ICARUS 130, 36–48 (1997)ARTICLE NO. IS975787

Radiative Balance and Dynamics in the Stratosphere of Jupiter:Results from a Latitude-Dependent Aerosol Heating Model1

Fernando Moreno and Jose Sedano

Instituto de Astrofısica de Andalucıa, CSIC, Granada, SpainE-mail: fernando@iaa.es

Received February 4, 1997; revised May 17, 1997

I. INTRODUCTIONAn updated dynamical model for the circulation in the jovian

Previous calculations of the radiative equilibrium tem-stratosphere has been developed. For computation of the heat-perature profile in the jovian stratosphere were limited bying and cooling rates in the stratosphere, required to obtain the

radiative flux convergence, the model makes use of exponential- two facts: first, all of the models were based on a limitedsum derived coefficients from laboratory and correlated-k dis- knowledge of the stratospheric aerosol distribution; andtributions from line listing data for the various atmospheric second, the models were based on early methane absorp-gases. The aerosol distribution at different latitudes was deter- tion coefficient estimates and derived band model parame-mined from comparisons of results from microphysical models ters. Much of the earlier work simply parameterized theand near-UV jovian images obtained by the Wide Field and

aerosol distributions (e.g., Wallace et al. 1974, ApplebyPlanetary Camera 2 on the Hubble Space Telescope. The largestand Hogan 1984), without including any latitudinal depen-aerosol content is found at latitudes south of 658S planeto-dence of the aerosol heating. Based on estimates of aerosolgraphic, the aerosols being produced at higher atmosphericdistribution from International Ultraviolet Explorer mea-levels and at higher rates than those at the corresponding north-

ern latitudes. At midlatitudes, the aerosol production rate is surements by Tomasko et al. (1986), West et al. (1992)less than about two orders of magnitude than that found at were the first to include a latitudinal dependence of aerosolhigh latitudes. The distinct imaginary refractive index spectra heating in the models, although due to fact that the obser-of the aerosols found at the different latitudes reflect a composi- vational data were limited to only two latitudes on Jupiter,tional difference in the material being produced as a result of they had to scale the results at other latitudes taking intochemical reactions. This difference is evident in the shortest

account a north–south Voyager 2 PPS scan and assumingwavelength explored (leff 5 230 nm) between low to midlati-latitudinal variations in the total column density of parti-tudes and the polar regions.cles. In this work, we extended the microphysical codesThe resulting heating rates are much higher in the strato-used to obtain the aerosol distribution at two latitudes onsphere than those given by previous estimates. The correspond-

ing radiative equilibrium temperatures are therefore hotter than Jupiter from Hubble images (Moreno 1996) to severalpreviously reported, mainly above the 10-mbar level. A north– other latitudes to gain a better knowledge of the depen-south asymmetry in the stratospheric aerosol distribution was dence of the aerosol distribution on latitude. Methane ab-found, which, in turn, produces a different pattern in the de- sorption in the range 1–2.5 em is the most important con-rived quantities from the dynamical model. In particular, the

tribution to the gaseous heating. Many of the previousEliassen–Palm flux divergence («) shows a different patternmodels are based on incomplete line listing data or arewhen compared with that inferred by Conrath et al. (1990,based on or employ band model formulations similar toIcarus 83, 255–281) and West et al. (1992, Icarus 100, 245–259).that of Wallace et al. (1974) for the near-infrared bandsAt the base of the stratosphere we inferred the same circulation

pattern as found by Gierasch et al. (1986, Icarus 67, 456–483) longward of 1.5 em, which were based on early laboratoryand West et al. (1992) with upwelling over the zones and subsi- methane data by Kuiper and Cruikshank (1964). We showdence in belts, but with higher values in the magnitude of the in Section III that the heating rates above the 30-mbarvertical winds at low latitudes. 1997 Academic Press level corresponding to the band complexes at 1.7 and 2.3

em computed by Wallace et al. (1974) are a factor of about2 smaller than that computed with an exponential-sum

1 Based on observations made with the NASA/ESA Hubble Space model (Baines et al. 1993) applied to recent laboratoryTelescope, obtained from the data archive at the Space Telescope Sciencespectra by Giver et al. (1990) and Strong et al. (1993). AsInstitute (STScI), which is operated by the Association of Universities

for Research in Astronomy, Inc. under NASA Contract NAS 5-26555. a result of the higher heating rates derived, we show that

360019-1035/97 $25.00Copyright 1997 by Academic PressAll rights of reproduction in any form reserved.

JOVIAN STRATOSPHERE DYNAMICS 37

the corresponding horizontally-averaged (area-weighted)equilibrium temperature is hotter than previously inferredby other authors (Appleby and Hogan 1984, Conrath et al.1990). Sections II, III, and IV describe the exponential-sum model and the heating and cooling rate computationsand the procedure used to obtain the horizontally averagedequilibrium temperature profile.

The last portion of the paper is devoted to obtainingthe various quantities describing the large-scale circulationin the jovian stratosphere. The dynamical model used hereis based on the same grounds as that of West et al. (1992),so that a direct comparison of the magnitudes of thesequantities can be made. A comparison with the frictionalmodel of Conrath et al. (1990) is also made.

II. THE EXPONENTIAL-SUM MODEL

The basis of the exponential-sum fitting method is thatFIG. 1. Root-mean-square errors of the exponential-sum model fitsthe gaseous transmission function in a given spectral inter-

to the laboratory data of Strong et al. (1993) at T 5 190 K and at threeval is expressed as (see, e.g., Wiscombe and Evans 1977)spectral regions, as labeled.

T(u) 5 Oi5N

i51wi exp(2ki u), (1)

tables, coefficients at intermediate pressures and tempera-tures are obtained by a two-dimensional linear interpola-tion. Figure 1 shows the root-mean-square error of thewhere T is the transmittance, u is the gas abundance, wi

are the weights of a given quadrature (here we use N 5 exponential-sum fit derived transmittances to the Stronget al. (1993) laboratory transmittances at 190 K. These10 Gaussian quadrature weights), and ki are the absorption

coefficients to be determined by a fitting algorithm to ex- errors are generally confined to values less than 0.02 unitin transmittance which can be considered as acceptableperimental or band model data. For the outer planet atmo-

spheres, methane gas is the primary absorber in the near taking into account the fact that these values are compara-ble to the estimated errors in the measured transmittancesinfrared and the most important gaseous contributor to

the stratospheric heating. To obtain the coefficients for as described by Strong (1992).Since there is a spectral region of overlap between boththe exponential-sum model from the available laboratory

methane data, we followed the same approach as described the Strong et al. (1993) and the Giver et al. (1990) datasets, it is important to verify that the resulting syntheticby Baines et al. (1993). Essentially, the laboratory methane

transmittance data are fitted to a quasi-random band model spectra obtained from the exponential-sum fits in that spec-tral region from those laboratory data sets are in close(e.g., Crisp 1990) first, and then exponential-sum absorp-

tion coefficients are derived from the band model. The agreement. Figure 2 shows the resulting spectra in theinterval 4000–6260 at three temperatures and fixed pres-technique was applied to the pure methane laboratory data

of Giver et al. (1990) and Strong et al. (1993). The Giver sure and path length for both the Giver et al. derivedcoefficients and the Strong et al. derived coefficients. Theet al. data cover the spectral region 4000–6260 cm21 at

three temperatures, 112, 188, and 295 K, and the Strong agreement is remarkable. For all the computations pre-sented here, the exponents derived from the Strong et al.et al. data cover the full near-IR range between 2000 and

10,000 cm21, at temperatures of 190, 240, and 296 K. Both data were used, except for those at 80 and 112 K in theinterval 4000–6260 cm21, where the Giver et al. data weredata sets were obtained at several pressure–path length

combinations. The coefficients from the exponential-sum used. As we are dealing with jovian stratospheric tempera-tures (ranging from 110 to 180 K), an important matter offits were obtained at five temperatures, namely, 80, 112,

190, 240, and 296 K, and 7 pressures from 1025 to 10 atm, concern is the use of exponential-sum coefficients extrapo-lated to temperatures lower than those reached in theseparated by a decade. The coefficients at 80 and 112 K

were obtained by band-model extrapolations from the de- Giver et al. (1990) measurements (112 K) or to the Stronget al. (1993) measurements (190 K). It is then interestingrived parameters at the lowest temperature data available

in the spectral region under consideration. From these to compare the synthetic spectra with other available labo-

38 MORENO AND SEDANO

FIG. 3. Transmittance spectra in the 2.3-em methane band. Theheavy solid line corresponds to the laboratory measurements of McKellar(1989) at 77 K, a CH4 abundance of 0.29 m-am, a CH4 partial pressureof 0.13 kPa, and a N2 partial pressure of 60.4 kPa. The dashed linecorresponds to the line-by-line results of Apt et al. (1981), and the thinsolid line corresponds to the spectra derived from the exponential-summodel. The quantity s corresponds to the root mean square of the expo-nential-sum spectrum to the laboratory spectrum.

FIG. 2. Transmittance spectra computed from exponential-sum coef- strength. For the 1.7-, 1.35-, and 1.15-em bands, closeficients for a methane abundance of 10 m-am, a pressure of 0.1 atm, and agreement was also found (see Figs. 4 and 5). Of course,temperatures of 296, 210, and 140 K, as labeled. The solid lines are the

this does not guarantee that the lower-temperature band-spectra derived from the Giver et al. (1990) laboratory measurements;model extrapolations will always work for all the atmo-the dotted lines correspond to the spectra derived from the measurements

by Strong et al. (1993).

ratory methane spectra at the lowest temperature condi-tions. To do that, we compared the synthetic spectra ob-tained with the data of McKellar (1989), who obtainednitrogen-broadened methane spectra at 77 K in the region1.1–2.6 em. To consider the fact that these data pertainto methane broadening with nitrogen gas, we applied theprescription given in Baines et al. (1993) by which for atotal pressure p1 the exponents corresponding to pressurep0 are used, p0 being given by p0 5 (c1 p1)/c0, where c0

and c1 are the broadening coefficients for methane andnitrogen, respectively. The broadening coefficients weretaken from an average of values corresponding to variousmethane lines or bands as shown in Table 3 of VujkovicCvijin et al. (1993) at 113 and 77 K. This gave a c1/c0

ratio of 0.7, the same value at both temperatures. TheFIG. 4. Transmittance spectra in the 1.73-em methane band. Thecomparison with the laboratory spectrum at the 2.3-em

heavy solid line corresponds to McKellar’s (1989) laboratory measure-methane band is shown in Fig. 3, which also shows anments for 2.5 m-am of CH4, a CH4 partial pressure of 0.83 kPa, a N2earlier low-temperature line-by-line calculation by Aptpartial pressure of 35.5 kPa, and a temperature of 77 K. The thin solid

et al. (1981). As seen, although the agreement is not com- line shows the corresponding results from the exponential-sum model.plete, the exponential-sum model reproduces most of the The quantity s corresponds to the root mean square of the exponential-

sum spectrum to the laboratory spectrum.features seen in the laboratory spectrum with the right

JOVIAN STRATOSPHERE DYNAMICS 39

used to retrieve the aerosol size distribution profiles atother latitudes. We considered that the aerosols at latitudesnorth of 408N and south of 558S were charged with a chargeof 3 electrons per particle of 0.1-em in radius, being chargeproportional to the radius, as was found by Moreno (1996)for the particles at 658S. For the region between the 408Nand the 658S latitude circles, the particles are assumed tocarry a charge between 0 and 1 in the same units. Wealso assumed the same hydrazine production rates at thoselocations as reported by Moreno (1996) for 658S and theequator, respectively. Thus, for different latitudes wesearched for the best-fitting embryo production rate profileand imaginary refractive indices. We started the procedureat the highest northern latitudes. At these latitudes wefirst tried models having the same embryo production rateprofile and imaginary refractive indices as found by Mor-eno (1996) at 658S, based on the similar appearance ofFIG. 5. Transmittance spectra in the 1.35- and 1.15-em methanethe planetary regions north of 408N and south of 558S.band groups. The heavy solid line corresponds to McKellar’s (1989)

laboratory measurements for 3.5 m-am of CH4, a CH4 partial pressure However, the resulting modeled limb-to-limb reflectivitiesof 1.15 kPa, a N2 partial pressure of 36.8 kPa, and a temperature of 77 were too low compared with the measured profile. Specifi-K. The thin solid line shows the corresponding results from the exponen- cally, at 758N for the F218W filter, the model was a factortial-sum model.

of 2.6 less reflective than the measured reflectivity at 708relative longitude and a factor of 1.4 less reflective thanthe measured reflectivity at the central meridian. By con-sidering smaller values for the imaginary refractive indexspheric conditions, but it at least gives an idea of the magni-at those high northern latitudes it was possible to fit thetude of the errors involved in the transmittance calcula-reflectivity values at the central meridian, but not at thetions.limbs; i.e., the modeled profiles gave the wrong center-to-In all the calculations presented here pertaining to jovianlimb variation. We then varied both the embryo productionstratospheric conditions, we used an average c1/c0 ratiorate profile and imaginary refractive indices. The best-(where c1 is now the H2-broadening coefficient) of 0.6,fitting models at high northern latitudes have embryo pro-which is an average of hydrogen-to-self broadening coeffi-duction rate profiles that peak at much lower altitudes thancients for 113 and 190 K from the data shown in Table 3those at the high southern latitudes and have differentof Vujkovic Cvijin et al. (1993).values of the refractive indices (see Table II). After fittingmodels at those highest northern latitudes, we proceededIII. COMPUTATION OF THE HEATING RATESby modeling the highest southern latitudes, specifically at558S and 758S. While the model at 758S is rather similarAerosol heating rates are computed from the obtained

aerosol size distribution profiles at different latitudes. A to that found at 658S by Moreno (1996), the productionrate profile at 558S peaks at a much lower atmosphericset of Hubble Space Telescope archive images in the near

UV were used to extract the limb-to-limb reflectivity (I/F) height, being more similar to the models at the northernprofiles at different latitudes at the wavelengths under con-sideration. The images used, the corresponding filters andeffective wavelengths, and the geometric albedo at those TABLE I

Hubble Space Telescope Images Used in the Present Work awavelengths are listed in Table I. The reduction and cali-bration of the images are described by Moreno (1996),

Effectiveand are not repeated here. For each latitude, the fourImage Filter wavelength Geometric

wavelength-dependent limb-to-limb I/F scans were used denomination name (nm) albedoas input to a radiative transfer model in which scattering

U2EB0407 F218W 230 0.31parameters by atmospheric particulates are computed byU2EB0408 F255W 275 0.28Mie theory. The particle size distribution at each height isU2EB0409 F336W 335 0.29given by the output of a one-dimensional microphysicalU2EB040A F410M 410 0.36

code as described by Moreno (1996), who obtained aerosolprofiles at the equator and at 658S planetographic. A proce- a Effective wavelengths and geometric albedoes are from West et al.

(1995).dure similar to that described by Moreno (1996) was then

40 MORENO AND SEDANO

TABLE IIProperties of the Best-Fitting Aerosol Models at Various Latitudes

Integrated mass ni

production rate p0 py

Latitude (g cm22 sec21) (mbar) (mbar) 230 nm 275 nm 335 nm 410 nm

758N 4.1 3 10215 20 10 0.04 0.02 0.00001 0.00001658N 1.2 3 10214 25 1 0.04 0.017 0.003 0.0005608N 1.4 3 10214 45 1 0.04 0.02 0.007 0.0015558N 1.4 3 10214 45 1 0.04 0.02 0.007 0.0015458N 7.1 3 10215 70 1 0.045 0.025 0.007 0.0045308N 4.5 3 10216 1 0.1 0.08 0.03 0.003 0.0001158N 4.5 3 10217 1 0.1 0.08 0.03 0.003 0.0001

08N 4.5 3 10217 1 0.1 0.08 0.03 0.003 0.0001158S 4.5 3 10217 1 0.1 0.08 0.03 0.003 0.0001308S 4.5 3 10216 1 0.1 0.08 0.03 0.003 0.0001458S 7.0 3 10216 1 0.1 0.08 0.03 0.003 0.0001558S 1.4 3 10214 40 2 0.02 0.012 0.003 0.0005658S 1.8 3 10214 3 0.8 0.027 0.018 0.008 0.0045758S 2.0 3 10214 1 0.8 0.027 0.018 0.003 0.0008

Note. Models at latitudes north of 408N and south of 558S have charge and hydrazine production rates as in Moreno andMolina’s (1996) south polar region model. Models at latitudes equatorward of 358N and 508S have charge and hydrazineproduction rates as in Moreno and Molina’s (1996) equatorial model. The production rate profile is parameterized by q(z) 5

C exph20.5[(p 2 p0)/py]2j g cmmi3 sec21, where C is the integrated mass production rate.

high latitudes. It is therefore remarkable that the only polar respectively. Model results at other latitudes can also beseen in the work of Moreno (1996).regions having a large aerosol content at high altitudes

(pressures near 1 mbar) are those confined to latitudes To find the aerosol distribution at latitudes other thanthose shown in Table II, we interpolate the model inputsouth of 658S. The next step for the application of the

aerosol model fits was to select various latitudes in the parameters at those latitudes and generate the correspond-ing aerosol size distribution profiles. Once these profilesbroad range from temperate to equatorial regions. To have

a sample of visually different regions, including belt and were obtained from 858N to 858S at 58 step, we proceededto compute the heating rates. Based on the low obliquityzones, we selected the limb-to-limb scans at 158N (in the

North Equatorial Belt), 158S (in the South Equatorial and low eccentricity of the jovian orbit, for all the computa-tions we assumed a mean Jupiter–Sun distance of 5.2 AUBelt), 308N (in the North Tropical Zone), and 308S and

458S (which did not display a clear belt or zone character). and a zero obliquity. The incident solar fluxes (Thekaekara1976) were divided by 2 to account for the diurnal variationAt all these latitudes, we employed as starting point the

equatorial aerosol model as reported by Moreno (1996). on a rapidly rotating planet near equinox. The effectivesolar zenith angle x at different latitudes was determinedThe regions at 308S, 458S, and 308N required production

rates higher than found at the equator, while the belt re- by averaging cos x over the daylight hours.The heating rates were computed by considering scatter-gions at 158N and 158S did not require modifications in

the production rate profile, but did require modifications ing and absorption processes by methane and aerosols inthe range 0.175–1.0 em, and absorption by methane in thein the single scattering albedo and the Henyey–Greenstein

phase function parameters of the lower cloud. Specifically, range 1–4 em. The collision-induced absorption bands dueto H2–H2 and H2–He collisions near 2.1 em were alsowe found that the fits improved when the phase function

parameters corresponding to the South Equatorial Belt included. The collision-induced absorption coefficientswere computed from codes sent by Borysow (1991). In thein the blue, as reported by Tomasko et al. (1978), were

considered. This is important, as it implies that the visual range 0.175–1 em we used the low-temperature methanecoefficients of Karkoschka (1994) averaged over 100-Abelt/zone contrasts are in fact due to variations in the cloud

properties below the 400-mbar level, and that there is a intervals. For the near-IR range between 1 and 4 em wederived exponential-sum fits to laboratory methane mea-ubiquitous haze, as has been previously suggested by vari-

ous authors (see, e.g., West et al. 1986). Examples of the surements as described in the previous section.The heating rates were calculated from the divergencemodel fits to the data are given in Figs. 6 and 7, correspond-

ing to the fits at latitudes 758N and 308S planetographic, fluxes by using the discrete-ordinates code DISORT

JOVIAN STRATOSPHERE DYNAMICS 41

FIG. 6. Aerosol model fit at 758N planetographic latitude. The variation of the mean radius (labeled rmed) and cumulative optical depth withpressure, as well as the results on reflectivity (I/F) versus longitude relative to the central meridian of the planet, at the four wavelength channelsindicated in the top labels, are shown. In the panel showing the variation of cumulative optical depth with pressure, the solid line corresponds tothe F218W channel, the dashed line to F255W, the dash–dotted line to F336W, and the dotted line to F410M. In the panels showing reflectivityversus longitude, the dots are the observed I/F values, while the solid lines represent the model results.

(Stamnes et al. 1988). Mie theory was used to obtain the northern latitudes aerosol heating is comparable to gas-eous heating in the ranges 1–1.6 and 1.6–2.4 em aroundphase function, single scattering albedo, and optical thick-

ness for every layer in the model from 0.3 to 404 mbar. 20 mbar, a consequence of the fact that aerosol produc-tion is found to be maximum at that altitude. TheWe used a total of 15 layers between those pressure levels

equally spaced in altitude. The mixing ratios of the relevant resulting heating rates in the 1.7- and 2.3-em bands atthe equator can be compared with those of Wallace et al.gases are listed in Table III.

Some heating rate profiles at various latitudes and (1974) in the same spectral range. While both profilesgive similar values below the 30-mbar level, they showwavelength ranges are shown in Fig. 8. As can be seen,

at the equator, the heating rates are dominated by the large differences at altitudes above that level. For in-stance, at the 10-mbar level, they gave a heating ratenear-IR methane bands at the spectral ranges 1–1.6 and

1.6–2.4 em. At high southern latitudes, aerosol heating of about 0.5 erg cm22 sec21 per cm-am of methane, whilewe found value twice as high.dominates in the pressure range 1–10 mbar, and at

42 MORENO AND SEDANO

FIG. 7. As for Fig. 6, but for 308S planetographic latitude.

IV. COMPUTATION OF THE COOLING RATES AND sphere. To obtain the line-by-line absorption coefficientprofile, the HITRAN 1992 line compilation (RothmanTHE RADIATIVE BALANCEet al. 1992) for the relevant atmospheric gases was em-

The most important processes in diabatic cooling are ployed as input to the GENLN2 code (Edwards 1992).those due to the pressure-induced absorption by H2–H2 That code was used to obtain the line-by-line spectra withand H2–He collisions, as well as the vibration–rotation a resolution of 0.0005 cm21. To perform the computations,bands n4 CH4 at 7.8 em, n9 C2H6 at 12.2 em, and n5 C2H2 a Voigt line profile was used. The contribution of wing ofat 13.7 em. We also considered the most intense band lines out as far as 25 cm21 from the considered spectralgroups of NH3 between 526 and 24 em, at 10.7 and 10.3 interval was included in the absorption coefficient compu-em, and at 6.1 em. The mixing ratios of these gases relative tation. From those spectra, a table of correlated-k coeffi-to molecular hydrogen are listed in Table III. Correlated- cients were obtained. The resolution of those correlated-k coefficients for those gases in the spectral regions consid- k coefficients was 10 cm21. An example of the goodnessered were derived following the procedures described by of the fits of the correlated-k derived spectra with thoseMoreno and Molina (1996). Briefly, line-by-line absorption constructed by direct line-by-line calculations (degradedcoefficient spectra were derived for a variety of pressure– to 10 cm21) for several atmospheric conditions is shown in

Fig. 9. While these comparisons are made here for homoge-temperature conditions pertaining to the jovian atmo-

JOVIAN STRATOSPHERE DYNAMICS 43

FIG. 8. Heating rates profiles at various latitudes, as labeled. Thethin solid line shows the heating by the aerosols plus the contribution ofthe methane bands in the range 0.175–1 em, the dashed line correspondsto the heating by the 3.3 em methane band, the dash-dotted line to thecontribution of the 1.7- and 2.3-em methane bands, and the dotted lineto the contribution of the band groups between 1 and 1.6 em. The heavysolid line represents the sum of the different contributions.

neous paths, both Goody et al. (1989) and Lacis and Oinas(1991) demonstrated the accuracy of the correlated-k ap-proach over inhomogeneous media for a variety of differ- FIG. 9. A comparison of line-by-line spectra computed with theent conditions between atmospheric slabs. The infrared GENLN2 code (Edwards 1992) degraded in resolution to 10 cm21 (solid

lines) with those derived from the correlated-k technique (dotted lines),cooling was computed by using these correlated-k coeffi-for various pressure–temperature–path length combinations, as labeled,cients along with the H2–H2 and H2–He collision-inducedfor the 7.7-em methane band.absorption coefficients generated from computer codes by

Borysow for the rototranslational bands (see Borysow etal. 1985, Borysow and Frommhold 1991). The hydrogen

To find the radiative equilibrium temperature, we con-coefficients depend on the ortho–para ratio. We adoptedsidered an iterative process in which we started by comput-the ortho–para ratio profile as given by Carlson et al.ing the horizonal average of the heating plus cooling rates(1993), which is valid for relatively low latitudes. We didfrom a zonally averaged temperature array that was madenot include any latitudinal dependence in the ortho–paraavailable to us by R. West (private communication, 1996).ratio profile. The cooling rates were also computed byThe radiative equilibrium of the horizontally averagedusing the discrete-ordinates code DISORT, which permitstemperature field is a necessary requirement to preservethe inclusion of the thermal component in the calculationsmass continuity in a diabatic circulation. West furnishedof the flux divergence. Cooling rate profiles were evaluatedtables of temperatures from 2908 to 908 at 58 intervals inat 58 step in latitude from 2858 to 858.latitude and pressures between 0.3 and 270 mbar. Theeffective spatial resolution in temperature was 108, al-though a cubic spline interpolation was used by West et al.

TABLE III (1992) to derive temperatures at 58 intervals. These tablesMixing Ratios Relative to H2 of the Gases Pertaining to were based mostly on infrared radiances measured by Voy-

Heating and Cooling Rate Computations ager 1 and 2 spacecraft (Pirraglia et al. 1981). Using thosetables we found that the horizontal average of the heatingSpecies Mixing ratio to H2 Referenceplus cooling rates was far from zero (radiative equilibrium

He 0.156 Niemann et al. (1996) condition) at levels above 30 mbar. Therefore, we madeCH4 2.1 3 1023 Niemann et al. (1996) an iterative process by which we modified the originalNH3 Variable Kunde et al. (1982) temperature array to find the radiative equilibrium condi-C2H6 5.56 3 1026 Appleby and Hogan (1984)

tion. The procedure consisted of modifying the whole arrayC2H2 3.34 3 1028 Appleby and Hogan (1984)by adding a factor that depended on height, but not on

44 MORENO AND SEDANO

FIG. 10. Horizontally averaged equilibrium temperature profile FIG. 11. Horizontally averaged infrared cooling (dashed line) and(solid heavy line) compared with the Voyager 1 ingress profile (solid thin solar heating (dotted line) profiles, and the net contribution (solid line).line), the thermal equilibrium profile of Conrath et al. (1990) (dashedline), the dust-free model of Appleby and Hogan (1984) (their model‘‘b,’’ dotted line), and the uniform aerosol heating model of Applebyand Hogan (1984) (their model ‘‘c,’’ dash–multidotted line). 11. The departures from zero in the net profile are negligi-

ble at most altitudes, as can be seen. The two-dimensionalmaps on the resulting heating rates and radiative flux con-vergence obtained after imposing the condition of radiativelatitude, i.e., keeping the horizontal temperature differ-equilibrium in the horizonal mean are those shown in Figs.ences as they were originally in the temperature tables. The12 and 13.procedure continued until the horizontal average profile of

In Fig. 14 we present the cooling rate profiles at thethe cooling plus heating rates was less than a certain presetequator and high latitudes, showing the contribution ofvalue at all the atmospheric levels in the model. At atmo-several gaseous species as a function of pressure. The mainspheric levels deeper than 150 mbar, the temperature ad-contributors to the cooling rates are methane CH4 andjustments needed to meet radiative equilibrium wereC2H6 at levels above 4 mbar. From that level to about 150smaller than the error bars indicating the standard devia-

tion in temperature for the six bins in longitude from Voy-ager 1 and 2 zonal mean temperatures considered by Gier-asch et al. (1986) (see their Fig. 2). At the 1-mbar level,the longitudinal variations in temperature at latitudes pole-ward of 6608 (see Fig. 1 of West et al. 1992) are comparableto the temperature adjustments at those atmospheric levelsto reach the radiative equilibrium condition.

The horizontally averaged equilibrium temperature pro-file obtained by the above approach is that shown in Fig.10, along with the Voyager 1 ingress profile and the thermalequilibrium profiles by other authors. As can be seen, thederived horizontally averaged equilibrium profile is hotterthan previous estimates mainly above the 10-mbar level.This is mostly a consequence of the different gaseous heat-ing formulations and, to less extent, the inclusion of adetailed structure of the stratospheric aerosol distribution.Model ‘‘c’’ of Appleby and Hogan (1984) is within 28 ofthat derived here in the region 10–100 mbar, possibly dueto the inclusion of uniform aerosol heating in their model.

The corresponding horizontally averaged heating and FIG. 12. Heating rate contour map in the stratosphere and uppertroposphere. Units are erg/g/sec.cooling rates and the net contribution are graphed in Fig.

JOVIAN STRATOSPHERE DYNAMICS 45

r0v* cos l 5 2­c9

­z1

1H

c9, (2)

r0w* cos l 51a

­c9

­l, (3)

where l is the latitude, z the altitude, r0 is the basic statedensity [r0 ; rs exp (2z/H), where rs is the density at astandard reference level taken here as 1 bar, z is the alti-tude, and H is the scale height], a is Jupiter’s radius, v* isthe meridional residual velocity, and w* is the verticalresidual velocity. The mass streamfunction c is obtainedfrom c9 as c 5 c9 exp(2z/Hs), where Hs is the scale heightat the reference level. Substitution of the mass streamfunc-tion into the steady-state thermodynamic energy equationyields the following second-order elliptic equation for c9:

FIG. 13. Radiative flux convergence contour map. Units are erg/ ­T­lH­2c9

­z­l2

1H

­c9

­lJ2

­2T­l2 H­c9

­z2

c9

HJ1­

­lHN 2H

R­c9

­lJg/sec.

5­

­l(r0 Qrad a cos l). (4)

mbar, H2–H2 collision-induced absorption constitutes themain source of cooling, while NH3 is mainly responsiblefor cooling below 150 mbar to the bottom of the model. Here, T is the zonally-averaged temperature, N 2 is the

Brunt–Vaisala frequency, R is the gas constant, and Qrad

V. RESULTS OF THE DYNAMICAL MODEL is the radiative flux convergence as given in Fig. 13. Theupper and lower boundary conditions are obtained from

The formalism used here to infer the jovian large-scale the same equations by West et al. (1992), i.e.,stratospheric circulation is the same as that proposed byWest et al. (1992), and the derivation of the equations that

w*(l) QR

N 2HQrad(l), (5)permit the computation of the relevant quantities is not

repeated here. Briefly, starting from the ‘‘transformed Eu-lerian mean’’ continuity equation, a velocity streamfunc- which, as those authors indicate, implies neglecting hori-tion (c9) is defined as given by zontal relative to vertical advection of heat in the thermo-

dynamic energy equation. To obtain the mass streamfunc-tion from the elliptic equation, we employed the successiveoverrelaxation technique (Press et al. 1992), as done byWest et al. (1992). The resulting mass streamfunction mapis given in Fig. 15, and the vertical velocity map is shownin Fig. 16. These graphs show upwelling in the regionswere solar heating dominates, and subsidence where thereis net radiative cooling. Close to the tropopause, the re-gions of upwelling/subsidence are associated with the belt/zone-scale temperature gradients. The main differencewith respect to the mass streamfunction map derived byWest et al. (1992) is in the atmospheric regions above 30mbar at high northern latitudes, as they found a regionof upwelling at those locations associated with a largerabundance of aerosols at these locations than is inferredhere. At levels close to the tropopause, the absolute value

FIG. 14. Cooling rate profiles at various latitudes, as labeled. The of the radiative flux convergence is much smaller than atthin solid line represents the cooling by CH4, the dashed line that by

other locations, due to the lower abundance of aerosols,NH3, the dotted line that by C2H2, the dash–dotted line by H2–H2 plusand the circulation is dominated by the meridional varia-H2–He collision-induced absorption, and the dash–multidotted line that

by C2H6. The thick solid line represents the total cooling rate. tion of the infrared cooling due to variations in the belt/

46 MORENO AND SEDANO

FIG. 17. Vertical velocity profiles at 270 and 150 mbar, as labeled,as a function of latitude.

heat equation but based on a rough estimate of the radia-tive time constant, which is inversely proportional to theFIG. 15. Mass streamfunction contour map. Units are g/cm/sec.amplitude of the vertical velocity, and an uncertain valueof the radiative equilibrium temperature, which causes ar-bitrary vertical displacement of the velocities. Neverthe-

zone temperature contrasts. To show this in detail, theless, the velocity profile of Gierasch et al. is useful for

vertical residual velocities at 270 mbar and 150 mbar arequalitative comparisons. Most of the features seen in the

shown in Fig. 17, in which the vertical velocities at pressuresGierasch et al. high-spatial-resolution data are also recov-

of 270 and 150 mbar are graphed, for a direct comparisonered in the West et al. data, although some features are lost.

with the derived velocities of West et al. (1992). BecauseOur data show good agreement with the Gierasch et al.

of the higher spatial sampling in our model (58 in latitude)profile in its trend, but not in the absolute values. The

compared with the West et al. (1992) model (108), thestrong subsidence peaks at 108–158N and 108–158S are re-

vertical velocity profile shows more details than the profilesproduced in our profile, as are the upwelling peaks at

of these authors, mainly at the 270-mbar level. Our veloci-latitudes near 258S and 208N. There is also a relative mini-

ties are comparable to those reported by West et al. atmum at 258N in the Gierasch et al. data that is recovered

most latitudes at the 150- and 270-mbar levels. However,in our computations. The relative maximum at 308N in the

these velocities are higher than those reported by GieraschGierasch et al. data does not appear in our profile at that

et al. (1986) at 270 mbar, which were derived from thelatitude, but at about 358N. There are differences betweenour results and those of West et al. in the amplitude ofthe vertical velocities and the different behavior at highlatitudes. Their data show a relative maximum at 608Swhich does appear in our computations, but show subsi-dence at both polar regions, while our data show subsi-dence at latitudes north of 458N at the 270-mbar level andupwelling south of 258S. We found a stronger subsidencenear the equator than found by West et al. at the 270-mbarlevel. On the other hand, the profiles at 150 mbar of Westet al. compare well with that shown here. In particular, therelative maxima at 6208 and 608S are also shown in our150-mbar graph, and both polar regions show strong subsi-dence. Also, the subsidence near the equator at 270 mbaralmost vanished in our data at 150 mbar, in accordancewith the findings of West et al.

Sources of possible systematic errors in the modelinginclude the uncertainties in the gas mixing ratios, the aerosolcontent, and the derived exponential-sum coefficients. Theerror in these coefficients arises from the standard deviation

FIG. 16. Vertical residual velocity contour map. Units are cm/sec. of the modeled transmittances as compared with the labora-

JOVIAN STRATOSPHERE DYNAMICS 47

tory-measured transmittances, as for methane in the near-infrared region, and from the derivation of the correlated-k coefficients, as for all the spectroscopically active joviangases in the midinfrared region. As explained in SectionII, the error in the fit to the laboratory transmittances isabout the same as the experimental errors in the measuredtransmittances themselves. Considering the uncertainties inthese coefficients as the main source of error in the derivedquantities, we estimated that the 1-s errors in the radiativeflux convergence are of 10% near the bottom of the modelat the 270-mbar level and increase up to 40–50% near the1-mbar level. We have verified that all the other derivedquantities, such as the mass streamfunction and the verticalvelocities, have similar uncertainties.

The last step in our dynamical computations was to esti-mate the Eliassen–Palm flux divergence. This quantity re-flects the magnitude of transient and irreversible eddy pro-cesses on the zonal wind. It provides a useful diagnostic FIG. 18. Eliassen–Palm flux divergence contour map. Units are 1024

cm sec22.of wave–mean flow interaction. This quantity was esti-mated by West et al. (1992) using the approximation « Q2fv*, which is valid if the time derivative of the zonal with the jet structure. The results of West et al. (1992) didwind and the advection by the zonal wind by the residual not show a complete correlation of « with the jet structurecirculation are neglected in the momentum balance equa- either. As pointed out by those authors, the reasons couldtion. We readily checked this approach, obtaining « by be the low effective spatial resolution in the model, whichsolving the zonal component of the momentum equation does not permit resolution of the jet structure, and the[cf. Eq. (1a) in West et al. 1992] by neglecting the time inclusion of the global-scale component of the meridionalderivative and substituting the calculated v* and w* with circulation associated with the global variation of radiativetheir values obtained from the mass streamfunction in the equilibrium temperature, which was not included in theelliptic equation. The zonal wind was estimated from the frictional model of Gierasch et al. (1986).thermal wind equation [cf. Eq. (6) in Gierasch et al. 1986]. As mentioned by West et al. (1992), the present approachTo do that, the cloudtop measured winds (Limaye, 1986) used to calculate « does not elucidate the nature of thewere used as boundary condition. Under these assump- eddies that force the mean flow. Therefore, nothing cantions, it is seen that the approximation « 5 2fv* is valid be said about the observed dramatic changes in the derivedexcept for latitudes equatorward of about 6108. The errors Eliassen–Palm flux divergence patterns with respect to theat 6108 are about 10% and increase dramatically toward source of the eddy forcing mechanisms. It is demonstrated,the equator owing to the fact that the Coriolis parameter however, that the north/south asymmetries we found invanishes. The resulting Eliassen–Palm flux divergence is the aerosol heating have a key role in the derived Eliassen–that depicted in Fig. 18, which shows large differences with Palm flux divergence.respect to the patterns found by Conrath et al. (1990) and In the future, we plan to update the model by investigat-West et al. (1992). The differences with the pattern found ing these forcing mechanisms, as well as to extend theby Conrath et al. (1990) are mostly attributable to the fact model to the other methane-rich planet stratospheres bythat they did not include aerosol heating in their model. first developing microphysical models applicable to thoseThe pattern found by West et al. (1992) differs from that planets. For that purpose, we also plan to use Hubblefound here in two respects. First, the magnitude of the Space Telescope images, which were essential for the mi-eddy forcing on the zonal winds that we find is larger by crophysical model developed for the jovian stratosphere.a factor varying between 5 and 10, depending on latitude.Second, the distribution of the regions with positive and ACKNOWLEDGMENTSnegative « is markedly different from that found by Westet al. (1992). Gierasch et al. (1986) found an anticorrelation We express our gratitude to Robert West, who furnished the codes

to obtain the exponential-sum near-infrared methane coefficients andbetween zonal winds at the cloud level and frictional dragprovided us with thermal profiles at different latitudes. We thank Kimin the upper troposphere. This would suggest that weStrong and Larry Giver for providing us with the methane laboratory

should find a correlation between jet structure and «, at data in the near infrared. The hydrogen and helium collision-inducedleast in the upper troposphere. However, the Eliassen– absorption coefficients at several spectral ranges were computed by using

computer codes kindly sent to us by Aleksandra Borysow. We are gratefulPalm flux divergence pattern does not show any correlation

48 MORENO AND SEDANO

to David Edwards for providing us with the GENLN2 code. The Principal sion, and multiple scattering in vertically inhomogeneous atmospheres.J. Geophys. Res. 96, 9027–9064.Investigator of the Hubble Space Telescope images used in this work,

Harold Weaver, and the STScI staff are gratefully acknowledged. We Limaye, S. 1986. Jupiter: New estimates of mean zonal flow at the cloudgratefully acknowledge the comments and suggestions on the paper by level. Icarus 65, 335–352.Kevin Baines and an anonymous referee. This work was supported by McKellar, A. R. W. 1989. The spectrum of gaseous methane at 77 K inthe Comision Nacional de Ciencia y Tecnologıa under Contracts ESP94- the 1.1–2.6 em region: A benchmark for planetary astronomy. Can.0719 and ESP94-0803. J. Phys. 67, 1027–1035.

Moreno, F. 1996. The structure of the stratospheric aerosol layer in theequatorial and South Polar Region of Jupiter. Icarus 124, 632–644 .REFERENCES

Moreno, F., and A. Molina 1996. Correlated-k coefficients for modellingAppleby, J. F., and J. S. Hogan 1984. Radiative–convective equilibrium the ammonia absorption at 2 em in the jovian planets. J. Quant.

models of Jupiter and Saturn. Icarus 59, 336–366. Spectrosc. Radiat. Transfer 55, 267–272.Apt, J., J. V. Martonchik, and L. R. Brown 1981. Comparison of band Niemann, H. B., S. K. Atreya, G. R. Carignan, T. M. Donahue, J. A.

model and integrated line-by-line synthetic spectra for methane in the Haberman, D. N. Harpold, R. E. Hartle, D. M. Hunten, W. T. Kasprzak,2.3 em region. J. Quant. Spectrosc. Radiat. Transfer 26, 431–442. P. R. Mahaffy, T. C. Owen, N. W. Spencer, and S. H. Way 1996. The

Galileo Probe Mass Spectrometer: Composition of Jupiter’s atmo-Baines, K. H., R. A. West, L. P. Giver, and F. Moreno 1993. Quasi-randomnarrow-band model fits to near-infrared low-temperature laboratory sphere. Science 272, 846–849.methane spectra and derived exponential-sum absorption coefficients. Pirraglia, J. A., B. J. Conrath, M. D. Allison, and P. J. Gierasch 1981.J. Geophys. Res. 98, 5517–5529. Thermal structure and dynamics of Saturn and Jupiter. Nature 292,

677–679.Borysow, A. 1991. Modelling of collision-induced infrared absorptionspectra of H2–H2 pairs in the fundamental band at temperatures from Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery 1992.20 to 300 K. Icarus 92, 273–279. Numerical Recipes. Cambridge Univ. Press, Cambridge.

Borysow, A., and L. Frommhold 1991. Pressure-induced absorption in Rothman L. S., R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H.the infrared: A data base for the modelling of planetary atmospheres. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret,J. Geophys. Res. 96, 17,501–17,506. A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth

1992. The HITRAN database: Editions of 1991 and 1992. J. Quant.Borysow, A., L. Trafton, L. Frommhold, and G. Birnbaum 1985. Model-ling of pressure-induced far infrared absorption spectra: Molecular Spectrosc. Radiat. Transfer 48, 469–507.hydrogen pairs. Astrophys. J. 296, 644–654. Stamnes, K., S. Tsay, W. Wiscombe, and K. Jayaweera 1988. Numerically

stable algorithm for discrete-ordinate-method radiative transfer in mul-Carlson, B. E., A. A. Lacis, and W. B. Rossow 1993. Tropospheric gascomposition and cloud structure of the jovian North Equatorial Belt. tiple scattering and emitting layered media. Appl. Opt. 27, 2502–2509.J. Geophys. Res. 98, 5251–5290. Strong, K. 1992. Spectral Parameters of Methane for Remote Sounding of

the Jovian Atmosphere. Ph.D. thesis, Univ. of Oxford, Oxford, England.Conrath, B. J., P. J. Gierasch, and S. S. Leroy 1990. Temperature andcirculation in the stratosphere of the outer planets. Icarus 83, 255–281. Strong, K., F. W. Taylor, S. B. Calcutt, J. J. Remedios, and J. Ballard

1993. Spectral parameters of self- and hydrogen-broadened methaneCrisp, D. 1990. Infrared radiative transfer in the dust-free martian atmo-sphere. J. Geophys. Res. 95, 14,577–14,588. from 2000 to 9500 cm21 for remote sounding of the atmosphere of

Jupiter. J. Quant. Spectrosc. Radiat. Transfer 50, 363–429.Edwards, D. 1992. GENLN2: A General Line-by-Line AtmosphericTransmittance and Radiance Model. NCAR Tech. Note NCAR/TN- Thekaekara, M. P. 1976. Solar radiation measurement: Techniques and

instrumentation. Solar Energy 18, 309–325.3671SRT. NCAR, Boulder, CO.

Gierasch, P. J., B. J. Conrath, and J. A. Magalhaes 1986. Zonal mean Tomasko, M. G., E. Karkoschka, and S. Martinek 1986. Observations ofthe limb darkening of Jupiter at ultraviolet wavelengths and constraintsproperties of Jupiter’s upper troposphere from Voyager infrared obser-

vations. Icarus 67, 456–483. on the properties and distribution of stratospheric aerosols. Icarus,65, 218–243.Giver, L. P., D. C. Benner, M. G. Tomasko, U. Fink, and D. Kerola

Tomasko M. G., R. A. West, and N. D. Castillo 1978. Photometry and1990. Gaussian Quadrature Exponential-Sum Modelling of Near-Infra-polarimetry of Jupiter at large phase angles. I. Analysis of imagingred Methane Laboratory Spectra Obtained at Temperatures from 106data of a belt and a zone from Pioneer 10. Icarus 33, 558–592.to 297 K. NASA Conf. Publ. CP-3077, pp. 147–156.

Vujkovic Cvijin, P., M. K. Wells, I. Mendas, J. K. Delaney, J. I. Lunine,Goody, R., R. West, L. Chen, and D. Crisp 1989. The correlated-k methodD. M. Hunten, and G. H. Atkinson 1993. Determination of line intensityfor radiation calculations in nonhomogeneous atmospheres. J. Quant.and pressure broadening of the 618.68 nm methane overtone absorptionSpectrosc. Radiat. Transfer 43, 191–199.line at low temperatures using intracavity laser spectroscopy. J. Quant.Karkoschka, E. 1994. Spectrophotometry of the jovian planets and TitanSpectrosc. Radiat. Transfer 49, 639–650.at 300- to 1000-nm wavelength: The methane spectrum. Icarus 111,

Wallace, L., M. Prather, and M. J. S. Belton 1974. The thermal structure174–192.of the atmosphere of Jupiter. Astrophys. J. 193, 481–493.Kuiper, G. P., and D. Cruikshank 1964. Laboratory spectra for testing

West, R. A., A. J. Friedson, and J. F. Appleby 1992. Jovian large-scalethe presence of minor constituents in planetary atmospheres. I. CH4,stratospheric circulation. Icarus 100, 245–259.NH3, N2O, CO, COS, region 1–2.5 em. Commun. Lunar Planet. Lab.

2, 141–165. West, R. A., E. Karkoschka, A. J. Friedson, M. Seymour, K. H. Baines,and H. Hammel 1995. Impact debris particles in Jupiter’s stratosphere.Kunde, V., R. Hanel, W. Maguire, D. Gautier, J. P. Baluteau, A. Marten,Science 267, 1296–1301.A. Chedin, N. Husson, and N. Scott 1982. The tropospheric gas compo-

sition of Jupiter’s North Equatorial Belt (NH3, PH3, CH3D, H2O) and West, R. A., D. F. Strobel, and M. G. Tomasko 1986. Clouds, aerosols,the jovian D/H isotopic ratio. Astrophys. J. 263, 443–467. and photochemistry in the jovian atmosphere. Icarus 65, 161–217.

Lacis, A. A., and V. Oinas 1991. A description of the correlated-k distribu- Wiscombe, W. J., and J. W. Evans 1977. Exponential-sum fitting of radia-tive transmission functions. J. Comput. Phys. 24, 416–444.tion method for modelling nongray gaseous absorption, thermal emis-