*4.3. Simulation Results*

#### 4.3.1. Effect of Snow Cover on VI

Figure 10 compares the changes in the five VIs under different SCF conditions as the FVC increases from 0 to 1. For all indices, the values of the five VIs generally decreased with increasing SCF. In the presence of snow cover, the larger the FVC was, the greater the decrease in the VI value. The deviation of the data points from the 1:1 line showed the effect of snow cover on VI values. The dashed line in each subplot of Figure 10 indicates the difference in VI values between SCF = 0% and SCF = 100%, denoted as |ΔVI|max. MIS values were further calculated for FVC = 0 and FVC = 1 to show the maximum possible influence of snow on VI values using Equation (3). Thus, the sensitivity of the five VIs to snow cover is NDPI (MIS range 0.0466–0.9534) < NDGI (MIS range 0.0122–1.0122) < NIRv (MIS range 0.2335–1.2335) < EVI2 (MIS range 0.3320–1.3320) < NDVI (MIS range 0.5280–1.5280).

**Figure 10.** Comparison of simulated VIs under different SCFs with snow-free cases. (**a**–**e**) are the changes of the five VIs as the FVC increases from 0 to 1 under different SCF conditions.

#### 4.3.2. Effect of Snow Cover on SOS Detection

Figure 11 shows the temporally filtered time curves of the five VIs and the detected SOS dates in simulation experiments I and II. Under snow-free conditions, the SOS detected by the different VIs ranged from DOY 144 to DOY 152, indicating small differences in snowfree SOS detected by the different VIs. Under snow conditions, the SOS dates detected by NDVI and EVI2 were earlier, while those detected by NDGI and NDPI were later, and those detected by NIRv were in between, as shown in all subplots of Figure 11.

Considering the differences in the SOS between SCF = 0 and SCF > 0 in Figure 11, the effect of snow on the detected SOS generally follows the order of NDPI/NDGI < NIRv < EVI2/NDVI. Generally, the presence of snow significantly reduced the VI values during the pregrowth period and advanced the SOS for all five VIs. For all five VIs, the greatest advances in the SOS were found for the earliest snow season (i.e., for ESS at DOY 104), which ranged from 16 to 56 days. As the ESS increased from DOY 104 to 168, the advances in the detected SOS decreased rapidly. For the ESS at DOY 168, the SOS estimated by NDVI, EVI2, and NIRv was only 4–6 days earlier than the snow-free SOS, while those estimated by NDPI and NDGI were 6 and 2 days later than the snow-free SOS, respectively. This indicates that the ending date of persisting snow is very important. When persisting snow ends earlier than the snow-free SOS, the presence of snow reduces the minimum VI value during the pregrowth period but does not affect the maximum VI value during the peak growth period, which would increase the gradient of the time curve of VI significantly and cause the SOS to be detected earlier. As analyzed in Section 4.3.1, the snow-induced decrease in the VI value is very small at small VI values and is relatively larger at large VI values. When the snow season ends later than the snow-free SOS, the decrease in VI values around the SOS is larger than that of the pregrowth period. This may locally smooth the time curve of VI and delay the detected SOS compared to the case of an early snow season.

**Figure 11.** Time curves and the detected SOS of the five VIs under different SCF and ESS cases in experiments I and II. (**a**–**c**), (**d**–**f**), (**g**–**i**), (**j**–**l**), and (**m**–**o**) are the time curves of five VIs, for each of which three ESS cases at DOY 104, 136, and 168 and five cases of SCF = 0%, 25%, 50%, 75%, and 100% were plotted.

To further investigate the mechanism of how snow affects SOS detection, simulation experiment III was implemented to analyze the ΔSOS under different snow scenarios defined by SCDc, ESS, and SCF, and the results are shown in Figure 12. It clearly shows that ΔSOS changes with varying SCDc, ESS, and SCF values. Using the absolute values of ΔSOS as a standard, the effect of snow on SOS detection followed the order of NDPI/NDGI < NIRv < EVI2 < NDVI, which is consistent with the effect of snow on VI values analyzed in Section 4.3.1. Both SCDc and ESS are very important in determining the ΔSOS. In general, the larger the SCDc value was, the larger the absolute value of ΔSOS. This is reasonable because the reduction in VI values during a short snow period (i.e., small SCDc) can be better recovered by time series filtering performed prior to SOS detection. Specifically, for short snow with SCDc = 32, ΔSOS was very close to 0 for all VIs, except NDVI, for which ESS was earlier than the snow-free SOS. For longer snow with SCDc = 64 and 96, ΔSOS increases from negative to positive values as ESS increases. This also indicates that an earlier ESS generally advances the SOS, while an ESS much later than the snow-free

SOS delays the SOS, and ΔSOS approaches 0 when ESS approaches the snow-free SOS. These findings were consistent with the results of experiments I and II as analyzed above.

**Figure 12.** Changes in ΔSOS with increasing ESS under different SCF and SCDc cases derived from simulation experiment III. (**a**–**c**), (**d**–**f**), (**g**–**i**), and (**j**–**l**) are the changes in the ΔSOS with ESS for four cases of SCF = 25%, 50%, 75%, and 100%, in each group of which three cases of SCDc = 32, 64, and 96 were plotted.

To further investigate the different effects of ESS and SCDc on ΔSOS, we also analyzed the time curves of Vis under different ESS scenarios based on simulation experiment III. The medium SCDc = 64 was used. As the ΔSOS was close to 0 around the ESS at DOY 144, the ESS was varied as DOY 144 minus or plus three 16-day intervals, corresponding to three cases of ESS at DOY 96, 144, and 192. Figure 13 shows the temporally filtered time curves of VIs and the detected SOS. It clearly shows that the snow season ending much earlier than the snow-free SOS (ESS at DOY 96) advanced the SOS by up to 56 days, while the snow season ending much later than the snow-free SOS (ESS at DOY 192) delayed the SOS by up to 38 days. When the ESS approached the snow-free SOS (ESS at DOY 144), the changes in SOS caused by snow were very small. Therefore, the effect of snow cover on SOS detection depends on snow parameters, specifically SCDc, ESS, and the snow-free SOS. Because the presence of snow increases the local gradient of the VI growth curve and causes SOS to be detected, ESS and snow-free SOS determine where and to what extent the gradient of the VI growth curve increases.

**Figure 13.** Time curves and the detected SOS of the five VIs under different SCF and ESS cases at SCDc = 64. (**a**–**c**), (**d**–**f**), (**g**–**i**), (**j**–**l**), and (**m**–**o**) are the time curves of five VIs, for each of which three ESS cases at DOY 96, 144, and 192 and five cases of SCF = 0%, 25%, 50%, 75%, and 100% were plotted.
