The methane distribution and polar brightening on Uranus based on HST/STIS, Keck/NIRC2, and IRTF/SpeX observations through 2015
Lawrence A. Sromovsky, Erich Karkoschka, Patrick M. Fry, Imke de Pater, Heidi B. Hammel
aa r X i v : . [ a s t r o - ph . E P ] J un Journal reference: Icarus (2018) Under review.
Preprint typeset using L A TEX style emulateapj v. 12/16/11
THE METHANE DISTRIBUTION AND POLAR BRIGHTENING ON URANUS BASED ON HST/STIS † ,KECK/NIRC2, AND IRTF/SPEX OBSERVATIONS THROUGH 2015 L. A. Sromovsky , E. Karkoschka , P. M. Fry , I. de Pater , H. B. Hammel Journal reference: Icarus (2018) Under review.
ABSTRACTSpace Telescope Imaging Spectrograph (STIS) observations of Uranus in 2015 show that the de-pletion of upper tropospheric methane has been relatively stable and that the polar region has beenbrightening over time as a result of increased aerosol scattering. This interpretation is confirmedby near-IR imaging from HST and from the Keck telescope using NIRC2 adaptive optics imaging.Our analysis of the 2015 spectra, as well as prior spectra from 2012, shows that there is a factor ofthree decrease in the effective upper tropospheric methane mixing ratio between 30 ◦ N and 70 ◦ N.The absolute value of the deep methane mixing ratio, which probably does not vary with latitude,is lower than our previous estimate, and depends significantly on the style of aerosol model thatwe assume, ranging from a high of 3.5 ± ± ± µ m, a realrefractive index near 1.65, and a total column mass of 0.03 mg/cm , while the large-particle solutionhas a particle radius near 1.5 µ m, a real index near 1.24, and a total column mass 30 times larger.The pressure boundaries of the main cloud layer are between about 1.1 and 3 bars, within which H Sis the most plausible condensable.
Subject headings:
Uranus, Uranus Atmosphere; Atmospheres, composition, Atmospheres, structure INTRODUCTION
The visible and infrared spectra of Uranus are bothdominated by the absorption features of methane, itsthird most abundant gas. In some spectral regions, how-ever, the effects of collision-induced absorption (CIA) byhydrogen can be seen competing with methane. Thosewavelengths provide constraints on the number den-sity of methane with respect to hydrogen, and thus onthe volume mixing ratio of methane. From analysis of University of Wisconsin - Madison, Madison WI 53706, USA University of Arizona, Tucson AZ 85721, USA University of California, Berkeley, CA 94720, USA AURA, 1212 New York Ave. NW, Suite 450, Washington,DC 20005, USA Space Science Institute, Boulder, CO 80303, USA † Based in part on observations with the NASA/ESA Hub-ble Space Telescope obtained at the Space Telescope ScienceInstitute, which is operated by the Association of Universitiesfor Research in Astronomy, Incorporated under NASA ContractNAS5-26555.
HST/STIS spatially resolved spectra of Uranus obtainedin 2002, 5 years before equinox and limited to latitudessouth of 30 ◦ N, Karkoschka and Tomasko (2009), hence-forth referred to as
KT2009 , discovered that good fitsto the latitudinal variation of these spectra required alatitudinal variation in the effective volume mixing ratioof methane. They inferred that the southern polar regionwas depleted in methane with respect to low latitudes byabout a factor of two. This suggested a possible merid-ional circulation in which upwelling methane-rich gas atlow latitudes was dried out by condensation then movedto high latitudes, where descending motions brought themethane-depleted gas downward, with a return flow atdeeper levels.Because post equinox groundbased observations re-vealed numerous small “convective” features in the northpolar region that had not been seen in the south polarregion just prior to equinox, Sromovsky et al. (2012b)suggested that the downwelling movement of methane-depleted gas would suppress convection in the south po-lar region, providing a plausible explanation for the lackof discrete cloud features there, and further suggestedthat the presence of discrete cloud features at high north-ern latitudes might mean that methane is not depletedthere. However, using 2012 HST/STIS observations de-signed to test that hypothesis, Sromovsky et al. (2014)showed that the depletion was indeed symmetric, withboth polar regions depleted by similar amounts, and fromimaging observations taken near equinox using discretenarrow band filters that sampled methane-dominatedand hydrogen-dominated wavelengths, they showed thatthe symmetry was also present at equinox and thus prob-ably a stable feature of the Uranian atmosphere.In spite of the apparent general stability of the lat-itudinal distribution of methane, there were significantpost-equinox increases in the brightness of the north po-lar region, as well as some evidence for brightening at lowlatitudes. New HST/STIS observations were obtainedin 2015 to further investigate possible changes in themethane distribution and the nature of the polar bright-ening that was taking place.Other relevant developments occurred since our lastanalysis of the HST/STIS spectra of Uranus. The firstis the inference of new mean temperature and methaneprofiles for Uranus by Orton et al. (2014a), which arein disagreement with the occultation-based profiles ofLindal et al. (1987) and also with those using a reducedHe/H volume mixing ratio derived by Sromovsky et al.(2011). The second development is an independent deter-mination of the methane volume mixing ratio in the lowerstratosphere and upper troposphere by Lellouch et al.(2015) using Herschel far infrared and sub-mm obser-vations. Since both of these results question the valid-ity of Uranus occultation results in general, and morespecifically the validity of using them at all times andall latitudes, we decided to modify our analysis so thatmodels would be constrained by STIS spectral observa-tions alone, and abandoned the requirement that our low-latitude methane profiles also be consistent with occul-tation constraints. We also took a fresh look at how tobest model the aerosol structure, and found that a muchsimpler 2-3 layer structure could produce fits as accurateas the more complex five-layer structure we had used inour previous analysis of the 2012 STIS observations.In the following we first describe the approach to con-straining the methane mixing ratio on Uranus, then dis-cuss the new thermal profile for Uranus and its im-plications. We follow that with a discussion of our STIS, WFC3, and Keck supporting observations, thecalibration of the STIS spectra, direct comparisons ofSTIS spectra, comparisons of imaging observations atkey wavelengths, description of our approach to radia-tive transfer modeling, results of modeling cloud struc-ture and the distribution of methane, interpretation ofthose results, how models can be extended to longerwavelengths to match spectra obtained at NASA’s In-frared Telescope Facility (IRTF), comparisons with othermodels, and a final summary and conclusions. HOW OBSERVATIONS CONSTRAIN THE METHANEMIXING RATIO ON URANUS
Constraining the mixing ratio of CH on Uranus isbased on differences in the spectral absorption of CH and H , illustrated by the penetration depth plot of Fig.1. There methane absorption can be seen to dominateat most wavelengths, while hydrogen’s Collision InducedAbsorption (CIA) is relatively more important in nar-row spectral ranges near 825 nm, which is covered by ourSTIS observations, and also near 1080 nm, which we wereable to sample with imaging observations using the NIC-MOS F108N filter and Keck He1 A filter. Model calcula-tions that don’t have the correct ratio of methane to hy-drogen lead to a relative reflectivity mismatch near thesewavelengths. Karkoschka and Tomasko (2009) used the825-nm spectral constraint to infer a methane mixing ra-tio of 3.2% at low latitudes, but dropping to 1.4% at highsouthern latitudes. Sromovsky et al. (2011) analyzed thesame data set, but used only temperature and mixingratio profiles that were consistent with the Lindal et al.(1987) refractivity profiles. They confirmed the depletionbut inferred a somewhat higher mixing ratio of 4% at lowlatitudes and found that better fits were obtained if thehigh latitude depletion was restricted to the upper tropo-sphere (down to ∼ ◦ S, which was 32 ±
24% above the min-imum found at 44 ◦ N. These low IRTF-based values forthe latitudinal variation might be partly a result of lowerspatial resolution combined with worse view angles intohigher latitudes than obtained by HST observations. HST/STIS 2015 OBSERVATIONS µ m) -1 P r e ss u r e ( ba r s ) Level at which 2-way Optical Depth=1.00 (all gas absorption + Rayleigh)CH4 onlyCIA only
Jan17-112804-2018 F N F N H E A HC O N T PABE T A Fig. 1.—
Penetration depth vs. wavelength as limited by different opacity sources assuming the Orton et al. (2014a) temperature profileand a 3.5% deep methane mixing ratio. Where absorption dominates, penetration is about one optical depth, but when Rayleigh scatteringdominates, light can penetrate many optical depths. Transmission profiles of key HST/NICMOS (dot-dash) and Keck NIRC2 (solid)narrow-band filters are also plotted.
Our 2015 spectral observations of Uranus (Cycle 23HST program 14113, L. Sromovsky P.I.) used four HSTorbits, three of them devoted to STIS spatial mosaicsand one devoted to Wide Field Camera 3 (WFC3) sup-port imaging. The STIS observations were taken on 10October 2015 and the WFC3 observations on 11 October2015. Observing conditions and exposures are summa-rized in Table 1.
STIS spatial mosaics.
Our STIS observations used the G430L and G750Lgratings and the CCD detector, which has ∼ ′′ × ′′ squarefield of view (FOV) and a spectral range from ∼
200 to1030 nm (Hernandez et al. 2012). Using the 52 ′′ × ′′ slit, the resolving power varies from 500 to 1000 over eachwavelength range due to fixed wavelength dispersion ofthe gratings. Observations had to be carried out withina few days of Uranus opposition (12 October 2015) whenthe telescope roll angle could be set to orient the STISslit parallel to the spin axis of Uranus.One STIS orbit produced a mosaic of half of Uranususing the CCD detector, the G430L grating, and the52 ′′ × ′′ slit. The G430L grating covers 290 to 570nm with a 0.273 nm/pixel dispersion. The slit wasaligned with Uranus’ rotational axis, and stepped fromthe evening limb to the central meridian in 0.152 arcsec-ond increments (because the planet has no high spatialresolution center-to-limb features at these wavelengthswe used interpolation to fill in missing columns of themosaic). Two additional STIS orbits were used to mo-saic the planet with the G750L grating. We intended touse the 52 ′′ × ′′ slit (524-1027 nm coverage with 0.492nm/pixel dispersion) for both orbits, but an error in theprogram resulted in half of the half-disk covered with the nominal 0.05 ′′ slit. This produced a higher spectralresolution at the cost of a significant reduction in signalto noise ratio. The limb to central meridian steppingwas at 0.0562 arcsecond intervals for the G750L grating.Aside from the slit width error, this was the same proce-dure that was used successfully for HST program 9035 in2002 (E. Karkoschka, P.I.) and for HST program 12894 in2012 (L. Sromovsky, P.I.). As Uranus’ equatorial radiuswas 1.85 arcseconds when observations were performed,stepping from one step off the limb to the central merid-ian required 13 positions for the G430L grating and 36for the G750L grating. Two orbits were needed to com-plete the G750L grating observations, spanning a totaltime of 2 h 17 m, during which Uranus rotated 47 ◦ . Thisrotation was not a problem because of the high degreeof zonal symmetry of Uranus and because our analysisrejected any small scale deviations from it.Exposure times were similar to those used in the 2002and 2012 programs, with 70-second exposures for G430Land 84-second exposures for G750L gratings, using the1 electron/DN gain setting. These exposures yieldedsingle-pixel signal-to-noise ratios of around 10:1 at 300nm, > < ′′ from the planet center to the central meridian)the signal to noise at continuum wavelengths was reducedby a factor of ∼ ∼ ∼ Supporting WFC3 imaging.
TABLE 1Science exposures from 2015 HST program 14113.
Relative Start Start Instrument Filter or Exposure No. of PhaseOrbit Date (UT) Time (UT) Grating (sec) Exp. Angle ( ◦ )1 2015-10-10 13:54:06 STIS MIRVIS 5.0 1 0.091 2015-10-10 14:09:48 STIS G430L 70.0 13 0.092 2015-10-10 15:28:02 STIS G750L 84.0 19 0.093 2015-10-10 17:03:25 STIS G750L 84.0 19 0.0919 2015-10-11 18:30:59 WFC3 F336W 30.0 1 0.0419 2015-10-11 18:32:44 WFC3 F467M 16.0 1 0.0419 2015-10-11 18:34:24 WFC3 F547M 6.0 1 0.0419 2015-10-11 18:35:48 WFC3 F631N 65.0 1 0.0419 2015-10-11 18:38:17 WFC3 F665N 52.0 1 0.0419 2015-10-11 18:40:24 WFC3 F763M 26.0 1 0.0419 2015-10-11 18:42:11 WFC3 F845M 35.0 1 0.0419 2015-10-11 18:44:05 WFC3 F953N 250.0 1 0.0419 2015-10-11 18:50:43 WFC3 FQ889N 450.0 1 0.0419 2015-10-11 19:02:25 WFC3 FQ937N 150.0 1 0.0419 2015-10-11 19:09:25 WFC3 FQ727N 210.0 1 0.04 On October 10 the sub-observer planetographic latitude was 31.7 ◦ S, the observer range was 18.984AU (2.8400 × km), and the equatorial angular diameter of Uranus was 3.7126 arcseconds. Thefirst two STIS orbits used the 52 ′′ × ′′ slit and the third inadvertently used the 52 ′′ × ′′ slitThe complex radiometric calibration of the STIS spec-tra relies on calibrated WFC3 images to provide the finalwavelength dependent correction functions. To ensurethat this function was determined as well as possible forthe Cycle 23 observations in 2015, and to cross checkthe extensive spatial and spectral corrections that arerequired for STIS observations, we used one additionalorbit of WFC3 imaging at a pixel scale of 0.04 arcsecondswith eleven different filters spread over the 300-1000 nmrange of the STIS spectra. These WFC3 images are dis-played in Fig. 2, along with synthetic images with thesame spectral weighting constructed from STIS spatiallyresolved spectra, as described in the following section.The filters and exposures are provided in Table 1. Supporting near-IR imaging
HST/NICMOS and groundbased Keck and Geminiimaging at near-IR wavelengths help to extend and fillgaps in the temporal record of changes occurring in theatmosphere of Uranus. Fig. 3 shows that the differ-ence between polar and low latitude cloud structureshas evolved over time. The relatively rapid decline ofthe bright “polar cap” in the south and its reforma-tion in the north is faster than seems consistent withthe long radiative time constants of the Uranian atmo-sphere (Conrath et al. 1990). In following sections wewill show that the polar brightness in 2015 (and presum-ably also in 1997) is not due very much to latitudinalvariations in aerosol scattering, but is mainly due to amuch lower degree of methane absorption at high lati- tudes. This latitudinal variation of methane absorptionappears to be stable over time according to infrared ob-servations (Sromovsky et al. 2014). Thus, at times whenthe polar region was as dark as low latitudes (comparedat the same view angles), it appears not that methane ab-sorption was greater then, but instead that aerosol scat-tering was reduced, a causal relationship we will herefurther confirm regarding polar brightness increases be-tween 2012 and 2015.The aforementioned interpretation of the bright polarregion on Uranus can be partly inferred from the charac-teristics of near-IR images at key wavelengths that havedifferent sensitivities to methane and hydrogen absorp-tion, as illustrated in Fig. 4. Images at hydrogen dom-inated wavelengths (panels A and E) reveal relativelybright low latitudes, and high latitudes that were eitherdarker, as at equinox (A), or comparably bright, as in2015 (E). At methane dominated wavelengths, low lati-tudes are relatively darker, especially in 2015, where theexcess methane absorption at low latitudes is obviousfrom comparing panels E and F. STIS DATA REDUCTION AND CALIBRATION.
The STIS pipeline processing used at STScI is justthe first step of a rather complex calibration procedure,which is described by KT2009 for the 2002 observations,and by Sromovsky et al. (2014) for the 2012 observa-tions. Essentially the same procedure was followed forthe 2015 observations. Additionally, 2002 and 2012 STIScubes were recalibrated using WFPC2 and WFC3 im-
TABLE 2Near-IR observations from HST, Keck, and Gemini observatories.
Telescope Obs. Phase S.O./Instrument PID Obs. Date Time Filter Angle CLat PI, NotesHST/NICMOS 7429 1997-07-28 09:50:24 F165M -40.3 Tomasko, 1Keck II/NIRC2 2003-10-06 07:14:51 H -18.1 Hammel, 2Keck II/NIRC2 2004-07-11 11:30:32 H -11.1 de Pater, 2HST/NICMOS 11118 2007-07-28 04:39:xx F095N 2.0 0.61 Sromosvky, 3HST/NICMOS 11118 2007-07-28 04:22:30 F095N 0.58 Sromovsky, 3HST/NICMOS 11118 2007-07-28 04:39:13 F108N 0.58 Sromovsky, 3Keck II/NIRC2 2007-07-31 14:39:28 PaBeta 1.87 0.51 Sromovsky, 2Keck II/NIRC2 2007-07-31 14:32:33 Hcont 0.49 Sromovsky, 2HST/NICMOS 11190 2007-08-16 07:32:32 F165M -0.0 Trafton, 3Gemini-N/NIRI 2010B-Q-110 2010-11-02 07:08:57 H G0203 9.3 Sromovsky, 4Keck II/NIRC2 2014-08-06 13:42:06 H 28.4 de Pater, 2Keck II/NIRC2 2015-08-29 12:09:05 He1A 31.96 de Pater, 2Keck II/NIRC2 2015-08-29 12:04:41 PaBeta 31.96 de Pater, 2Keck II/NIRC2 2015-08-30 10:56:55 H 31.9 de Pater, 2NOTES: 1: pscale = 0.0431 as/pixel; 2: pscale = 0.009942 as/pixel ; 3: pscale = 0.0432 as/pixel; 4: pscale= 0.02138 as/pixelages newly reduced using the best available detector re-sponsivity functions and filter throughput functions. Allthree calibrated STIS cubes and related information canbe found online in the HST MAST archive as describedin the supplemental material section at the end of thepaper. In the discussion that follows, we first describethe processing of supporting WFC3 imaging. In the caseof 2012 recalibration, WFC3 imaging was also utilized,but for the 2002 recalibration, WFPC2 images were used.We then describe the creation of our calibration correc-tion function, describe our spectral cube construction,and finally our comparison of STIS synthetic images withbandpass filter images.Each WFC3 image was deconvolved with an appro-priate Point-Spread Function (PSF) obtained from thetiny tim code of Krist (1995), optimized to result indata values close to zero in the space view just off thelimb of Uranus. To match the spatial resolution of theSTIS images, the WFC3 images were then reconvolvedwith an approximation of the PSF given in the analysissupplemental file of Sromovsky et al. (2014). The im-ages were then converted to I/F using the best availableheader PHOTFLAM values [given in WFC3 ISR 2016-001] and the Colina et al. (1996) solar flux spectrum, av-eraged over the WFC3 filter band passes. (PHOTFLAMis a multiplier used to convert instrument counts of elec-trons/second to flux units of ergs/s/cm /˚A.) To obtain adisk-averaged I/F, the planet’s light was integrated outto 1.15 times the equatorial radius, then averaged over the planet’s cross section in pixels, which was computedusing NAIF ephemerides (Acton 1996) and SPICELIBlimb ellipse model (SPICELIB is NAIF toolkit softwareused in generating navigation and ancillary instrumentinformation files.) The disk-averaged I/F (using the ini-tial calibration) was also computed for each of the STISmonochromatic images, and the filter- and solar flux-weighted I/F was computed for each of the WFC3 filterpass bands that we used.By comparing the synthetic disk-averaged STIS I/F,using the initial calibration, to the corresponding WFC3values, we constructed a correction function to improvethe radiometric calibration of the STIS cube. Figure 5Cshows the ratios of STIS to WFC3 disk-integrated bright-ness, and the quadratic function that we fit to these ratiosas a function of wavelength, for the 2015 data set and re-calibrations of the previous two data sets. We heavilyweighted the broadband filters, and computed an effec-tive wavelength weighted according to the product of thesolar spectrum and the I/F spectrum of Uranus. TheRMS deviation of individual filters from the calibrationcurve given in Fig. 5 is about 1% RMS for 2012 and 2015correction curves, but about 2 % RMS for the 2002 cal-ibration curve (fit points not shown). For narrow filterssuch as FQ937N, typical deviations are some three timeslarger. The difference between the 2002 and the latercalibration curves is mostly due to use of different slit lo-cations, which result in different light paths through themonochrometer. The 2012 and 2015 curves use the same WFC3 15 A
F336W B F467M C F547M D F631N E F665N F FQ727N
STIS 15 G
F336W H F467M I F547M J F631N K F665N L FQ727N
STIS/WFC3
F336W
F467M
F547M
F631N
F665N
FQ727N
WFC3 15 M
F763M N F845M O FQ889N P FQ937N Q F953N
STIS 15 R
F763M S F845M T FQ889N U FQ937N V F953N
STIS/WFC3
F763M
F845M
FQ889N
FQ937N
F953N
Fig. 2.—
WFC3 images of Uranus taken on 11 October 2015 (A-F and M-Q) compared to synthetic band-pass filter images (G-L andR-V) created from weighted averages of STIS spectral data cubes using WFC3 throughput and solar spectral weighting. The north pole isat at the right. Portions of the synthetic images east of the central meridian are obtained by reflection of the images west of the centralmeridian. The ratio images are stretched to make 0.8 black and 1.2 white. A B C D E F Fig. 3.—
H-band (1.6- µ m) images of Uranus from 1997 through 2015, from observatories/instruments given in the legends. The brightsouth polar region seen in 1997 (A), 10 years before equinox, is similar to the bright north polar region seen in 2015 (F), eight years afterequinox. Images taken during the 2007 equinox year (C) found that neither polar region was bright. The longitude and planetographiclatitude grid lines are at 30 ◦ and 15 ◦ intervals respectively. A B C D E F Fig. 4.—
Near-IR narrow-band images of Uranus obtained near the 2007 equinox (A-D) and in August 2015 (E, F) from observato-ries/instruments given in the legends. The NICMOS F108N image (A) and the Keck II He1 A image (E) sample wavelengths at whichhydrogen absorption dominates. The remaining images sample wavelengths of comparable absorption but due entirely to methane. Notethat low latitudes are relatively darker than high latitudes at methane dominated wavelengths (e.g. in B and F), which is not the case forwavelengths dominated by hydrogen absorption (as in A and E). Grid lines are the same as in Fig. 3. slit location and thus should be the same, and indeedthey are consistent to about 1%.If one assumes that the spectrum of Uranus varies onlyslowly with time, one can add many other filters to plotsof Fig. 5 where images are available somewhat close tothe time of STIS spectroscopy. The medium and widefilters plot quite consistently near the same curve whilemany narrow filters show significant offsets, suggestingthat an improved calibration weights the narrow filtersmuch less in the fitted curve. This consideration changesthe calibration by about 1% and thus does not make a bigdifference with respect to our previous adopted calibra-tion, but our new calibration is more reliable because itis less dependent on unreliable data from narrow filters.The final calibrated cubes contain 150 pixels parallel tothe spin axis of Uranus and 75 pixels perpendicular to itsspin axis, with a spatial sampling interval of of 0.015 × R U km/pixel (384 km/pixel), which is equivalent to 0.028 arcseconds per pixel for 2015 observations. (Here R U is theequatorial radius of Uranus). The center of Uranus islocated at coordinates (74, 74), where (0, 0) is the lowerleft corner pixel. The spatial resolution of the final cubeis defined by a point-spread function with a FWHM of3 pixels. The cube contains an image for each of 1800wavelengths sampled at a spacing of 0.4 nm, with a uni-form spectral resolution of 1 nm. Navigation backplanesare provided, in which the center of each pixel is given aplanetographic latitude and longitude, solar and observerzenith angle cosines, and an azimuth angle.As a sanity check on the STIS processing we comparedWFC3 images to synthetic WFC3 images created fromour calibrated STIS data cubes, as shown in Fig. 2. Ra-tio plots of STIS/WFC3 show the desired flat behavior,except very close to the limbs, where STIS I/F values ex-ceed WFC3 values. The most significant discrepancy isin the overall I/F level computed for the FQ937N filter(note the dark ratio plot in the bottom row), a conse-quence of our calibration curve being 10% high for thatfilter. CENTER-TO-LIMB FITTING
The low frequency of prominent discrete cloud fea-tures on Uranus and its zonal uniformity make it possi-ble to characterize the smooth center-to-limb profiles ofthe background cloud structure without much concernabout longitudinal variability, even though we observedonly half the disk of Uranus. These profiles provide im-portant constraints on the vertical distribution of cloudparticles and the vertical variation of methane comparedto hydrogen. Because our observations were taken veryclose to zero phase, these profiles are a function of justone angular parameter, which we take to be µ , the co-sine of the zenith angle (the observer and solar zenithangles are essentially equal). They also have a relativelysimple structure that we characterized using the same3-parameter function KT2009 used to analyze the 2002STIS observations, and which we also used to fit the 2012observations. For each 1 ◦ of latitude from 30 ◦ S to 87 ◦ N, all image samples within 1 ◦ of the selected latitudeand with µ > I ( µ ) = a + bµ + c/µ, (1)assuming all samples were collected at the desired lati-tude and using the µ value for the center of each pixelof the image samples. Fitting this function to center-to-limb (CTL) variations at high latitudinal resolutionmakes it possible to separate latitudinal variations fromthose associated with view angle variations.Before fitting the CTL profile for each wavelength, thespectral data were smoothed to a resolution of 2.88-nm toimprove signal to noise ratios without significantly blur-ring key spectral features. (Our prior analysis was con-ducted in the wavenumber domain and used smoothingto a resolution of 36 cm − .) Sample fits are provided inFig. 6. Most of the scatter about the fitted profiles isdue to noise, which is often amplified by the deconvo-lution process. Because the range of observed µ values P r e li m . S T I S / ( W F P C | W F C ) C STIS Photometric Correction Functions400 600 800 1000Wavelength (nm)0.900.951.001.05 C a l . S T I S / ( W F P C | W F C ) F W F M F M F N F N F M F M F N F Q N F Q N F Q N D G eo m e t r i c A l bedo A A l bedo / A l bedo B Fig. 5.— A: Radiometrically calibrated disk-averaged I/F spectra for three year of STIS observations. STIS observations from 2002 and2012 have been recalibrated from previous incarnations (Karkoschka and Tomasko 2009; Sromovsky et al. 2014). B: Ratio of each year’sdisk-averaged I/F to 2015. C: STIS photometric calibration functions (raw stis albedo divided by WFC3 albedo). The functions are afit to ratios constructed using synthetic band-pass filter disk-integrated I/F values (preliminary-calibration) divided by corresponding I/Fvalues obtained from WFC3 measurements (circles and horizontal bars indicate filter effective wavelength and full-width half maximumtransmission for 2012 and 2015). D: Ratio of final calibrated STIS synthetic disk-averaged I/F values to WFC3 reflectivities, showingscatter of ratios relative to the fits, for 2012 and 2015. decreases away from the equator at high southern andnorthern latitudes, we chose a moderate value of µ =0.7 as the maximum view-angle cosine to provide a rea-sonably large unextrapolated range of 16 ◦ S to 77 ◦ N.Ranges for other years and for a µ range of 0.3 to 0.6 aregiven in Table 3. Unless otherwise noted all our resultsare derived without extrapolation.The CTL fits can also be used to create zonallysmoothed images by replacing the observed I/F for eachpixel by the fitted value. Results of that procedure aredisplayed in a later section. TABLE 3Latitude ranges for two different view-angle cosineranges.
Year 0.3 ≤ µ ≤ ≤ µ ≤ ◦ S – 33 ◦ N 67 ◦ S – 26 ◦ N2012 35 ◦ S – 72 ◦ N 28 ◦ S – 65 ◦ N2015 23 ◦ S – 77 ◦ N 16 ◦ S – 77 ◦ N DIRECT COMPARISONS OF STIS SPECTRA
CTL curves at glat 0.00 o I/ F wlen res = 2.88 nmlimbcorr 552.0 nm, X 1.0 620.0 nm, X 1.0 826.8 nm, X 2.0 890.0 nm, X 4.0 935.2 nm, X 2.0 Aug11-100905-2016PS file: minn_ctl_diag.ps CTL curves at glat 60.00 o I/ F wlen res = 2.88 nmlimbcorr 552.0 nm, X 1.0 620.0 nm, X 1.0 826.8 nm, X 2.0 890.0 nm, X 4.0 935.2 nm, X 2.0 Aug11-101023-2016PS file: minn_ctl_diag.ps Fig. 6.—
Sample center-to-limb fits for 0 ◦ N (left) and 60 ◦ N (right), as described in the main text. STIS I/F samples and fit lines withuncertainty bands are shown for five different wavelengths indicated in the legends. The latitude bands sampled for these fits are darkenedin the inset images of the half-disk of Uranus.
A rough assessment of the changes between 2012 and2015 and the differences between high and low latitudesin these two years can be made with the help of directcomparisons of STIS spectra, as in Fig. 7. Note thatat 10 ◦ N there is almost no difference between 2012 and2015 spectra (panels A and B). This is also the case for µ values of 0.3 and 0.5, which are not shown in the figure.For 2015, (see panel E) the lack of any I/F difference be-tween 10 ◦ N and 60 ◦ N at 0.83 µ m, which is a wavelengthat which hydrogen absorption dominates, suggests thatthere is not much difference in aerosol scattering betweenthese two latitudes. A similar lack of difference at 0.93 µ m, a wavelength of weak (but dominant) methane ab-sorption, suggests that at very deep levels, there may notbe much of a latitudinal difference in methane mixing ra-tios, or that there is an aerosol layer blocking visibilitydown to levels that might sense such a difference. Yet thefact that wavelengths of intermediate methane absorp-tion do show a significant increase in I/F with latitudesuggests that at upper tropospheric levels the methanemixing ratio does decline with latitude, which is a knownresult from previous work, and is refined by the analysispresented in following sections. Somewhat different re-sults are seen, for 2012 (in panel G). The 10 ◦ N and 60 ◦ N I/F values at 0.83 µ m and 0.93 µ m do differ (panelsG and H), which we will later show is a result of differ-ences in aerosol scattering. The small size of continuumdifferences between 2012 and 2015 (panels D and H) ispartly a result of the relatively smaller impact of par-ticulates at short wavelengths where Rayleigh scatteringis more significant. At absorbing wavelengths for whichgas absorption is important, the optical depth and verti-cal distribution of particulates have a greater fractionaleffect on I/F and thus small secular changes in these pa-rameters can be more easily noticed. DIRECT COMPARISON OF METHANE ANDHYDROGEN ABSORPTIONS VS. LATITUDE.
If methane and hydrogen absorptions had the same de-pendence on pressure, then it would be simple to estimatethe latitudinal variation in their relative abundances bylooking at the relative variation in I/F values with lati-tude for wavelengths that produce similar absorption atsome reference latitude. Although this idea is compro-mised by different vertical variations in absorption, whichmeans that latitudinal variation in the vertical distribu-tion of aerosols can also play a role, it is neverthelessuseful in a semi-quantitative sense. Thus we explore sev-eral cases below.
Image comparisons at key near-IR wavelengths in2007 and 2015
Our first example compares an HST/NICMOS imagemade with an F108N filter (centered at 1080 nm), whichis dominated by H CIA, to a KeckII/NIRC2 image madewith a PaBeta filter (centered at 1290 nm), which is dom-inated by methane absorption. The images are shown inpanels A and B in Fig. 4 and latitude scans at fixedview angles are shown in Fig. 8. The NICMOS obser-vation was taken on 28 July 2007 at 4:39 UT and theKeck observation on 31 July 2007 at 14:39 UT (see Ta-ble 2 for more information). That these two observationssense roughly the same level in the atmosphere is demon-strated by the penetration depth plot in Fig. 1, whichalso displays the filter transmission functions. The ab-solute (unscaled) I/F profiles for these two images nearthe 2007 Uranus equinox are displayed for µ = 0.6 and µ = 0.8 by thinner lines in Fig. 8. At high latitudes inboth hemispheres, profiles at the two wavelengths agreeclosely, and both increase towards the equator. Butas low latitudes are approached the two profiles divergedramatically, with the I/F for the hydrogen-dominated0 I/ F o N, µ = 0.72012 I/F at 10 o N, µ = 0.7 D i ff e r en c e I/ F o N, µ = 0.72012 I/F at 60 o N, µ = 0.7 µ m)-0.06-0.04-0.020.000.020.040.06 D i ff e r en c e DCBA I/ F o N, µ = 0.72015 I/F at 60 o N, µ = 0.7 D i ff e r en c e I/ F o N, µ = 0.72012 I/F at 60 o N, µ = 0.7 HGFE µ m)-0.06-0.04-0.020.000.020.040.06 D i ff e r en c e Fig. 7.—
Comparison of 2012 and 2015 STIS spectra at 10 ◦ N (A) and 60 ◦ N (C), and comparison of STIS 10 ◦ N and 60 ◦ N spectrafrom 2015 (E) and 2012 (G), with difference plots shown in panels B, D, F, and H respectively. The dotted curve in panel H is a copy ofthe 2015 difference curve from panel F. Latitudes are planetographic. Note the nearly exact equality (in A) of 10 ◦ N spectra from 2012and 2015. wavelength ending up 50% greater than for the methane-dominated wavelength, indicating much greater methaneabsorption at low latitudes than at high latitudes. Asnoted by Sromovsky et al. (2014) this suggests that up-per tropospheric methane depletion (relative to low lat-itudes) was present at both northern and southern highlatitudes in 2007, at least roughly similar to the patternthat was inferred by Tice et al. (2013) from analysis of2009 IRTF SpeX observations. Latitudinal variations inaerosol scattering could distort these results somewhat,but because they affect both wavelengths to similar de-grees, most of the effect is likely due to methane varia-tions.A second example is shown by the thicker lines in Fig.8, which display latitudinal scans of 2015 images shownin panels E and F of Fig. 4. These were made by theKeckII/NIRC2 camera with He 1A and PaBeta filterson 29 August 2015 (see Table 2). The He 1A filter issimilar to the NICMOS F108N filter, as shown in Fig. 1.The 2015 observations present a picture that is somewhatdifferent from the 2007 observations, with high north-ern latitudes much brighter (at the same view angles)than in 2007. This change appears to be entirely dueto increased aerosol scattering. This conclusion is sup-ported by the characteristics of images obtained withH -dominated filters (NICMOS F108N filter and Keck He1 A filter). In 2015 the I/F in the He1 A filter isrelatively independent of latitude as shown by the im-age in panel E of Fig. 4, indicating that aerosol scatter-ing must have a relatively weak latitudinal dependence.Note that latitude scans at fixed view angles for these fil-ters (shown in Fig. 8) exhibit a low-latitude divergence ofthe hydrogen-dominated and methane-dominated wave-lengths which has about the same magnitude in 2015 asseen for the 2007 observations, indicating a similar in-crease of methane absorption at low latitudes. Direct comparison of key STIS wavelength scans
A comparison of the STIS latitude scans at methanedominated wavelengths with scans at H CIA domi-nated wavelengths is also informative. By selecting wave-lengths that at one latitude provide similar I/F valuesbut very different contributions by H CIA and methane,one can then make comparisons at other latitudes to seehow I/F values at the two wavelengths vary with lati-tude. If aerosols did not vary at all with latitude, thenany observed I/F variation would be a clear indicatorof variation in the ratio of CH to H . Fig. 9 displaysa detailed view of I/F in the spectral region where hy-drogen CIA exceeds methane absorption (see Fig. 1 forpenetration depths). Near 827 nm (A) and 930 nm (C)the I/F values are similar but the former is dominated1 -60 -40 -20 0 20 40 60 80Planetographic Latitude ( o )0.000.020.040.060.080.100.12 µ = 0.80 o )0.000.020.040.060.080.100.12 R e l a t i v e R e f l e c t an c e µ = 0.60 A B )Keck/NIRC2 PaBeta (1290 nm, all CH )Keck/NIRC2 He1_A (1080 nm, mostly H )Keck/NIRC2 PaBeta (1290 nm, all CH ) Solid lines: mostly H absorptionDashed lines: all CH absorption Fig. 8.—
Latitudinal profiles at fixed zenith angle cosines of 0.6 (A) and 0.8 (B) for F108N (HST/NICMOS) and PaBeta (Keck/NIRC2)filters (light solid and dashed lines respectively) taken near the Uranus equinox in 2007, and Keck/NIRC2 filter He1 A and PaBeta filters(thick solid and dashed lines respectively) in 2015. In 2007 the southern hemisphere was still generally brighter than the northern hemisphereand the 38 ◦ S - 58 ◦ S southern bright band was still better defined and considerably brighter than the corresponding northern bright band.The relatively low equatorial I/F values for the methane-dominated PaBeta filter (1290 nm) implies greater CH /H absorption at lowlatitudes. We scaled the Keck 2015 observations to approximately match the 2007 observations at 10 ◦ N, where we found almost nochange between 2012 and 2015 at CCD wavelengths (Fig. 7A). Note that between 2007 and 2015, the north polar region has brightenedby comparable amounts at both hydrogen-dominated and methane-dominated wavelengths, indicating that it the brightening is due toincreased aerosol scattering, not a temporal change in the methane mixing ratio at high latitudes. More information about the observationsis given in Table 2. by hydrogen absorption (dot-dash curve) and the latterby methane absorption (dashed curve). Near 835 nm(B) there is a relative minimum in hydrogen absorption,while methane absorption is still strong. For the lati-tude and view angle of this figure (50 ◦ N and µ = 0.6),I/F values are nearly the same at all three wavelengths,suggesting that they all produce roughly the same atten-uation of the vertically distributed aerosol scattering.Figure 10 displays the latitudinal scans for the threewavelengths highlighted in Fig. 9 for the STIS obser-vations in 2002 (shown by thin lines), 2012 (thick graylines), and 2015 (thick black lines). This is for a viewangle cosine of µ = 0 .
6, chosen as a compromise be-tween amplitude of variation and coverage in latitude.The 2012 I/F for the hydrogen-dominated wavelengthincreases towards low latitudes, while the I/F for themethane-dominated wavelength decreases substantially,indicating an increase in the amount of methane relativeto hydrogen at low latitudes. Similar effects are seen in2002 (providing the best view of southern latitudes) and2015 (providing the best view of the northern latitudes).The hydrogen-dominated wavelengths have relatively flatlatitudinal profiles of I/F in the southern hemisphere in2002 and in the northern hemisphere in 2015, while themethane-dominated wavelengths show strong decreases towards the equator, beginning at about 45 ◦ S and 50 ◦ N. For µ =0.8 (not shown), which probes more deeply, thelatitudinal variation for the methane dominated wave-lengths is somewhat greater (a 30% decrease in I/F atlow latitudes vs. a 20% decrease for µ = 0.6).The spectral comparisons in Fig. 10 also reveal sub-stantial secular changes between 2002 and 2012 and be-tween 2012 and 2015. At wavelengths for which methaneand/or hydrogen absorption are important, the north-ern low-latitudes have brightened substantially, while thesouthern low latitudes have darkened. The bright bandbetween 38 ◦ and 58 ◦ N continued to brighten. Its bright-ening and the darkening of the corresponding southernband was already apparent from a comparison of 2004and 2007 imaging (Sromovsky et al. 2009). The mostdramatic change between 2012 and 2015 is the increasedbrightness of the polar region. The nearly identicalbrightening at all wavelengths, shown by the ratio plot inpanel B of Fig. 10, argues that the brightening is due toaerosol scattering rather than a decrease in the amountof methane. We will confirm this with radiation transfermodeling in Section 9.A color composite of the highlighted wavelengths (us-ing R = 930 nm, G = 834.6 nm, and B = 826.8 nm) isshown in Fig. 11, where the three components are bal-2
800 820 840 860 880 900 920 940Wavelength (nm)0.000.050.100.150.20 I/ F Latitude= 50 o , µ = 0.60 solid = I/F spectrumdashed = CH abs. coeff., (km-am) -1 dot-dash = scaled H CIA, (km-am ) -1 A B C
Fig. 9.—
I/F and absorption spectra comparing the equilibrium H CIA coefficient spectrum (divided by 1.2 × − , shown as dot-dashcurve) and methane absorption coefficient spectrum (dashed). Note that the I/F spectrum has nearly equal I/F values at 826.8 nm (A),834.6 nm (B), and 930 nm (C), but H absorption is much greater at A than at B, while the opposite is true of methane absorption, andat C only methane absorption is present. In a reflecting layer model, changes in cloud reflectivity should affect wavelengths A-C by thesame factor, but changes in methane mixing ratio would affect C most and A least. From Sromovsky et al. (2014). -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80Planetographic Latitude ( o )0.100.150.20 I/ F µ = 0.60 , solid) 834.6 nm (mostly CH , dot-dash) 930.0 nm (all CH , dotted) A B -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80Planetographic Latitude ( o )0.40.60.81.01.21.41.6 I/ F r a t i o t o Fig. 10.—
I/F vs. latitude at µ = 0 . /H ratios at low latitudes. Also note the increasednorth polar brightness at all displayed wavelengths between 2012 and 2015, indicating that the temporal change is due to increased aerosolscattering. RADIATIVE TRANSFER MODELING OF METHANEAND AEROSOL DISTRIBUTIONS
Radiation transfer calculations
In contrast to our prior analysis (Sromovsky et al.2014), which was carried out in the wavenumber do-main to accommodate our Raman scattering code, herewe worked in the wavelength domain, which is bettersuited to the uniform wavelength resolution of our cali-brated STIS data cubes. We also used an approximationfor the effects of Raman scattering rather than carryingout the full Raman scattering calculations. We againused the accurate polarization correction described bySromovsky (2005b) instead of carrying out the time con-suming rigorous polarization calculations. To assess theadequacy of our approximations, we did sample calcu-lations that included Raman scattering and polarizationeffects on outgoing intensity using the radiation transfercode described by Sromovsky (2005a). Examples in Fig.12 show that at most wavelengths the errors from theseapproximations do not exceed a few percent.We improved our characterization of methane ab-sorption at CCD wavelengths by using correlated-kmodel fits by Irwin et al. (2010), which are availableat http://users.ox.ac.uk/ ∼ atmp0035/ktables/ in filesch4 karkoschka IR.par.gz and ch4 karkoschka vis.par.gz.These fits are based on band model results ofKarkoschka and Tomasko (2010). To model collision-induced opacity of H -H and He-H interactions, we in-terpolated tables of absorption coefficients as a functionof pressure and temperature that were computed with aprogram provided by Alexandra Borysow (Borysow et al. 2000), and available at the Atmospheres Node of NASA’SPlanetary Data System. We assumed equilibrium hydro-gen, following KT2009 and Sromovsky et al. (2011).After trial calculations to determine the effect of differ-ent quadrature schemes on the computed spectra, we se-lected 12 zenith angle quadrature points per hemisphereand 12 azimuth angles. Test calculations with 10 and14 quadrature points in each variable changed fit param-eters by only about 1%, which is much less than theiruncertainties. Thermal profiles for Uranus
Assuming the helium volume mixing ratio (VMR)of 0.152 inferred by Conrath et al. (1987), Lindal et al.(1987) used radio occultation measurements of refrac-tivity versus altitude to infer a family of thermal andmethane profiles, with each profile distinguished by theassumed methane relative humidity above the cloudlevel, and the resultant deep volume mixing ratio (VMR)of methane below the cloud level. The cloud was posi-tioned at the point where the refractivity profile had asharp change in slope. None of these profiles achievedmethane saturation inside the cloud layer, even the pro-file with the highest physically realistic humidity level(limited by the requirement that lapse rates could not besuperadiabatic). This high-humidity profile also had thehighest deep temperatures and the largest deep methaneVMR of 4%. By allowing the He/H ratio to take onvalues near the low end of the uncertainty range givenby Conrath et al. (1987), Sromovsky et al. (2011) wereable to find solutions that achieved methane saturationinside the cloud layer, as well as deep methane mixingratios somewhat greater than 4%.The above results are based on the Voyager ingressprofile, which sampled latitudes from 2 ◦ S to 6 ◦ S. As towhether this local sample can be taken to roughly rep-resent a global mean profile, some guidance is providedby the results that Hanel et al. (1986) derived from theVoyager 2 Infrared Interferometer Spectrometer (IRIS)observations. Inversion of spectral samples near bothpoles and near the equator yielded temperature profilesthat differed by less than 1 K from about 150 mbar to600 mbar, and the equator and south pole profiles re-mained within 2 K from 60 mbar to 150 mbar, withthe north polar profile deviating up to 4 K above thetropopause. More significant variations can be seen atmiddle latitudes, however, especially in the 60 – 200mbar range where average temperatures are 3.5 K higherthan the latitudinal average near the equator and 4.5 K4 A B C Fig. 11.—
Color composites of fitted center-to-limb smoothed images for 2002 (A, right), 2012 (B, right), and 2015 (C, right), using colorassignments R=930 nm (all methane) G=834.6 nm (methane and hydrogen), and B=826.8 nm (mostly hydrogen). The blue tint at lowlatitudes in all years is due to locally increased methane absorption. We also show near-IR NIRC2 H-band images for 2003 (A, left), 2012(B, left), and 2015 (C, left). The NIRC2 images are rotation removed averages following Fry et al. (2012) and processed to enhance thecontrast of small spatial scales, by adding k times the difference between the original image and a 0.13-arcsecond smoothed version, wherek was taken to be 30 for 2003 and 2012 images, but only 22.5 for the 2015 image because of better seeing conditions during its acquisition. I/ F µ = 0.4 µ = 0.6 µ = 0.8 A µ m)0.850.900.951.001.051.101.151.20 i gno r e po l , r a m / t r ue po l + r a m an line = Raman scattering and Polarization ignored + = true Raman + true Polarization B I/ F µ = 0.4 µ = 0.6 µ = 0.8 C µ m)0.850.900.951.001.051.101.151.20 app r o x po l + r a m an / t r ue po l + r a m an line = modified Wallace + Sromovsky pol. correction + = true Raman + true Polarization D Fig. 12.—
Trial calculations showing errors produced by ignoring Raman scattering and polarization (A and B) and greatly reduced errorsachieved by employing the modified Wallace approximation of Raman scattering (Sromovsky 2005a) and the approximation of polarizationeffects following Sromovsky (2005b). ◦ S (Conrath et al. 1991). In the 200 – 1000mbar range latitudinal excursions are within 1–1.5 K.Thus it appears that in the most important region of theatmosphere for our applications, the thermal structurewas not strongly variable with latitude, at least in 1986.Models of seasonal temperature variations on Uranus byFriedson and Ingersoll (1987) suggest that the effectivetemperature variation at low latitudes will be extremelysmall, only 0.2 K peak-to-peak at the equator, increasingto a still relatively small 2.5 K at the poles. Thus, it isplausible to analyze observations during the 2012 – 2015period with thermal profiles obtained as far back as 1986,even though they are local, but probably more appropri-ate to use thermal structures derived from observationsin 2007, averaging over a wide range of latitudes, such asthose inferred by Orton et al. (2014a) from nearly disk-integrated spectral observations.Sample thermal and methane profiles are displayed inFig. 13. The profile of Orton et al. (2014a), hereafter re-ferred to as
O14 , is based on nearly disk-integrated spec-tral observations obtained with the Spitzer Space Tele-scope near the Uranus equinox in 2007. Among the oc-cultation profile sets, it is only those with high methaneVMR values that provide decent agreement with the O14deep temperature structure, but none of the occultationprofiles are compatible with the O14 profile in the 0.30 –1.0 bar range. One might argue that if radio occultationresults agree with O14 at 100 mb and at pressures beyond1 bar, then the disagreement in temperatures at interme-diate pressure levels is more likely due to an error in theOrton et al. profile because that profile is inferred fromdifferent spectrometers in different spectral regions thatsample different altitudes, which might suffer from dif-ferences in calibrations, while the radio occultation usesthe same measurement (the frequency of a radio signal)throughout the pressure range. It seems more likely thatthe errors in the radio profile would be in the altitudescale or in offsets due to uncertain He/H ratios, ratherthan varying in the way the differences between the ra-dio and Orton et al. profile do. A similar argumentmight be made in favor of the Conrath et al. (1987) pro-file over the O14 profile because the former is based oninterferometric measurements using the same instrumentover the entire spectral range. And the former profile isin good agreement with the occultation-based profiles inthe 300–600 mbar range, where the latter is not. On theother hand, the Orton et al. profile allows higher CH mixing ratios without saturation in the 0.3 – 1 bar re-gion (Fig. 13) and are thus more compatible with the recent Lellouch et al. (2015) CH VMR profile derivedfrom Herschel far-IR and sub mm observations.The methane VMR in the stratosphere was estimatedto be no greater than 10 − by Orton et al. (1987). Abest fit estimate for the tropopause value of the methaneVMR, based on more recent Spitzer observations, is(1 . +0 . − . ) × − according to Fig. 4 of Orton et al.(2014b), which is the value we assumed here in deriv-ing the new F0 profile. However, the even more recentLellouch et al. (2015) result is three times larger. Interms of relative humidity (ratio of vapor pressure to sat-uration vapor pressure) these stratospheric mixing ratioscorrespond to humidities of 25% and 75% at the Ortonet al. tropopause temperature of 52.4 K. The F profileof Lindal et al. (1987) was derived assuming a constantmethane relative humidity of 53% above the cloud topsand a constant stratospheric mixing ratio equal to thetropopause value. In deriving the F0 profile we usedlinear-in-altitude interpolation of the methane humidityvalues between the cloud top and tropopause. The F1profile of Sromovsky et al. (2011) followed the same pro-cedure except that the value of the tropopause mixingratio was taken to be the earlier upper bound of 10 − and the He VMR was taken to be 0.1155 instead of 0.152.The lower He VMR was chosen to produce a saturatedmethane mixing ratio inside the cloud layer.Our analysis for this paper is primarily based on theO14 thermal profile, although we did consider the effectsof using these alternative profiles. From trial retrievalswe found no significant difference in the absolute mixingratios inferred for different thermal profiles. The maindifferences occurred when these mixing ratios were con-verted to relative humidities. We often found supersatu-ration above the condensation level for the cooler occul-tation profiles, whereas the same mixing ratios did notlead to supersaturation for the warmer O14 profile, orfor the F0 profile. The F0 profile would also have beena decent baseline choice, as long as we did not also usethe F0 methane profile, and instead let the STIS spectraconstrain the methane mixing ratios without regard tooccultation consistency. Vertical Profiles of Methane
In our prior analysis the vertical profile of methanewas generally coupled to the vertical temperature pro-file so that the vertical variation of atmospheric re-fractivity was consistent with occultation measurementof refractivity. In our current analysis we uncoupledtemperature and methane profiles because of questions6
60 80 100 T (K)1.000.100.01 P ( ba r) Conrath et al. 1987Orton et al. 2014F1 profileD profileF0 profile -10 -5 0 5 10T - T O (K) 10 -5 -4 -3 -2 -1 CH VMR1.0 0.1 dotted = saturation VMRLellouch et al. 2015
A B C
Fig. 13.— A: Alternate Uranus T(P) profiles. F0 and D profiles were derived from radio occultation measurements (Lindal et al. 1987)assuming a helium VMR of 0.152. The F1 profile was also derived from radio occultation measurements, but using a lower helium VMR0.1155, following Sromovsky et al. (2011). The Voyager IRIS profile of Conrath et al. (1987) (thick gray curve) is in best agreement withthe F0, D, and F1 profiles. The Orton et al. (2014a) profile (solid black curve), is based on Spitzer Space Telescope spectral observations. B: Temperatures relative to the Orton et al. (2014a) profile, which strongly disagrees with the radio occultation profiles in 500 mbar – 1bar region, where it is 3 K warmer. C: Methane VMR profiles corresponding to temperature profiles shown in A, using the same line styles,with an additional estimated profile by Lellouch et al. (2015), based on Herschel far-IR and sub-mm observations. raised about the reliability of the occultation results,especially by the new temperature structure results ofOrton et al. (2014a), and by the new methane measure-ments of Lellouch et al. (2015), which imply supersatu-ration for the cooler temperature profiles obtained fromoccultation analysis. Another difference in our currentanalysis is that we included the parameters describingthe methane vertical distribution as adjustable param-eters in the fitting process. We first carry out fits ofspectra at different latitudes assuming a vertically in-variant (but adjustable) methane VMR ( α ) below thecondensation level. Slightly above the condensation levelwe fit a relative humidity rh c , and assume a minimumrelative humidity of rh m at the tropopause between 20%and 60%, which yields mixing ratios within a factor oftwo of Orton et al. (2014a)). The high end of this rangeis in better agreement with Lellouch et al. (2015). TheSTIS spectra themselves are not very sensitive to theexact value at the tropopause, as evident from Fig. 1.Between the tropopause and the condensation level weinterpolate relative humidity between rh c and rh m using the function rh ( P ) = rh m + ( rh c − rh m ) × (2) (cid:2) − log( P c /P ) / log( P c /P m ) (cid:3) , where P c is the pressure at which CH condensationwould occur for the given thermal profile and a givenuniform deep methane VMR, and P m is the pressure atwhich the relative humidity attains its minimum valuenear the tropopause. Given a deep methane VMR ( α )and a temperature profile from which a condensationpressure can be defined, Eq. 3 then defines a methaneVMR as a function of pressure for P < P c , denoted by α ( P ). That profile is generated prior to application ofthe Sromovsky et al. (2011) “descended profile” functionin which the initial mixing ratio profile α ( P ) is droppeddown to increased pressure levels P ′ ( α ) using the equa-tion P ′ = P × [1 + ( α ( P ) /α ) vx ( P d /P c − P tr < P < P d , P d is the pressure depth at which the revised mix-ing ratio α ′ ( P ) = α ( P ′ ) equals the uniform deep mixingratio α , P c is the methane condensation pressure be-fore methane depletion, P tr is the tropopause pressure(100 mb), and the exponent vx controls the shape ofthe profile between 100 mb and P d . Sample plots of de-scended profiles are displayed in Fig. 14. The profileswith vx = 1 are similar in form to those adopted byKarkoschka and Tomasko (2011). Our prior analysis ob-tained the best fits with vx =3, while our current analysisobtains a latitude dependent value ranging from ≥ ± ◦ N.Fig. 14B displays an alternative step-function deple-tion model in which the methane mixing ratio decreasesfrom the deep value to a lower vertically uniform valuebeginning at pressure P d and continuing upward untilthe condensation level is reached for that mixing ratio.This is parameterized by four variables: the deep mixingratio α , the pressure break-point P d , the upper mixingratio α , and the relative humidity immediately abovethe condensation level rh c . The parameters of all threeof these vertical profile models are summarized in Table4. Cloud models
Prior cloud models
Our prior analysis used an overly complex five-layermodel that was based on the KT2009 four-layer model,with the main difference being replacement of theirmain Henyey-Greenstein (HG) layer with two layers, thehigher of which was a Mie-scattering layer that wasa putative methane condensation cloud, as illustratedin Fig. 15A. In this model the scattering properties ofthe three remaining Henyey-Greenstein layers were takenfrom KT2009, with no adjustment to improve fit qual-ity. This model was partly based on parameters tunedto fit the 2002 STIS observations, taken 13 years beforeour most recent ones, and thus it was appropriate toreconsider the aerosol structure. In addition, the five-layer model actually has too many parameters to mean-ingfully constrain independently with STIS observations.Our starting point consisted of three Mie-scattering sheetclouds, as illustrated in Fig. 15B. But we obtained fits ofcomparable quality using for the tropospheric aerosols asimpler single cloud of uniform scattering properties anduniformly mixed with the gas between top and bottomboundaries, as in in Fig. 15C. As a result, that simplermodel became our baseline model. Tice et al. (2013),Irwin et al. (2015), and de Kleer et al. (2015) were suc- cessful in using a similar model structure to fit near-IRspectra.
Simplified Mie-scattering aerosol models
We have two options for our 2-cloud baseline modeldisplayed in Fig. 15C. Both options use a sheet cloudof spherical Mie-scattering particles to approximate thestratospheric haze contribution. The parameters defininga sheet cloud of spherical particles are the size distribu-tion of particles, their refractive index, effective pressure,and optical depth. We chose the Hansen (1971) gammadistribution, characterized by an effective radius and ef-fective dimensionless variance. As spectra are not verysensitive to the variance, we chose an arbitrary value of0.1. Based on preliminary fits we chose a particle sizeof 0.06 µ m. Other researchers have selected a slightlylarger size of 0.1 µ m. We also found generally low sen-sitivity to the effective pressure as long as it was suffi-ciently low. We thus chose a somewhat arbitrary valueof 50 mbar, putting the haze above the tropopause. Wemade an arbitrary choice of 1.4 for the layer’s refractiveindex. At wavelengths shorter than our lower limit, thehaze undoubtedly provides some absorption, as noted byKT2009, but we did not need to include stratospherichaze absorption to model its effects in our spectral range.Usually the only adjustable parameter for this layer wetook to be the optical depth. Test calculations showedthat an extended haze spanning pressures from 1 mbarto 200 mbar worked almost as well as our sheet cloudmodel. It did produce a slightly larger χ but using adiffuse stratospheric haze model had little effect on de-rived parameter values. The optical depth of the hazeonly increased by 2%, and the fractional changes in allthe other fitted parameters were less than 0.4%, puttingthese changes well below their estimated uncertainties.In any case, our aim with the haze model was to ac-count for its spectral effects, not to accurately describethe physical characteristics of the haze itself.For a tropospheric sheet cloud of conservative particlesthe fitted parameters would be particle size, real refrac-tive index, effective pressure, and optical depth (4 pa-rameters). For a pair of tropospheric sheet clouds, as inFig. 15B, there would be 8 parameters to constrain. As-suming both layers had the same scattering properties,that would drop the number of fitted parameters to 6.Replacing the pair of sheet clouds with a single diffuselayer with uniform scattering properties, as in Fig. 15C,reduces the number of optical depths to one, but keepsthe number of pressure parameters to two, this time used8 -5 -4 -3 -2 -1 Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) -5 -4 -3 -2 -1 Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) CH HePcond= 1.21 bars Pd = 5 barsvx = 0.5 1 3CH RHM = 0.35 CH RHC = 0.6 A -5 -4 -3 -2 -1 Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) -5 -4 -3 -2 -1 Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) CH HePcond= 0.93 bars Pd = 2.72 barsCH RHM = 0.22 CH RHC = 0.35 B CH S a t u r a t i on P r o f il e Fig. 14.— A: Sample “descended gas” methane profiles with pd = 5 bars and vx = 0.5 (dashed), 1 (dot-dash), and 3 (solid). Thestarting profile before descent is shown in solid gray and is based on the F1 T(P) profile with methane constrained by its deep mixing ratioand the humidities above the condensation level (CH RHC) and at the tropopause (CH RHM), with linear in log P interpolation betweenthese levels. B: Sample step-function vertical methane profile using the T(P) profile of Orton et al. (2014a) to define the saturation vaporpressure profile (dotted curve). This particular example fits the 2015 spectra at 40 ◦ N. See text for further explanation.
TABLE 4Methane vertical profile model parameters.
Model Type Parameter (description) Value α (deep mixing ratio) adjustable P c (condensation pressure) derived from α , P ( T ) profileuniform deep P t (tropopause pressure) derived from P ( T ) profile rh c (relative humidity at 0 . × P c ) adjustable rh m (relative humidity at P t ) adjustable, or from Orton et al. (2014a) α (mixing ratio for P > P d ) adjustable α (mixing ratio for P c < P < P d ) adjustable P d (transition pressure) adjustable2-step uniform P c (condensation pressure) derived from α , P ( T ) profile rh c (relative humidity at 0 . × P c ) adjustable rh m (relative humidity at P t ) fixed at various values α (mixing ratio for P > P d ) adjustable P d (transition pressure) adjustabledescended vx (exponent of shape function) adjustable α ′ ( P ) (descended VMR profile) derived by inverting Eq. 4 rh c (relative humidity at 0 . × P c ) adjustable rh m (relative humidity at P t ) fixed at various valuesNOTE: we assumed the same mixing ratio for P < P t as for P = P t . For the 1 and 2-step uniform models rh ( P )for P t < P < . × P c is obtained from Eq. 3. for top and bottom boundaries, yielding a new total of5 parameters for the tropospheric aerosols. Instead offitting top and bottom pressures to control the verticaldistribution, Tice et al. (2013) chose to fit the base pres-sure and the particle to gas scale height ratio. Whichapproach is more realistic remains to be determined. Atthis point we have a nominal total of 6 adjustable pa-rameters to describe our aerosol particles, one for the stratospheric sheet, and five for the vertically extendedtropospheric layer. These are named m r , m r , m pb , m pt , m od , and m nr , where the characters preced-ing the number indicate the type of particle ( m denotesMie scattering spherical particle), the number is the layernumber, and the type of parameter is indicated after theunderscore ( r for radius, pb for bottom pressure, pt fortop pressure, od for optical depth, and nr for real refrac-9 P r e ss u r e ( ba r) CH cloudH S?NH SH? m1hg1 m2, m2_p, m2_rhg2, hg2_phg3
A B C
Fig. 15.— A: Comparison of the KT2009 model (dotted) with the similar but more complex 5-layer model used by Sromovsky et al.(2014), which replaced two diffuse layers with 3 compact layers. B: A preliminary simplified model with three compact layers, mostlydefined by the two lower layers. This model was constructed with the possibility in mind that m m S. C: Our baseline simplest model in which the tropospheric cloud is uniformly mixed between top and bottom pressures and hasthe same particle properties throughout layer 2. tive index).For these spherical (Mie-scattering) particles, wave-length dependent properties are controlled by particlesize and refractive index. Even if both of these arewavelength-independent, scattering cross section (or op-tical depth) and phase function do have a wavelengthdependence because of the physical interaction of lightwith spherical particles. Where our chosen parametersfail to provide sufficient wavelength dependence, we willalso add another parameter, namely the imaginary re-fractive index m ni , which will in general be wavelengthdependent, and have its main influence over the single-scattering albedo ̟ . We also have between two and fourparameters chosen to constrain the vertical methane pro-file, yielding generally between eight and ten total pa-rameters to constrain by the non-linear regression rou-tine. Non-spherical aerosol models.
Because the particles in the atmosphere of Uranus arethought to be mostly solid particles, they are unlikely tobe perfect spheres, and thus we also considered a moregeneralized description of their scattering properties. Toinvestigate non-spherical scattering, we employed thecommonly used double Henyey-Greenstein phase func- tion, in which three generally wavelength-dependent pa-rameters need to be defined: the scattering asymme-try parameter ( g >
0) of a mainly forward scatter-ing term, the asymmetry parameter ( g <
0) of themainly backscattering term, and their respective frac-tional weights ( f and 1 − f respectively). An addi-tional fourth parameter is the single-scattering albedo( ̟ ), which might also be wavelength dependent. Thedouble Henyey-Greenstein (DHG) phase function is givenby P ( θ ) = f × (1 − g ) / (1 + g − g cos( θ )) / (4)+(1 − f ) × (1 − g ) / (1 + g − g cos( θ )) / , where θ is the scattering angle. KT2009 modeled theirresults assuming g = 0 . g = − . f to adjust the phase function oftheir tropospheric cloud layers so that they would ap-pear relatively bright enough at short wavelengths. Forhaze layers composed of fractal aggregate particles, asinferred to exist in Titan’s atmosphere, one would ex-pect both phase function and optical depth to be wave-length dependent, and modeling the fractal aggregatephase function variation with double Henyey-Greensteinfunctions would require wavelength dependence in g and g as well as f , judging from the aggregate models of0Rannou et al. (1999). An alternate approach to match-ing observed spectra with spherical particles is to makethe particles absorbing at longer wavelengths and con-servative at shorter wavelengths.The simplest DHG particle is just an HG particle char-acterized by an asymmetry parameter g, and a singlescattering albedo ̟ , and for a limited spectral range, awavelength dependence parameter, which can be taken asa linear slope in optical depth, which amounts to threeparameters ( g , ̟ , d τ /d λ ). This is the same numberneeded to characterize scattering by a Mie particle ( r , nr , ni ). However, if we use a full DHG formulation, thenthere are five particle parameters to constrain ( f , g , g , ̟ , and d τ /d λ ).An alternative way to produce the wavelength depen-dence of a spherical particle without its potentially com-plex phase function, containing features like glories andrainbows, which would not be seen in randomly orientedsolid particles, is to follow the procedure of Irwin et al.(2015). They computed scattering properties of sphericalparticles to determine the wavelength dependence of thescattering cross section, but fit the phase function to adouble HG function to smooth out the spherical particlefeatures. The refractive index they assumed was the typ-ical value of 1.40 at short wavelengths, but was modifiedby the Kramers-Kronig relation to be consistent with thefitted variation of the imaginary index. Whether thereare any cases of randomly oriented solid particles actuallydisplaying these modified Mie scattering characteristicsremains to be determined. Fractal aggregate particles
For those layers that are produced by photochemistry,it is also plausible that the hazes might consist of fractalaggregates, which have phase functions that are stronglypeaked in the forward direction, but are shaped at otherangles by the scattering properties of the monomersfrom which the aggregates are assembled. It is a con-venience to assume identical monomers, and to parame-terize the aggregate scattering in terms of the number ofmonomers, the fractal dimension of the aggregate, andthe potentially wavelength dependent real and imaginaryrefractive index of the monomers (Rannou et al. 1999).If the refractive index were wavelength independent, thiswould require fitting of potentially five parameters (rm,Nm, dim, nr, ni), the same number as for the most gen-eral DHG particle. Assuming ni = 0, rm = fixed size, thiswould require fitting just three parameters (Nm, dim,nr), a tractable task, but one which we have not so far implemented in our fitting code.To better understand the wavelength dependent prop-erties of aggregates we made some sample calculations.We first considered an aggregate of 100 monomers 0.05 µ m in radius with a real refractive index of 1.4, anda fractal dimension of 2.01. These particles have themass of a particle of 0.23 µ m in radius. This providesa physical connection between monomer parameters andthe wavelength dependent aggregate phase function andscattering and absorption cross sections. We foundthat it is possible to at least roughly characterize thefractal aggregate phase functions with double Henyey-Greenstein functions, although this provides no physicalconnection to a wavelength dependent cross-section andsingle-scattering albedo unless DHG fits to the fractal ag-gregates are done for each wavelength. We found for thisexample that the backscatter phase function amplitudedeclines as wavelength decreases, opposite to the modelof KT2009, while the scattering efficiency (and thus op-tical depth) has a strong wavelength dependence, alsocontradicting the KT2009 model, which assumed wave-length independence for optical depth. By increasing thenumber of monomers from 100 to 500 (mass equivalentto a particle 0.4 µ m in radius), the asymmetry param-eter can be made relatively flat over the 0.5 µ m to 1 µ m range, but the strong wavelength dependence of theextinction efficiency remains, suggesting that it is opti-cal depth dependence on wavelength that offers the bestlever for adjusting model I/F spectra, rather than thephase function. It is also clear that no spherical parti-cle can simultaneously reproduce both the fractal phasefunction and scattering efficiency and their wavelengthdependencies. Photochemical vs. condensation cloud models
According to Tomasko et al. (2005), the dominantaerosol in Titan’s atmosphere is a deep photochemicalhaze extending from at least 150 km all the way to thesurface, with a smoothly increasing optical depth reach-ing a total vertical optical depth of 4-5 at 531 nm, withno evident layers of significant concentration that mightsuggest condensation clouds (only a thin layer of 0.001optical depths was seen at 21 km). KT2009 argued for asimilar origin for the dominant aerosols on Uranus. Thefact that the main aerosol opacity on Uranus is foundsomewhat deeper than would be expected for a methanecondensation cloud certainly suggests that the aerosolsin the 1.2-2 bar region are either H S, which might con-dense as deep as the 5-bar level or higher, or some pho-1tochemical product, or both. And residual haze parti-cles might serve as condensation nuclei for H S. This pu-tative deeper photochemical haze is apparently not thehaze modeled by Rages et al. (1991), which is producedat very high levels of the atmosphere and has UV ab-sorbing properties that do not seem to be characteristicof the deeper haze. In fact, it is not clear that thereis enough penetration of UV light to the 1.2-bar levelto produce significant photochemical production of anyhaze material. Ignoring the issue of production rate, themain arguments for a photochemical haze are based onthe following expected characteristics of such a haze: (1)a strong north-south asymmetry before the 2007 equinox,with more haze in the south compared to the north; (2)a declining haze near the south pole as solar insolationdecreased towards the 2007 equinox (this assumes thatthe lag between production and insolation is only a fewyears); (3) an increasing haze near the north pole as itstarts to receive sunlight after the 2007 equinox; (4) slowchanges because the sub-solar latitude changes by only4 ◦ /year; (5) a time lag with respect to solar insolationbecause haze particles accumulate after production butdo not exist at the beginning of production (equilibriumwould be reached when the fall rate of particles equalsthe production rate). All five characteristics are indeedobserved for Uranus, at least qualitatively, while thesechanges are not obvious expectations for condensationclouds.Given our preferred explanation for the polar methanedepletion, namely that there is a downwelling flow fromabove the methane condensation level, the mixing ratioof methane would be too low to allow any methane con-densation in the polar region at pressures greater thanabout 1 bar. Thus it is challenging to explain the in-crease in haze in the polar region after equinox as anincrease in the mass of condensed particles in that re-gion. One possibility is that the clouds are formed belowthe region of downwelling methane, and instead in a re-gion of upwelling H S. But microwave observations sug-gest that the polar subsidence extends deeper than thedeepest aerosol layers that we detect, which would seemto inhibit all cloud formation by condensation. Anotherpossibility is that meridional transport of condensed H Sparticles at the observed pressures, if it occurred at a suf-ficiently high rate, could resupply the falling particles.One odd feature of the putative tropospheric photo-chemical haze in the KT2009 model, is the concentrationof optical depth within the 1.2-2 bar region, which hasabout 2 optical depths per bar, which far exceeds the density of any of the other four layers in the KT2009model. A possible explanation of this effect is that thephotochemical aerosols absorb significant quantities ofmethane, as appears to have occurred in Titan’s atmo-sphere (Tomasko et al. 2008), growing larger and also di-luting the UV absorption of the particles originating fromthe stratosphere. The bottom boundary of this region ofenhanced opacity may be where the methane that wasadsorbed into the photochemical aerosols is released andevaporated. A problem with this concept is that it is alsohard to explain the growth of the haze following equinoxin a region of greatly reduced methane abundance.Another mystery is why the methane mixing ratio is sostable over time, if methane is involved in fattening thephotochemical particles that have a time varying produc-tion. This might just be due to the fact that it takes verysmall amounts of condensed material to produce a signif-icant optical depth of particulates. The rate limiting fac-tor might be the arrival rate of UV photons, rather thanthe amount of methane either as the parent molecule ofthe photochemical chain of events in the stratosphere, oras the adsorbed material needed to enhance the opticaldepth of the haze particles in the troposphere. We canhope that some clues can be gleaned from the character-istics of the time dependence and latitude dependenceobserved in the model parameters.
Fitting procedures
To avoid errors in our approximations of Raman scat-tering and the effects of polarization on reflected inten-sity, we did not fit wavelengths less than 0.54 µ m. Anupper limit of 0.95 µ m was selected because of significantuncertainty in characterization of noise at longer wave-lengths. To increase S/N without obscuring key spectralfeatures, we smoothed the STIS spectra to a FWHMvalue of 2.88 nm. We chose three spectral samples of theCTL variation, at view and solar zenith angle cosinesof 0.3, 0.5, and 0.7, which are fit simultaneously. In itssimplest form our multi-layer Mie model has three ad-justable parameters per layer (pressure, particle radius,and optical depth). Each layer is assumed to be a sheetcloud of insignificant vertical thickness.We also fit adjustable gas parameters, illustrated inFig. 14 and described in Table 4. For the verticallyuniform mixing ratio model (up to the CH condensa-tion level) we have two adjustable parameters: the deepmethane volume mixing ratio and the relative methanehumidity above the condensation level (methane relativehumidity is the ratio of its partial pressure to its satu-2 TABLE 5Summary of 2 layer cloud model parameters
Layer Description Parameter (function) ValueStratospheric haze m p (bottom pressure) fixed at 60 mbof Mie particles m r (particle radius) fixed at 0.06 µ m1 with gamma size m b (variance) fixed at 0.1distribution (m1) n m od (optical depth) adjustable m pt (top pressure) adjustableUpper tropospheric m pb (bottom pressure) adjustablehaze layer of Mie m r (particle radius) adjustableparticles (m2) m b (variance) fixed at 0.1 m nr (real refractive index) adjustable m ni (imag. refractive index) adjustable2 m od (optical depth) adjustable hg pt (top pressure) adjustableAlternate upper trop. hg pb (bottom pressure) adjustablehaze of HG particles ̟ ( λ ) (single-scatt. albedo) adjustable or fixed(hg2) g (defines HG phase func.) adjustable hg od (optical depth) adjustable hg kod (optical depth slope) adjustableSecond alternate hg pt (top pressure) adjustableupper tropospheric hg pb (bottom pressure) adjustablehaze of double-HG particles ̟ ( λ ) (single-scatt. albedo) adjustable or fixed(hg2) P ( θ, λ ) (phase function) DHG function of KT2009 hg od (optical depth) adjustable ration pressure). For the 2-layer Mie-scattering aerosolmodel, this yields a total of 8-9 adjustable parameters(the top Mie layer has a fixed pressure and often a fixedparticle size as well, with optical depth remaining asthe only adjustable parameter because the others are sopoorly constrained). For the step-function 2-mixing ratiogas model, we use three adjustable gas parameters: thebreak point pressure, and the upper CH mixing ratio,and the relative methane humidity above the conden-sation level, for a total of nine adjustable parameters.The third parameterization of the methane distribution,the descended gas model, also uses three adjustable pa-rameters: the pressure limit of the descent, the methanerelative humidity above the condensation level (prior todescent), and the shape exponent vx .We used a modified Levenberg-Marquardt non-linearfitting algorithm (Sromovsky and Fry 2010) to adjust thefitted parameters to minimize χ and to estimate uncer-tainties in the fitted parameters. Evaluation of χ re-quires an estimate of the expected difference between amodel and the observations due to the uncertainties inboth. We used a relatively complex noise model followingSromovsky et al. (2011), which combined measurementnoise (estimated from comparison of individual measure-ments with smoothed values), modeling errors of 1%,relative calibration errors of 1% (larger absolute calibra- tion errors were treated as scale factors), and effects ofmethane absorption coefficient errors, taken to be ran-dom with RMS value of 2% plus an offset uncertaintyof 5 × − (km-amagat) − . This is referred to in thefollowing as the COMPLX2 error model. FIT RESULTS FOR 2012 AND 2015 STIS OBSERVATIONS
Here we first consider conservative fits over a wide540-980 nm spectral range, which identifies a problemin matching the needed particle properties to fit such awide range. That problem is then deferred by fittingthe critical 730-900 nm wavelength range that providesthe strongest constraints on the methane/hydrogen ra-tio, first using Mie scattering particles for all cloud lay-ers, then using an alternative model in which the maintwo tropospheric layers are characterized by adjustableDHG phase functions. If we assume that the methanemixing ratio is uniform up to the condensation level, wefind that it must decrease with latitude by factors of 2-3from equator to pole with different absolute levels, de-pending on whether particles are modeled as spheres orwith DHG phase functions. We then consider two mod-els that restrict methane depletions to an upper tropo-spheric layer, and find that improved fits are obtainedwith models that restrict depletions to the region abovethe 5-bar level.3
Initial conservative fits to the 540-980 nmspectrum.
Assuming a real refractive index of m nr = 1.4, andan imaginary index of zero, we fit our simplified 2-layermodel to spectra covering the 540-980 nm range by ad-justing the seven remaining parameters. We obtained abest fit model spectrum with significant flaws that areillustrated in Fig. 16. The parameter values and uncer-tainties are listed in Table 6. The best-fit value for themethane mixing ratio was a remarkably low 1.27 ± /H ratio is very poorly fit.Additional flaws are seen near 750 nm, as well as at othercontinuum features at shorter wavelengths. Almost ex-actly the same fit quality and the same specific flawswere obtained when we replaced the single troposphericcloud with two sheet clouds with two more adjustableparameters.Better results were obtained by letting the real refrac-tive index be a fitted parameter as well. This is in con-trast to the common procedure of fixing the refractiveindex, most often at a value of 1.4, as we also did in ourinitial fit. Irwin et al. (2015), for example, justified theirchoice of 1.4 by noting that most plausible condensableshave real indexes between 1.3 (methane) and 1.4 (ammo-nia). Other simple hydrocarbons are also in this range.However, at the levels where we see significant aerosol op-tical depth, ammonia is not very plausible, and methaneis in doubt because most particles are found at pressuresexceeding the condensation level. On the other hand, theplausible condensable H S has a significantly larger realindex of 1.55 (Havriliak et al. 1955) at the 80 K – 100K temperatures characteristic of the main cloud layeron Uranus. Another possible cloud particle is a com-plex photochemical product, one example of which is thetholin material described by Khare et al. (1993), whichhas a real index near 1.5. Thus, it seems premature tosettle on a fixed value at this point.When the initial fit is redone with starting values of m r = 1 µ m and m nr = 1.4, as documented in Ta-ble 6, we obtain a final large particle solution of m r = 1.918 ± µ m and m nr = 1.184 ± ± χ /N to 0.91. This solution was obtained byusing an initial guess of m r = 0.5 µ m and m nr = 1.4. As also shown in Table 6, these parameters adjusted tobest-fit values of m r = 0.235 ± µ m and m nr =1.83 ± S, and the methane VMR hasincreased to a more credible 1.90 ± Fitting the 730–900 nm region
Our next step was to concentrate on the spectral re-gion where the ratio of methane to hydrogen is best con-strained, i.e. the 730–900 nm region. As shown if Fig. 1,the short-wavelength side is free of CIA and sensitive tothe deep methane mixing ratio, while the middle regionfrom about 810 to 835 nm is strongly affected by hy-drogen CIA, and the long-wavelength side of the regionis sensitive to the methane mixing ratio at pressure lessthan 1 bar. By using this entire region we expect to ob-tain good constraints on both the ratio of methane to hy-drogen as well as on the vertical cloud structure. Resultsfrom fitting this region should not be strongly affected bywavelength-dependent particle properties, given the rel-ative modest spectral range we are considering here. Ifthe assumption of Mie scattering over this limited rangeis seriously flawed, that should show up in an inabilityto get high quality fits. This relatively narrow spectralrange also weakens constraints on particle size, as mightbe expected.
Effects of different aerosol models
We were somewhat surprised to find that the kind ofaerosol model chosen to fit the observations has a signif-icant effect on the derived vertical and latitudinal dis-tribution of methane. To investigate these effects wedid model fits at two key latitudes: 10 ◦ N and 60 ◦ N.From more detailed latitudinal profiles discussed later,we know that the apparent methane mixing ratio peaksnear 10 ◦ N and is approaching its polar minimum near60 ◦ N. These are also two latitudes for which 2012 and2015 observations provide good samples at the three viewangle cosines we selected.4 I/ F Measured Spectrum at mu= 0.3 0.5 0.7Best fit model with n1 = n2 = 1.4 + 0i at µ = 0.3 µ = 0.5 µ = 0.7 M ode l / M ea s . µ m)-4-202 ( M ode l - M ea s . ) / U n c e r t. stis_fitctl_spec_glats-30.00to87.00year2015mulim0.175Jun10-155158-2016limbcorr2.88nm.unf_lmfit_Dec27-142120-2017.tabPlanetographic Latitude = 10 o Nplot_spec_anal.pro: CASENUM = 13 χ = 469.29 CBA
Fig. 16.—
Top:
Model spectra at three view angle cosines (colored as noted in the legend) compared to the 10 ◦ N 2015 STIS spectra(black curves).
Middle:
Ratio of model to measured spectra.
Bottom:
Difference between model and measured spectra divided byexpected uncertainty. The aerosol model used the baseline 2-cloud model, except that m nr was fixed at a value of 1.4. Best fit parametervalues are given in Table 6. Note the significant discrepancies at short wavelength continuum peaks, near 740 nm, and within the criticalregion near 830 nm which is most sensitive to the methane to hydrogen ratio. Better fits were obtained with m nr allowed to adjust aspart of the fitting process. TABLE 6Preliminary fits to the 540-900 nm part of 2015 STIS 10 ◦ N spectra.
Parameter Value Value for LP soln. Value for SP soln.Name m nr fixed at 1.4 with m nr fitted with m nr fitted m od at λ = 0.5 µ m 0.046 ± ± ± m od at λ = 0.5 µ m 5.155 ± ± ± m pt (bar) 1.149 ± ± ± m pb (bar) 4.137 ± ± ± m r ( µ m) 0.382 ± ± ± m nr ± ± α (%) 1.270 ± ± ± ch rhc ± ± ± χ χ /NF 1.16 1.07 0.91NOTES: In the last two columns LP soln. denotes large particle solution and SP soln. denotes smallparticle solution. The χ values given here are based on fitting points spaced 3.2 nm apart. Fitting the spherical particle 2-cloud model assuminga uniform CH distribution. We first consider a methane vertical distribution thathas a constant mixing ratio from the deep atmosphereto the condensation level. Above that level (at lowerpressures) we assume a drop in relative humidity to anadjustable fraction of the saturation vapor pressure, and from there to the tropopause we interpolate from theabove cloud value to the tropopause minimum as de-scribed in Section 8.2. The key parameters describingthe methane distribution are then the above cloud rela-tive humidity and the deep mixing ratio.We first consider a simple aerosol model in whichthe tropospheric contribution is characterized by an ad-5justable optical depth and a single layer of spherical par-ticles bounded by top and bottom pressures and uni-formly mixed with the gas. We assume initially thatthese particles scatter light conservatively, but allow thereal refractive index to be constrained by the spectralobservations.The results of this series of fits for both 2015 and 2012observations are given in Table 7 where small particle so-lutions are given in the first four rows and large-particlesolutions in the remaining four rows. The model spec-tra are compared to the observations in Fig. 17. Thesefits do achieve their intended result of providing moreprecise constraints on the above-cloud methane humid-ity, which is high at 10 ◦ N and about 50% of those levelsat 60 ◦ N. The temporal change between 2012 and 2015in the effective methane mixing ratios is very small andwell within uncertainty limits. The low latitude valuesof 3.14 ± ± ◦ N values, which are 0.99 ± ± ± S, although the 60 ◦ Nvalues exceed that value by slightly more than their un-certainties. Perhaps this is an indication of a cloud com-position difference between the two latitudes. A quitedifferent result is obtained for the large-particle fit. Inthis case the average index is 1.23 ± ◦ N, providing the main driver forthe increase. According to Fig. 7, near 750 nm the I/Fincreased by about 20%, and according to the deriva-tive spectra in Fig. 18, the optical depth increase wouldaccount for about 11%, while the increase in refractiveindex by just 2.8% would increase the I/F by an ad-ditional 10%, accounting for the 20% total. However,these derivatives were computed for a latitude of 10 ◦ N;somewhat different derivatives might be found at 60 ◦ N.A similar increase of 33% is seen in the optical depth de-rived for the large particle solution, although in this casethere is also an increase in particle size by 22%, whichwould also contribute significantly. Weighting these byrespective factors of 0.42 and 0.45 (from Fig. 18) we ob-tain from just these parameters an I/F increase of about24%, which is again close to the entire change observed.The small changes in inferred methane mixing ratios areincreases of 6% for the small particle solution and about10% for the large particle solution, which would yield I/Fdecreases of 1.2% and 1.5% for the small and large par-ticle solutions respectively, both of which are well belowuncertainties. The fitting errors at high latitudes, whichare most evident in the 0.75- µ m region are highlightedby blue dotted ovals in Fig. 17. Fitting the 2-cloud non-spherical model assuming auniform CH distribution. We next consider fits in which the main troposphericlayer consists of a single particle type characterized bythe simplest possible Henyey-Greenstein function, whichis a one-term version of Eq. 5 characterized by a singleasymmetry parameter. The vertical structure parame-terization and stratospheric haze layer parameterizationare both unchanged from the spherical particle exampleused in the previous section. Because some wavelengthdependence is required, we introduce a wavelength de-pendent optical depth using a simple linear slope, whichis a parameter that is adjusted to optimize the fit. Ourmodel is given by τ ( λ ) = τ o × (1 + k OD × ( λ − λ )) (5)where λ is taken to be 800 nm. This also makes τ o the optical depth at 800 nm. We could also have madethe asymmetry parameter wavelength dependent insteadof, or in addition to, the optical depth, but found ex-6 TABLE 7Single tropospheric Mie layer fits to 10 ◦ N and 60 ◦ N STIS 730 - 900 nm spectra.
Lat. m od m pt m pb m r α ( ◦ ) × m od (bar) (bar) ( µ m) m nr (%) ch rhc χ YR10 2.8 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± NOTE: The optical depths are given for a wavelength of 0.5 µ m. These fits used 318 points ofcomparison and fit 8 parameters, for a nominal value of NF=310, for which the normalized χ /NFranged from 0.48 to 0.802.cellent fits without adding any further complexity. Wewill not be making any claims regarding the true sourceof wavelength dependence in any case. Our main objec-tive is to find out how this different kind of model affectsthe methane distribution, and to determine the averageasymmetry parameter of these particles. We will also tryto infer a single-scattering albedo.Best-fit parameter values and uncertainties for fits at10 ◦ N and 60 ◦ N for 2012 and 2015 are presented in Ta-ble 8. Best-fit model spectral are compared to observa-tions in the left panel of Fig. 19, while fractional deriva-tive spectra are displayed in the right panel. These fitsare comparable in quality to the spherical particle fitspresented in the previous section, and have the sameproblem fitting the high-latitude spectra, most notablyin the 750-nm region. This region senses more deeplythan other parts of this limited spectral range (see Fig.1), and thus is most likely to be affected by vertical vari-ations in the methane mixing ratio. According to thederivative spectra, an increase in the methane mixingratio with depth would reduce the I/F in this region,which we would expect to produce a better fit, and wewill later show that this does in fact improve the spectralfit in this region.The methane mixing ratio values for this model averagesomewhat higher than found for the model using spher-ical particles, although all are within uncertainty limitsfor a given latitude, and all results indicate an effectivemixing ratio decrease by slightly more than a factor ofthree from 10 ◦ N to 60 ◦ N. The best-fit asymmetry parameter for this model isgenerally near 0.4, well below the commonly assumedvalue of 0.6 for near-IR analysis, which is in partbased on an analysis of limb-darkening measurementsby Sromovsky and Fry (2008). That analysis predatesthe significant improvement in methane absorption coef-ficients seen in the last decade (Sromovsky et al. 2012a)and may no longer be valid. It seems unlikely that thisdifference is merely a wavelength dependence. For thesizes inferred for spherical particle solutions, the asym-metries either decrease with wavelength (small particlesolution), or remain relatively flat (large particle solu-tion). While the asymmetry parameter is highly nega-tively correlated with the optical depth parameter, thesetwo parameters do have sufficiently different ratios be-tween peaks and valleys to allow them to be indepen-dently determined (shown in Fig. 19F). The asymme-try was determined to within about 10% and the opticaldepth to within slightly better accuracy. The opticaldepths for this model appears to be considerably lowerthan for the spherical particle models, which were at ashorter wavelength of 500 nm. If we convert those Miescattering optical depths to a wavelength of 800 nm, wefind that the 0.3- µ m particle optical depth drops from 3.1to 2.6 and the 1.54 µ m particle optical depth increasesfrom 6.1 to 7.5. Thus, the wavelength difference doesnot explain the low optical depths of the non-sphericalmodel. It is more likely due to the latter’s more symmet-ric scattering. The Mie particle models have asymmetriesof about 0.68 and 0.87 for the small and large particle7 I/ F LAT = 10 o , χ = 140.80, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 256.71, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 196.26, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 192.54, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 Case 22: 2-layer Mie model large r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)
IHGF I/ F LAT = 10 o , χ = 148.39, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 248.62, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 192.65, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 196.02, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 Case 23: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)
IHGF
Fig. 17.—
Comparison of observed spectra (curves) with model fits (points) for the large particle solutions (left) and the small particlesolutions (right), both using the model parameterization defined in Table 7. Fits to 2015 STIS observations are shown in the top pair ofpanels and fits to 2012 observations in the bottom pair of panels. Blue dotted ovals identify regions of high-latitude fitting errors, whichcan be greatly reduced by using a non-uniform vertical distribution of methane. solutions respectively, both adjusted to a reference wave-length of 800 nm. The particles of KT2009, which usea DHG phase function, with their adopted values of g = 0.7 and g = -0.3, yield an asymmetry of 0.6, whichis much closer to that of our small particle solution forspherical particles, and much larger than our HG par-ticle solutions. We tried to find an HG solution withlarger asymmetry by using a first guess with g = 0.63,but the regression again converged on g = 0.43. It isapparently the case that very different scattering proper-ties can lead to very nearly the same fit quality, but verydifferent optical depths and asymmetry parameters. Atphase angles near zero, there is a considerable ambiguitybetween more forward scattering particles with larger op-tical depths and more backward scattering particles withsmaller optical depths.The best-fit optical depth slope parameter hg kod isnegative, as generally expected, and is around -2/ µ m at 10 ◦ N but -3.2 / µ m to -4/ µ m at 60 ◦ N. A spherical par-ticle of radius 0.3 µ m and real index 1.4 would have aslope of about -2.4/ µ m. For spherical particles, some ofthe wavelength dependence in scattering is provided bywavelength dependence in the phase function. This sug-gests a possible decrease in particle size at high latitudes.There is better agreement between the HG solutionand the small particle Mie solutions regarding other pa-rameters, including pressure boundaries, methane mixingratios and above cloud humidities. Thus, the preponder-ance of evidence suggests that the cloud particles canbe roughly approximated by the small particle Mie solu-tions, which is the solution type we will use to investigatethe latitude dependent characteristics in more detail. Latitude-dependent fits
To illustrate the latitude dependence of the effectivemethane mixing ratio and the inferred aerosol distribu-8 I/ F -0.2-0.10.00.10.20.3 dln(I/F)/dlnm1_od -1.0-0.50.00.51.0 dln(I/F)/dlnm2_pb -1.0-0.50.00.5 dln(I/F)/dlnm2_pt -0.50.00.51.01.5 dln(I/F)/dlnm2_od -0.50.00.51.01.5 dln(I/F)/dlnm2_r dln(I/F)/dlnm2_n µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4v0 µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4rhc Derivs. taken at: m1_od= 0.028 m2_pb= 2.686 m2_pt= 1.111 m2_od= 4.954 m2_r= 1.093 m2_n= 1.275 ch4v0= 0.027 ch4rhc= 0.671
A BC DE FG HI µ =0.7 glat= 10 o I/ F -0.2-0.10.00.10.20.3 dln(I/F)/dlnm1_od -1.0-0.50.00.51.0 dln(I/F)/dlnm2_pb -1.0-0.50.00.5 dln(I/F)/dlnm2_pt -0.50.00.51.01.5 dln(I/F)/dlnm2_od -0.50.00.51.01.5 dln(I/F)/dlnm2_r dln(I/F)/dlnm2_n µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4v0 µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4rhc Derivs. taken at: m1_od= 0.028 m2_pb= 2.458 m2_pt= 1.125 m2_od= 3.070 m2_r= 0.343 m2_n= 1.553 ch4v0= 0.031 ch4rhc= 0.684
A BC DE FG HI µ =0.7 glat= 10 o Fig. 18.—
Derivative spectra for uniform mixing ratio models evaluated for the large-particle solution (Left group) and small particlesolution (Right group). In each group we show I/F model spectrum (A) and derivatives of fractional changes in I/F with respect tofractional changes in parameters m od (B), m pb (C), m pt (D), m od (E), m r (F), m nr (G), ch v ≡ α (H) and ch rhc (I).All the derivative panels are scaled the same, except for panel B, which has been expanded by a factor of 4, and panel G, which has beencompressed by a factor of 5 because of their unusually small and large effects, respectively, on the I/F spectrum. In panels F and G, thedotted curve represents a version of the m od derivative spectrum scaled to match the lower features of the m r and m nr derivativespectra respectively, to illustrate their strong correlations but resolvable differences. TABLE 8Single tropospheric HG layer fits to 10 ◦ N and 60 ◦ N STIS spectra.
Lat. m od hg pt hg pb hg kod α ( ◦ ) × hg od (bar) (bar) hg g (/ µ m ) (%) ch rhc χ YR10 2.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± NOTE: The optical depth is for a wavelength of 0.8 microns for hg od , and for 0.5 µ m for thestratospheric haze ( m od ). These fits used 318 points of comparison and fit 8 parameters, for anominal value of NF=310, for which the normalized χ /NF ranged from 0.48 to 0.802.tion we selected the simple 2-layer model using a compactstratospheric haze and an extended diffuse layer of spher- ical tropospheric particles, characterized by Mie scatter-ing parameters of radius and refractive index. We also9 I/ F LAT = 10 o , χ = 151.51, STIS 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 252.65, STIS 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 192.22, STIS 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 193.30, STIS 2012 µ = 0.30 µ = 0.50 µ = 0.70 HG Case 7: Mie stratospheric haze, ONE HG layer, 730-900 nm,Orton T(P), uniform deep CH4vmr
JIHG I/ F -0.2-0.10.00.10.20.3 dln(I/F)/dlnm1_od -1.0-0.50.00.51.0 dln(I/F)/dlnhg2_pd -1.5-1.0-0.50.00.5 dln(I/F)/dlnhg2_pt -0.50.00.51.01.5 dln(I/F)/dlnhg2_od -1.0-0.50.00.51.0 dln(I/F)/dlnhg_g -0.2-0.10.00.10.20.3 dln(I/F)/dlnhg_kod µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4v0 µ m) -1.0-0.50.00.51.0 dln(I/F)/dlnch4rhc Derivs. taken at: m1_od= 0.026 hg2_pd= 2.325 hg2_pt= 1.126 hg2_od= 1.580 hg_g= 0.426 hg_kod=-2.230 ch4v0= 0.035 ch4rhc= 0.651
A BC DE FG HI µ =0.7 glat= 10 o Fig. 19.—
Left: HG Model spectra compared to observations at 10 ◦ N and 60 ◦ N for 2012 (bottom pair) and 2015 observations (top pair),with models plotted as points with error bars. Right: Derivative spectra showing the ratio of a fractional change in I/F to the fractionalchange in the parameter producing the change (here ch v ≡ α ). The dotted curve in panel F of the derivative group is an inverted plotof the curve in panel E, with minima scaled to match the solid curves. Note that the maxima do not match, making them distinguishable. chose the small-radius solution set because of their highquality fits and relative consistency between 2012 and2015, as well as their better agreement with HG fits asnoted in the previous section. Other models show similarcharacteristics, except that they contain more variationbetween years, as can be surmised from the table of fitparameters from fits at 10 ◦ N and 60 ◦ N, shown in Ta-ble 7 for large Mie particle fits and in Table 8 for HGmodel fits. We assumed a methane profile that has avertically uniform fitted deep mixing ratio, a fitted rela-tive humidity immediately above the condensation level,a minimum relative humidity of 30%, with linear inter-polation filling in values between the condensation leveland the tropopause. Above the tropopause we assumed amixing ratio equal to the tropopause value. From fittingspectra every 10 ◦ of latitude for both 2012 and 2015 ob-servations we obtained the best-fit parameters and theirformal uncertainties given in Table 9. The parametersare also plotted in Fig. 20, where panels A-E display the fit parameter values and their estimate errors, and pan-els F-I display samples of model and observed spectra for10 ◦ N and 60 ◦ N for 2015 (F and G) and 2012 (H and I).Most of the model parameters are found to have onlyweak variations with latitude. The top pressure of thesole tropospheric cloud layer is surprisingly invariantfrom low to high latitudes as well as from 2012 to 2013,even though there are substantial variations in opticaldepth between years as well as with latitude. Thisboundary pressure is also very well constrained by theobservations. The bottom pressure of this cloud is morevariable, but its variation is not much more than its un-certainty which is much larger than that of the cloudtop pressure. The larger uncertainty is consistent withthe derivative spectra given in Fig. 18, which shows that,compared to the top pressure, the bottom pressure has asmaller fractional effect on the I/F spectrum for a givenfractional change in pressure.0 [!t]
TABLE 9Single tropospheric Mie layer fits to the 730-900 nm spectra as a function of latitude assuming vertically uniform CH below the condensation level. Lat. m od m pt m pb m r α ( ◦ ) × m od (bar) (bar) ( µ m ) m nr (%) ch rhc χ YR-10 2.4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± NOTE: The optical depths are for a wavelength of 0.5 µ m. These fits used 318 points of comparisonand fit 8 parameters, for a nominal value of NF=310, for which the normalized χ /NF ranged from0.44 to 0.90.The most prominent latitudinally varying parameteris the effective deep methane mixing ratio, which attainsa low-latitude maximum of about 3.15%, dropping toabout 2% by 30 ◦ N, reaching a high-latitude value ofabout 1% at between 50 ◦ N and 60 ◦ N. Close behind, is thevariation in methane humidity above the condensationlevel, which was found to be 60-100% at low latitudes,declining to about 30-40% for regions poleward of 50 ◦ N.This decline towards the north pole is also seen in othermodel types as well.There is also close agreement, for this model, betweenbetween 2012 and 2015 results for both the extremes inthe methane mixing ratio and in its latitudinal variation.The slight dip at the equator is also present in results forboth years, as is the peak at 10 ◦ N. The agreement of the2012 and 2015 methane profiles (on both the deep mix-ing ratio and the above cloud humidity) is close enough that we must look elsewhere to explain the brightening ofthe polar region between 2012 and 2015. The most likelyaerosol change responsible for the polar brightening is theincrease in the bottom cloud layer optical depth ( m od )by about 60% at latitudes north of 50 ◦ , a factor alreadydiscussed in Section 9.2.2. However, because multipleaerosol parameters differ between 2012 and 2015, it isuseful to show that the combined effect of layer m2 pa-rameter changes does indeed result in the increased scat-tering that produced the observed brightness increase.This was done by starting with the model spectrum for2012 and computed a new model spectrum in which onlythe layer-m2 parameters were changed to match thoseof 2015, leaving other parameters unchanged. We alsocomputed the spectrum change when only the opticaldepth of the m2 layer was changed to the 2015 value.We did this at latitudes of 50 ◦ N, 60 ◦ N, and 70 ◦ N. The1 -20 0 20 40 60 80 3.02.52.01.51.00.5 P r e ss u r e ( ba r) Case 25: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)m2_pbm2_ptm2_n m2_pbm2_ptm2_n -20 0 20 40 60 8010 -2 -1 R ad i u s ( µ m ) , o r O p t i c a l dep t h m1_odm2_odm2_r m1_odm1_odm2_odm2_rm2_r -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 CH RH ch4rhcch4rhc ch4rhc -20 0 20 40 60 800.010.020.030.04 M e t hane V M R ch4v0 ch4v0STIS 2012STIS 2015 -20 0 20 40 60 80Planetographic Latitude (deg)0.40.60.81.01.21.4 χ / ( N F ) complx2 error model Nfree= 310Nfree= 310 EDCBA I/ F LAT = 10 o , χ = 148.39, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 248.62, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 192.65, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 196.02, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 Case 25: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)
IHGF
Fig. 20.—
Left: Single tropospheric Mie model fits as a function of latitude under the assumption that the methane VMR is constantfor pressures exceeding the condensation level. Parameter values are also given in Table 9. Right: sample spectra, with blue dotted ovalsidentifying regions of larger I/F errors. results are summarized in the following figures. The left-hand figure provides a sample spectral view at 60 ◦ N.It shows the measured spectral difference between 2012and 2015 as a shaded curve, with shading range indicat-ing uncertainties. Also shown are the difference in modelfits (+), the difference due only to layer m2 differences( × ), and the difference due only to the change in opticaldepth (o). The right hand plot displays the latitude de-pendence for two pseudo-continuum wavelengths. Againare shown the measured differences (shaded curves), themodel difference ( × ), and the brightness change due onlyto layer m2 (+). This figure shows that layer m2 isclearly responsible for the vast majority of the brightnessincrease between 2012 and 2015 , but changes in the m2layer optical depth are only responsible for about half ofthe total scattering increases of that layer (as in the lefthand plot), except at 50 ◦ N, where even though the opti-cal depth decreased, the layer still brightened because ofchanges in particle size and refractive index).At low latitudes, the fit quality for both years is better than expected from our uncertainty estimates, but fitquality decreases significantly at high northern latitudes,especially for the 2015 fits, which have increased aerosolscattering. The high latitude fitting problem is mostobvious just short of 750 nm, as shown in panels G and Iof Fig. 20, where the model values exceed the measuredvalues (note the encircled regions). This problem canbe greatly reduced by using an altered vertical profile ofmethane, as discussed in Section 9.3.
Summary of uniform methane results
Both spherical particle and HG models for the uppertropospheric layer lead to declining effective methane vol-ume mixing ratios with latitude by similar factors, butare in some disagreement with respect to magnitudes,as shown in greater detail in Fig. 22. The more detailedlatitudinal fit results in Fig. 20 for the small-particle solu-tion, show that the effective methane mixing ratio peaksnear 10 ◦ N in both years, has a local minimum at theequator and declines with latitude by more than a factor2 µ m)0.000.020.040.060.08 I/ F ( ) - I/ F ( ) shaded = measured difference for µ = 0.7RED x = model differenceBLK + = difference due to m2 model changesGRN o = difference due to m2_od change only o N
50 55 60 65 70Planetographic latitude ( o )0.000.020.040.060.08 I/ F d i ff e r en c e ( - ) shaded = measured difference for µ = 0.7RED x = model differenceBLK + = difference due to m2 model changes830 nm I/F - 0.01750 nm Fig. 21.—
Left: spectral difference at 60 ◦ N between 2012 and 2015 observations at a zenith angle cosine of 0.7 (shaded curve) comparedto all model differences ( × ), to those contributed only by layer m2 (+), and to those due only to the m2 optical depth change (o). Right:latitudinal variation of observed temporal differences at 750 nm (upper shaded curve) and 830 nm (lower shaded curve offset by 0.01),compared to total model differences ( × ) and differences due to all changes in layer m2 only (+). This shows that increased scattering bylayer m2 is primarily responsible for the observed brightening of the polar region between 2012 and 2015. of two by 50-60 ◦ N. For each year, the two aerosol modelslead to similar shapes, and in the 50-70 ◦ range the twomodels agree that there is a crossover in which the 2015vmr declines from 50 ◦ to 70 ◦ , while the 2012 vmr risesslightly over the same interval.The fitted values of the methane relative humidity justabove the condensation level, shown in Fig. 22B, haveconsiderable uncertainty. But both results indicate apeak near 20 ◦ N, a clear local minimum near the equa-tor, and a strong decline towards the north pole. Thisis suggestive of rising motions near 20 ◦ and descendingmotions near the equator and poles, with the latter beingmore significant. The effects of particle absorption on derived methaneamounts
The modeling results presented so far are for conser-vative particles ( ̟ = 1.0). Particles that absorb somefraction of the incident light will act to darken the at-mosphere and reduce the amount of methane neededto fit the spectrum. This is true even if the parti-cles are not distributed vertically in the same fashionas methane, and even though they lack the band struc-ture of methane. The aerosol optical depths and derivedpressure locations of the layers are also altered. To in-vestigate the magnitude of these effects we did fits of the2 Mie layer model to the 2015 STIS observations, underthe assumption of vertically uniform methane, but withthe imaginary index of the tropospheric layer increasedfrom zero to 0.0049, which, for a 0.3- µ m radius particlewith a real refractive index of 1.8 corresponds to a de-crease in single scattering albedo at 0.8 µ m from ̟ = 1.0 to ̟ ≈ ◦ N, where m nr has increased by almost10% (and m nr - 1 by 28%), increasing the scatteringefficiency substantially. For 60 ◦ N, the changes in m r , m nr , and m od are all substantially smaller. Mostimportantly, the effective deep methane mixing ratio isdecreased by 3% at 10 ◦ N and 7% at 60 ◦ N, which sug-gests that a fair approximation of the latitudinal profilefor absorbing cloud particles can be obtained by scal-ing the profile we derived from conservative scattering.Whether the cloud particles are actually absorbing in the730-900 nm region remains to be determined.For the large-particle solution, we made a similar com-parison, but just for 10 ◦ N and for 2012. In this casethe increase of imaginary index needed to adjust thewavelength dependence (as described above for the small-particle solution) is only from 0 to 6.2 × − , which de-creases the single-scattering albedo for a 1.535 µ m par-ticle with real index 1.225 to ̟ = 0.990 at 0.8 µ m. Al-3 o N 1 diffuse Mie layer (small r, n fit) 148.39 (2015)1 diffuse Mie layer (large r, n fit) 140.80 (2015)1 diffuse HG layer (k_od fit) 151.51 (2015)2 compact Mie layers (small r, n=1.4) 175.05 (2015)2 compact DHG layers (w KT2009 fn) 153.41 (2015)1 diffuse Mie layer (small r, n fit) 192.65 (2012)1 diffuse Mie layer (large r, n fit) 196.26 (2012)1 diffuse HG layer (k_od fit) 192.22 (2012)2 compact Mie layers (small r, n=1.4) 199.77 (2012)2 compact DHG layers (w KT2009 fn) 195.79 (2012) A o N 1 diffuse Mie layer (small r, n fit) 248.62 (2015)1 diffuse Mie layer (large r, n fit) 256.71 (2015)1 diffuse HG layer (k_od fit) 252.65 (2015)2 compact Mie layers (small r, n=1.4) 275.59 (2015)2 compact DHG layers (w KT2009 fn) 253.40 (2015)1 diffuse Mie layer (small r, n fit) 256.71 (2012)1 diffuse Mie layer (large r, n fit) 192.54 (2012)1 diffuse HG layer (k_od fit) 193.30 (2012)2 compact Mie layers (small r, n=1.4) 227.90 (2012)2 compact DHG layers (w KT2009 fn) 187.22 (2012) B Fig. 22.—
Effective deep methane VMR for different aerosol model parameterizations at 10 ◦ N (A) and 60 ◦ N (B). Vertical lines showunweighted mean values for 2015 (dashed) and 2012 (dotted). though this seems like a small change, it produces a 50%increase in optical depth, a 56% increase in the cloudbottom pressure, and a 10.6% decrease in the best-fitmethane mixing ratio, as shown in Table 11. For non-spherical particles in which wavelength-dependent op-tical depths or wavelength dependent phase functionsmight be used to adjust the wavelength dependent I/Fspectrum, there may be no need for absorbing particles,in which case the somewhat higher methane mixing ra-tios may apply.
Fitting latitude-dependent vertically non-uniformmethane depletion models
Alternative models of vertically varying methane
The fits discussed in previous sections have assumedthat the methane profile is vertically uniform from thebottom of our model atmosphere all the way up to themethane condensation level. We have already notedproblems with those fits in the 750 nm region of thespectrum, which suggest that the methane mixing ra-tio likely increases with depth at high latitudes. Thereare also independent physical arguments suggesting thesame characteristic. Sromovsky et al. (2011) pointed outthat extending the very low high latitude mixing ratios to great depths would result in horizontal density gradi-ents over great depths. As a consequence of geostrophicand hydrostatic balance, these gradients would lead tovertical wind shears (Sun et al. 1991). This would re-sult in an enormous wind difference with latitude atthe visible cloud level, which would be inconsistent withthe observed winds of Uranus. Thus, we would ex-pect that the polar depletion would be a relatively shal-low effect, as we have inferred from our previous work(Karkoschka and Tomasko 2009; Sromovsky et al. 2011,2014). As indicated by KT2009, the 2002 spectral obser-vations did not require that methane depletions extend togreat depths, and Sromovsky et al. (2011) showed thatshallow depletions were preferred by the 2002 spectra.This was further supported by de Kleer et al. (2015),who used our descended profile parameterization, fixedthe shape parameter at vx = 2, and constrained thedepth parameter vs latitude using H band spectra. Theyfound a clear latitude trend, with a low-latitude value of1.7 ± ± ◦ Nband, and as deep as 26 +11 − bars in the 60–70 ◦ N band,although at that extreme value the depth parameter isconstrained more by the shape of the profile at muchlower pressures than by any direct sensing of sunlight4
TABLE 10Changes in small-particle best-fit parameter values derived from the STIS 2015 observations, as a result of addingabsorption to aerosol layer 2 by increasing m ni from 0.0 to 0.005. ◦ N Latitude 60 ◦ N LatitudeParameter Value Value Value ValueName m ni = 0 m ni = 0.005 Difference m ni = 0 m ni = 0.005 Difference m od m pt (bar) 1.126 1.127 0.14% 1.023 1.032 0.87% m pb (bar) 2.450 2.993 22.12% 2.519 2.968 17.79% m r ( µ m) 0.342 0.307 -10.16% 0.248 0.256 2.89% m nr α ×
100 3.160 3.060 -3.16% 0.989 0.916 -7.38% ch rhc χ TABLE 11Changes in large-particle best-fit parameter valuesderived from the STIS 2015 observations, as a result ofadding absorption to aerosol layer 2 by increasing m ni from zero to 6.2 × − . ◦ N LatitudeParameter Value ValueName m ni = 0 m ni = 6.2 × − Difference m od m pt (bar) 1.094 1.112 1.64% m pb (bar) 2.675 4.183 56.39% m r ( µ m) 1.535 1.597 4.01% m nr α ×
100 2.560 2.290 -10.55% ch rhc χ reflected from the 26-bar level.From the previous discussion, we expect a reasonablephysical model has some pressure value P d for whichthe methane mixing ratio is independent of latitude for P > P d , but allows a decline in mixing ratio with lat-itude for P < P d . We assume that the highest mixingratio we observe at low latitudes (which turns out to beat 10 ◦ N) is representative of the deep mixing ratio andassume all of the variation with latitude is a depletionrelative to that level. Here we describe the results of fit-ting two alternative vertically varying depletion models:the descended profile model described in Fig. 14A andEq. 4, and the step function depletion described in Fig.14B. Both options result in improved fit quality at highlatitudes, with depletions confined to the upper tropo-sphere.We first consider the stepped depletion model shownin Fig. 14B because it is easier to constrain its bottomboundary at all latitudes. A more detailed look at the60 ◦ N spectrum from 2012 in comparison with a model fitusing a vertically uniform methane mixing ratio is shown in Fig. 23A-C, while our best fit model for the steppedmethane profile is displayed in Fig. 23D-F. Here we as-sume that the deep mixing ratio is equal to the 10 ◦ Nbest fit uniform VMR value of 3.14%, and optimize thedepleted mixing ratio α and the depth of the depletion P d to minimize χ . The result is seen to be a substan-tial improvement of the fit in the 750-nm region, withminor improvements in other areas, with an overall sig-nificant reduction in χ for the entire fit from 196.02 to160.72. The fact that the difference plots show strongfeatures in the vicinity of large slopes in the spectrum,particularly at 0.88 µ m, suggests that there may be aslight error in the STIS wavelength scale. If we move theobserved spectrum just 0.24 nm towards shorter wave-lengths, these χ values can be reduced to 170.02 and137.93 respectively. (Although the STIS wavelengths arevery accurate up to 653 nm because of the availabilityof numerous Fraunhofer calibration lines, longer wave-lengths require extrapolation that allows errors of thissize.) The best fit values for the methane profile parame-ters are ch vx = 0.73 ± P d = 3.0 +3 . − . bars. Themethane value is a little below the 0.93 ± ±
16% for the uniform case and 67 ±
32% for theupper tropospheric depletion case. The uncertainty inthe depth of depletion ( P d ) is much larger on the highside because the sensitivity to that parameter decreaseswith depth.We also tried fits with the descended depletion functiondescribed in Fig. 14A and Eq. 4, which is defined bya shape parameter vx and a depth parameter P d . Wefound the depth parameter difficult to constrain becausethe rate of change of mixing ratio with depth can become quite small for large depths due to the shape of thefunction. However, fixing P d at 5 bars, and using just the5 I/ F -0.010.000.010.02 M ode l - M ea s µ m) -2-1012 D i ff/ U n c χ = 196.02STIS OBS from 60 o N 2012UNIFORM METHANE MODELCH VMR = 0.93 % for P > Pcond
ABC I/ F -0.010.000.010.02 M ode l - M ea s µ m) -2-1012 D i ff/ U n c χ = 160.72STIS OBS from 60 o N 2012UPPER TROPOSPHERICMETHANE DEPLETION MODELCH VMR = 0.73% from Pcond to 3 bars,CH VMR = 3.15% for P > 3 bars.
DEF
Fig. 23.—
Detailed comparison of 60 ◦ N 2012 STIS observations with best-fit model spectra assuming vertically uniform methane VMR(A-C) and with model calculations assuming a step-function change in methane VMR (D-F), where observations are plotted as continuouscurves and models as colored points, using red, green, and blue for µ values of 0.3, 0.5, and 0.7 respectively. Below each spectral plot areplots of model minus observation (B and E) and the same difference divided the expected uncertainty (C and F). Methane profiles aredescribed in the legends. shape parameter to control the depletion, we obtaineda χ value of 167.34 and a shape parameter of vx =1.22 ± ◦ N observation as inFig. 23. Thus, a descended depletion fit is also viable,and probably a more realistic vertical variation than thestep function. The advantage of the step function is thatboth parameters can be fit without too much difficulty.
Latitude dependent fits with a stepped depletion ofmethane
Here we describe the results of assuming a stepped de-pletion of methane, parameterized by one fixed parame-ter ( α , the deep methane VMR, which is set to 0.0315)and two adjustable parameters ( P d , the pressure at whichthe step occurs and α , the decreased mixing ratio be-6tween that level and the condensation level (which is afunction of the decreased methane VMR). In addition tofitting these two parameters, we fit the usual aerosol pa-rameters and the methane relative humidity above thecondensation level, resulting in a net increase of one ad-justable parameter, for a new total of nine. The best-fitparameter values and their uncertainties are given at 10 ◦ latitude intervals for both 2012 and 2015 in Table 12.These are plotted versus latitude in the left column ofFig. 24 and comparisons of model and observed spectraare displayed in the right column.The best-fit methane depletion depth parameter valuesare shown by dashed lines in panel B of Fig. 24 for P d and by dotted lines in panel D for α . At high latitudesthe latter is near 0.8%, and increases somewhat at lowlatitudes, but becomes very uncertain at low latitudes,which is a result of having less and less influence on thespectrum as the depth of the depletion decreases towardsthe condensation level. As shown in panel D, the deple-tion depth is in the 3-5 bar range from 70 ◦ N down toabout 50 ◦ N, and then declines to nearly the condensa-tion level by 20 ◦ N, and at low latitudes there is almost nodepletion. The improvement in fit quality is significantat high latitudes.In comparison with the uniform methane fit results, wesee only minor changes in most of the other parameters.The top pressure of the tropospheric cloud layer is nearlythe same for both models, although the stepped depletionmodel results show a little more variability. The retrievedbottom pressure shows more significant changes. Thenew results show much closer agreement between years,but more change with respect to latitude, increasing fromabout 2.5 bars at low latitude to 3 bars at high latitude.The prior results showed no consistent trend with lati-tude, averaging about 2.7 bars. The optical depth forthat layer shows about the same trend with latitude andthe same increase at high latitudes between 2012 and2015. The particle size generally remains between 0.2and 0.4 µ m for both models, but the descended modelfits indicate that particles in the northern hemisphere areabout 40% larger in 2015 than in 2012, while the uni-form model showed much less difference between years.All these particle size differences are within uncertain-ties, however. The relative humidity results for methaneare roughly similar for the two model types, with higher,near saturation levels at low latitudes and a factor of twodecline in the polar region. Both find the methane hu-midity depressed at the equator, with a slightly sharperdecline seen in the descended profile results. The refractive index results differ a little. For the de-scended depletion model fits for 2012 and 2013 are insomewhat better agreement than for the uniform model,and do not show as much trending towards slightly highervalues at high latitudes. Latitude dependent fits with descended depletion ofmethane
Because the descended depletion function approachesthe deep mixing ratio on a tangent, it is hard to constrainthe depth parameter for this model at most latitudes.Thus, from preliminary fits we found a P d value thatworked well at high latitudes ( P d = 5 bars) and keptthat constant, while using just the shape parameter ( vx )as the additional adjustable parameter in maximizing fitquality as a function of latitude. The results for best fitparameter values and uncertainties are given in Table 13and plotted in Fig. 25.These two depletion model fits are compared in Fig. 26,with descended model fits in panel A and the steppeddepletion model fits in panel B. The descended modelfits yield slightly lower χ values, especially at 70 ◦ N,although even there the difference is smaller than theexpected uncertainty of p χ , which is 22 in this case.Both models imply that the high latitude depletion isof limited depth, and both imply that the methane hu-midity above the 1 bar level is near saturation at lowlatitudes and decreases poleward. Not only can we ob-tain good fits with a shallow depletion of methane, theyare preferred on the basis of fit quality. Not only doesthe high latitude fit near 745 nm improve significantlywhen the vertically varying depletion models are used,but the overall χ at high latitudes is also significantlyimproved, as illustrated in Fig. 27. This is especially ap-parent at the higher latitudes and in comparing averagesover the 50 ◦ – 70 ◦ latitude range. Although the steppeddepletion model is seen to yield slightly better χ val-ues than the descended depletion models, the differenceis less than the expected uncertainty. The virtue of thestepped depletion model is that it can be well constrainedat all latitudes, while the virtue of the descended deple-tion model is that it makes more sense physically. Wewere able to extend the latitude range of the descendedmodel fits by fixing the value of the depth parameter P d to 5.0 bars. We then found that both depletion modelsdo not quite yield zero depletion at low latitudes, whichone might interpret to mean that we should have cho-sen a slightly lower deep methane VMR value. However,the χ values for the vertically uniform values are just as7 -20 0 20 40 60 80 3.53.02.52.01.51.00.5 R ea l i nde x o r P ( ba r) Case 24: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)m2_pbm2_ptm2_n m2_pbm2_ptm2_n -20 0 20 40 60 8010 -1 R ad i u s ( µ m ) , op t i c a l dep t h , o r p ( ba r) m2_odm2_rpd m2_odm2_rm2_rpdpd -20 0 20 40 60 80 0.00.51.01.52.0 CH RH ch4rhcch4rhc ch4rhc -20 0 20 40 60 80 0.0000.0050.0100.0150.020 D ep l e t ed CH v m r α α STIS 2012STIS 2015 -20 0 20 40 60 80Planetographic Latitude (deg)0.40.60.81.01.21.4 χ / ( N F ) complx2 error model Nfree= 309Nfree= 309 EDCBA I/ F LAT = 10 o , χ = 144.54, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 239.38, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 192.40, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 160.72, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 Case 24: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P)
IHGF
Fig. 24.—
Stepped depletion model of vertical methane distribution fit to STIS spectra from 2012 and 2015. Conservative cloud modeland gas profile parameters for a Mie-scattering haze above a single diffuse Mie-scattering tropospheric layer, assuming a deep mixing ratioof α = 0.0315, and a methane profile characterized by a pressure depth parameter P d and a depleted mixing ratio α (defined in Fig. 14)and constrained by spectral observations from 730 nm to 900 nm. The parameter values are in panels A-E, with red (open circle) pointsdisplaying results of fitting 2012 STIS observations and black (filled circle) points displaying the results of fitting 2015 observations. Samplecomparisons between measured and large-particle model spectra are in panels F-I. Note the great improvement in the high latitude fitsnear 745 nm, compared to results given in Fig. 20. good or slightly better than the depleted models at lowlatitudes. Wavelength dependence issues
Although the best-fit parameters given in Table 7 pro-vide great spectral matches over the fitted range (730–900 nm), they do not provide good matches over theentire range. As expected, and as illustrated in Fig. 28,the corresponding model spectra fit even worse over therest of the wavelength range than the initial fit shown inFig. 16. The problem with both the small-particle andlarge-particle models is that they do not produce a largeenough I/F at the short wavelength side of the spectrum(from 0.54 µ m to 0.68 µ m) for the two largest zenith an-gle cosines, and produce too high an I/F in the deeplypenetrating region near 0.94 µ m for all three zenith an- gles. The problem is less extreme for the small-particlesolution because it produces a larger increase in I/F atshorter wavelengths.One way to solve the short wavelength deficit prob-lem is to abandon spherical particles and use awavelength-dependent phase function that provides in-creased backscatter at short wavelengths, which is theapproach followed by KT2009, and one which we willreturn to in a later section. An alternative approachconsidered here is to use a wavelength-dependent imagi-nary index that is small at short wavelengths and largerat long wavelengths, an approach used by Irwin et al.(2015) to solve a similar problem in fitting near-IR spec-tra. The utility of this approach is that the increasedoptical depth required to compensate for the small ab-sorption at long wavelengths leads to a needed increase8 TABLE 12Single tropospheric Mie layer fits to the 730-900 nm spectra as a function of latitude assuming stepped depletion of CH below the condensation level. Lat. m od m pt m pb m r α P d ( ◦ ) × m od (bar) (bar) ( µ m ) m nr ch rhc (%) (bar) χ YR-10 3.5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± NOTE: The optical depth is for a wavelength of 0.5 µ m. These fits used 318 points of comparisonand fit 8 parameters, for a nominal value of NF=310, for which the normalized χ /NF ranged from0.426 to 0.87.in the I/F at short wavelengths where the absorptionis absent. To follow up on this approach we added anadjustable imaginary index to cloud particles in the m2Mie layer, and then optimized model parameters to fitboth the 730–900 nm region and the 540-580 nm regionsimultaneously, as described in the following section. Controlling wavelength dependence with particulateabsorption
The first example of controlling wavelength depen-dence over a larger spectral range is based on adjustmentof particulate absorption. For this example, we assumetwo Mie scattering clouds, with the top layer (m1) lo-cated at an arbitrary pressure of 50 mbar and containingconservative particles with an assumed effective radius of0.06 µ m, and an adjustable optical depth. The top layerhas a very small optical depth and its particle size is notvery well constrained by our observations. We chose a somewhat arbitrarily value based on preliminary fittedvalues. The Rages et al. (1991) haze model estimates aparticle size closer to 0.1 µ m at 50 mbar. The other Mielayer is assumed to be composed of a non-conservativematerial, characterized by a refractive index of m nr +0 × i for λ <
700 nm and n = m nr + m ni × i for λ >
710 nm. The tropospheric Mie layers (m2) is charac-terized by three additional fitted parameters: pressure,particle size, and optical depth. We then simultaneouslyfit just two sub regions of the spectrum: the 540-580nm region, where we assume the particles are conser-vative, and the 730–900 nm region, where we assumea locally wavelength-independent imaginary index thatis adjusted to minimize χ . We also allowed m nr tobe adjustable. This process produced a best-fit value of(4.9 ± × − for the imaginary index and 2.7 ± -20 0 20 40 60 80 3.53.02.52.01.51.00.5 P r e ss u r e ( ba r) Case 26: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P), descended CH4 with CH4v0=3.15% and Pd=5 barsm2_pbm2_ptm2_n m2_pbm2_ptm2_n -20 0 20 40 60 8010 -2 -1 R ad i u s ( µ m ) , o r O p t i c a l dep t h m1_odm2_odm2_r m1_odm1_odm2_odm2_rm2_r -20 0 20 40 60 80 0.00.51.01.5 CH RH ch4rhcch4rhc ch4rhc -20 0 20 40 60 80 110 S hape pa r a m e t e r vx vx vxSTIS 2012STIS 2015 -20 0 20 40 60 80Planetographic Latitude (deg)0.40.60.81.01.21.4 χ / ( N F ) complx2 error model Nfree= 310Nfree= 310 EDCBA I/ F LAT = 10 o , χ = 153.03, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 60 o , χ = 242.69, YEAR = 2015 µ = 0.30 µ = 0.50 µ = 0.70 I/ F LAT = 10 o , χ = 193.20, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 µ m)0.00.10.20.3 I/ F LAT = 60 o , χ = 168.19, YEAR = 2012 µ = 0.30 µ = 0.50 µ = 0.70 Case 26: 2-layer Mie model small r2 fit to 730-900 nm, 2012, 2015 STIS obs.Orton T(P), descended CH4 with CH4v0=3.15% and Pd=5 bars
IHGF
Fig. 25.—
Descended depletion model of vertical methane distribution fit to STIS spectra from 2012 and 2015. Conservative cloud modeland gas profile parameters for a Mie-scattering haze above a single diffuse Mie-scattering tropospheric layer, assuming a deep mixing ratioof 0.0315, and a methane profile characterized by a pressure depth parameter P d and a shape parameter vx (defined in Eq. 4 and illustratedin Fig. 14) and constrained by spectral observations from 730 nm to 900 nm. The parameter values are in panels A-E, with red (open circle)points displaying results of fitting 2012 STIS observations and black (filled circle) points displaying the results of fitting 2015 observations.Sample comparisons between measured and large-particle model spectra are in panels F-I. Note the great improvement in the high latitudefits near 745 nm, compared to results given in Fig. 20. cess slightly degraded the fit in the 730-900 nm region.To better constrain the methane mixing ratio for the casewith absorbing aerosols we adopted the imaginary indexobtained from the dual fit, then refit the remaining pa-rameters using the 730-900 nm region for our spectralconstraints, yielding the results given in Table 10. Ap-plying these parameters over the entire spectral rangefrom 540 nm to 960 nm, we then obtained a much im-proved match to the observations, with a χ of 724.50.This was further improved to 586.32 by optimizing valuesof m pt (1.09 ± m pb (3.35 ± m od (0.030 ± m od (3.91 ± m r (0.30 ± m nr (1.69 ± m nilw (0.0051 ± S does not appear to exhibit such a trend either. Thuswe have some motivation to consider other ways to gen-erate wavelength dependence.
Controlling λ dependence with optical depthvariations Although Mie scattering calculations for spherical par-ticles produce wavelength dependent optical depth andscattering phase functions, if these do not yield needed0
TABLE 13Two-cloud spherical particle fits as a function of latitude assuming descended depletion of CH as a function oflatitude. Lat. m od m pt m pb m r ( ◦ ) × m od (bar) (bar) ( µ m ) m nr ch rhc vx χ YR-10 3.3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± NOTE: The optical depth is for a wavelength of 0.5 µ m. These fits used a fixed value of P d = 5bars, α = 3.15%. There were 318 points of comparison and 8 fitted parameters, for a nominal valueof NF=310, for which the normalized χ /NF ranged from 0.42 to 0.83.dependencies, and if particle size is constrained, andwavelength-dependent absorption is not acceptable, thennon-spherical particles need to be considered.The simplest option is to use a single HG scatteringphase function and simply adjust the wavelength depen-dence of the optical depth to match the observed spectralvariation. An increase in optical depth with size param-eter (2 πr/λ ) is certainly a characteristic shared by mostparticles and by aggregates in our trial calculations. Italso is plausible that a non-spherical particle might ex-hibit a greater λ dependence in optical depth than aspherical particle for the case in which both particlessatisfy the other constraints in the 730-900 nm region.To define the needed τ ( λ ) function we began by tak-ing our best fit vertical structure and asymmetry fit forthe 730-900 nm region, then computed a series of modelspectra with optical depths increasing until we could find an optical depth at any wavelength that would matchthe observed I/F at that wavelength. But we found aproblem with this approach. At short wavelengths, theoptical depth needed to match two successive continuumregions (e.g. at 560 nm and 585 nm) was about 4-5 timesthe value at 800 nm that was derived from fits to the 730-900 nm region. But to match the intervening absorptionfeature at 576 nm would require about half of that opti-cal depth. Thus a smoothly varying optical depth func-tion could not be created in this fashion, and a functionthat included wiggles at all the methane features wascompletely implausible. The fix to this problem was todistribute the cloud particles over a greater atmosphericdepth. This would not change the continuum I/F valuesvery much, but in the weakly absorbing regions, therewould be more absorption. At longer wavelengths thisrequired an increase in the cloud’s optical depth, which1 -5 -4 -3 -2 -1 Methane Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) -5 -4 -3 -2 -1 Methane Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) Pcond= 1.13 bars A DESCENDED PROFILE MODELS o N χ = 173.1130 o N χ = 152.9050 o N χ = 213.4670 o N χ = 235.07 CH S a t u r a t i on P r o f il e -5 -4 -3 -2 -1 Methane Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) -5 -4 -3 -2 -1 Methane Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) B CH S a t u r a t i on P r o f il e STEPPED DEPLETION MODELS o N χ = 168.4730 o N χ = 154.6450 o N χ = 212.3270 o N χ = 235.58 Fig. 26.—
A: Best-fit descended profiles at 4 latitudes, using average parameter fits for 2012 and 2015. B: Best fit stepped depletionprofiles, using average parameter fits for 2012 and 2015. The profiles in A are overlain in light gray in B for reference. Both sets of fitsshow decreasing methane humidity with latitude above the 1 bar level, and both indicate that the depletion is of limited depth ( ∼ χ values for 2012 and 2015 are given in the legend. -20 0 20 40 60 80Planetographic Latitude (deg)100150200250300 χ Vertically uniform CH Descended depletionStepped depletion o - o A v g . -20 0 20 40 60 80Planetographic Latitude (deg)100150200250300 χ Vertically uniform CH Descended depletionStepped depletion o - o A v g . Fig. 27.—
Comparison of 2012 (left) and 2015 (right) χ versus latitude values for for three different methane vertical distributionmodels: uniform (solid line), descended depletion (dotted line), and stepped depletion (dashed line). Corresponding averages over the 50 ◦ – 70 ◦ latitude range are also shown near 80 ◦ N in each panel. The depleted profile values are slightly shifted in latitude to avoid error baroverlaps. This shows that the overall fit quality is improved by use of the descended profile, in addition to the more obvious improvementnear 750 nm. The small overall improvement seen in fits to the 2015 observations is likely due to the increased noise level at high latitudesand low signal levels for this data set. in turn required readjustment of the optical depth ratiobetween 800 nm and 540 nm. The result of this processapplied to our model of the 2015 STIS spectrum at 10 ◦ Nis shown in Fig. 30.
Controlling λ dependence with phase functionvariations KT2009 assumed that the main tropospheric cloudlayer had a wavelength-independent optical depth, whichis a plausible assumption for large particles, and used awavelength dependent phase function to match the ob-served spectral variation. A general form of their func- tion can be written as f ( λ ) = a − b × sin α [ π λ o − λ ) / ( λ − λ )] , (6) λ ≤ λ ≤ λ o in which KT2009 assumed α = 4, a = 0 . b = 0 . λ = 1 µ m, and λ = 0 . µ m, which makes f reach amaximum of 0.94 at a wavelength of 1 µ m and a mini-mum of 0.513 at 0.3 µ m. They applied this to a doubleHG function with adopted values of g = 0.7 and g =-0.3. (Note that there is no basis for applying this func-tion to wavelengths greater than 1 µ m or less than 0.3 µ m.) We found that this function was able to fit low2 I/ F χ = 1732.43 (for total range)Measured spectrum displayed as solid linesBest fit model displayed as colored points: µ = 0.3 µ = 0.5 µ = 0.7 M ode l / M ea s . µ m)-8-6-4-202 ( M ode l - M ea s . ) / U n c e r t. fitted rangeParams_from_Mie_conservative_730-900nm_fit_Dec10-191250-2017.tabPlanetographic Latitude = 10 o Nplot_spec_anal.pro: CASENUM = 2
Fig. 28.—
As in Fig. 16, except 10 ◦ N spectral comparisons are shown for a conservative cloud model that provide the best match to the10 ◦ N 2015 STIS spectra from 730 nm to 850 nm, using the small particle solution. Note the significant model falloff at shorter wavelengths.See text for implications. I/ F M ode l / M ea s µ m)-6-4-2024 D i ff/ U n c χ = 586.32 χ = 159.10 (0.54 - 0.67 µ m)STIS obs. from 10 o N 2015 stis_fitctl_spec_glats-30.00to87.00year2015mulim0.175Jun10-155158-2016limbcorr2.88nm.unf_lmfit_May14-184627-2018.tabplot_spec_comparisons.proCASENUM = 10
Fig. 29.—
Extended range wavelength dependent model, using imaginary index variations to adjust the wavelength dependence. Theimaginary index m ni , multiplied by a factor of 100, is shown by the dashed curve. latitude spectra over the 730 nm to 900 nm range quitewell, but that the a and b constants needed to vary withlatitude and that we needed to increase g , leading us toadopt a new value of 0.8. When applied to the extendedspectral range, we needed to increase λ to about 0.45 and α to 5. The resulting spectral match was intermedi-ate between those shown in Figs. 29 and 30. A problemwith this formulation is that extending the idea to longerwavelengths would require the particles to become moreand more forward scattering at longer wavelengths (in3 I/ F M ode l / M ea s µ m)-6-4-2024 D i ff/ U n c χ = 889.49STIS OBS from 10 o N 2015 stis_fitctl_spec_glats-30.00to87.00year2015mulim0.175Jun10-155158-2016limbcorr2.88nm.unf_lmfit_Dec14-111419-2017.tabplot_spec_comparisons.proCASENUM = 8
Fig. 30.—
Extended range wavelength dependent model for HG particles, using an optical depth variation with wavelength adjusted tomatch the 2015 STIS observations at 10 ◦ N. The dashed curve displays the wavelength dependent optical depth normalized by its value at800 nm, then scaled downward by a factor of 10. order to produce the same effect that absorbing Mie par-ticles produce, as discussed later). This is not a plausibletrend. For large enough wavelengths the particles mustbecome less forward scattering.We also considered whether the HG model could usea wavelength-dependent asymmetry parameter insteadof a wavelength dependent optical depth to match theobserved spectrum over a wider spectral range. How-ever, matching the shorter wavelengths required a nega-tive asymmetry parameter, which is an implausible con-dition, and thus not an acceptable solution.Thus over the longer spectral ranges it is most likelythat optical depth variation and possible particulate ab-sorption will be needed to model reflected spectra. Phasefunction variations will also be present, but cannot be thesole way to produce the needed wavelength dependencein scattering properties.
Two-layer Mie model applied to Near-IR spectra
To test whether our 2-layer Mie models would be capa-ble of fitting near-IR spectra, we extended model calcula-tions to 1.6 µ m and compared them to a central meridianSpeX spectrum covering the 0.8–1.65 µ m range. [We ob-tained this spectrum from the Infrared Telescope Facilityon 18 August 2013, using the cross-dispersed mode of theSpeX spectrometer. The spectrum was spatially aver- aged over the central 0.4 arcseconds of the central merid-ian covered by the 0.15-arcsecond slit, corresponding toan average latitude of 24 ◦ N. It was spectrally smoothedto the same spectral resolution as the smoothed STISspectrum (a FWHM of 2.88 nm). The spectrum wasscaled to match the 1.09 × − I/F center-of-disk H-bandI/F from Sromovsky and Fry (2007).] The initial small-particle model parameters we used were from the 20 ◦ Nspectrum and used an imaginary index of 0.0046 at allwavelengths longer than 730 nm. For the initial large-particle model, we used a fit to the 10 ◦ N spectrum andused an imaginary index of 6.2 × − for λ >
730 nm.The smaller index for the large particle solution is a resultof the lower real refractive index for the best-fit largerparticles.Fig. 31 shows that the extended models agree well inthe dark regions of the spectrum, indicating that littlechange in stratospheric haze properties is needed, butis far too bright in the longer wavelength continuum re-gions, indicating that the real cloud particles have, atlonger wavelengths, a lower optical depth or greater ab-sorption than the model particles. The large particlesolution is the worst offender because its scattering effi-ciency is a relatively weak function of wavelength, whilethe scattering efficiency of the smaller particles declinessubstantially, though not enough to match the falloff in4pseudo continuum I/F values with wavelength.The excess model I/F at these wavelengths can be re-duced by increasing the imaginary index as indicated inthe bottom panel of Fig. 31. Our procedure for devel-oping these solutions was to start with a conservativesolution constrained by the 730-900 nm spectrum. Wethen used that as an initial guess for a split fit of the540-580 nm plus 730-900 nm region, assuming that theimaginary index was zero for λ ≤
580 nm and had anadjustable value of m nilw for for λ ≥
730 nm. Fromthat we obtained an estimate for the imaginary index inthe 730-900 nm region. We then fixed that imaginaryindex and did a new fit within the 730-900 nm region toget a revised estimate of the methane profile. We thenfixed the methane profile and used a second split fit toimprove the optical depth and vertical aerosol distribu-tions, as well as particle size and real index. We thenadjusted the imaginary index in the 670-730 nm rangeto optimize the fit to that part of the spectrum. Thatprovided the parameters used for the initial near-IR cal-culations. To match the near-IR spectrum we did a suiteof forward calculations with different constant imaginaryindex values to find in each wavelength region the imag-inary index that provided the best model match to theobservations. This was not done at a fine wavelengthresolution in an attempt to match every detail becausethe solid materials making up the cloud particles wouldnot likely have such fine-scale absorption features.This figure shows that the STIS-based model with twolayers of small spherical particles can match the observedinfrared spectrum out to 1.65 µ m by increasing the imag-inary index with wavelength as shown in Fig. 31, reach-ing a maximum of 0.1 for the H-band region. Our in-dex is generally larger than the imaginary index esti-mated by Irwin et al. (2015) although of roughly sim-ilar shape. Our mean value in the H band is similarto the adopted value of de Kleer et al. (2015). Our fit-ted real index of 1.72 ± µ m particles. Irwin et al.suggested that the refractive index spectrum would allow us to determine the composition of the cloud particles.However, the most likely cloud material (H S) does nothave well characterized (quantitative) absorption proper-ties, and frost reflection spectra between 1.2 and 1.6 µ m(Fink and Sill 1982) provide little qualitative evidencefor significant absorption of the type we seem to need tomatch the observed spectrum.We could also have modeled the drop in I/F at longerwavelengths using a HG particle scattering model, eitherby varying the single-scattering albedo with wavelength,or by varying the optical depth as a function of wave-length. It is left for future work to evaluate which sortof variation provides the best overall compatibility withthe observations.Although our modified imaginary index allows our twocloud model to closely reproduce the observed spectrumin most regions, there are some problems that need fur-ther work to address. First, note that at the 1.08- µ m con-tinuum peak, the model contains modulations that arenot observed in the measured spectrum. This is also thecase for model calculations shown by Tice et al. (2013),and is an indication of a possible flaw in our commonlyused absorption coefficients in this region.There is also a relatively sharp feature at 1.1 µ m that ismuch larger in the model than in the observations. Fur-ther, the detailed shape of the pseudo continuum peaknear 1.27 µ m is not fit very well. DISCUSSION
Why occultation constrained fits produced largermethane VMR values
Given the previous discussion of methane depletionprofiles, this might be a good point at which to com-pare the methane profiles in Fig. 26 with those obtainedfrom the occultation analysis of Lindal et al. (1987) orSromovsky et al. (2014). This is provided in Fig. 32,where we also show the results of Orton et al. (2014b)and Lellouch et al. (2015). The main regions of sen-sitivity to the methane VMR values are indicated bythicker lines for our current STIS results and those ofLellouch et al. (2015). Note that our current STIS re-sults at 30 ◦ N are in very good agreement with the Lel-louch et al. results where they have overlapping sen-sitivity (roughly the 200–700 mbar range). Both haverelatively high methane relative humidities compared tothe saturation vapor pressure profile computed for theOrton et al. (2014a) thermal profile. The occultation re-sults for methane are at much lower levels at pressuresless than the putative methane condensation pressure5 I/ F λ ) as in C M ode l / M ea s . µ m)0.0010.0100.100 I m ag i na r y i nde x I r w i n e t a l . ( ) This work (small r)This work (large r) de Kleer et al. (2015)
Planetographic Latitude = 24 o Nplot_spec_anal.pro: CASENUM = 10
CBA
Fig. 31.—
A: Our 2013 SpeX near-IR spectrum of Uranus from latitude 24 ◦ N (black) compared to model spectra for the same observinggeometry but using the gas and aerosol parameters from the 20 ◦ N two-layer Mie scattering model for two particle size solutions: small-particle (line only) and large-particle (lines with points). The same models, extended to the near-IR by adjusting the imaginary index ofthe cloud particles, are shown in red. In the first model set of models, a vertically uniform methane mixing ratio of 2.65% was assumed upto the methane condensation level. In the second set (red curves) a deep mixing ratio of 3.15% was assumed and a descended depletionprofile shape was used, with vx = 7.34 an Pd = 5 bars. B: ratio of model spectra to the SpeX observed spectrum. C: Imaginary indexspectra assumed in the second set of models (red), compared to imaginary index values derived by Irwin et al. (2015) and a value inferredfrom a single scattering albedo used by de Kleer et al. (2015). (about 1.2 bars). In the occultation analysis, temper-ature and methane profiles are linked. Both tempera-ture and composition affect density, which in turn af-fect refractivity versus altitude, which is the main resultproduced from the radio measurements. The refractiv-ity profile can be matched by a family of thermal andcorresponding methane profiles. A hotter atmosphere isless dense, and thus allows more methane to produce thesame refractivity. Because the occultation profiles havesuch low relative methane humidities above the cloudlevel compared to what the STIS spectra require to ob-tain the best fits, the hottest occultation profile is fa-vored. If the only allowed adjustment of methane is se-lection of the optimum occultation profile, as was the case for our previous analyses (Sromovsky et al. 2011,2014), then we obtain a deep mixing ratio that is rela-tively high (4%) so that the methane mixing ratio nearand above the cloud level can approach closer to the levelneeded to provide the best spectral match. As an exam-ple of this behavior, we carried out fits of STIS spectraat 10 ◦ N, using STIS spectral fit quality as the only con-straint, and compared that to the best fits obtained forprofiles with fixed occultation consistent methane verti-cal profiles. The results, tabulated in the legend of Fig.32, show that all the occultation fits are much worsethan the STIS-only constrained fits, and that the best ofthe occultation constrained fits (for the F profile) is forthe hottest profile, which provides the most upper tropo-6spheric methane, even though that has a deep methaneVMR that is much higher than is needed if one does notforce the methane to fit an occultation profile. Just be-low the cloud level, the methane VMR at low latitudesis closer to 2% at least in the region above the lowertropospheric clouds (near 2.5 bars) and perhaps deeper,although the STIS spectra are not sensitive to valuesdeeper than that. -5 -4 -3 -2 -1 Methane Volume Mixing Ratio -1 A t m o s phe r i c P r e ss u r e ( ba r) F1D1FD 3.42 9.42 1.72 5.51 χ ratioto STIS fitOccultationprofiles Lellouch et al. (2015)STIS fit at 30 o NOrton et al. (2014)
Fig. 32.—
Comparison of methane profiles derived from STIS-constrained and other spectral observations by Lellouch et al.(2015) and Orton et al. (2014b) compared to those derived from oc-cultation observations by Lindal et al. (1987) and Sromovsky et al.(2011). The 4% deep methane VMR occultation profiles providebetter agreement with STIS-constrained results in the upper tro-posphere. But without occultation constraints, the preferred deepmixing ratio is closer to 3% for most aerosol models fit to the 730-900 nm spectrum.
Evidence for a deep cloud layer
In our previous paper dealing with earlier STIS obser-vations (Sromovsky et al. 2014), we found that the fitquality at short wavelengths was improved by adding adeep cloud layer, which we fixed at the 5 bar level and as-sumed had the same tropospheric scattering parametersas KT2009. The only adjustable parameter for that layerwas its wavelength-independent optical depth, which wefound to vary from about 4 at low latitudes to about halfthat at high latitudes. It is possible in our current mod-eling that the more extended vertical extent of our uppertropospheric cloud layer serves to reduce the need for thecontribution of a deeper cloud. The main function of thedeeper cloud is to improve the fit in the 540 to 600 nmrange where matching weak methane band depth is eas- ier if some of the aerosol scattering is moved to higherpressures.To provide a better test of the existence of a deepercloud, we looked at spectra with deeper penetration.Choosing a spectrum with a nearly vertical view ( µ =0.9 at 10 ◦ N), we computed simultaneous model spectrafor view angle cosines of µ = 0.3, 0.5, and 0.9, basedon the fit we obtained using the standard set of viewangle cosines ( µ = 0.3, 0.5, and 0.7). That model didnot fit the weak methane bands very well even with thestandard view angles and was even worse for this moredeeply penetrating set. The χ values rose from 586.32to 714.59, with an expected χ uncertainty of 35-40. This χ increase by 128.3 is about three times its uncertainty.However, by refitting the same model (still without adeep cloud) to the new set of view angles, we reducedthe χ value for this new set of angles to 705.84, andthus reducing the difference to 119.5, which is still aboutthree times the expected uncertainty in χ . After in-serting an optically thick deep cloud with an adjustablepressure, a new fit further reduced χ from 705.84 to645.62, a decrease of 59.52, which is about 1.6 times itsuncertainty. A comparison of the latter and initial fitsto the measured spectra is displayed in Fig. 33. The χ improvement is even more dramatic when computed justfor the region from 540 nm through 670 nm. In thatcase the χ change is from 180.53 to 125.17, a decreaseof 75.46, which is over three times the expected uncer-tainty of about 22 for this more limited range that has243 comparison points. The model with a deep cloudalso improved fits at the original set of view (and zenith)angles. Adding that layer to the model plotted in Fig.29 and refitting, decreased χ from 586.32 to 529.95, adecrease of 56.37, with most of this change taking placein the 540-670 nm region where χ dropped from 159.10to 102.47, a decrease by 56.63, which is about 2.6 timesthe expected uncertainty. Thus both sets of view angleslead to significant local fit improvements, with derivedeffective pressures of 10.6 ± ± ± ± µ m)0.20.40.60.8 I/ F Model w/o deep cloud Model with deep cloud χ = 705.84 (0.54 - 0.96 µ m) χ = 180.53 (0.54 - 0.67 µ m) χ = 645.62 (0.54 - 0.96 µ m) χ = 125.17 (0.54 - 0.67 µ m) STIS obs. from 10 o N 2015 (shaded) µ = 0.3, 0.5, 0.9 stis_fitctl_spec_glats-30.00to87.00year2015mulim0.175Jun10-155158-2016limbcorr2.88nm.unf_lmfit_May10-163352-2018.tabstis_fitctl_spec_glats-30.00to87.00year2015mulim0.175Jun10-155158-2016limbcorr2.88nm.unf_lmfit_May10-174307-2018.tabplot_spec_comparisons.proCASENUM = 16 Fig. 33.—
STIS 2015 observations at 10 ◦ N (green shading indi-cating uncertainties), compared to fitted model results without adeep cloud layer (red) and with a deep cloud layer (blue). Theseare for non-standard, more deeply penetrating, zenith angle cosinesof 0.3, 0.5, and 0.7, with largest cosines corresponding to largestI/F values at continuum wavelengths. The legend gives χ valuesfor the entire spectral range that was fitted (0.54 - 0.96 µ m) andfor the region most influenced by the deep cloud (0.54 - 0.70 µ m). cluding its latitude dependence, is left for future work.A plausible composition for such a cloud is NH SH.
Comparison with other models of gas and aerosolstructure on Uranus.
Models of 0.8-1.8 µ m SpeX spectra of Uranus byTice et al. (2013) and more recently by Irwin et al.(2015) and recent models of H-band (1.47-1.8 µ m) spec-tra by de Kleer et al. (2015) present what appear to bedifferent views of the cloud structure from that derivedfrom our STIS observations. Some fraction of the dif-ferences are due to different constraining assumptions.The other authors typically constrain the upper cloudboundary pressure and fit the scale height ratio, whilewe have here mainly assumed a unit scale height ratio(particles uniformly mixed with gas) and treated the up-per boundary pressure as adjustable. The differences areprobably not due to very different conditions on Uranus,as the spectral observations are generally very similar,as illustrated in Fig. 34. These spectra are all obtainednear the center of the disk, and all near latitude 20 ◦ N.In most of the spectral range they are all within 10%of each other. The main exception is the de Kleer et al.(2015) spectrum, which is much brighter than the othertwo spectra in the 1.63-1.8 µ m region. This would pre-sumably lead to a model with much greater stratospherichaze contributions than would be needed to match theother spectra. To better characterize these differencesand better understand their origin, we attempted to re- produce results from these near-IR analyses.The first attempt was to match the Irwin et al. (2015)retrieval of a two-cloud structure from the Tice et al.(2013) 2009 SpeX central meridian data (0.8-1.8 µ mrange). They used 1.6% deep CH with 30% RH abovecondensation level and the Lindal et al. (1987) Model DT(P) profile. They retrieved self-consistent refractiveindexes for their Tropospheric Cloud (TC) and Tropo-spheric Haze (TH), similar to Tice et al. 2-cloud model.They retrieved particle sizes, but used ”combined H-G”phase function fits in the forward modeling, rather thanMie calculations. An additional complication was thattheir plots of optical depth vs pressure were incorrectin the paper (estimated to be about an order of mag-nitude too large, P.G.J. Irwin private communication).That and the uncertain way double HG phase functionswere obtained from the Mie phase functions, led us tonot attempt detailed quantitative comparisons.We decided to make our quantitative comparisons with2-cloud results of Tice et al. (2013). This was moretractable, as the phase functions for both TC (tropo-spheric cloud) and UH (Upper Haze, called TH in Ir-win et al.) were simply H-G phase functions with anassumed asymmetry parameter g = 0.7. They alsoutilized wavelength-dependent optical depths based onMie calculations of extinction efficiency, but they didnot use the wavelength-dependent phase functions orwavelength-dependent asymmetry parameters for eitherparticle mode. Although, for the larger particles in theTC, the asymmetry parameter obtained from Mie calcu-lations is close to their chosen value, the 0.1- µ m parti-cle model has a very small asymmetry, which leads toa backscatter phase function value about ten times thatfor an HG function with g = 0.7. Since their UH (orTH) particles have such small optical depths, their con-tribution can be well approximated by single-scattering,in which case the observed I/F contribution is given by I/F = 14 ̟P ( θ ) τ /µ (7)where θ is the scattering angle (about 180 ◦ in this case), τ is the vertical optical depth, and µ is the cosine of the ob-server zenith angle. This makes the modeled I/F stronglydependent on the assumed phase function, specifically itsbackscatter amplitude. While there is substantial varia-tion in scattering efficiency with wavelength for a 0.1- µ mparticle, such a particle would not have such a stronglyforward peaked phase function, and would probably re-quire roughly a factor of ten lower optical depth thanTice et al. (2013) found for their UH layer. However,8 I/ F o N spectrum2009 SpeX 8 o N from Tice et al. (2015)2010 OSIRIS 10 o S-10 o N spectrum from de Kleer et al. (2015)0.8 1.0 1.2 1.4 1.6 1.8Wavelength ( µ m) S pe c t r u m / S pe X plot_spec_anal.pro: CASENUM = 7 Fig. 34.—
Comparison of near-IR spectra of Uranus. Our 2013 central-disk spectrum is shown in black. The 2009 SpeX central-diskspectrum of Tice et al. (2013) is shown in blue, and the 2010 OSIRIS 10 ◦ S - 10 ◦ N spectrum of de Kleer et al. (2015) in red. The bottompanel plots the ratio of each spectrum to our 2013 SpeX spectrum. using their peculiar scattering characterization for thislayer, and using their more plausible characterizationfor the lower layer, and their chosen single-scatteringalbedos, we were able to roughly match our own 2013SpeX center-of-disk spectra (which are quite similar tothe spectra shown in the Tice paper). Thus we have twodifferent vertical structures that can match the spectra.Ours has a single tropospheric layer uniformly mixed be-tween 1.06 and 3.3 bars (small particle solution), whiletheirs has a very strongly varying optical depth per barbetween their assumed cloud top of 1 bar and their fit-ted bottom at 2.3 bars. We did not attempt to reproducethe more complex structures based on Sromovsky et al.(2011) three- and four-cloud models.We also tried to reproduce de Kleer et al. (2015) re-sults for a 2-cloud model. Their retrievals were for amore limited H-band wavelength range (H-band spec-tra). Their spectra were also similar to our 2013 SpeX re-sults, except their dark regions were as much as 3-4 timesbrighter (see Fig. 34). They used a two-stream radiativetransfer model, with wavelength dependent H-G param-eters based on Mie calculations. Using their retrievedoptical depths, we roughly matched their window I/F.However, we used correlated-k coefficients for Hartmanntype line-shape wings, while de Kleer et al. used the hybrid wing shape from Sromovsky et al. (2012a) thatproduces more absorption in the H-band window. Usingthese c-k coefficients, our I/F values in the methane win-dow were lower than those of de Kleer et al. by a factorof 2 or so. The origin of these differences remain to bedetermined. It is likely that it is not entirely a result ofvery different numbers of streams, as de Kleer et al. didtrial calculations showing that their approximation wasgood to within ∼ n = τ / ( πr Q ext ), where r is the particle radius and Q ext is the extinction efficiency (extinction cross sectiondivided by geometric cross section). From n the mass9loading (mass per unit area) is computed as m = nρπr ,assuming that the particle density ρ is 1 g/cm . Oursmall-particle tropospheric cloud is one of very low main-tenance. It needs very little material to form, the parti-cles fall slowly because they are small, and thus probablya low level of mixing is needed to sustain it. It also hasthe virtue of having a refractive index similar to that ofits potential main component, H S. The large particlecloud is thirty times more massive, with larger particlesthat fall much more quickly, needing much more verticaltransport to be sustained.If these clouds are to be made of H S, it is worth con-sidering whether there is enough H S available to makethem. For a mixing ratio α H S , the mass per unit areaof H S between two pressures separated by ∆P would be(M H S /M) α H S ∆ P/g , where g is gravity (9.748 m/s ),and the ratio of molecular weights of H S to the totalis given by 34/2.3 = 14.78. For H S to condense at thetropospheric (layer-2) cloud base its mixing ratio musthave a minimum value that depends on base pressure asshown in Fig. 36. To condense at the 3.3 bar level wouldrequire the H S VMR to be equal to its the solar mixingratio of 3.1 × − (Lodders 2003). About 10 times thatVMR would be needed to condense as deep as the 5 barlevel and about ten times less would lead to condensa-tion no deeper than the 2.4 bars. Microwave observationsby de Pater et al. (1991) suggest H S is at least a factorof ten above solar. Even for just a 10 ppm mixing ratio,this yields an H S mass loading of 169 mg/cm per bar ofpressure difference. Thus, condensing all the H S in justa 1-bar interval would make 170 times the cloud massthat is inferred for the large-particle solution and morethan 5000 times the mass needed for the small-particlecloud. Thus, none of these clouds is immediately ruledout by lack of condensable supply. A more sophisticatedmicrophysical analysis would be needed to evaluate them,accounting for eddy mixing, coagulation, sedimentation,and other effects. Another test would be to comparemodel spectra for these various distributions with STISspectra at CCD wavelengths. We have verified that ourSTIS-based models can fit near-IR spectra, but the re-verse has not yet been demonstrated for near-IR basedmodels.
SUMMARY AND CONCLUSIONS
We observed Uranus with the HST/STIS instrument in2015, following the same approach as in 2012 and 2002.We aligned the instrument’s slit parallel to the spin axisof Uranus and stepped the slit across the face of Uranusfrom the limb to the center of the planet, building up an image of half the disk with each of 1800 wavelengths from300.4 to 1020 nm. The main purpose was to constrainthe distribution of methane in the atmosphere of Uranus,taking advantage of the wavelength region near 825 nmwhere hydrogen absorption competes with methane ab-sorption and displays a clear spectral signature. Ourrevised analysis approach used a considerably simplifiedcloud structure, relaxed the restriction that methane andthermal profiles should be consistent with radio occul-tation results, considered the new Uranus global meanprofile of Orton et al. (2014a) that was inconsistent withradio occultation results, and included parameters defin-ing the methane profile as part of the adjusted parame-ter sets in fitting observed spectra. This revised analysisapplied to STIS observations of Uranus from 2015 andcomparisons with similar 2002 and 2012 observations, aswell as analysis of HST and Keck/NIRC2 imaging ob-servations from 2007 and 2015, and IRTF SpeX spectrafrom 2013, have led us to the following conclusions.1. TEMPORAL CHANGES1.1 A direct comparison of 2012 STIS spectra with2015 STIS spectra reveals no statistically significantdifference at low latitudes. At 10 ◦ N and a zenithcosine of 0.7, the spectra from the two years arewithin the noise level of the measurements.1.2 A different result is obtained by comparing 2012and 2015 STIS spectra at high latitudes. Therewe find significant differences at pseudo-continuumwavelengths beyond 500 nm, where weaker methanebands are present, and where the 2015 I/F exceeds2012 I/F values by up to 0.04 I/F units (about 15-20%). However, no difference is seen in the strongmethane bands that would be sensitive to changesin stratospheric aerosols.1.3 The brightening of high latitudes at pseudo con-tinuum wavelengths between 2012 and 2015 is a re-sult of increased scattering by tropospheric aerosols,and not due to a change in the effective methanemixing ratio. This is shown by radiation transfermodeling as well as by direct comparisons of imag-ing at wavelengths with different fractions of hydro-gen and methane absorption.1.4 The polar brightening from 2012 to 2015 thatwe found in comparisons of STIS spectra is partof a long-term trend evident from comparisons ofH-band images from the 2007 equinox and on-ward, including recent images obtained in 2017(Fry and Sromovsky 2017).0 -4 -3 -2 -1 Optical depth/bar at 1.6 µ m10.01.00.1 P r e ss u r e ( ba r) This work (small particle)This work (large particle)Tice et al. (2013)Irwin et al. (2015)de Kleer et al. (2015) 0.26 1.52 1.35 0.89 1.00 0.83 13.38 7.00 5.48 2.00 4.42E+08 6.95E+07 3.84E+07 8.09E+07 2.27E+07 0.0329 1.0229 0.3962 0.2390 0.0952r ( µ m) τ TOT
N (/cm ) mg/cm A µ m543210 P r e ss u r e ( ba r) B Fig. 35.—
Comparison of tropospheric cloud density vertical profiles on log scales (A) and linear scales (B). Our small-particle fit isshown with solid lines in both panels, while results from other investigators are shown using lines defined in the legend. The Irwin et al.(2015) result has been scaled downward by a factor of 10, which is a rough correction from what is shown in the left panel their Fig. 2,suggested by P.G.J. Irwin (personal communication). Their profile was derived for a deep methane mixing ratio of 1.6% and would moveupward by several hundred mbar for double that mixing ratio. The Tice et al. (2013) profile was derived using a deep methane mixing ratioof 2.2%, which is also the case for the de Kleer et al. (2015) profile. As noted in the legend, our small-particle model has much less opticaldepth at 1.6 µ m and much less total mass than the other results shown. The estimated total column cloud mass per unit area assumes adensity of 1 g/cm . S cloud base pressure (bar)10 -6 -5 -4 -3 H S c onden s a t i on V M R H S solar abundance
Fig. 36.—
Minimum H S VMR required to condense at the cloudbase versus cloud base pressure.
2. METHANE DISTRIBUTION:2.1 While the increased brightness of the polar region between 2012 and 2015 is due to increased aerosolscattering, the fact that the polar region is muchbrighter than low latitudes in 2015 is due to thelower mixing ratio of upper tropospheric methaneat high latitudes.2.2 We found that the STIS spectra from 2015 and2012 can be well fit by relatively simple aerosolstructures. We used a two-layer cloud structurewith an optically thin stratospheric haze, and onetropospheric cloud, the latter extending from near1 bar to several bars. This is similar to the 2-cloudmodel of Tice et al. (2013) except that we fit theupper boundary instead of fixing the upper bound-ary and fitting the scale height ratio. The parti-cles in the tropospheric cloud were modeled eitheras spherical particles uniformly mixed with the gasand with a fitted real index, or as non-sphericalparticles using an HG phase function with a fittedasymmetry parameter.2.3 Our initial fits to the 2015 STIS spectra over theentire range from 540 nm to 980 nm using either atwo-cloud or three-cloud model using spherical par-1ticles of real refractive index of n = 1.4 producedgood overall fits that were especially bad near 830nm, just where the spectrum is especially sensitiveto the methane to hydrogen ratio. Much better fitswere obtained by allowing the refractive index of thetropospheric aerosols to be adjusted, which yieldedtwo solutions, one a large-particle low-index solu-tion and second small-particle high-index solution,the latter providing the better fit and somewhatcloser match to the refractive index of H S.2.4 Our preliminary 2-cloud models using sphericalparticles found little variation as a result of usingdifferent temperature profiles, as long as we didnot force the deep methane mixing ratio or themethane humidity above the condensation level tobe constrained either by occultation results or bya prohibition against supersaturation. We chose touse the Orton et al. (2014a) profile, even thoughit is inconsistent with occultation results, becauseits higher upper tropospheric temperatures allowedmore methane without supersaturation.2.5 For subsequent models containing a stratospherichaze and just a single tropospheric conservativeMie-scattering layer mixed uniformly with the gas,we did preliminary fits to spectra at 10 ◦ N and60 ◦ N over the 730 nm to 900 nm range, and forboth 2012 and 2015, assuming that methane wasuniformly mixed below the condensation level. Wefound two classes of solutions, one with large par-ticles of 1.1-1.75 µ m in radius and a real indexof 1.22 ± ± ± µ m to0.34 ± µ m in radius with much larger real in-dex values from 1.55 ± ± S,a prime candidate for the cloud’s main constituent.2.6 The above preliminary fits with uniform methanemixing ratios found those ratios ranged from2.56% ± ± ◦ N, and from0.74% ± ± ◦ N, with lowervalues in both cases obtained from the large par-ticle solutions, but good agreement between 2012and 2015 in both cases.2.7 Preliminary fits using non-spherical HG parti-cles for the single tropospheric cloud layer pro-duced similar results, with a methane mixing ra-tio from 2.85% ± ± ◦ N andfrom 0.97% ± ± ◦ N, and in this case differences between 2012 and 2015 arewithin estimated uncertainties.2.8 All the above preliminary fits found methane hu-midities in the 68% to 95% at 10 ◦ N, and 30% to 56%at 60 ◦ N, generally with uncertainties of 12-16% and18-26% respectively.2.9 STIS results in the upper troposphere are in goodagreement with the Lellouch et al. (2015) resultsbased on Herschel observations. For 2015, the rela-tive methane humidity above the nominal conden-sation level, which is roughly at the 1-bar level, forthe Orton et al. thermal profile is roughly 50%north of 30 ◦ N but near saturation from 20 ◦ N andsouthward, but becomes supersaturated for the F1and F0 profiles.2.10 Latitude dependent fits assuming a uniformmethane mixing ratio below the condensation levelshow that a local maximum value of about 3% isattained near 10 ◦ N latitude. From that point theeffective mixing ratio smoothly declines by a factorof 2 by 45 ◦ N, and by a factor of three by 60 ◦ N,attaining a value of about 1% from 60 ◦ to 70 ◦ N.However, if particle absorption is present, the de-rived mixing ratios are lowered by up to 10% oftheir values, or possibly more, depending on mod-els. Thus, it is not possible to give a firm value ofthe mixing ratio without a deeper understanding tothe aerosols within the atmosphere.2.11 For a vertically uniform methane mixing ratio,the high-latitude model fits failed to accurately fol-low the observed spectra in the 750 nm region, sug-gesting that the upper tropospheric methane mix-ing ratio increased with depth. This was espe-cially obvious for the 2012 observations, probablybecause of reduced aerosol scattering in 2012. Amodel profile containing a vertical gradient abovethe 5-bar level, using either what Sromovsky et al.(2011) called a descended depletion profile or a stepdecrease at the 3 bar level made a substantial im-provement in the fit quality.2.12 When the methane depletion with latitude ismodeled as a stepped depletion, we find that thestep change occurs at pressures between 3 and 5bars, although the uncertainty is typically 2 bars.This level applies between about 50 ◦ and 70 ◦ N, butmoves to lower pressures between 50 ◦ N and 20 ◦ N,and remains near the condensation level from thatpoint to 20 ◦ S. The mixing ratio above the break2 point pressure is near 0.75% in the 60 ◦ N to 70 ◦ Nrange, increasing to about 1.2% at low latitudes, al-though by that point the depleted layer is so thinthat it is hard to distinguish from the uniformlymixed case with a single mixing ratio up to the con-densation level.2.13 Because the shape of the descended profilemakes the depth parameter of that profile difficultto constrain with the spectral observations, we wereguided by the stepped depletion results to choosea fixed depth parameter of 5 bars, and fit justthe shape parameter vx as a function of latitude.The results show a relatively smooth variation fromslightly greater than 1 at high latitudes, increasingto about 4 by 30 ◦ N, then rising to very high val-ues at low latitudes, which yields a nearly verticalprofile that produces negligible depletion.3. AEROSOL PROPERTIES:3.1 Preliminary fits with non-spherical particles witha simple HG phase function yielded asymmetry pa-rameters that ranged from 0.43 ± ◦ N to0.26-0.39 at 60 ◦ N. These are smaller values than thecommonly used value of g = 0.7, e.g. by Tice et al.(2013). It is also smaller than the asymmetry pa-rameters of even the small-particle solutions for thetropospheric aerosols, which ranged from about 0.4at 1.6 µ m to 0.6 at 0.8 µ m. The large-particle asym-metry values were near 0.86 at 0.8 µ m and 0.9 at1.6 µ m.3.2 The cloud pressure boundaries varied with modelstructure. When a vertically uniform methane pro-file is assumed, the top boundary of the cloud isprecisely constrained and nearly invariant with lat-itude, moving from slightly greater than 1 bar atlow latitudes to almost exactly 1 bar at high lati-tudes. The lower boundary is more uncertain vary-ing about a mean near 2.6 bars. The optical depthof the tropospheric cloud declines by roughly a fac-tor of two from low to high latitudes, when 2012 and2015 results are averaged. For the stepped deple-tion models, the top boundary behavior is similar tothat of the uniform model, but the bottom bound-ary moves from 2.5 bars at low latitude to 3 bars athigh latitude.3.3 A very different characteristic is seen for the de-scended methane fits as a function of latitude. Inthis case the upper boundary of the tropospheric cloud moves significantly downward with latitudeinstead of slightly upward, with the pressure in-creasing from about 1.1 bar to 1.3 bar. We alsofound that the refractive index increased with lat-itude, from 1.6 to about 2.0, perhaps a result ofa low-index coating evaporating from a high indexcore as the cloud descends to warmer temperatures.The particle radius also decreases somewhat withlatitude, which would be consistent with that spec-ulation. The tropospheric cloud optical depth isalso seen to decline somewhat at high latitudes, asseen for other models.3.4 The real refractive index of the main cloud has arelatively flat latitude dependence for the steppeddepletion model, but significant increases with lat-itude are seen for uniform and descended depletionmodels. Better agreement is obtained at low lati-tudes, where weighted averages over 2012 and 2015from 20 ◦ S to 20 ◦ N are 1.65 ± ± ± S byamounts that are not much greater than combineduncertainties.3.5 The way aerosol contributions produce the in-creased polar brightness between 2012 and 2015 issimplest to understand within the context of themodels assuming vertically uniform methane. Inthese cases an increased amount of scattering in themain cloud layer produces the brightness increase.And at 60 ◦ N and 70 ◦ N this is due to a combina-tion of increased optical depth and increased par-ticle size. Similar effects are seen in the steppeddepletion model model (small particle solution). Inthe descended depletion model it appears that anincrease in the cloud top pressure over time may bea significant factor. For the simple non-sphericalHG particle cloud we found a 37% increase in opti-cal depth coupled with a 33% decrease in the asym-metry parameter from 0.39 to 0.26. These effectswould produce a combined rise in pseudo continuumI/F of about 32% (= 0.45 × (0.37+0.33)), which iscomparable to the observed change.3.6 The association of high-latitude methane deple-tions with descending motions of an equator-to-poledeep Hadley cell does not seem to be consistent withthe behavior of the detected aerosol layers, at leastif one ignores other cloud generation mechanismssuch as sparse local convection. Both on Uranus3and Neptune (de Pater et al. 2014), aerosol layersseem to form in what are thought to be downwellingregions on the basis of the effective methane mixingratio determinations.3.7 Models using conservative spherical particles inthe tropospheric cloud layer have significant flawswhen fit to the wider spectral range from 540 nmto 980 nm and assuming a real index of refractionof n = 1.4. Much smaller flaws are seen with smallparticles with a larger refractive index, but moreaccurate fits require additional wavelength depen-dent scattering characteristics. This can be done byadding absorption in the longer wavelength regions,which allows increasing optical depths enough tobrighten the shorter wavelength regions. For smallparticles with high real index values we needed toincrease the imaginary index from zero at shortwavelengths to 1.09 × − between 670 to 730 nmand to 4.9 × − from 730 nm to 1 µ m. Fornon-spherical HG particles, we were able to matchthe same spectral region by creating an appropri-ate variation in optical depth with wavelength. Itis also possible to produce a similar fit for DHGparticles by appropriate wavelength dependence inthe phase function, following an approach used byKT2009.3.8 We were able to extend Mie model fits to thenear-IR spectral range by further adjustments ofthe imaginary index with wavelength. For smallparticles the imaginary index had to be elevated to0.1 at 1.6 µ m, where its single-scattering albedo de-scends to 0.64. For large particles, the needed imag-inary index increase was to a level eight times lessthan for small particles, and the single-scatteringalbedo was decreased to a more modest value of0.90.3.9 Our two solutions for cloud structures that canmatch spectra from visible to near-IR wavelengthsto at least 1.6 µ m, require vast differences in thetotal optical depth and cloud mass. These so-lutions bound solutions from other investigators,which have different vertical structures that in mostcases match spectra from 0.8 to 1.6 µ m. The col-umn masses of particles in these clouds range from500 to 17 times smaller than the total mass of H Sin a 1-bar pressure interval, and thus, even the mostmassive of these clouds cannot be ruled out on thebasis of insufficient parent condensate. 3.10 We found evidence for a deep cloud layer in the9 bar to 11 bar range if optically thick and possi-bly composed of NH SH. Including this layer in ourmodels has the main effect of improving our fits tothe weak methane band structure at wavelengthsfrom 540 nm to 600 nm. Placing the deep cloud at5 bars yields an optical depth near 4 but a worsefit to the spectra. Further work is needed to betterconstrain the properties of this cloud.4. CONSTRAINTS ON H S:4.1 If the tropospheric cloud is a condensation cloud,H S is the likely main component. This conclusionis based on the fact that virtually all of the modelcloud mass is below the level at which methanecan condense, but likely within the pressure rangeat which H S can condense. It is also the casethat our preferred small-particle solutions are inrough agreement with the refractive index of H Sat low latitudes, although that agreement worsensat high latitudes and thus does not provide com-pelling support. More compelling support for H Sas the main constituent of this cloud is the recentdetection of H S vapor at saturation levels abovethis cloud (Irwin et al. 2018). What remains un-clear is whether the spectrally varying imaginaryindex that seems to be required for this cloud iscompatible with the absorbing properties of con-densed H S.4.2 Based on the estimated bottom boundary of thetropospheric aerosol layer, if the small particle solu-tion is to be consistent with a composition of H S,the mixing ratio of H S at the 3.3-bar level and im-mediately below must be at least ∼
30 ppm. To beconsistent with the large particle solution would re-quire around an order of magnitude higher VMRnear the 5-bar level.Advancing our understanding of the distribution andcomposition of Uranus’ aerosols would be helped bygood measurements of the optical properties of H S, themost likely primary constituent of the most visible tropo-spheric cloud layer. Another helpful undertaking wouldbe microphysical modeling of photochemical haze for-mation and seasonal evolution as well as microphysicalmodeling of condensation clouds. The variety of verticalaerosol structures and mass loadings that can producemodel spectra matching the observations is surprisinglylarge and it seems likely that not all of these options4would satisfy microphysical constraints. A better under-standing of the aerosols is also the key to better con-straints on the distribution of methane because differ-ent aerosol models yield different methane mixing ratios,with deep VMR values mostly falling between 2% and4%. As Uranus seems to be continuing to change, espe-cially the continued brightening of the north polar regionthrough at least 2017, and many uncertainties remain,continued observations are also warranted.
ACKNOWLEDGMENTS
This research was supported primarily by grantsfrom the Space Telescope Science Institute, managed by AURA. GO-14113.001-A supported LAS and PMF.Partial support was provided by NASA Solar SystemObservations Grant NNXA16AH99G (LAS and PMF).EK also acknowledges support by an STScI grant un-der GO-14113. I.dP was supported by NASA grantNNX16AK14G. We thank staff at the W. M. Keck Obser-vatory, which is made possible by the generous financialsupport of the W. M. Keck Foundation. We thank thoseof Hawaiian ancestry on whose sacred mountain we areprivileged to be guests. Without their generous hospi-tality none of our groundbased observations would havebeen possible.
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