Constraint from the Phase function.
For the costraints btw 144 - 80km I used slightly more restricted thresholds filter the matching models. Namely, for the backscattering I used 10% error margin. The reason why I did not apply 5% error is because firstly since we are extrapolating our model to the mononer numbers that is few times larger than the maximum tested t-matrix model. Secondly since in the previous titan haze models old parameterization is used although the phase functions include some corrections and based on the observations. Therefore This may not be true ( I am still not sure). Moreover, our model is although very accurate in the forward scattering in the tested range, it is slighlty less accurate in the backscattering region especieally when it comes to backscattering enhancement due to weak localization effect. The weak localization effect is not directly modelled in our model although it is somewhat included to a limited degree in the statistical correction made at the backscattering angles between 135 - 180.
As for the w0, I allowed 10% error. (Why?)
For the constraints below 80km I allowed even larger error for the backscattering angles, about 15% due to increased uncertainity in the observed DISR model which results from the increased optical depth at these altitudes, especially at the blue channel. This was also required to avoid eliminating too many model runs. Otherwise, with 10% error limit we would only have less than 10 model matching the all criteria.
constraints
For Blue 144, Red 144 Red 80
vars()[wl+alt] = eval(wl)[eval(wl)['w0{}_Rerr'.format(alt)] <= 0.05]
vars()[wl+alt] = eval(wl+alt)[eval(wl+alt)['Rel_err_b'.format(alt)] <= 0.155]
For red channel best fiting model is pm3975_02689_175_00060 (and some other close neighboorhood combinations)
For Blue 80, 5% error is too restricted when combined with 10% error limit in the backscattering in a way that almost no model particle can match the observation within the error limits. This could be due to increased uncertainty in the solar aerolo measurements which results from the increased optical depth at these lower altitudes, especially at the blue channel. As a result perhaps the w0 value provided at table 2 in tomasko 2008a may not be accurate for 80km at 491 nm. Or perhaps the phase function is slighlty different at these altitude due to increase in the size of the aggregates. I therefore allowed a larger error margin both for w0 and phase function to account for these uncertainties. As a result, at Blue channel constraints suggest that
"
Tomasko et al. (2008b) shows that the single scattering albedo also increases below 80 km. This change in single scattering albedo indicates that the indices of
refraction are also changing which is consistent with condensation of a non-absorbing material onto the aerosols. Our present model does not include condensation onto aerosols, however, we believe it is the most likely source of the discrepancies between our model and the observations below 80 km.
We explored 20 to 218 monomers by factors of 4, with our best fit
having 4096 monomers. We explored fractal dimensions from 1.6 to 3.0 with fractal dimensions of 2.0, 2.4, and 2.8 being the best fits to altitudes above 80 km, 30–80 km, and below 30 km respectively (
Fig. 12). Using the larger fractal dimensions (2.4 and 2.8) gives much better fits to the observations below 80 km than does the model with fractal dimensions of 2.0.
"\citep{Larson_2014}
Results And Discsussion
Get Constraints for phase&Rm and nr,ni independentl
As expected, constraints from the observations from 80km and below is rather less accurate since in this level the optical thickness is too large especially for blue channel. Therefore the multiple scattering significantly contributes to the observed radiation which makes it more difficult to obtain the single scattering properties. Nevertheless, combining all the constraints from both the Blue and Red channel helps narrowing down the parameters significantly. Here in the following table s the range of parameters are shown that passes the filters. In the Figure x the best fitting particles are drawn which have the smallest combined errors from all the constraints.
As it is shown in the Figure x, constraints from both the Red and Blue channels suggest that the haze particles between 80-30km have around 3000 monomers with monomer size around 0.041.
Constraint from Red is expected to give a larger size range since the size parameter is smaller at this wavelength as a result strong polarization is observed with much larger particles comparing to the particles produces the polarization similar to one observed in Blue channel. Therefore, I use the Blue channel to constraint the monomer size in the haze particles.