Impacts of topographic factors on regional snow cover characteristics

Muattar Saydi ,Jian-li Ding *

a College of Resources and Environmental Sciences,Xinjiang University,Urumqi 830046,China

b School of Geography and Planning,Sun Yat-sen University,Guangzhou 510275,China

c Key Laboratory of Oasis Ecology,Xinjiang University,Urumqi 830046,China

Received 20 September 2019;accepted 30 March 2020

Available online 25 September 2020

Abstract At a local scal e,snow cover is influenced by terrain properties,and it affects water availability across some arid and semiarid regions.This study aimed to quantify the spatial heterogeneity of snow cover due to topographic effects based on moderate-resolution image spectroradiometer(MODIS)daily snow cover products,processed with spatial and backward temporal filters.A snow-dominant region in the middle section of the northern Tianshan Mountains in China was selected,and the snow cover ratio(SCR)and the number of snow cover days(SCD)were investigated.The results suggest that MODIS images are biased toward underestimation of the snow cover in the study region,and the error is primarily manifested within the elevation band of 1 500-2 500 m.The snow cover is mainly affected by elevation,and snow mostly accumulates above 3 800 m.In addition,the differences in SCR and SCD between the south-and north-facing slopes are more significant than those between the east-and west-facing slopes.Notably,the north-facing slopes have the maximum values of SCR and SCD,whereas the south-facing slopes have the minimum values of SCR and SCD.Furthermore,the impact of slope gradients on snow cover varies across seasons.Snow cover on a sloped surface decreases with the slope gradient during winter,while it tends to increase with the slope gradient during the other seasons.Overall,this study presents a useful perspective on the variance in regional snow cover and provides guidance for the water resources management of snow meltwater with different terrain features.

? 2020 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Snow cover;Snowmelt;Surface runoff;MODIS;Topographic effect;Elevation;Aspect;Tianshan Mountains

1.Introduction

Global warming has become evident(Xu et al.,2008;Mishra et al.,2014;Hasan and Wyseure,2018),and its impact on hydrologic systems with snow cover has been extensively recognized(Whetton et al.,1996;Dankers and Christensen,2005;Adam et al.,2009).Owing to its thermal and water storage properties(Liu and Chen,2011),the accumulated snow in high mountainous areas is an important source of surface runoff(Datt et al.,2008;Jain et al.,2009;Negi et al.,2009;Maskey et al.,2011).It affects the water cycle process over most continental mountainous areas in the northern hemisphere(Adam et al.,2009;Hall and Riggs,2007;Frei et al.,2012).Accumulated snow in high mountainous areas during cold seasons becomes runoff during the melting season,supplying water for different water usages(Saydi et al.,2019).More than one-sixth of the global population and nearly one quarter of the gross domestic products depend on water supply from snow and glacier meltwater(Adam et al.,2009;Immerzeel et al.,2012).The available water resources rely significantly on the snow accumulation and ablation processes in these regions.

Snow accumulation and ablation processes are primarily dominated by geographic latitude(Jain et al.,2009)and air temperature(L′opez-Moreno et al.,2013,2014).Local topographic factors,including elevation,aspect,and slope,significantly influence the snow cover through the distribution of incoming solar radiation(Hock,1999;Wang et al.,2006;Jain et al.,2009;Pu and Xu,2009;Lee et al.,2013;Zhang et al.,2017).Owing to its critical impact on local microclimates,especially in mountainous areas(Li et al.,2011),elevation is the primary factor to be investigated.Snow accumulation is more common in high mountainous areas because higher locations have lower temperatures,and precipitation tends to increase with elevation(Li et al.,2011).The terrain properties of aspect and slope affect the incoming solar radiation on the surface by changing the intensity and duration of sun exposure at a given location(Li et al.,2011).Usually,snow on sunward aspects lasts for a shorter period than that on shaded slopes owing to temperate discrepancy(Zhang et al.,2017);windward slopes receive more snow than leeward slopes because of the direction of incoming water vapor(Li et al.,2011;Zhang et al.,2017);and steeper slopes tend to have less snow than flatter slopes because of gravity.Therefore,the influences of topographic factors should be considered in a quantified way for investigation of snow cover characteristics and their variability(Dankers and Christensen,2005).

To date,some studies have highlighted the significance of topography in the snow cover distribution and focused on the influence of elevation.For example,Pu and Xu(2009)examined the variability of snow cover fraction(SCF)at different elevations over the Tibetan Plateau,demonstrating that SCFs were mostly concentrated in high-elevation bands and lasted for a longer period.Maskey et al.(2011)investigated the trend of change in snow cover over vertical elevation zones in the Himalaya region and reported that different elevation zones exhibited various trends of change in snow cover.Tahir et al.(2016)explored the spatiotemporal changes in snow cover across three basins in Pakistan,with regard to the changes in elevation,and investigated the trend of change in snow cover in different elevation zones.In addition,Liu et al.(2017)explored the dynamics of snow cover in Central Asia and assessed the rate of snow cover change at different elevations.Zheng et al.(2017)examined the snow cover area(SCA)and the number of snow cover days(SCD)at different elevations in a mountainous watershed in northwestern China and defined vertical zones where the snow cover is sensitive to altitude.

The terrain features of aspect and slope are crucial in local topography and closely correlated with the snow cover distribution,especially in rugged terrain.Jain et al.(2009)examined the role of aspect in the snow cover distribution in the Western Himalayas,revealing that aspect is a major factor in snow accumulation and that snow accumulated mostly on northeast-and northwest-facing slopes.Pu and Xu(2009)used four basic aspects and different slope gradients to investigate the SCF distribution over the Tibetan Plateau and quantified the variance in snow cover.L′opez-Moreno et al.(2014)examined the influence of aspect on snowpack accumulation and duration based on the energy and mass balance;the findings demonstrated that snow accumulation on south-facing slopes was more sensitive to temperature increment than that on north-facing slopes because of the more intensive solar radiation on the surface of south-facing slopes.Zhang et al.(2017)explored the SCA variation over the Qinghai-Tibetan Plateau with regard to aspect and reported that snow cover on south-and west-facing slopes changed at higher rates than that on north-facing slopes.However,the role of slope gradients in the snow cover distribution has been investigated less,and relevant studies are limited.Usually,the elevation,aspect,and slope are related to one another and act in unison to exert an overall topographic effect(Jain et al.,2009).Thus,it is necessary to conduct a more comprehensive study to elucidate the relationship between snow cover characteristics and terrain properties.

The monitoring of snow cover characteristics is based on either routinely available ground observations or images obtained from various remote-sensing satellites.The ground observation of snow is an arduous and expensive task,which is limited in areal extent(Pu et al.,2007;Negi et al.,2009;Frei et al.,2012;Liu et al.,2015).Recent advancements in remotesensing techniques and satellite capabilities have augmented snow detection with various scales of imagery at a high temporal frequency and spatial resolution,which makes it feasible to monitor snow in data-sparse areas,such as complex mountain terrains and cold regions(Frei et al.,2012).Using remote-sensing techniques,snow mapping can be obtained mainly by using either a combination of visible and infrared bands or microwave band of the electromagnetic spectrum(Frei et al.,2012).The algorithm of visible and infrared snow mapping uses the discrimination between the reflectances of snow and clouds,as well as the impacts of vegetation cover and surface heterogeneity(Hall et al.,1995,2002;L′opez-Burgos et al.,2013).Passive microwave detection differentiates between the intensities of microwave emission of snowcovered and snow-free land surfaces at a large scale(Frei et al.,2012).As the visible and infrared bands have a higher spatial resolution than a microwave,snow monitoring at a regional scale frequently uses optical instruments working in visible and infrared bands(Wang and Xie,2009;Frei et al.,2012).One of the most important sensors used for this purpose is the moderate-resolution image spectroradiometer(MODIS),which is carried by both Terra and Aqua satellites.

MODIS snow mapping is based on an algorithm developed by Hall et al.(1995).It is suitable for snow monitoring,primarily because MODIS data are readily and freely available and have been enhanced in their spatial resolution and geolocation accuracy(Hall et al.,2002;Tekeli et al.,2005;Zhang et al.,2017).Several studies have investigated the accuracy of Terra and Aqua daily snow cover products,and positive results have been obtained in different areas worldwide(Klein and Barnett,2003;Tekeli et al.,2005;Hall and Riggs,2007;Wang et al.,2007,2009).Nonetheless,the major drawback of MODIS daily snow cover products is cloud obstruction.To date,several methodologies have been developed to reduce cloud cover by merging the Terra and Aqua data on a pixel base and further using spatial and temporal filters(Parajka and Bl¨oschl,2008;Wang et al.,2009;Liang et al.,2008;Gafurov and B′ardossy,2009;Hall et al.,2010;Parajka et al.,2010;Gao et al.,2010;Tekeli and Tekeli,2012;L′opez-Burgos et al.,2013;Morriss et al.,2016).All these approaches are eff icient choices of cloud removal,enabling routine snow monitoring with less cloudy or cloud-free images.

The Tianshan Mountains of China,stretching across arid and sem iarid Xinjiang Uyghur Autonomous Region,are one of the three stable SCAs in China(Liu and Chen,2011).The mountains feed 373 inland river streams w ith snow and ice meltwater,accounting for 53.6% of the total river runoff in Xinjiang(Hu,2004).Thus,the snow accumulation and ablation processes in the Tianshan Mountains affect the tim ing and amount of released meltwater.Generally,the discharge at the outlet of an inland river closely denotes the total available surface runoff of the basin(Dou et al.,2011).Thus,the total amount of water at a river outlet is highly dependent on the abundance of seasonal snow cover at headwaters.Some recent studies have demonstrated that the air temperature in arid northwestern China has increased at a rate of 0.32°C per decade over the last 50 years,which is nearly tw ice the overall rate in China and three times the average global rate(Chen et al.,2019;Li et al.,2012).Such accelerated warm ing has markedly affected the regional snow cover and increased water stress(Chen et al.,2017,2019).Hence,it is imperative to have a robust understanding of snow cover characteristics for better planning and management of water resources in this region.

Toward these ends,this study aimed to explore the variation in snow cover characteristics across the m iddle section of the northern Tianshan Mountains in China based on local topography,from the follow ing aspects:(1)reducing cloud obstructions by merging and f iltering the Terra and Aqua daily snow cover products and validating data accuracy;(2)assessing the snow cover characteristics w ith the snow cover ratio(SCR)and SCD;and(3)analyzing the relationships between snow cover characteristics and topographic factors,including elevation,aspect,and slope.

2.Study site

The Tianshan Mountains in China stretch around 1 800 km from the east to the west(Zhang et al.,2004).They are divided into three parts:the northern,central,and southern Tianshan Mountains(Hu,2004).The study area is located at the m iddle section of the northern Tianshan Mountains,between the latitudes of 42°50′N(xiāo) and 44°27′N(xiāo) and longitudes of 83°57′E and 90°25′E,covering an area of 92 944 km2.The study area includes parts of two mountains,Yilianhabierga Mountain in the west and Bogeda Mountain in the east,w ith the Junggar Basin to the north and the Turpan Depression below sea level to the southeast(Fig.1).The elevation of the study area ranges between－119 and 5 071 m,extracted from a digital elevation model,w ith an average value of 1 809 m,and the slope gradient varies from 0°to 46.6°,w ith an average value of 7.4°.The study area,along w ith the Tailan Glacier on the southern slopes of the Tuomuer Peak and the Ili River Basin,comprises three main areas w ith stable seasonal snow cover in the Tianshan Mountains(Hu,2004).The area relies partly on snow and ice meltwater for its water resources supply(Hu,2004).

Fig.1.Location of study area and distribution of meteorological stations.

3.M aterials and methods

3.1.Removal of cloud obstruction and accuracy assessment of MODIS data

We used the Terra and Aqua daily snow cover products of MOD10A1 and MYD10A1(V005 version)in the hierarchical data format(HDF)from the NASA Distributed Active Archive Center(DAAC)at the National Snow and Ice Data Center(NSIDC).For the study period of 2003-2012,3 638 MOD10A1 and 3 648 MYD10A1 data were available,while 15 images for Terra and f ive images for Aqua were m issing.To remove cloud obstruction,we used the combined spatial and backward temporal f ilters proposed by Parajka and Bl¨oschl(2008)and implemented f iltering by(1)merging the Terra and Aqua data on the same day on a pixel base and updating the cloud pixel values of Aqua w ith non-cloud(snow or land)pixel values of Terra;(2)using a spatial f ilter to replace the cloud pixel values of the merged data w ith neighboring cloudfree pixel values;and(3)using backward temporal f ilters to replace the cloud pixel values of the merged data w ith the most recent non-cloud pixel values within one to seven preceding days.For data verif ication,we evaluated three indicators of accuracy:underestimation error,overestimation error,and overall accuracy.The underestimation error indicates the proportion(%)of snow classif ied as non-snow,the overestimation error indicates the proportion(%)of non-snow classif ied as snow,and the overall accuracy denotes the proportion(%)of the accurately classif ied snow or non-snow data.Further details on the method and data verif ication are available in Parajka and Bl¨oschl(2008).We collected daily snow depth data from January 2003 to August 2011 at 18 routine meteorological stations(Fig.1).The elevations of the meteorological stations varied in the range of 411-3 539 m,with an average elevation of 1 083 m.However,because of the rugged topography and extreme climatic conditions in high mountainous areas,only six stations had elevations ranging from 1 104 to 3 539 m,whereas the other 12 stations were scattered in plains with elevations lower than 1 km.

3.2.Evaluation and validation of snowcover characteristics

SCR indicates the proportion of SCA and can be calculated using the following equation:

where Rcis the SCR,Acis the snow cover area,A is the total area of the study site,Psis the number of snow pixels,and P is the number of total pixels.

SCD indicates the number of days at a specific location covered by snow within a hydrologic year.In the study area,the hydrologic year spans from September 1 to August 31 of the following year.The study period of 2003-2012 included nine hydrologic years,and SCD for each hydrologic year was evaluated using the cloud-filtered MODIS data with a 500-m spatial resolution.Accordingly,first,we reclassified cloudfiltered MODIS data into snow and non-snow classes.Second,the pixel value of each grid cell in the snow class was assigned a value of 1 and that in the non-snow class was assigned a value of 0.Finally,all available reclassified cloudfiltered MODIS data within a hydrologic year were overlaid with one another to obtain SCD of each grid cell.

We validated the SCD accuracy using the proportion of agreement(%)between the ground-measured SCD and the MODIS-retrieved SCD.The ground-measured SCD was assessed using the daily snow depth records of 18 meteorological stations(S1 through S18),with a snow depth threshold taken as 1 cm at each station for each precipitation day(Wang and Xie,2009).The MODIS-retrieved SCD was extracted from the SCD map based on the locations of meteorological stations.Following Wang and Xie(2009),the proportion of agreement at each station was defined using the following equation:where RDis proportion of agreement,DMis the MODISretrieved SCD,and DGis the ground-measured SCD.

3.3.Topographic effects

To investigate the impact of topographic effects,each of the three basic topographic characteristics,elevation,aspect,and slope,was divided into several groups based on the properties of local topography.It should be noted that the extraction of topographic characteristics was completed using DEM data.The study area was divided into six vertical zones by means of elevation,orientations were grouped into four basic aspects,and slope gradients were clustered into four consecutive groups(Tables 1 and 2).Although the characteristics of local topography varied from site to site,the classification of terrain features in such a way could provide a clear perspective on quantifying the relationships between topographic effects and snow cover characteristics.

Table 1 Classification of vertical elevation zones in study area based on DEM data.

4.Results

4.1.MODIS cloud removal and data validation

The MODIS cloud removal using the spatial and backward temporal filters exhibited a strong performance during 2003-2012.The long-term average cloud coverage was 44.0%for Terra,47.3%for Aqua,and 35.3%for the merged images.After the merged images were filtered with spatial and temporal filters,the cloud obstruction was removed by 33.8% and decreased to a small fraction of 1.5%.For data validation,the accuracy of snow classification was assessed,respectively,for the Terra and Aqua daily snow cover products under clear sky conditions and for the cloud-filtered MODIS data on each day.Table 3 shows that the MODIS data are biased toward the underestimation of snow cover in the study area.Under clear sky conditions,we found that the average underestimation errors were 5.2%and 7.5%for Terra and Aqua images,respectively,and the proportion of overestimated snow was less than 1%for each satellite.The cloud-filtered MODIS data therefore also tended toward a larger underestimation error(9.6%)and were capable of correctly identifying 89.1%of snow.

4.2.Extraction and validation of SCD

We evaluated SCD in each grid cell for each hydrologic year and averaged the results for nine hydrologic years to obtain the SCD map of the study area,as shown in Fig.2.The spatial resolution of each grid cell is 500 m,and the SCD values are classified into six ranges to form a color map.Meanwhile,the SCD accuracy was validated for each hydrologic year at each station,and the results were averaged for the nine hydrologic years(Fig.3).

Table 2 Classification of aspects and slope gradients in study area based on DEM data.

Table 3 Accuracy of snow classification in study area during 2003-2011.

Fig.2 shows that the lowest SCD values of less than 30 d were detected in the Turpan Depression and at some riverbeds in the mountainous watersheds,accounting for 24.1%of the total area.The areas with SCD ranging from 91 d to 120 d covered the northern part of the Yilianhabierga and Bogeda mountains,accounting for the largest proportion of 27.3%.In addition,the areas with SCD ranging from 121 d to 180 d crossed the northern foothills of Bogeda Mountain and southwestern foothills of Yilianhabierga Mountain,and had a proportion of 17.0%.Furthermore,the areas with the largest SCD values of more than six months were mainly distributed in the high mountainous areas and had the smallest proportion of 8.0%.

Fig.2.Spatial distribution of average SCD in study area during 2003-2012.

Fig.3 shows agreement between the MODIS-retrieved and ground-measured SCDs.The average proportion of agreement across 18 stations was 85.9%,while the average proportion of disagreement was 14.1%.Of the 18 stations,eight had a proportion of agreement greater than 90%,among which one station(station S10)displayed full agreement(100%).Also,the average MODIS-retrieved SCD across 18 stations was 95 d,which was 17 d less than the average ground-measured SCD,with the value of 112 d.

4.3.Snow cover characteristics in relation to elevation

We evaluated SCR for each elevation zone at daily step during 2003-2012,and the annual average values were calculated,as shown in Fig.4.

Across the study area,SCR did not increase with elevation below 2 500 m.For example,zones B and C at higher elevations had smaller SCRs(18.5% and 17.3% on average,respectively)compared with the lower-elevation zone A(23.4% on average).Above the elevation of 2 500 m,SCR increased with altitude.The long-term annual average SCR in zone D was 23.0%,which increased at a rate of 1.37% per 100 m to 32.0% in zone E.Zone F was at elevations higher than 3 800 m,where SCR continued to increase at a higher rate of 3.27%per 100 m and reached 53.2%.Compared with other elevation zones,zone F had the highest SCR,and more than 60% of the zonal area was covered by snow during autumn(September to November),winter(December to January),and spring(March to May).Summer(June to August)also had a considerable SCR of 31.6%,implying that one-third of the zonal area was covered by snow throughout a year.However,below the elevation of 3 800 m,SCR during the summer was tiny,and snow existed in a tiny region,coving 0.1%-5.1% of the entire study area.

Fig.3.Proportion of agreement between average MODIS-retrieved and ground-measured SCDs at each meteorological station during 2003-2012.

Fig.4.Annual average SCR distribution across vertical elevation zones during 2003-2012.

The SCD distribution across vertical zones(Table 4)corroborated that of SCR.Areas below the elevation of 1 500 m(zone A)had an average SCD of 81 d.At higher elevations of 1 500-2 500 m,the average SCD decreased to 64 d for zone B and 60 d for zone C.At elevations higher than 2 500 m,SCD tended to increase with elevation.For example,zone D had an average SCD of 81 d,which was equal to that of zone A.In the elevational bands E and F,SCD increased dramatically.For zone E,SCD for each hydrologic year was greater than 100 d,and it reached a maximum of 132 d during 2005-2006.For zone F,SCD varied between 169 d and 207 d,and the average SCD reached 191 d,implying that areas above the elevation of 3 800 m were covered by snow for more than six months of a year.

Table 4 Distribution of SCD across vertical elevation zones during 2003-2012.

Elevation controls the vertical distribution of air temperature and liquid and solid precipitation(Ding et al.,2014).During cold seasons,precipitation falls as snow across most parts of the study area.In warm seasons,however,snow occurs more often in higher-elevation zones,while lowerelevation bands receive precipitation in the form of rain(Ding et al.,2014;Sospedra-Alfonso et al.,2015).The snow cover distribution at different elevations thus has a seasonal pattern(Table 5).

The average SCR across four seasons in each elevation zone revealed that winter had the highest average SCR of 52.2%,followed by spring with 28.8% and autumn with 22.1%,and summer had the lowest average SCR of 6.6%.These findings suggested that autumn and winter are snow accumulation seasons,while spring and summer are snow ablation seasons.Nearly one half of the accumulated snow melts in spring,contributing to snowmelt runoff in the middle section of the northern Tianshan Mountains.

Table 5Seasonal average SCR distribution across vertical elevation zones during 2003-2012.

4.4.Snow cover characteristics in relation to aspect

Snow cover is sensitive to aspect(Li et al.,2011).Table 6 lists statistics of the average SCRs of different aspects for each month during 2003-2012.SCR varied significantly on differently oriented slopes.The snow accumulation on the northern slopes was higher than that on the southern slopes.In addition,the long-term annual average SCR on the northern slopes was 30.0%,which was 13.5% higher than that on the southern slopes.However,the long-term annual average SCRs on the western and eastern slopes were comparable,with the values of 26.8% and 24.3%,respectively,throughout a year.

Fig.5 displays the SCDs of four aspects in each hydrologic year during 2003-2012.The findings revealed that northfacing slopes had the maximum average SCD of 104 d,followed by 93 d for west-facing slopes.East-facing slopes had an average SCD of 84 d,and south-facing slopes had the minimum average SCD of 59 d.There was a difference of 45 d in SCD between north-and south-facing slopes,and the difference was 9 d between west-and east-facing slopes.

4.5.Snow cover characteristics in relation to slope

We evaluated the annual average SCR of the four slope gradient groups in the study area(Table 7).In the relatively flat area with a slope gradient of 0°-5°,the long-term annual average SCR was 24.4%.On the steeper slopes with gradients of 5°-10°and 10°-15°,SCR increased and reached 26.1%and 28.3%,respectively.As the slope gradient exceeded 15°,SCR tended to decline and decreased by 3.2% compared with that on flatter slopes with a gradient of 10°-15°.

Terrain slopes influence the snow cover seasonality.A steeper slope receives less radiation than a flatter surface,but is less favorable for snow accumulation because snow moves downslope due to gravity.SCRs during 2003-2012 for different slope gradients revealed seasonal variation(Fig.6).As discussed in Section 4.3,winter has the most snowfall.However,with the increase in slope gradient,the accumulated snow on steeper slopes tends to slide,and the amount is less than that on flatter surfaces.Thus,SCR decreased with an increase in slope gradient in winter.For example,on flat terrain with slope gradients of 0°-5°,SCR reached its highest value at 72.2% during winter.As the slope got steeper,SCR started to decrease and fell to its lowest value at 41.6% on a steep slope with a gradient greater than 15°.Across the other three seasons,SCR mostly increased with the slope gradient.For example,in the gradient range of 0°-5°,SCR was 15.4%for spring,0.4% for summer,and 9.7%for autumn.When the slope gradient was greater than 15°,SCR increased by 1.95,14.00,and 2.39 times in spring,summer,and autumn,respectively.SCR increased on steeper slopes across warmer seasons,probably because snow occurs more often over high mountainous areas with steeper slopes.

Table 6Monthly average SCRs of four aspects during 2003-2012.

5.Discussion

Under different topographic conditions,the snow cover distribution varies significantly,and the quantified relationship between topography and snow cover characteristics strongly depends on the quality of data used for snow cover evaluation.This study used the MODIS Terra and Aqua daily snow cover products,in combination with spatial and backward temporal filters,to obtain cloud-free or less-cloudy snow data.The findings show that MODIS snow cover products exhibited a strong performance in snow classification in the study site.The MOD10A1 and MYD10A1 data could identify more than 90%of snow correctly on clear-sky days,while the cloud-filtered MODIS data could identify nearly 90% of snow correctly on each day.These accuracies match other studies(Klein and Barnett,2003;Zhou et al.,2005;Hall and Riggs,2007;Liang et al.,2008;Parajka and Bl¨oschl,2008;Wang and Xie,2009;Gafurov and B′ardossy,2009),which had accuracies ranging from 80% to 100% in evaluation of snow distribution.

Our MODIS-retrieved SCD map exhibited an overall agreement of 85.9% with the ground-measured SCD and was biased toward the SCD underestimation.Liu and Chen(2011)investigated the spatiotemporal variation of SCD in China using MODIS data during 2001-2006 and found that the MODIS-retrieved SCD was usually lower than the groundmeasured SCD by 10% in Xinjiang and some other regions in China.In addition,Marcil et al.(2016)detected a larger underestimation error of MODIS snow cover products in a Canadian mountainous watershed.However,the results of partial errors(overestimation and underestimation errors)suggested that the smaller SCD value retrieved from MODIS data was partly due to the snow presence underestimation by the Terra and Aqua daily snow cover products.In addition,the daily merged Terra and Aqua images were subjected to cloud filtering,and 93.5%(3 348 images)of all merged images were cloud-free or had less than 5% of cloud coverage after filtering.However,6.5%(233 images)of the merged images still contained some cloud obstructions,ranging from 5.2% to 26.9%,with an average of 9.7%.For SCD retrievals from MODIS data,the remaining cloud pixels were reclassified into a non-snow class,which might have caused a small fraction of underestimation error in the MODIS-retrieved SCD.

Fig.5.SCDs of four aspects in each hydrologic year during 2003-2012.

Both SCR and SCD had smaller values in areas with elevations of 1 500-2 500 m(zones B and C)compared with elevations lower than 1 500 m.However,three meteorological stations(stations S15,S16,and S17 in Fig.3)were available within the elevation range of 1 500-2 500 m.These three stations had a relatively high percentage of disagreement between the MODIS-retrieved and ground-measured SCDs,nearly 34% on average.At the much higher elevation of station S18(3 539 m),the proportion of disagreement decreased to 7.7%,implying that the underestimation of snow cover by MODIS data might be concentrated within the elevational band of 1 500-2 500 m,encompassing the transitional zones from less snow-covered plains to snow-dominated mountainous areas.Similar results were reported by Wang et al.(2009)in northern Xinjiang in a cloud removal and data validation task on the Terra and Aqua daily snow cover products.They revealed that the snow classification accuracies of both the Terra and Aqua daily snow cover products were compromised in the transitional zones from land to snowcovered areas;high agreement could be found in either landor snow-dominant areas,and major disagreement occurred in the transitional zones.

Table 7Annual average SCRs for different slope gradients during 2003-2012.

Fig.6.Seasonal average SCR distribution in relation to slope gradient during 2003-2012.

Regarding the relationship between aspects and snow cover,the north-facing slopes had remarkably large SCR and SCD values compared with those of the south-facing slopes,corroborating previous studies that emphasized that snow accumulates most on north-facing slopes(Jain et al.,2009;L′opez-Moreno et al.,2014).The seasonal variations in snow cover on differently oriented slopes also followed the same pattern.In winter,the north-facing slopes were mostly covered with snow,and the average SCR was 78.0%.However,the south-facing slopes had the lowest SCR of 38.4%,which was less than one half of that of the north-facing slopes.In addition,the average SCR was 63.1% for the west-facing slopes and 54.8%for the east-facing slopes,with a smaller difference of 8.3% between the two aspects.During the other three seasons,SCRs of the north-facing,west-facing,and eastfacing slopes were nearly equal to one another,whereas the south-facing slopes had the lowest SCR.These findings indicate that the spatial variability of SCR with aspect is most significant during winter.SCR varying with aspect is primarily affected by the distribution of solar radiation and the direction of incoming water vapor(Pu and Xu,2009).The water vapor arrives to the Tianshan Mountains primarily from two sources:water vapor transported with westerlies and moisture from the north(Chen et al.,2019;Hu,2004).The impact of water vapor on precipitation decreases along the Tianshan Mountains from the west to east and from the north to south(Hu,2004).Hence,the northern slopes of the Tianshan Mountains have more precipitation than the southern slopes,and the western slopes have more precipitation than the eastern slopes.The remarkably low SCR and short snow cover duration of the southern slopes account for the fact that water resources of the southern slopes of the Tianshan Mountains are much scarcer than those of the northern slopes(Hu,2004).

6.Conclusions

The main findings of this study are as follows:

(1)Elevation is the major regulator of snow presence.The amount and duration of snow cover share the same pattern in their vertical distribution across the middle section of the northern Tianshan Mountains in China.Both SCA and SCD increase with elevations higher than 2 500 m,and most snow accumulates in high mountainous bands.The areas with elevations higher than 3 800 m(zone F)are covered by snow for more than six months each year,and approximately one-third of the total zonal area is covered by snow throughout a year.

(2)The magnitudes of SCR and SCD vary significantly between the four aspects and can be listed in the following decreasing order:north-facing slopes,west-facing slopes,eastfacing slopes,and south-facing slopes.The difference in snow cover between the south-and north-facing slopes is more significant than that between the east-and west-facing slopes.Meanwhile,the snow cover in relation to aspect is most pronounced during winter.

(3)The impact of slope gradients on snow cover is clear.Flatter slopes facilitate snow accumulation,and SCR shows a sharp decline during the winter as the slope gets steeper.However,across the other three seasons,SCR tends to increase with the slope gradient.

Acknowledgements

We truly thank Professor Juraj Parajka at the Institute of Hydraulic Engineering and Water Resources Management,at the Technical University of Vienna,Austria for his help with MODIS data processing and coding.We also thank Professor Xiaodong Huang at the College of Pastoral Agriculture Science and Technology,Lanzhou University,for his data support.The DEM and MODIS data were obtained,respectively,from the United States Geological Survey(USGS)and the Distributed Active Archive Center(DAAC)at the National Snow and Ice Data Center(NSIDC).

Declaration of competing interest

The authors declare no conflicts of interest.