## 2 Models and Data
### Synthetic Snow Dataset
#### 2.3.2 Illustrative Examples  
To gain a sense of how the various parameters affect radiances and the albedo, several computations were carried out at designated 10 nm increments of the parameter values. To this end, radiance versus wavelength plots for upward radiances at the TOA are provided in Figure 2. Also, albedo versus wavelength plots for varying solar zenith angle, snow grain size, and impurity concentration are provided in Figure 3. Figure 2 shows that variability in radiance is largely affected by the solar zenith angle and snow grain size, with the impurity concentration also having a significant impact in the visible part of the spectrum. Changes to the relative azimuth and viewing zenith angle have a relatively minimal observable effect on the TOA radiance; however, the forward reflection (BRDF)  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **Data Range** & **Distribution** & **Mean** \\ \hline Relative azimuth angle & 0 to 180 (degrees) & Uniform & 89.87\({}^{\circ}\) \\ Viewing zenith angle & 0 to 45 (degrees) & Uniform & 22.55\({}^{\circ}\) \\ Solar zenith angle & 20 to 75 (degrees) & Uniform & 47.62\({}^{\circ}\) \\ Snow grain size & 50 to 2500 (\(\upmu\)m) & Log-normal & 835 \(\upmu\)m \\ Snow impurity concentration & \(10^{-9}\) to \(10^{-5}\) (ratio) & Log-normal & \(9.27\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of parameters used to generate the synthetic training dataset.  
is generally stronger, especially along the principal in NIR, which can lead to significant differences depending on the viewing/azimuth angles. Figure 3 shows that these findings are also true for the snow surface albedo. It is worth noting that only snow grain size seems to have a significant impact on radiance past 1500 nm, and only when the grain size is quite small, in the 50-300 nm range. Impurity concentration has the biggest impact on the albedo for wavelengths in the visible part of the spectrum, while a decrease in snow grain size caused the albedo to increase. This albedo enhancement is most dramatic in the near-infrared nm range. Changes in the solar zenith angle cause noticeable changes in the albedo across all wavelengths.  
Figure 3: Albedo vs. wavelength plots for a variety of conditions. The black lines in all plots have constant relative azimuthal angle of 90\({}^{\circ}\), viewing zenith angle of 22.5\({}^{\circ}\), solar zenith angle of 45\({}^{\circ}\), grain size of 300 nm, and impurity concentration of 10\({}^{-8}\). In all plots, four of the parameters are held to the constant values listed above, while the fifth is varied. (**A**) Varied solar zenith angles from 20 to 75\({}^{\circ}\). (**B**) Varied snow grain size from 50 to 2500 nm. (**C**) Varied impurity concentration from 10\({}^{-9}\) to 10\({}^{-5}\).  
Figure 2: Radiance vs. wavelength plots at TOA, the black lines in all plots have constant relative azimuthal angle of 90\({}^{\circ}\), viewing zenith angle of 22.5\({}^{\circ}\), solar zenith angle of 45\({}^{\circ}\), grain size of 300 μm, and impurity concentration of 10\({}^{-8}\). In all plots, four of the parameters are held to the constant values listed above, while the fifth is varied. (**A**) Varied relative azimuthal angles from 0 to 180\({}^{\circ}\). (**B**) Varied viewing zenith angles from 0\({}^{\circ}\) to 45\({}^{\circ}\). (**C**) Varied solar zenith angles from 20\({}^{\circ}\) to 75\({}^{\circ}\). (**D**) Varied snow grain size from 50 to 2500 μm. (**E**) Varied impurity concentration from 10\({}^{-9}\) to 10\({}^{-5}\).