## 2 Methodology
### Orbital Configuration and Sensor Type
#### 2.2.3 LiDAR Altimetry  
The fourth hypothetical sensor is a wide-swath (imaging) LiDAR with a 20 km swath width. This specific configuration (and the assumed instrument errors) for use in space may not be achievable given the engineering requirements of today, but this aspirational sensor is considered here as a feasible part of a future, hypothetical snow constellation configuration and, as such, is explored in this study. The fifth evaluated sensor is an ICESat-2-like narrow-swath LiDAR [47]. It has a similar orbit as ICESat-2, but with better spatial coverage assuming the use of a hypothetical 6 km continuous swath width to replace the original ICESat-2 observations that are sampled by six laser beams, each with a 10-meter footprint across a 6 km field of view. The sixth evaluated sensor is a GEDI-like (Global Ecosystem Dynamics Investigation onboard the International Space Station) low-inclination angle LiDAR [38]. As a low-inclination angle platform, it only views regions within \(\pm\)51.6\({}^{\circ}\) latitude. Although it loses the ability to monitor snow over high latitudes, it yields a higher revisit frequency in low latitude areas of snow. The orbital configurations for each of these sensors are provided in Table 1.  
Among the existing spaceborne altimetry and LiDAR instruments, ICESat-2 has a 6 km total swath width [48], and GEDI has a total swath width of 6.5 km [49]. Therefore, the assigned swath width of the hypothetical LiDAR is set to 6 km in order to appropriately represent the current, state-of-the-art technology. The swath width of the hypothetical \"wide-swath\" LiDAR is assigned as 20 km. Even though such a spaceborne LiDAR does not currently exist, it is worth conducting this experiment to consider the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & **Sensor** & **Orbit** & **Inclination** & **Swath** & **Prototype** \\  & **Type** & **Altitude [km]** & **Angle [\({}^{\circ}\)]** & **Width [km]** & **(Status)** \\ \hline \multirow{2}{*}{1} & PMW & & & & \\  & Radiometer & 510 & 97 & 1450 & \begin{tabular}{c} AMSR2 \\ (Existing) \\ \end{tabular} \\ \hline \multirow{2}{*}{2} & Ku-band & & & & & \\  & SAR & 705 & 98 & 500 & \begin{tabular}{c} TSMM \\ (Hypothetical) \\ \end{tabular} \\ \hline \multirow{2}{*}{3} & C-band & & & & & \\  & SAR & 705 & 98 & 250 & \begin{tabular}{c} Sentinel-1 A/B \\ (Existing) \\ \end{tabular} \\ \hline \multirow{2}{*}{4} & Wide & & & & & \\  & LiDAR & 481 & 92 & 20 & \begin{tabular}{c} ICESat-2 \\ (Hypothetical) \\ \end{tabular} \\ \hline \multirow{2}{*}{5} & Narrow & & & & & \\  & LiDAR & 481 & 92 & 6 & \
\begin{tabular}{c} ICESat-2 \\ (Existing) \\ \end{tabular} \\ \hline \multirow{2}{*}{6} & Low-inclination & & & & & \\  & LiDAR & 415 & 51.6 & 6.5 &
\begin{tabular}{c} GEDI \\ (Existing) \\ \end{tabular} \\ \hline \hline \end{tabular}  
* PMW = passive microwave; SAR = synthetic aperture RADAR; LiDAR = light detection and ranging; AMSR2 = Advanced Microwave Scanning Radiometer 2 (AMSR2); TSMM = Terrestrial Snow Mass Mission; ICESat-2 = Ice, Cloud and land Elevation Satellite-2; GEDI = Global Ecosystem Dynamics Investigation.  
\end{table}
Table 1: Orbital configurations of the tested sensors. The sensor prototype and its status (existing or hypothetical) is marked in “Prototype” column.  
added value associated with a hypothetical increase in swath width relative to that which is currently operational.