DISR Phase Functions, single scattering albedo Modified in a 2015 paper \citet{Doose_2016}

"Finally, the single scattering phase functions and the variations of the single scattering albedo, -0, with altitude have been refined by including the photometry from the imagers, constraints from Titan’s geometric albedo, and measurements of Titan’s disk size variation with wavelength"
"In the bottom range, between 0 and 20 km altitude, the upward-looking radiance field is significantly influ- enced by light scattered up from surface albedo features, which makes a reliable analysis of aerosol properties difficult. Thus, we restrict most of our analysis to data taken from altitudes above 20 km"
"The main DISR imagers acquired more than 300 images cover-ing nadir angles 6–96° (Karkoschka and Schröder, 2016) in one spectral band of 640–960 nm with an effective wavelength of 770 nm. They primarily recorded surface features, but their photo- metric accuracy also allows us to use them to refine Titan’s aerosol parameters"
"The DISR observations we concentrate on in this work areexpected to be accurate to 3–5% in a photometric sense. The uncer- tainty in absolute calibration is probably twice as large. The sources of uncertainty include the pre-flight calibration and changes in instrument sensitivity during the 7-year flight to Titan. Some sources of uncertainty also vary during the descent. For example, uncertainties in pointing arose because the probe swung unpredictably with high frequency under the parachutes. Measure- ments that require averaging of several observations, such as azi- muthal averages of measured radiance at a particular altitude, are more accurate if the descent velocity is slower through that altitude"
"The forward scattering part of the phase function was directlymeasured by the upward-looking solar aureole camera that mea- sured the radiance of the light scattered at small angles from the solar beam at 510 and 930 nm wavelength at 83 and 60 km alti- tude. As"
"These two observa- tional requirements on the scatterers are satisfied if the aerosols are fractal aggregate particles containing some 2000–3000 mono- mers, according to a scattering model developed by Tomasko et al. (2008). This model for scattering by fractal aggregate particles was used to give the angular dependence of the phase function for mid- and back-scattering regions and also the variation with wave- length outside the two wavelength regions where the measure- ments were made. The phase function is not as constrained at lower altitudes, although nothing in the DISR measurements requires that it changes with altitude"
"In our previous study we adopted the- oretical phase functions above 80 km altitude and increased the backscattering part below 80 km at wavelengths where the obser- vations required it. In this study, we chose an intermediate phase function for all altitudes that fits the data just as well as the two- phase-function model. The new phase function is a mix of 85% of the upper and 15% of the lower altitude phase functions used in Tomasko et al. (2008), throughout the atmosphere."

Finding w0 and Tau

"The procedure for searching for a run of optical depth with alti-tude for a given phase function is to vary the optical depth to fit the ULVS measurements and -0 to fit both the ULVS and DLVS obser- vations. This is done at continuum wavelengths first, and then at wavelengths where significant absorption by methane occurs. In this work we adopted published absorption coefficients for methane together with pressure and temperature variations (Karkoschka and Tomasko, 2010). Finally, we find functions which fit the changes in optical depth and -w0 with altitude and wavelength. We note that model parameters we find using this method are non-unique. A more complex variation of parameters can often fit the data as well. Our method is to find the simplest aerosol struc- ture with the fewest free parameters that best fit the observations."

Condensing materials over aggregate particles

Beginning near 80 km, several authors (Maguire et al., 1981; Sagan and Thompson, 1984; Anderson and Samuelson, 2011; \citet{Lavvas_2011}) predict the condensation of HCN. C4H2 and HC3N may condense at a similar altitude, and C6H6 may condense even higher. These materials may coat the aggregate particles and might possibly contribute to a change in the extinction profile seen toward lower altitudes. \citep{Doose_2016}

New w0

"The geometric albedos we aim to fit should be larger than those measured by Karkoschka (1998) in 1995 (shown in Fig. 5), at least in the blue. Lockwood and Thompson (2009) measured a 3% bright- ening between 1995 and 2005 in the blue. The new model was designed to fit the geometric albedo by adjusting -0 as shown in Fig. 6. Here -0 continues to decrease with altitude as shown up to 200 km. The dependence of -0 on altitude is not required to be a linear change. There is so little absorption that we cannot measure it very well. It could be a more complex function, but this is not justified by the observations. At altitudes above 80 km the measurements are very sensitive to the tip/tilt, making anything beyond a linear fit unjustified"