## 3 Results
### Evaluation of Single Sensor  
#### 3.3.1 Viewed Snow Coverage Percentage Analysis  
To quantitatively assess the seasonal variation of the viewed snow area, the total snow area and viewed snow area by each individual sensor over different periods is illustrated in Figure 5. The total snow cover area in the northern hemisphere varies as a function  
Figure 4: Viewing example for a single day using a C-band SAR (No.3 in Table 1) overlying the snow-covered area via IMS; blue is sensor coverage; green is snow-covered terrain according to IMS. Figure 3: Example of daily viewing extent of sensors listed in Table 1.  
of season and reaches a peak of about (5.4 \(\times\) 10\({}^{7}\) km\({}^{2}\)) during February with a minimum value of about (0.2 \(\times\) 10\({}^{7}\) km\({}^{2}\)) during August. As a result, the spatial coverage for snow varies correspondingly, and yields the largest difference between different sensors during peak snow accumulation. For example, a single PMW sensor could observe more than 80% of the snow-covered terrain in a single day in February, while a single SAR sensor could observe between 20% and 40%, depending on the swath width. A single LiDAR sensor views less than 5% of the snow-covered terrain area in a single day. When the integration time increases to three days, a PMW radiometer can view all of the terrestrial snow across the northern hemisphere. However, a single LiDAR sensor coverage is still limited to less than 15%. For a 30-day integration period, the wide-swath LiDAR could cover more than 50% of terrestrial snow in the northern hemisphere, while the narrow-swath LiDAR views approximately 38%. In short, a single PMW sensor views most of the northern hemisphere snow-covered terrain in a 1-day period; a single SAR sensor views most of the snow-covered area in a 3-day period; and a 20-km swath width LiDAR sensor cannot view most of the snow-covered terrain even in a 30-day period. The difference between their coverage mainly results from the swath width configurations of each sensor. Figure 6 highlights the viewed snow percentage as a function of swath width. This result is computed using an inclination angle of 97\({}^{\circ}\) and a 510 km altitude as a function of swath widths ranging from 50 km to 1500 km. The increase in viewed snow cover percentage is nearly linear as the swath width increased during a 1-day integration  
Figure 5: Seasonal variation in viewed terrestrial snow area for different types of existing and hypothetical sensors. Subplot (**a**) shows coverage based on a 1-day integration period; (**b**) shows a 3-day integration period; (**c**) shows a 30-day integration period. period. The growth rate of percent coverage is asymptotic when the swath width is large for a 3-day or 30-day integration period due to the successive overlaps between different days. When arbitrarily drawing a line of 80% of snow-covered percentage, the swath width required is about 1100 km, 550 km, and 200 km for a 1-day, 3-day, and 30-day integration period, respectively. This result provides a useful benchmark of snow mission demands when considering daily, synoptic, and seasonal variations of snow. This analysis assumes a peak snow period. For other days of the year, the extent of low-latitude snow decreases. We employ the effective coverage as presented in Section 2.5.2 to reflect the effect of sensor efficacy on different snow classes, along with consideration of cloud attenuation. The effective coverage not only indicates the snow extent viewed by the sensor(s) but also shows the skill of each sensor to detect the snow in different snow classes. The simulated results for effective snow coverage percentage are shown in Table 4. It shows poor percent coverage for all sensors over taiga since we assume only LiDAR sensors, whose swath widths are limited, work well for this class. The PMW sensor provides considerable viewing for the tundra, ephemeral, and prairie classes within one day.