## 4 Results and Discussion
### Discussion  
Our sensitivity study's findings indicate that using continuous (hyperspectral) channels when developing an SPR algorithm offers some improvements over selecting specific (multispectral) wavelengths like those available for sensors such as MODIS and SGLI. It is likely that the SBG algorithm outperformed the other three algorithms when it comes to snow impurity because of its channel configuration. Figure 2E shows that for impurity values in the \(10^{-9}\) to \(10^{-8}\) range, radiances in the 380-600 nm range are significantly affected by the impurity, while the impact is insignificant at longer wavelengths. The SBG algorithm has twenty-three channels in this spectral range, while the Min-Max and SGLI algorithms have six channels and the MODIS algorithm has only two. Both the MODIS,  
Figure 11: Performance of Max-Min snow parameter retrieval algorithm predictions versus model synthetic data (N = 5000). Figure 10: Performance of SGLI snow parameter retrieval algorithm predictions versus model synthetic data (N = 5000). Figure 9, and SGLI, Figure 10, algorithms tended to overestimate very low impurity values and underestimate values near and around \(10^{-8}\), leading to an S-like curve in the plots. This tendency is most noticeable for the MODIS algorithm where the underestimation continues past \(10^{-8}\) up to \(10^{-7}\). To a lesser extent, this S-like curve is also present in the Max-Min plots shown in Figure 11. The SBG algorithm, Figure 8, performed better in these ranges with an APD of 14.1% compared to 30.3%, 23.3%, and 18.5% for MODIS, SGLI, and Max-Min, respectively. However, the SBG algorithm still overestimates very low impurities near \(10^{-9}\). The use of channels based on a continuous spectrum configuration also shows small improvements in predicting snow grain size. When comparing the SBG algorithm to the other algorithms, we observe a tighter grouping of data in the SBG plots (Figure 8). This tighter clustering becomes more noticeable as snow grain size increases, with the SBG algorithm having an MAE of 31.9 \(\upmu\)m for snow grains ranging from 1500 to 2500 \(\upmu\)m compared to 48.7 \(\upmu\)m, 45.8 \(\upmu\)m, and 43.9 \(\upmu\)m for the MODIS, SGLI, and Max-Min algorithms. Figure 2D shows that the variation in radiance across all wavelengths becomes less pronounced as the grain size increases. We observe a much larger shift when grain sizes increase from 50 to 300 \(\upmu\)m than for when it increases from 900 to 2500 \(\upmu\)m. This behavior likely made it harder for the MLNNs to precisely evaluate changes in radiance caused by large snow grains, leading to a larger deviation of prediction values from the model data for large grain sizes for the three multi-band algorithms. All four algorithms were able to accurately predict the albedo in the visible, near-infrared, and shortwave infrared spectral ranges. The reason is likely that the variation of albedo vs. wavelengths is much smoother than the variation of radiance vs. wavelength, making the albedo easy to predict from only a few wavelength channels. However, since the albedo mainly depends on the physical properties of snow, to get an understanding of the global climate system it is not enough to solely predict this value. It is possible that a snow sample with small grain size and high impurity could produce the same albedo as a different snow sample with large grain size and low impurity. An illustration of this circumstance is shown in Figure 12. Despite the large differences in grain sizes and impurity concentrations, the two very different snow configurations are shown to yield the same VSWIR (380-2500 nm) albedo. The Max-Min algorithm contains channels at all of the peaks and valleys observed in our illustration plots, Figures 2 and 3. These channels should contain the most contrasting values and make it easy for a neural network to identify differences in retrieval parameters.