudeof 270N and those of the actual distribution measuredover Laramie (410N) at about the same time. Howev-er, we have already shown that as far as the 8 -13-Mimwindow region is concerned, such details do not notice-ably affect the spectral behavior. Furthermore, if in-stead of the OBDEC13 distribution we employ theHRLNSP2 distribution, which was actually measuredover Laramie a couple of months later, the variation inthe calculated scaling factors is only -3%.
Also shown in Fig. 5, curve b is the vertical profile ofthe volume extinction coefficient at X = 0.525 4m,measured over Laramie two years later.23 In spite ofthe slightly different wavelength and approximate es-timate of n(r) in obtaining curve a, a comparison be-tween the two profiles is useful when attempts aremade to treat the time-dependent aerosol vertical pro-file as an adjustable parameter. This topic is dis-cussed further in the next section.
B. Limb Radiance Simulations
Figure 6 shows an observed spectral radiance curveobtained on a balloon flight on 22 Sept. 1982 overPalestine, TX (320N).9 This is a typical limb scan
Fig. 7. Calculated vs observed spectral radiance for a limb geome-try (Hob, = 40 km, obs = 95.4°). The observed radiance is redrawnfrom Fig. 6 and is presented by sparse crosses. The calculatedradiances correspond to a case with no stratospheric aerosols (curve0) and to an aerosol vertical profile of 23 Oct. 1982 with normalizedsize distributions described by OBSEP23 (curve 1), the two-layermodel (curve 2), HROCT23 (curve 3), and OBDEC13 (curve 4).Solid curves correspond to 75% H 2S0 4 and dashed curves to 62%
H2 SO4 . A mid-latitude winter profile is assumed.
obtained on that flight, where the observation altitudewas 40 km and the zenith angle was set at either 90.5 or95.4°. Admittedly, from a computational point ofview, this geometry is not ideal for stratospheric aero-sols studies for two main reasons: (1) A small butfinite vertical field of view about a zenith angle near950 results in a significant spread of the tangentheights, which consequently may drop well below thetropopause. (2) The line of sight intersects manystratospheric sublayers, thereby introducing a greatnumber of potentially unknown profile parameters forboth the temperature and mixing ratios of stratospher-ic gaseous components. Unfortunately, this has beenthe only geometric setup employed for radiance mea-surements at that time and since the main eruption ofEl Chichon 6 months earlier. However, the fact thatthe amount of aerosol present in the stratospherereached its maximum value at about that period, andindependent in situ measurements of the aerosolsproperties were concurrently made by other investiga-tors, renders a theoretical study of these radiance ob-servations valuable and distinctive in spite of theaforementioned limitations.
The aerosols contribution to the observed radiancein Fig. 6 should be mostly perceivable in the far wingsof and between the main bands of 03, HNO3, and CO2.(For convenience, these bands along with the potentialregions for aerosol contributions are marked on thefigure.) Thus regions to be investigated are near thelower wavelength edge of the figure (8.7 Mm) and thetwo minima at 10.6 and 12 m. It is unfortunate thatthe main absorption band of the H2SO4 aerosols at X 8.5 ,um (see Fig. 4) falls outside the measured spectral
window region, but still a significant contribution isretained near 9 m.
Due to the finite field of view of the spectrometer(<1o), the observed radiance is an average over a rangeof zenith angles about that of the optical axis with acorresponding spread of a few kilometers in the tan-gent height. However, the absence of strong water-vapor lines indicates that contributions from zenithangles larger than 95.4° are negligibly small. Thus theactual zenith angle of the optical axis might have beensomewhat smaller than indicated.
Results of calculated spectral radiances for the nom-inal geometry of H = 40 km and = 95.40 are shown inFig. 7. The computations have been performed usingthe LOWTRAN-6 code but replacing the standardstratospheric aerosol data sets by the optical modelscalculated by us for the various maturity states of thepost El Chichon aerosols. A common vertical profileof the stratospheric aerosols was assumed in all thecurves shown in the figure given by the profile mea-sured by Hofmann and Rosen over southern Texas on23 Oct. 1982.6 The vertical profiles of the temperatureand mixing ratios of the gaseous components weretaken as those corresponding to mid-latitude winterconditions.22 The computed radiance for the two-layer optical model, described in Sec. III.A, is shown bycurve 2 in Fig. 7. For comparison, results obtained bymeans of simplified optical models, where the normal-ized size distribution and composition (acidity per-centage) do not change with altitude, are also shown inthe figure (curves 1,3, and 4). The calculated radiancefor a case with no stratospheric aerosols is shown aswell (case 0). For convenience, the measured radianceis redrawn in Fig. 7 (sparse crosses), where regions ofdense lines have been replaced by their average radi-ance level.
It should be noted that the spectral resolution of theLOWTRAN data base is only 20 cm-' compared with theexperimental resolution of <1 cm-' with which thespectral radiance of Fig. 6 has been measured. Whilethe LOWTRAN resolution is definitely sufficient for de-scribing the aerosols emissive features (see Fig. 2), itintroduces some distortions in the ozone band shape,which appears broader compared with the observedemission band. Similar distortions are obtained atother geometries as well (see Sec. III.C). As will beshown, calculations made by a line-by-line code, whichhas a spectral resolution compatible with that of theobserved data, recover the correct ozone band shapewhile maintaining relative spectral features similar tothose of LOWTRAN-6 at the wavelength regions near8.5,10.6, and l 2 gm. Since the emphasis in the presentwork is on the effects of aerosols (rather than ozone orother gaseous constituents) on the observed spectralradiances, the LOWTRAN-based computations seemadvantageous from two main aspects. First, a com-parative study which examines the effects of manyaerosol optical models, including variations in otheratmospheric conditions, would be impractical to carryout by means of a high-resolution computation due tocomputer-time considerations. Second, since the
LOWTRAN code has gained worldwide familiarity, ex-tending its predictive capabilities in the IR windowregion to different posteruption conditions should beconsidered of prime importance from an applicabilitypoint of view.
Comparison between the observed and calculatedradiance curves in Fig. 7 shows that the observed ra-diances near 12, 10.6, and 8.7 m fall in the regionbetween the two-layer and OBSEP23 optical models.(One has to take into account the effect of the LOW-TRAN broadened ozone band near X 9 Mm.) Thisresult is encouraging, especially since no adjustableparameter has been used. We recall that the atmo-spheric profiles used for the temperature and gaseousconstituents are the standard ones for that period ofthe year and that the aerosol optical models (the two-layer model and OBSEP23 combined with the 23 Oct.vertical profile) are based on actual measurementsmade at about the same time and location. As can beseen from the figures, the calculated radiances corre-sponding to more mature aerosol distributions (in par-ticular, OBDEC13) are far above the observed values.Still, since the vertical profiles and size distributions ofthe aerosols employed in the optical model were notmeasured simultaneously with the radiance observa-tions, uncertainty estimates of the simulated radiancelevels are needed before a quantitative comparisonwith the observed radiance is done. Additional poten-tial error sources in the simulation include possibledeviations of the actual stratospheric temperaturesand gaseous constituents profiles from the standardmid-latitude winter profiles. The resulting uncertain-ty levels of the simulated radiance are discussed in thefollowing paragraphs.
We first refer to the vertical profiles of particle con-centration and relative size distributions measured insouthern Texas (27-291N) during a 2-month periodfrom 21 Aug. to 23 Oct. 1982.6 On a short-range alti-tude scale the profiles appear highly variable. Howev-er, for the purpose of calculating the aerosol contribu-tion to the observed radiance, especially in the limbscan under study, it is appropriate to consider aerosolvolume absorption coefficients, kab5 (X), averaged overlayers a few kilometers thick in accordance with therate of change of stratospheric temperatures. Follow-ing Eq. (4) and the discussion thereafter, variations inthe aerosol profile and size distribution affect kabs(X)
through only the aerosol mass loading within theselayers. Hence knowing the temporal and spatial var-iabilities of the latter quantities during the Sept.-Oct.1982 period at latitudes near 27-290 N enables one toestimate the uncertainty in the simulated radiance asfar as the vertical profiles and size distributions of theaerosols are considered. The vertically integratedaerosol mass (column mass) at these latitudes above15,20, and 25 km vs time after the eruption is shown inFig. 3 of Ref. 12. The variations in these values be-tween 21 Aug. and 23 Oct. 1982 did not exceed 25%.For example, the aerosol column mass above 25 kmdecreased from -1 X 10-2 to 7.5 X 10-3 g/m 2 , whileabove 20 km it increased from 2.3 X 10-2 to 2.5 X 10-2
g/m2. By comparison, the calculated values of theaerosol column mass for the two-layer model employedin the radiance simulation in Fig. 7 are 1 X 10-2 and 2 X10-2 g/m2 above 25 and 20 km, respectively. It thusappears that to account for uncertainties in the actualaerosol loading at 27-29°N during Sept. 1982, an errorof up to +25% should be associated with the two-layermodel simulation of the window regions limb radiance.It should be noted that at latitudes near 321N, theaerosol mass loading at that period was systematicallylower than that near 27-291N by -15%.2
Next we discuss uncertainties related to the strato-spheric temperature and gaseous constituent profiles.We computed radiance curves employing the sameaerosol models as those in Fig. 7, only this time mid-latitude summer and tropical model standard atmos-pheres replaced the mid-latitude winter profile for thetemperature and gaseous constituents. The relativevariations in the radiance values near 10.6 and 12 umwere by far less than those in the ozone band. It,therefore, appears that small deviations from the mid-latitude winter profile, which probably occurred dur-ing Sept. 1982 (in spite of the prominent fit betweenthe observed and calculated radiances near 9.5 Mm)had little effect on these window regions, where theaerosol contribution is dominant. We estimate theerror in the simulated radiance, originating from theseuncertainties, to be not more than a few percent. Werecall that an error of a similar magnitude results fromemploying room-temperature values of the H2SO4 re-fractive indices in the simulation. These relativelysmall error sources can be added to the above statederror of +25% to yield a conservative total error of
:30%.Finally, we analyzed the sensitivity of the calculated
radiance to small variations in the observer's zenithangle. It has been found that a decrease of the zenithangle by 0.50 (from 95.4 to 94.9° with an associatedincrease of the tangent height from 10.8 to 16.3 km)may result in an increase of -10% in the radiance near10.6 Am and an increase of -20% in the radiance near12 um without significantly affecting the intensity andshape of the ozone band. This increase in the windowregion radiance should be taken into account when acomparison is made between the simulated and ob-served radiances, since the latter is affected by thefinite field of view of the spectrometer. On the otherhand, we recall that the observed radiance in Figs. 6and 7 corresponds to a latitude of 320N, while thesimulated radiance employs aerosol profiles corre-sponding to latitudes between 27 and 290N at aboutthe same time. As mentioned above, the latter differ-ence implies that the simulated values near 10.6 and 12,m in Fig. 7 should be reduced by -15% before beingcompared with the observed ones. It thus appearsthat practically a mutual cancellation takes place be-tween the effects due to the finite field of view and thedifference in latitudes. Hence, for comparison withthe observation on 22 Sept. 1982, the simulated radi-ance can be taken as that represented by the two-layermodel curve in Fig. 7 with uncertainty limits of +30%.
Fig. 8. Observed spectral radiance obtained on a balloon flight overPalestine, TX (31.50N) -1.5 yr after the El Chichon eruption (10Oct. 1983). The observation altitude and zenith angle are 23.6 kmand 89°. The spectral resolution is -0.1%. Also shown are black-
body radiances calculated at 210 and 230 K.
It can be seen that within the stated uncertainty thesimulated radiance in the window regions near 12,10.6,and 8.7 Am agrees with the observed one.
C. Radiance Observations 1.5 yr after the EruptionFigure 8 shows a typical radiance scan observed on a
balloon flight over Palestine, TX -1.5 years after theEl Chichon eruption. Since by this time the aerosolloading was several times smaller compared with Sept.1982 (and also because of the different observationgeometry used), the radiance levels in the 8.7-, 10.6-,and 12-Am windows are small compared with those inFig. 6. Yet the present geometry is much more amena-ble to theoretical studies, because the line of sight isnearly locally horizontal. Hence the number of poten-tially unknown profile parameters (of the temperatureand gaseous components) is smaller than in the limbview case, and the spread in observation zenith anglesdue to the finite field of view has a much smaller effecton the observed radiance. However, unlike the previ-ous case, an independent measurement of the aerosolvertical profile at this period is not available in theliterature, and, therefore, it is treated as an adjustableset of parameters. The choice of the aerosol profileshould be consistent with the long-term temporal be-havior of the post El Chichon aerosol loading in thepertinent altitudes. As a guideline for this choice werefer to Fig. 5, which shows the temporal changes in thevertical profiles of the extinction coefficients (the so-called scaling factor in the LOWTRAN-6 program) over a2-yr period. As can be seen from the figure, at alti-tudes between 15 and 20 km the extinction coefficientshave decreased by a factor of 8-10, whereas at altitudesbetween 22 and 26 km, the decrease is by a factor of 25-40. At higher altitudes the decay factor is more than 2orders of magnitude. It is well understood that aero-sol particles of different sizes were subjected to some-what different decay rates during this 2-yr period.Nevertheless, as a crude approximation let us assumethat the temporal changes in the vertical profile of thevisible extinction coefficients reflect the decay rate ofthe vertical profile of the total aerosol distribution.Recalling that this decay rate is exponential12 it follows
21
U +~~~~~~++
N ~~~~~~~~++
10 +~~~~'
8 9 10 11 12 13X (am)
Fig.9. Calculated vs observed radiance for a nearly locally horizon-tal scan -1.5 yr after the eruption. The observed radiance is re-drawn from Fig. 8 (sparse crosses). The calculated radiances corre-spond to the following models: (1) no stratospheric aerosols (lowerbroken line); (2) an aerosol vertical profile 5 times smaller than thatof 9 Dec. 1982 and a mid-latitude winter profile; OBDEC13 normal-ized distribution; 75% H 2SO 4 (solid curve); (3) same as (2), but thecomposition is 62% H 2 SO 4 (dashed curve); (4) same as (2) but with amodified temperature profile, where temperatures at altitudes be-tween 20 and 30 km are 10 K higher than those of the standard mid-latitude winter (dotted curve); (5) aerosol distribution and loading
described by the two-layer model of Fig. 7 (sparse circles).
immediately that if 2 yr after Dec. 1982 the aerosolprofile has decayed by some factor x, 1 yr earlier itshould have decayed by a factor of -- Vx. Accordingly,to simulate the radiance spectra obtained in Oct. 1983the aerosol profile of 9 Dec. 1982 (see Fig. 5, curve a)should be reduced by a factor of -- /8 to -V10 foraltitudes between 15 and 21 km and be a factor of
/--\25 to V40 for altitudes between 22 and 26 km.Figure 9 shows the results of the calculated spectral
radiance for the same geometry as that of Fig. 8. Sincethe observation is nearly locally horizontal, the domi-nant contribution to the radiance originates fromstratospheric layers at altitudes close to Hobs. There-fore, we employed a constant reduction factor of 5 inresealing the aerosol profile above 23 km with respectto that of 9 Dec. 1982. The computations have beenperformed using the LOWTRAN-6 code, where again thestratospheric aerosol data set has been replaced, thistime by the optical model calculated for the OBDEC13normalized distribution with acidity percentages of75% (solid line in Fig. 9) and 62% (dashed line). Alsoshown in Fig. 9 are the calculated radiance for a casewith no stratospheric aerosols (lower broken line) andthe radiance which would have been obtained in thisgeometry if the aerosol distribution and loading werethose of the two-layer model of Fig. 7 (sparse circles).The latter calculation has been performed since itenables one to realize the expected effect due to a 1-yraerosol decay on the stratospheric radiance for a nearlylocally horizontal scan. Comparison between the cal-
culated radiance (solid curve in Fig. 9) and the ob-served radiance (redrawn by the sparse crosses in Fig.9) reveals that the standard mid-latitude winter pro-file does not satisfactorily reproduce the ozone andHNO3 emissions (near 9.6 and 11.3 gm, respectively) inthis case. From the radiance value near 9.6 Mm itappears that in reality the temperatures between 20and 30 km were -10 K higher than those of the stan-dard LOWTRAN model. Modifying the temperatureprofile so as to match the 03 emission (the HNO 3emission is still a factor of 2 smaller than observed) andcomparing the calculated (dotted curve) and observed(sparse crosses) radiances in the window regions near8.7, 10.6, and 12 Am, it is'seen that while a reasonableagreement appears near 8.7 and 10.6 Am, a noticeabledeviation shows up in the window region near 12 Am.This deviation is both in the absolute radiance value(the calculated radiance near 12 Am is a factor of -2.5smaller than the observed radiance) and in the relativespectral shape: the calculated radiance near 10.6 gmis larger than that near 12 ,m (by a factor of -1.8),whereas the observed radiances in this case show anopposite trend. To discuss these differences in moredetail, we first have to eliminate spectral distortionswhich might have originated from the LOWTRAN codeitself. It is well known that in spectral regions ofrelatively high transmittance, especially in the distantwings of strongly absorbing and overlapping bands,the atmospheric radiance calculated by LOWTRAN be-comes less accurate. 2 4 Moreover, radiance contribu-tions to the 10.6- and 12 -Am window regions originat-ing from Freon gaseous components are not includedin the present version of the LOWTRAN-6 code. Toaccount for these shortcomings of LOWTRAN and at thesame time improve the agreement between the calcu-lated and observed ozone and HNO3 emission bands,we refer to calculations made using a line-by-line lay-er-by-layer code.25 The results of these calculations,2 6
which have used an optical model for the stratosphericaerosols similar to that in Fig. 9 along with a modifiedtemperature profile to fit the radiance levels near 9.6Mm, are shown in Fig. 10. The calculated line-by-lineradiance for a case with no aerosols is shown as well.For comparison, the observed radiance curve of Fig. 8is redrawn by the dotted curve in Fig. 10. As can beseen in the figure, the agreement between the observedand calculated radiance levels in the 8.7- and 10.6-Amwindow regions is quite good, indicating that the aero-sol contribution to the radiance in these regions isconsistent with predictions based on long-term time-dependent models for the post El Chichon aerosols.12Similar conclusions can be drawn from comparisonsmade between calculated and observed radiances inthese window regions for other geometries (e.g., Hob, =
15.5 km and Oobs = 840).26 However, a common spec-tral feature of the calculated radiances by both theLOWTRAN and line-by-line codes employing the H2SO4optical models, which does not agree with the observedspectral radiance of Oct. 1983, is the previously men-tioned relative magnitude of the radiance at 12 Amcompared with that at 10.6,vm. We devote the rest of
l000
'E 100
1.
U
Zr I °Es
'V
a
9.0 (0.0 11.0 (2.0 13.0
X(Mm)
Fig.10. Calculated radiance by the line-by-line layer-by-layer code(solid curve, resolution 0.8 cm-') vs the observed radiance on 10 Oct.1983 over Palestine, TX (dotted curve). The calculation employs anaerosol optical model similar to that of the dotted curve in Fig. 9 butincludes also Freon gas contributions. The calculated line-by-lineradiance without stratospheric aerosols is shown as well (dashed
curve). The figure is taken from Ref. 26.
this section to discussing several alternative causes forthis difference.
The first possibility that one has in mind is investi-gation of the effect of having aerosol compositions ofacidity percentages lower than 75%. As can be seenfrom Fig. 4, the absorption coefficients (and hence theemissivities) at wavelengths X _ 11.5 Am decrease withlowering the acidity of the aerosols, while for 11.5 < X K16,um the opposite is true. This behavior is commonto all the post El Chichon aerosol distributions exceptfor HRMAY19, where the crossover point is shifted toX - 13.5 Am (see Fig. 2). The effect of lowering theacidity percentage to 62% on the calculated radiance isshown by the dashed curve in Fig. 9. Although therelative changes in the 10.6- and 12 -,m regions havethe desired trend, the ratio between the radiances at 12and 10.6 ,m is still smaller than 1 contrary to theobserved ratio. A further decrease in the acidity per-centage (toward 50%) might improve the situation,although even for 50% H2 SO4 the emissivity ratio isstill <1. Note, however, that an acidity percentage<<75% is not compatible with common water-vapormixing ratios and temperatures at altitudes above 20km. To appreciate this, we show in Fig. 11 the depen-dence of the equilibrium acidities of H 2SO4 -H2 0 aero-sols on water-vapor mixing ratios and ambient tem-peratures. The curves are based on results obtainedby Russell and Hamill,8 where we have replaced partialpressures by volume mixing ratios, using an air densitywhich corresponds to a standard mid-latitude winteratmosphere, 2 2 at an altitude of 24 km. As can be seenin the figure, for water-vapor mixing ratios which ataltitudes above 20 km are usually <10 ppmv and com-mon stratospheric temperatures (T > 200 K), the equi-librium acidity percentage is far above 50%.
Fig. 11. Equilibrium acidity percentage of H 2 SO4-H 2 0 aerosols asa function of temperature and water vapor mixing ratio. The acid-ity curves are based on results in Ref. 8. The saturation curvecorresponds to water vapor saturation pressure above ice. Partialpressures have been transformed into volume mixing ratios, assum-ing an air density of 46.24 g/m 3 (corresponding to an altitude of 24km of a standard mid-latitude winter atmosphere). The dashedrectangle indicates common stratospheric temperatures and water
vapor mixing ratios above 20 km.
Large values of water-vapor mixing ratios may bythemselves give rise to enhanced radiance levels near12 ,m. Both the water-vapor continuum and bandemissivities are larger at X = 12 m than X = 10.6 Am.
2 2
However, mixing ratios far above 10 ppm at altitudesabove 20 km would have shown up in the form ofintense emission lines in the radiance spectrum near 12,um. The absence of such lines in the observed spectralradiance (Fig. 8) indicates that the water vapor mixingratio was not unusually large on that occasion. As faras the water vapor continuum contribution is consid-ered, we have examined the sensitivity of the calculat-ed radiance to the continuum model22 by increasingthe amount of water vapor involved in it by factors ofup to 2 orders of magnitude (without changing thecontribution from the band emissivity). The resultingradiance near 12 m increased by not more than 30%,still failing to recover the observed ratio between the12- and 10.6-Mm radiances.
Finally, we looked into the possibility that H2SO4vapors are responsible for the enhanced radiance near12,um. From published IR absorption spectra of gas-eous H2 SO4,27 28 a value of '10 atm' cm' can beinferred, for the absorption coefficient at X = 12 m,which is a factor of -2 larger than that at X = 10.6,um.Number densities of H2SO4 vapors have been found torange from 105 cm-3 at altitudes between 23 and 27 kmup to 107 cm-3 around 33 km.29 The latter value hasbeen conjectured by Hofmann and Rosen5 to repre-sent post El Chichon number densities near 25 km.For temperatures of T 230 K it corresponds to anH2 SO4 partial pressure of 3.1 X 10-13 atm, which wewill take as an upper limit. Hence, for a line of sight ofa few hundred kilometers, the average emissivity ofH2SO vapors at X = 12 gmis <10-4. When multiplied
by a Planck function evaluated at X = 12 um and T <230 K, the contribution to the measured radiance willbe smaller than 0.1 MW cm-2 sr'i Am-'. This contri-bution is far below that necessary to account for thedifference between the calculated and observed ra-diances at 12 Am (Fig. 10).
It thus appears that the relative magnitudes of theradiances at 10.6 and 12 um observed on the Oct. 1983balloon flight have little to do with the pure H2SO4-H20 system. This is supported by the expectationthat solid H2SO4 particles exhibit similar spectral fea-tures to those of the liquid aerosols.30'3' One has,therefore, to look for potential spectral effects origi-nating from other species, which are capable of show-ing up only because the H2SO4 aerosol loading in thestratosphere at the period under study (1.5 yr after theeruption) has become relatively small (compared tothe Sept. 1982 observation). One such species is thecomplex system which may develop from the solutionof nitric acid vapors in droplets of sulfuric acid aque-ous solution.30 Radiance due to weak emission lines ofHNO3 vapors at the spectral region near 12 m andtemperature effects thereon may be an additional can-didate explanation for the enhanced intensity ob-served at this region.32 We have not further investi-gated these possibilities, which are beyond the scope ofthe present work. It should be noted that silicateparticles orginating from the El Chichon eruptionshould have been completely decayed by the periodunder study, especially at altitudes above 20 km.7Also, it has been indicated that little or no solid ammo-nium sulfate was present in background stratosphericaerosols.833 In any case, as can be seen from their IRabsorption spectra,3435 neither of these solid particleaerosols could have resolved the problem of the 10.6-12-,m radiance ratio.
IV. Multiple Scattering Effects
The relative importance of scattering, in the radia-tive transfer processes involving aerosol distributionsof different maturity states, can be recognized from therespective values of w0 , the single scattering albedo,shown in Fig. 3. As can be clearly seen in the figure,the eruption gave rise to a drastic change in the value ofcoo in the 8 -13-Am window region. From a fraction of apercent (HRPREER) it has increased to values near50% a couple of months after the El Chichon eruption(HRMAY19). A few months later, due to sedimenta-tion of large particles, the value of coo is found to be ofthe order of 1-2% with a gradual increase up to 10%after 1 yr (HRLNSP2).
Effects of multiple scattering in the thermal IR re-gion have rarely been examined in the past. For thisreason and in particular because of its potential ad-verse effects on the operation of remote sensing de-vices, it is interesting to find to what extent multiplescattering can affect the spectral radiance in the 8-13-,m window region shortly after an intense eruptionand 1 or 2 yr afterward. As typically maturity statesfor these time periods we chose the HRMAY19 andHRLNSP2 distributions, which have been shown to
have the largest o values. Multiple scattering com-putations are made, employing the DISORT code,36
which implements the discrete ordinate algorithm forsolving the radiative-transfer equation including ther-mal emission.
Figure 12 shows results of DISORT multiple-scatter-ing calculations involving the HRMAY19 normalizeddistribution and an aerosol vertical profile, which wastaken to be equal to that measured on 23 Oct. 1982.For comparison, LOWTRAN-6 calculations involvingthe same aerosol distribution and vertical profile alsoare shown, one curve (dashed line) computed with kext= kab5 (no attenuation due to scattering) and the othercurve (solid line) computed with kext > kabs. Thetemperature and ozone vertical profiles are those cor-responding to mid-latitude summer. Since the DIS-ORT code assumes a plane-parallel atmosphere, thegeometry chosen in this case is different from the pre-vious two cases to be compatible with neglect of earthcurvature effects. Due to computer-time consider-ations, DISORT computations have been done for a fewselected wavelengths only.
It is important to point out that, although the obser-ver's zenith angle is 0 = 700, the calculated radiancedepends not only on the atmospheric profiles for alti-tudes above Hobs (i.e., those of computational layersintersected by the line of sight) but also on the profilesbelow Hobs (13 km in this case), including the groundemissivity. To see the effects of these lower-lyinglayers on the multiply scattered radiance, three sepa-rate calculations have been performed for each wave-length, and the resulting radiances are displayed in thefigure. One computation was done taking the lowestatmospheric layer to extend down to 11 km only, whilethe other two computations take into account all layersdown to ground level with and without ground emis-sion. Aerosol data for altitudes below 10 km have beentaken from the standard LOWTRAN-6 data base (pro-files for tropospheric aerosols between 2 and 10 km andrural-type aerosols for the boundary layer between 0and 2 km assuming a visibility of 23 km). Theseinclude both optical depths (for extinction and scatter-ing to be used in the calculation of coo for each layer)and asymmetry factors of the scattering phase func-tions. The latter factors, as well as asymmetry factorscalculated for the HRMAY19 distribution (rangingbetween 0.4 and 0.5 for X between 13 and 9 Mm) havebeen employed in Henyey-Greenstein-type phasefunctions in the DISORT computations.
As can be seen from the different radiance computa-tions in Fig. 12, the contributions to the multiply scat-tered radiance originating from thermal emissionsfrom layers below 11 km, including the ground, may becomparable with those of the stratospheric sublayerswhich are intersected by the line of sight. This isespecially true in the window regions near 10.6 and 12Am, where the values of the total multiply scatteredradiances calculated by DISORT are found to be almosttwice as large as the values calculated by LOWTRAN.
On the other hand, close to the ozone emission band(9-10 Mm) the contributions from the low-lying layers
-E 120 - MID LAT. SUMMER(20 ~~~~~~ HRMAYI9
21. .1
Z N~~~~~~~~
/0 -
20
8 9 (0 I 12 13Mjasm)
Fig. 12. Results of DISORT multiple scattering calculations com-pared to LOWTRAN-6 calculations, where in both cases the strato-spheric aerosol relative size distribution is HRMAY19 and the com-position is 75% H2 SO4 . The results of the LOWTRAN calculations arepresented for kext > kabs (solid curve) and ket = kabs (dashed curve).The results of DISORT correspond to computations where (a) strato-spheric layers down to 11 km only are included (solid circles); (b) alllayers down to ground level are included, but the ground emissivityis zero (triangles); (c) as in (b) but the ground emissivity is equal to 1
(open circles).
become relatively small. This follows because most ofthe upward radiance, thermally emitted by the tropo-spheric and boundary-layer constituents, is being ab-sorbed by ozone mulecules either before or after beingscattered into the direction of observation.
It is interesting to note that the multiply scatteredradiances originating from the stratospheric sublayersalone are rather close to the values calculated by LOW-TRAN without taking into account attenuation due toscattering (dashed curve in Fig. 12). Thus it appearsthat in-scattering processes fully compensate for lossesdue to out-scattering, and the LOWTRAN algorithm inthis case largely overestimates the overall attenuation.
We have also carried out calculations for this case(HRMAY19 distribution, 8-13-Mm spectral region) inwhich solar scattering is taken into account. The ad-ditional contributions to the thermal radiances turnout to be at most of the order of 1%.
Figure 13 shows results of DISORT multiple scatter-ing calculations similar to those in Fig. 12, only thistime the normalized distribution function describingthe stratospheric aerosols was taken to be HRLNSP2.(The calculated asymmetry factors range between 0.05and 0.1.) LOWTRAN-6 calculations involving this aero-sol distribution are also shown for comparison. Nonoticeable differences have been obtained betweenLOWTRAN results calculated with or without attenua-tion due to scattering. Also, the contributions of thestratospheric sublayers alone to the multiply scatteredradiance calculated by DISORT coalesce with the LOW-TRAN results. The contributions originating from thelower-lying layers including ground emission are <10%even in the 10.6- and 12-Aum window region. Obvious-
X(ym)Fig. 13. Results of DISORT multiple scattering calculations com-pared with LOWTRAN-6 calculations where the stratospheric aerosolrelative size distribution is HRLNSP2 and the acidity is 75%. Thecurve presents the results of the calculations made with LOWTRAN(no noticeable difference between the cases kext > abs or kext = kabs).The other symbols present the results of the DISORT computations,
and their meaning is the same as in Fig. 12.
ly, the upward radiance emitted by the troposphericand boundary-layer constituents is similar to that ofthe HRMAY19 calculations, but the scattering effi-ciency into the direction of observation is much small-er in this case.
V. Conclusion
In this investigation we studied the impact of sulfu-ric-acid aerosols, formed and evolved in the strato-sphere following the El Chichon eruption, on the IRradiance in the 8-13-,gm window region.
The unique character of the calculations in this workis that they afford the opportunity to compare resultsof optical models based on Mie theory and reportedmeasurements of aerosol size distributions and verticalprofiles with actual data of IR radiance observed closeto the time and location of the aerosol measurements.The radiance observations were performed 6 monthsafter the eruption (Sept. 1982) and 1 yr later (Oct.1983). Since the period before Jan. 1983 was stillunsettled and the reported size distributions were notmeasured simultaneously with the radiance observa-tion, the uncertainty involved in the simulated radi-ance in the spectral regions near 8.7, 10.6, and 12 jamfor Sept. 1982 is estimated to be 30%. We demon-strated that within these uncertainty limits, the mag-nitude and main spectral features of the calculatedradiance for that period agree with the observed data.
The comparison between the observed and simulat-ed spectral radiances for Oct. 1983 demonstrates thatnear the window regions at 8.7 and 10.6 m the magni-tude of the observed radiance is compatible with theresults of calculations based on temporal evolutionmodels for the aerosols. However, the ratio betweenthe observed radiances at 12 and 10.6,gm is considera-bly higher than the calculated one. It appears that theadditional contribution to the observed radiance near12 m in this case results from species other than thoseof the pure H2SO4-H2O system and that it shows uponly because the H2SO4 aerosol contribution has been
reduced. It is possible that the additional radiance iscorrelated with the aerosol cloud but only through asecond agent, e.g., the complex system which may de-velop from the solution of nitric acid vapors in dropletsof sulfuric acid aqueous solution. Further studies areneeded to elucidate the source and mechanism respon-sible for this spectral feature. It should be noted thatdue to this additional radiance source and its possiblecorrelation with the aerosol cloud, it is impractical toattempt to estimate the acidity percentage of the sul-furic acid from the 10.6-12-Am radiance ratio, even inthe case of a relatively high aerosol loading.
Finally, it is instructive to note the time variation ofthe IR to the visible extinction ratio of the aerosoldistributions following the eruption and the high vari-ability of the IR single scattering albedo associatedwith these distributions. Aerosol distributions mea-sured a couple of months after the eruption are distinc-tive in exhibiting extinction ratios which are consider-ably higher than those of the preeruption period aswell as those of the more mature distributions. Ofparticular importance is the finding that the IR singlescattering albedo of the distribution measured in May1982 reaches values (50% at X - 12,Mm) significantlyhigher than hitherto assumed. We demonstrated theimpact of such high values of 0 on the multiply scat-tered stratospheric radiance, whose pattern becomesspectrally diffused due to a significant increase of theradiance level in the 10.6- and 12 -ptm window regions.Their role in radiative processes associated with cli-matic effects of volcanic clouds needs further investi-gation in the future.
We would like to thank A. Goldman for helpfuldiscussions and K. Stamnes and W. Wiscombe forproviding us with the DISORT code.
B. Halperin is on leave of absence from Soreq Nucle-ar Research Centre, Yavne, Israel.
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_ _ 7~~ . W OEAM
Wolfgang Kiefer of Karl Franzen University, Austria, photographed by F. S. Harris, Jr. at the 1986
