Snow is an important research interest in international cryosphere research. In China, cold region account for 43% of the total area (Yang et al., 2000). The area of stable snow where snow cover duration is greater than 60 days is approximately 420×104km2. In West China, the recharge to spring freshet from winter snow is a necessary regulation for spring drought (Qin et al., 2006). However, larger area but sparser stations in West China lead to a shortage of observations. Especially for snow, most of the regions where snow-dominated are located in mountainous regions that are quite inconvenient for people to establish observatory stations. All these result in a poor representative of station observations (Li, 1995). Therefore, application of Remote Sensing is absolutely necessary for snow research (Gao et al., 2010).
The data received and released by the Moderate-resolution Imaging Spectroradiometer (MODIS) with a spatial resolution of 250m, 500m and 1000m have been widely used for research. Huang et al (2007) combined Geographic Information System (GIS) and station observations to analyze the precision of snow identification of two types of MODIS snow products: MOD10A1 (daily snow cover data) and MOD10A2 (8-day snow cover data) in Northern Xinjiang area. 8-day data is proved to better eliminate the influence of amount of clouds and with a mean precision of snow identification about 87.5%. Wen et al (2006) assessed the seasonal variation of snow extent in parts of Nyainqntanglha Range (4720-5850m) based on MODIS data, and proved it feasible to monitor snow extent by MODIS data in this region. Zhang et al (2005) revealed that snow-cover area and snow line altitude change obviously with climate change in Qilian Mountains by adopting NOAA-AVHRR, EOS-MODIS data and station observation between May and August, 1997-2004. Han et al (2007) analyzed the feedback of regional snow-cover to climate in Northeast China during 2000-2005 by MODIS products.
Snowmelt hydrological model focus on snowmelt runoff processes and used to quantify snow-related variables in snow water equivalent (SWE). Anderton et al. (2002) developed a grid-based distributed energy balance snowmelt model and used distributed SWE as initial boundary condition. Bell and Moore (1999) developed an elevation-dependent snowmelt forecasting model, and used PACK snowmelt module, which conceptualizes snow storage to ‘dry’ and ‘wet’ snow reservoirs with different outflow rates. These methods provide a simple but quantitative relation between snow and water. However, both distributed SWE and reservoir calculate snow as water amount rather than its real state, hardly simulate the spatial pattern of snow covered area, and how it evolves with time. In fact, spatial distribution of snow is very important for hydrological cycle in snowmelt-dominated regions. Whether soil is covered by snow or not is a necessary boundary input for hydrological modelling. It determines the energy balance by albedo, inform whether rainfall runoff generation or snowmelt runoff.
Different factors dominate snow distribution at different scales. At macro-scales (10km–1000km), latitude, elevation, and water bodies primarily control spatial variation of snow. Terrain characteristics and vegetation cover determine at meso-scales (100m–10km), interception, sublimation, and wind redistribution dominate at micro-scales (10m–100 m) (McKay & Gray, 1981; Pomeroy et al., 2002; Liston, 2004). Based on the results of experiments, topographic factors (Marchand & Killingtveit, 2005) and vegetation cover (Jost et al., 2007) are considered to be the most important variables to explain snow pattern at the watershed-scale.
Among all the topographic factors, elevation provides a significant positive correlation with the spatial pattern of snow (Daugharty & Dickinson, 1982; D’ Eon, 2004; Varhola et al., 2010) because orographic cooling influence the accumulation and ablation processes of snow (Hendrick et al., 1971; Sloan et al., 2004). Linear lapse rate is regularly observed in mid-latitude mountainous regions (Hantel et al., 2000). Most often, the global mean lapse rate of approximately 6.5°/1000m is common used (Barry, 1992; Li & Williams, 2008). Bell and Moore (1999) adopted 5.9°/1000m in upland British. Based on a statistics of 27-year time series in 7 stations, temperature lapse rate in Eastern Tibet is 6.3°C per 1000 meters, a little smaller than that of 7.0°C per 1000m reported for Colorado Rocky Mountains (Williams et al., 2011; Gao et al., 2012).
Vegetation offers a negative indicator of snow distribution. Calculated from a physically based formulation, interception is closely related to vegetation cover (Hedstrom and Pomeroy, 1998; Pomeroy, 2002). Interception by canopies and increased sublimation reduce snow accumulation on the ground (Essery et al., 2003). In forested area, the amount of snow is 40% lower than in nearby clear-cut reference sites (Winker et al., 2005). Presence of snow affects both length of growing season, and primary plant production (Buus-Hinkler et al., 2006). Long snow-covered periods will shorten vegetative season, for snow-cover prevents the initiation of growing season until it disappears from vegetated areas (Palacios, 1997; Buus-Hinkler et al., 2006). Normalized Difference Vegetation Index (NDVI), an index of vegetation greenness derived from remote sensing data (Jia et al., 2004) is frequently employed. NDVI-related researches in cold regions are frequently conducted. Ones reveal the inter-annual (Myneni et al., 1997; Hope et al., 2003) and intra-seasonal variability of NDVI. Different latitudes (Hope et al., 2004) and vegetation types (Jia et al., 2004) are also assessed. Buus-Hinkler et al. (2006) monitored Snow-NDVI relations at Zackenberg in high Arctic Northeast Greenland at both high spatial and high temporal resolution, and developed a semi-empirical model to calculate snow-cover extent and NDVI. They contributed to establish a detailed relation between vegetation and snow in High Arctic areas. However, less work has been done to relate the spatial patterns of snow cover and NDVI together, and to the altitude in Alpine areas.
In our study, remote sensing data play a critical role in our data mining. Elevation as a variable is considered in spatial distribution of snow, vegetation will be used as a reference, or an indicator. We investigate: (1) quantification of SCA (Snow-Cover Area per unit area of elevation band) – Elevation relations and NDVI-Elevation relations; (2) comparisons among Snow-Elevation-Vegetation relations, to obtain a better understanding of snow-covered area vary with elevation, and the relation to vegetation.
2. Study area and data source
Yangbajain Basin locates at 90°00’E
Yangbajain Hydrological Station (90°33’E, 30°5’N) is located at the outlet of Yangbajain Basin with an elevation of 4250 m. According to temperature records of the station from 2003 to 2008, annual precipitation in the area averages 505.2 mm, 87.4% of which falls in the summer season from June to September. Monthly air temperature from June to August is above 10°C, with five months: January, February, March, November, and December, having temperatures below 0°C. Monthly average temperature at different elevation bands based on observations at Yangbajain station and interpolated with lapse rate of 6.3°C/1000m are shown in Table 1, elevation bands with air temperature above 0°C are marked in orange, which might indicate an intensive vegetative growth.
To examine the relation between SCA and elevation (SCA-Elevation) and Vegetation-Elevation relation, three types of dataset are required:
MODIS snow product: MYD10A2 (MODIS/Aqua Snow Cover 8-Day L3 Global 500 m SIN Grid V005) with a resolution of 500 m.
MODIS vegetation product: MYD13A1 dataset (MODIS/Aqua Vegetation Indices L3 Global 500 m SIN Grid V005) with a spatial resolution of 500 m and a temporal resolution of 16 days.
Digital Elevation Data (DEM) released by Shuttle Radar Topography Miss (SRTM) version 2 with a resolution of about 90 m.Table 1. Monthly average temperature at different elevation band based on observations at Yangbajain station and interpolated with lapse rate of 6.3°C/1000m.
The study area involves h25v05 and h25v06 blocks, 226 rows, 150 columns, 33900 grids. The original data are on a Sinusoidal projection. MODIS Reprojection Tools (MRT) provided by NASA is applied for re-projection, mosaic, and extraction. The command: hdftool and hdfread in Matlab is useful for processing the data in hdf format. Programs on C++ language are made to match the DEM and MODIS data (Fig. 3), calculating the average elevation of all the DEM pixels within one MODIS grid. As the spatial resolution of DEM is about 90m, and that of MODIS product is approximately 500m, every MODIS grid has 30 DEM pixels. Thus, we know the elevation for each grid in 6-year MODIS snow products with a time interval of 8-day and 3-year MODIS NDVI products with time interval of 16 days.
MODIS snow grids blurred by cloud are removed under the assumption that average snow cover percentage of cloud-affected grids is similar to average level of the ones without clouds. Finally, every grid in that 6-year/3-year time series contains three types of property: with/without snow, NDVI, and elevation.
3. Temporal distribution of snow and vegetation coverage
The regions below 4800 m have lower snow coverage, less than 20%. The region above 6400 m is covered by glaciers and permanent snow with snow coverage of more than 70%. In the elevation band between 5600 and 6400 m, the SCA varies but remains 20% at minimum. This is sometimes influenced by the temperature in warm seasons. Seasonal snow covers elevation band between 4800 and 5600 m, and is largely affected by precipitation in winter. The lack of precipitation may lead to snow-free.
A significant seasonality of vegetation is detected in elevations below 5200 m. NDVI values gradually increase from June to July when peak NDVI (>0.3) happens and then decreases. For high elevations (>6000 m), NDVI values remain less than 0.01 during the whole year.
Precipitation and temperature are considered to be the primary factors which influence snow distribution (Hope et al., 2003), especially winter precipitation and summer temperature. Based on monthly meteorological records from 2003 to 2008, air temperature stays above 0°C from April to October. Figure 6 depicts the monthly temperature anomaly from April to October which indicates melting temperature, while Figure 7 presents the precipitation in January, February, March, November, and December which indicates winter snowfall.
Obvious positive monthly temperature anomalies are recorded in April, August, and October of 2003, May and September of 2004, April and from June to September in 2005, from June to August in 2006, all the warm months except August in 2007 and April of 2008. Furthermore, the decline of SCA occurs within those months, especially in the elevation zone of [5600, 6400] m.a.s.l.
Higher precipitation in February and March of 2007 and 2008 is observed with the total amount of 10.8 and 13.0 mm, respectively. These values are much more than those during the same time of the other four years, which lead to a larger snow-cover percentage at the beginning of those two years. Shortage of snowfall in March 2004 results in the absence of snow below 5600 m.
4. Spatial distribution of snow and vegetation coverage
Under a given elevation interval, we sort all the MODIS grids into different elevation band. Therefore, snow cover percentage in one elevation band is counted from the information of with/without snow in the MODIS grids belong to that band. And average NDVI is calculated in that elevation band. In this way, SCA-Month/NDVI-Month relations in different elevation bands are transferred to SCA-Elevation/NDVI-Elevation relations in different months.
Generally, if resolution permitting, the division of a finer elevation interval will help to reveal the results in detail. The resolution of MODIS and DEM are 500 and 90 m, respectively. With a similar magnitude of resolution in both vertical and horizontal directions, the elevation intervals of 800, 400, and 200 m are chosen.
First, we use the elevation intervals 800 and 400 m to discover the relation of SCA-Elevation from 2003 to 2008. Then a comparison between SCA-Elevation and NDVI-Elevation is made based on elevation interval of 200 m from 2003 to 2005.
Two groups are depicted with elevation band intervals equal to 400 and 800 m. In each group, there are 12 figures denoting the 12 months in a year. In each figure, six lines represent the relations of SCA-Elevation in each year from 2003 to 2008 (shown in Fig. 8 and Fig. 9).
The following can be concluded:
Based on the division with an elevation interval of 800 m, an obvious positive relation between SCA and elevation is presented. This relation could be considered to be a three-segmented line (Fig. 8) with a slow increase below 5600 m, followed by a rapid rise between 5600 and 6400 m, and finally a lagging growth above 6400 m.
If 400 m is used as the elevation interval, the three-segmented line evolves into a smooth “S”-shaped curve in all the months and years (Fig. 9). This is expressed as follows:
where S is the ratio of SCA per unit area of elevation zone (Snow-cover percentage).
There exists a critical elevation
The relation of NDVI-Month at different elevation zones (Fig. 5) is converted to the relation of NDVI-Elevation in different months (Fig. 10). A pair of similar but reversed graphs of SCA-Elevation and NDVI-Elevation is preliminarily derived.
5. Correlation between SCA-elevation and NDVI-elevation
In this section, a finer interval of 200 m is adopted for elevation division in order to provide an insight into the relation among SCA-NDVI-Elevation. SCA-Elevation and NDVI-Elevation are obtained during the same time period of 2003-2005. For each elevation band, the expected values of snow-cover percentage (E(S)) and NDVI (E(ndvi)) and standard deviation of snow-cover percentage (
From Fig. 11, SCA increases, while vegetation cover decreases as elevation rises. Although a linear relationship between temperature and elevation is commonly used as “lapse rate”, and both snow and vegetation are closely related to temperature, neither Snow-Elevation nor Vegetation-Elevation seems to be linear, as shown in Fig. 11. Furthermore, as elevation increases, both snow and vegetation follow the changing style of being gradually varying, rapidly varying and gradual varying again.
Vegetation takes on a significant seasonality at low elevation, which leads to a high variance (
For expected value:
Knowledge in second derivative could offer a quantitative analysis. Second derivative illustrates how the rate of change proceeds for a given system. It could also be reflected by the curvature or concavity of a graph. A positive second derivative is illustrated by an upward curve (concave up), whereas a negative second derivative is denoted by a downward curve (concave down). The point switch from concave up to concave down is an inflection point. Based on the definition of the second derivative,
The expression on the right only involves two variables: S (snow-cover percentage / NDVI) and
The second derivative demonstrates one inflection point in SCA-Elevation curve and two inflection points in NDVI-Elevation curve. As shown in Fig. 14, SCA-Elevation curve varies from concave up to concave down, with inflection point in the band of [5600, 5800] m.a.s.l. It suggests an accelerated growth below 5600 m and decelerated growth above 5800 m. Two inflection points in the band of [4400, 4600] and [5400, 5600] m.a.s.l divide NDVI-Elevation curve into three segments, from concave up to concave down then to concave up again:
≤4400 m, vegetation decelerated decreases as elevation increase;
In the bands of [4600, 5400] m.a.s.l, vegetation acceleration decreases as elevation increase;
≥5600 m, vegetation decelerated decreases as elevation increase.
According to Section 3, less than 20% of the area below 4800 m is seasonally covered by snow, where air temperature keeps above 0°C for more than 6 months (see Table 1). In the regions above 6000m, NDVI value is less than 0.01 and air temperature remains below 0°C during the whole year (see Table 1). Therefore, the coincident regions [4800, 6000] m.a.s.l for both snow and vegetation are meaningful and highlighted (Fig. 14).
Within the bands of [4800, 6000] m.a.s.l, the negative NDVI-Elevation curve varies from concave down to concave up with an inflection point in the band of [5400, 5600] m.a.s.l. On the other hand, the positive SCA-Elevation curve changes from concave up to concave down with an inflection point in the band of [5600, 5800] m.a.s.l. A nearly completed reversed relation between NDVI-elevation and snow-elevation is obtained.
Based on the Snow-Vegetation-Elevation relation derived from MODIS snow and MODIS vegetation products with a spatial resolution of 500 m, we discovered the following:
A positive relation between snow and elevation exists because temperature decreases as elevation increases. However, the quantification of SCA-Elevation relation derived in Yangbajain Basin, a branch of Lhasa River Basin, Tibet, China, demonstrates an “S”-shaped curve. This means that the SCA-Elevation does not follow the supposed linear shape of temperature lapse rate to elevation.
Phenological traits of vegetation are closely related to temperature, followed by elevation. However, a complex nonlinear relation between NDVI (an index of vegetation greenness) and elevation is also discovered.
Combined with the analysis on temporal distribution of snow and vegetation in Section 3, the elevation zone of [4800, 6000] m.a.s.l seems sensitive to both snow and vegetation in our study area. Furthermore, within this elevation zone, both SCA-Elevation and NDVI-Elevation present an “S” shape, initially having an accelerated variation followed by a decelerated one, but in reversed directions. The inflection point of Vegetation-Elevation is located between 5400 and 5600 m, and that of Snow-Elevation is between 5600 and 5800 m. It reveals that the NDVI-Elevation relation could be an indication of Snow-Elevation relation. In fact, there is really a very close interaction between snow and vegetation, such as interception of vegetation could reduce snow accumulation and long snow-covered periods would shorten vegetative growing season (Palacios, 1997; Buus-Hinkler et al., 2006). That is why the inflection of NDVI-Elevation almost coincide with inflection of Snow-Elevation relation, which could help to develop the linear Snow-Temperature-Elevation relation into a more complex function for a better model input.
It is also consistent with the point that the forest cover is the most highly correlated variable with snow cover (Varhola, 2010) at meso-scales (100–10 km), but mainly in snow-vegetation sensitive elevation. At relatively high elevations such as from 801 to 1069m accounting for a maximum about 1000m and >851/1200 in southeast British Columbia (D’ Eon, 2004), or >6000 m/6970 m for Yangbajain Basin, greater snow versus reduced vegetation make the NDVI-Snow indication meaningless.
This book chapter provides a quantitative method to detect the Snow-NDVI-Elevation relation. It is a simple method that could be adopted in other watersheds for more comparisons and new findings.