Evidence of elevation-dependent warming from the Chinese Tianshan Mountains

The phenomenon in which the warming rate of air temperature is amplified with elevation is termed elevation20 dependent warming (EDW). It has been clarified that EDW can accelerate the retreat of glaciers and melting of snow, which can have significant impacts on the regional ecological environment. Owing to the lack of high-density ground observations in high mountains, there is widespread controversy regarding the existence of EDW. Current evidence is mainly derived from typical high mountain regions such as the Swiss Alps, the Colorado Rocky Mountains, the Tropical Andes and the Tibetan Plateau/Himalayas. Rare evidence in other mountains has been reported, especially in arid regions. In this study, 25 EDW features (regional warming amplification and altitude warming amplification) in the Chinese Tianshan Mountains (CTM) were detected using a unique high-resolution (1 km, 6-hourly) air temperature dataset (CTMD) from 1979 to 2016. The results showed that there were significant EDW signals at different altitudes on different time scales. The CTM showed significant regional warming amplification in spring, especially in March, and the warming trends were greater than those of continental China with respect to three temperatures (minimum temperature, mean temperature and maximum temperature). 30 The significances of EDW above different altitude thresholds are distinct for three temperatures in twelve months. The warming rate of the minimum temperature in winter showed a significant elevation dependence (p < 0.01), especially above 3000 m. The greatest altitudinal gradient in the warming rate of the maximum temperature was found above 4000 m in April. For the mean temperature, the warming rates in June and August showed prominent altitude warming amplification but with different significances above 4500 m. Within the CTM, the Tolm Mountains, the eastern part of the Borokoonu Mountains, 35

glaciers with an area of ~9225 km 2 and of 1011 km 3 water resources (ice volume) in the Chinese Tianshan Mountains (CTM, Fig. 1) (Shi et al., 2009). However, recently, most glaciers in the CTM are in a state of accelerated degradation due to 100 climate warming (Ding et al., 2006;Chen et al., 2016;Sorg et al., 2012). The warming rate of mean temperature in the entire CTM has reached 0.32-0.42 ℃10a -1 in the past 50 years, which is much higher than the national average (Gao et al., 2018a;Xu et al., 2018). However, the EDW in the CTM still lacks systematic detection. Current research on climate warming in the CTM does not provide sufficient solid evidence for the EDW phenomenon. Therefore, in this study, EDW features in the CTM were comprehensively and systematically detected based on a unique high-resolution (1 km, 6-hourly) air temperature 105 dataset (hereafter referred to as CTMD) (Gao et al., 2018a). The present study reveals the EDW characteristics for different temperature indicators at different time scales.

CTMD
The lack of sufficient ground observations is the biggest obstacle in the accurate detection of the EDW phenomenon. This is 110 one of the original intentions of the development of CTMD. Previous studies have shown that the ECMWF's thirdgeneration reanalysis product, ERA-Interim, has a relatively small large-scale error (±2.5 K) and can capture the annual and seasonal climatologies very well (Gao et al., 2012(Gao et al., , 2014(Gao et al., , 2017Simmons et al., 2010). Hairiguli et al (2019) concluded that the ERA-Interim could capture the inter-annual variations of monthly mean temperature in the CTM from via comparing with 45 observation sites from 1984 to 2016. Bai et al. (2013) also found that ERA-Interim temperature data are better than 115 NCEP/NCAR data based on a comparison with nine observation sites in the CTM from 2004 to 2006. The systematic bias of ERA-Interim is mainly due to the height discrepancy between the ERA-Interim model height and observations (Gao et al., 2012(Gao et al., , 2014(Gao et al., , 2017. Thus, the bias could be significantly reduced for local climate trend investigations via an appropriate elevation correction procedure. A robust approach based on internal vertical lapse rates derived from different ERA-Interim pressure levels was developed to downscale the 0.25° grid ERA-Interim temperature to a 1 km grid derived from SRTM 120 (Gao et al., 2018a). This scheme is fully independent of meteorological stations via Equation (1).
T ERA_025 is the original 6-hourly ERA-Interim 2-m temperature at a 0.25° grid. Г describes the ERA-Interim internal lapse rates derived from the temperatures and geopotential heights at different pressure levels. For example, Г 500_700 indicates the lapse rate between the 500 hPa and 700 hPa pressure levels, which is calculated by the temperature differences divided by 125 geopotential height differences between these two pressure levels. ∆h is the height difference between the ERA-Interim model height and the 1 km grid. Different Г values were used according to the altitude of the 1 km grid. In other words, if the 1 km grid is lower than 1500 m in altitude, Г 850_925 is applied because the geopotential height between the 850 and 925 hPa pressure levels ranges from 150 m to 1500 m. If the grid altitude is higher than 4000 m, Г 500_600 is applied to the downscaling model. The geopotential height at the 850 and 700 hPa pressure levels is the demarcation at altitudes of 1500 m 130 and 3000 m, respectively. In total, four lapse rates (Г 500_600 , Г 600_700 , Г 700_850 and Г 850_925 ) were used for different altitude ranges according to the 1 km grids (Gao et al., 2018a). Therefore, the unique high-resolution (1 km, 6-hourly) air temperature dataset (CTMD) for the Chinese Tianshan Mountains from 1979 to 2016 has a spatial resolution of 1 km (total 356133 grids) with 6-hourly time step at 00, 06, 12, and 18 UTC. More information regarding the downscaling scheme and on the CTMD can be found in Gao et al. (2012Gao et al. ( , 2017Gao et al. ( , 2018a. 135 Although, the CTMD was validated by 24 meteorological stations on a daily scale, indicating a high reliability for the climatology trend investigations, its limitations must be fully demonstrated. Whether the lapse rate accurately reflects the temperature changes at all altitudes is worth discussing. For example, the lapse rates of ERA-Interim are greater than observations from September to December, whereas the lapse rate in the free atmosphere is steeper than that near the surface because of the different radiation mechanisms (Gao et al., 2018a). The lapse rate may be positive rather than negative 140 because of the "Cold Lake" effect in winter, such as in the Turfan Basin, which may lead to a temperature inversion layer at night. In this situation, the downscaling model may be disabled during winter. Therefore, the opposite trend for minimum temperature during winter was captured by the CTMD compared to the slight positive warming trend from the 24 observation sites. Meanwhile, the trend of the diurnal temperature range (DTR) was not captured very well by the CTMD in spring and autumn (Gao et al., 2018a). We emphasise that the CTMD is only validated by 24 sites, which are mainly located 145 in low elevation terrain. Evaluating the credibility of the CTMD in the high peaks is difficult because few observations exist. reliable and has been widely applied in climatology studies since it was interpolated using the thin plate spline method based 160 on high-density ground stations (approximately 2400 national meteorological observation stations) since 1961 (Sun et al., 2015;Wu et al., 2017). A common time period 1979-2016 was extracted for the current study. Previous studies found that the Qinghai-Tibetan Plateau (QTP) has a significant temperature warming trend over China (e.g. You et al., 2010). To reduce the influence of warming, the Qinghai-Tibetan Plateau was eliminated. Thus, not only the whole continental China (WCC), but the low-altitude areas (LCC), represented by excluding the Tianshan Mountains and the Qinghai-Tibetan Plateau 165 from the whole continental China, were also used for comparison.

Snow cover and snow depth data
To further discuss the possible hypotheses and mechanisms with respect to EDW, snow cover and snow depth data in the CTM were collected. The snow cover fraction was calculated by dividing the snow cover area by the total area. The snow cover area was interpreted based on the MODIS/Terra Snow Cover 8-Day L3 product (MOD10A2, version 5) with a 500 m 170 spatial resolution from the NASA Snow and Glacier Data Centre (https://nsidc.org/data/MOD10A2/versions/5). The annual maximum and minimum snow cover fractions (only two values per year) in the CTM from 2002 to 2013 were calculated.
This dataset was processed and provided by Chen et al. (2016) and Deng et al. (2019).
The daily snow depth data at a spatial resolution of 25 km from 1979 to 2016 over the CTM were derived from the National Earth System Science Data Centre, National Science & Technology Infrastructure of China (Che 2015). The snow depth was 175 calculated based on the original daily passive microwave brightness temperature data (EASE-Grid) produced from SMMR (1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987), SSM/I (1987SSM/I ( -2007 and SSMI/S (2008-2019) from the National Snow and Ice Data Centre (NSIDC). The monthly snow depth calculated from daily depth was applied for the follow up analysis. Detailed information on the data production can be found in studies of Che et al. (2008), Dai et al. (2015) and Dai et al. (2017).

Analytical methods 180
In this study, the 6-hourly (00, 06, 12 and 18 UTC) data of the CTMD were aggregated to the minimum temperature (Tmin), maximum temperature (Tmax), and mean temperature (Tmean) on daily, monthly, seasonal, and annual time scales. A standard linear regression was applied to calculate the warming rate in each grid from 1979 to 2016 for the CTMD and CMA05 datasets. The corresponding equation is given as follows: where y is the temperatures (Tmin, Tmax and Tmean) on different time scales, x is the time series from 1979 to 2016, and the fitting coefficient (slope) α indicates the warming rate. Thus, in this study, EDW refers to the rate of warming over a multi-annual scale.
To detect the altitude warming amplification within the CTM, the entire altitude range was divided into 14 groups with 500 m intervals (Table 1). The numbers of grids in each group are listed in Table 1. Standard linear regression was also used to 190 assess different significance levels (p < 0.1, p < 0.05, and p < 0.01) of EDW for different altitude groups. In this analysis, y is the warming rate (calculated by the equation 2) from 1979 to 2016 for each altitude group. The average warming rate of each group was used for the regression because of the different number of grids in each altitude group. Here, x denotes the 14 altitude groups (natural positive integers 1 to 14). Thus, the fitting coefficient (slope) represents the magnitude of the significance of EDW. The coefficients of determination (R 2 ) and confidence tests (p-values) illustrate the goodness of fit. 195

Regional warming amplification of the CTM
The temperature trends on monthly, seasonal, and annual time scales with respect to Tmin, Tmax and Tmean were calculated using Eq. (2) based on the aggregated Tmin, Tmax and Tmean from 6-hourly (00, 06, 12 and 18 UTC) CTMD data for each grid. Table 2 shows the ratio of the sum of grids at different significance levels (p < 0.1, p < 0.05, and p < 0.01) to the total 200 grids (356133) with respect to monthly temperatures. All grids reached the significant levels for Tmax in March, followed by 99.35% of all grids for the Tmean. The number of grids that reached the significance level was the lowest in December, especially for Tmean and Tmax. For Tmin, more than half of the grids in only two months (March and June) reached the significance levels. For Tmean, five months (March, April, June, July and August) exceeded 50% grids at the significance levels. For Tmax, only February and March had more than half of all grids at the significance level. Although the 205 temperature trend at some grids in a certain month did not reach a statistically significant level, it can still reflect climate warming on a regional scale to a certain extent. Thus, the subsequent analysis depends on the temperature trend of all grids.
The annual and seasonal temperature trends in the CTM were weaker than those over WCC with respect to the mean temperature (Tmean), maximum temperature (Tmax), and minimum temperature (Tmin), except during spring (Table 3).
The warming rates in the Tmax and Tmin of spring both exceeded 0.6 ℃ 10a -1 , which is much higher than that of WCC and 210 LCC which is represented by excluding the Tianshan Mountains and the Qinghai-Tibetan Plateau from the whole continental China. The summer Tmin and Tmean trends of CTM were also higher than those of LCC. The annual Tmin showed the greatest warming trend with a rate of 0.347 ℃ 10a -1 , followed by Tmax and Tmean with warming rate of 0.323 and 0.245 ℃ 10a -1 , respectively, in the CTM (Table 3). While summer had a much higher trend than autumn for Tmean and Tmin, it showed a comparable rate for Tmax (Table 3). Winter had the lowest rates compared with other seasons for the three 215 The warming rates vary from month to month, which is more significant than that from season to season. All temperature trends were negative in January and December in the CTM, which was different from that in the WCC and LCC (Table 4). 220 The rate of decrease was more significant in January than in December. Notably, Tmax decreased slightly in May, whereas Tmin warmed significantly at a rate of 0.624 ℃ 10a -1 in the CTM. The largest warming rates were observed for both the CTM and land surface of China in March for all temperature types. However, the CTM had a higher magnitude of warming.
The warming trend was 1.339 ℃ 10a -1 , which was almost double that over the whole of China (Table 4). Both rates exceeded 0.8 ℃ 10a -1 for Tmean and Tmin in the CTM in March. April showed the second largest Tmax and Tmean 225 warming trends in the CTM, which were also higher than those over continental China. For Tmin, May and June had rates greater than 0.6 ℃ 10a -1 . The significant warming trends from March to May resulted in higher trends in CTM than in continental China, especially in March (Table 4). In general, a more significant increment in Tmin was observed from March to June compared to that in other months. March and April showed remarkable warming trends for Tmax and Tmean (Table   4). In the entire CTM, Tmin increased faster than Tmax and Tmean. In general, regional warming amplification was 230 significant in March and June at all temperatures. The trend for Tmax also increased faster in the CTM in February and April than over the entire land surface of China. The warming rates of Tmean and Tmin in the CTM were faster than those in the WCC and LCC in April and May, respectively. All temperature trends at different time scales in the WCC were higher than LCC, which implies that the warming rate of the Qinghai-Tibet Plateau contributes significantly to regional warming. It is worth noting that the warming trends are larger in both Tmin and Tmax than in Tmean in some months for CTM, WCC and 235 LCC (Table 3 and 4). The possible reason is very complicated. It is not only related to the local physical mechanisms that may change the diurnal cycle, but also related to the data resource which is dependent on the time of day (00, 06, 12, and 18 UTC). You et al (2020) also found this phenomenon over the Tibetan Plateau based on multiple data products.

Warming amplification with altitude within the CTM
The performances of different temperature types (Tmin, Tmean and Tmax) were diverse for different months. The monthly 240 and seasonal temperature trends were calculated for each grid based on the averaged 6-hourly data. To detect the altitude warming amplification features in the mountain areas, the CTM was divided into 14 groups with a 500 m altitude interval (Table 1). Notably, the temperature trends in the different elevation groups were significant distinct than those of the entire CTM. Table 5 to 7 summarized the warming amplification with altitude for monthly Tmin, Tmean and Tmax over different altitudes from 1979 to 2016, respectively. The slope of fitting line between monthly temperature warming trends and altitude 245 groups illustrated the significance of EDW above different altitude thresholds. For Tmin, the EDW could be found at full altitude (204-7100 m) in winter (January, February, and December). However, the most significant EDW appeared at altitudes above 3000 m in January and December (Table 5). The EDW was significant for April Tmin at altitudes below 3500 m. The EDW begins to appear above 2500 m altitude, but it is most significant above 4500 m in July (Table 5). The most significant EDW was found at the elevation higher than 3000 m in January (Table 6). The Tmax in January, March and April showed the EDW over the whole elevations, but at different altitudes for the most significant EDW (Table 7). Above 3000 m altitude, the most significant EDW was found in January while above 2000 m in March. The EDW become more and more significant from 2000 m to 4000 m in April. From August to October, the 4500 m was the threshold for the most 255 significant EDW (Table 7). In general, the altitudes at which the EDW phenomenon appeared are different for three temperatures in twelve months. The EDW differences (slope values) demonstrated the magnitudes of warming amplification at different altitudes. For example, for Tmin, the most significant EDW could be detected at the altitude 3000 m in winter.
For Tmax, the EDW could be detected above 2000 m and 2500 m in April and August, respectively. However, the most significant warming amplification with altitude was found above 4000/4500 m in these two months (Table 7). 260 As the further explication of Table 5 to 7, Fig. 2 to Fig. 4 intuitively provided the temperature trends at different altitude groups as well as the significance of EDW above different altitude thresholds. Fig. 2 showed the Tmin warming trends in January, February, April, and December from 1979 to 2016. The fitting between temperature trends and altitude groups above 3000 m illustrated the warming amplification with altitude. As the number of grids in each elevation group is different, the boxplots show the interquartile range (25% to 75%) and median values. To maintain consistent trend calculation for the 265 entire study, the average value was used for linear regression. Meanwhile, linear regression was applied based on the average values, which indicated the altitude dependence of the warming trend (i.e. the significance of EDW). In general, the EDW characteristics were significant for Tmin in January, February, April, and December. All lines of best fit are at the 0.01 significance level (p < 0.01). The temperature trends were positive at altitudes higher than 5000 m, with median values greater than 0 ℃ 10a -1 above 4000 m in January (Fig. 2a). The median values of most elevation groups were above the 270 reference line in February, although the corresponding line of fit had a lower slope (0.025) compared with that of January ( Fig. 2b). The 75% quartile ranges of the trends for all elevation groups in April were higher than 0 ℃ 10a -1 (Fig. 2c). All trends were positive for the regions above 4000 m in April. The prevalence of EDW was the most significant in December with the highest slope (0.096, p < 0.01). Although, most of lower altitude grids (< 4000 m) showed negative warming trends, the trends become positive at altitudes higher than 5000 m (Fig. 2d). 275 Fig. 3 showed the Tmean warming trends in January, June, August, and September from 1979 to 2016. The altitude threshold was 4500 m. The warming rates in January were only slightly above 0 ℃ 10a -1 at higher elevations. The significance of EDW was at the 0.05 significance level with a slope of 0.016 (Fig. 3a). The most significant EDW (slope = 0.045, p < 0.01) was found in June with all positive trends at all altitudes (Fig. 3b). The second significant EDW occurred above an elevation of 4500 m in August (slope = 0.037, Fig. 3c). The warming rates were above 0 ℃ 10a -1 at higher 280 elevations (> 4500 m). The fitting slope is 0.017 at the 0.05 significance level in September (Fig. 3d).
A threshold of 4000 m was applied for the significance of EDW investigation for Tmax in March, April, August, and September (Fig. 4). Although the slope (0.023) of the trend was not remarkable, all warming rates were greater than 0.8 ℃ 10a -1 in March (Fig. 4a). A significant elevation-dependent cooling could be observed in the altitude range of 0-2500 m for 285 Tmax in April. However, the most significant EDW also was detected above the altitude of 4000 m (slope = 0.09, Fig. 4b).
Most of the warming rates were higher than 0.4 ℃ 10a -1 in April. The EDW occurs at higher height of 4000 m in August and September ( Fig. 4c and 4d). However, the EDW is more significant above 4500 m in September than that above 4000 m (Table 7). The temperature trends for all months and seasons are also provided in the supplementary material (Fig. S1-S13).
Previous studies also found that EDW is significant at different altitudes. For example, Li et al (2020)

Spatial distribution pattern of the warming trend over the CTM
The spatial distribution of warming trends for all months and seasons can be found in the supplementary material ( Fig. S14-S30). In general, the warming trend of the mean temperature was not as dramatic as that of the minimum and maximum 295 temperatures in the CTM. To better detect altitude warming amplification, four typical zones with high mountains (above 3000 m) were selected: Zone 1 (represented by the Tolm Mountains), Zone 2 (central Tianshan, including the eastern part of the Borokoonu Mountains), Zone 3 (represented by the Bogda Mountains), and Zone 4 (represented by the Balikun Mountains) (Fig. 5). The monthly minimum temperature trends of January in the higher altitude mountains were greater than those in the surrounding LCCs, especially in Zones 3 and 4 (Fig. 5a). The highest warming trend (exceeding 1.0 ℃ 10a -1 ) 300 was observed around the eastern Bogda Mountains (above 3000 m) in Zone 3. The lowlands to the north of the Bogda Mountains showed a cooling trend (Fig. 5a). Zone 4 also showed a remarkable EDW phenomenon (0.3-0.6 ℃ 10a -1 ), wherein high mountains such as the Balikun were slightly warmer than the surrounding lowlands. Although the warming trend of Zone 1 was not as distinct as that of Zones 3 and 4, compared with the Ili Valley (cooling trend), the warming rate was still remarkable (~0.4 ℃ 10a -1 ). In December, the warming trend was more significant in Zone 1 than in the other zones 305 (Fig. 5b). The trend in the Tolm Mountains (exceeding 0.4 ℃ 10a -1 ) was much higher than that in the Ili Valley (cooling trend), which is located in the northern part of Zone 1. The warming rate at high altitudes in Zone 3 was higher (0.2-0.4 ℃ 10a -1 ) than that in the lowlands. There was no obvious warming amplification in the high-altitude mountains of Zone 4 to the low-altitude areas (Fig. 5b). However, it is worth noting that even in the same mountainous areas, such as in the Bogda Mountains in Zone 3, the warming rate in the east was notably higher than that in the northwest. It is clear that the minimum 310 temperature warming trends accelerated as the elevation increased in January and December. The warming trends become positive at an altitude of approximately 3000 m (Fig. 5).
Zones 1 and 4 tended to exhibit the altitude warming amplification phenomenon for the monthly mean temperature in January (Fig. 6a). The temperature decreased (by approximately −0.2 to −0.4 ℃ 10a -1 ) in the Ili Valley but increased (approximately 0.05 to 0.15 ℃ 10a -1 ) in the Tolm Mountains, especially in the high-altitude areas (Fig. 6a). Zone 4 warmed 315 faster than regions outside the zone. However, the warming trend was not notable in the high-elevation areas compared with that in the lowlands within this zone (Fig. 6a). The temperatures showed cooling trends in Zones 2 and 3. Nevertheless, the trend was amplified with an elevation in January in Zone 2. The high-altitude areas were warmer than the low-altitude regions, especially in the Bogda Mountains of Zone 3 (Fig. 6a). The spatial distribution of the warming rate in February was similar to that in January. However, the trend in most areas of the CTM was positive (Fig. 6b). Zones 3 and 4 showed 320 obvious EDW phenomena in February. The difference between the temperature warming rates in the high and low terrains of these two zones exceeded 0.2 ℃ 10a -1 . The trend in the high terrain of Zone 2 was greater than that in the valleys in the western part of the zone (eastern Ili Valley). However, the temperature in the south of the zone warmed faster than that in the high mountains in the northern part of Zone 2 (Fig. 6b). The southwestern Tolm Mountains in Zone 1 warmed up faster than the north-eastern mountains. 325 The maximum temperature in March in the entire CTM significantly increased with rates ranging from 0.9 to 2.0 ℃ 10a -1 (Fig. 7a). The highest warming rate was observed in western Ili Valley. However, all typical zones showed strong altitudewarming amplification features. The areas above 4500 m in Zone 1 showed trends higher than 1.4 ℃ 10a -1 . The smoothed contour at 3000 m corresponds to a distinct boundary in Zone 2. The temperature warming rates were almost higher than ~1.5 ℃ 10a -1 in the areas above 3000 m, whereas the rates were smaller in the low altitude areas (Fig. 7a). The trend was 330 higher than ~1.1 ℃ 10a -1 in March, whereas the trend became positive at approximately 2000 m in September (Fig. 7b). The difference between the warming rates in the high-altitude areas and low-altitude areas was the most remarkable in Zone 3.
The temperature warming trend on the hilltop of the Bogda Mountains was much higher than that at the foot of the mountains (Fig. 7a). The temperature warming rate in Zone 4 ranged from 1.3 to 1.6 ℃ 10a -1 . The trend differences between the high-altitude areas and low-altitude areas in Zone 4 were not as remarkable as those in Zone 3 (Fig. 7a). However, the 335 warming rate on the mountain peak was much higher than that in the neighbouring lowlands (Fig. 7a).
The spatial distribution of the maximum temperature in September showed distinctive east-west differentiation. The warming rates in Zones 3 and 4 were greater than those in Zones 1 and 2 (Fig. 7b). The EDW features were not notable in Zone 4. In contrast, the temperature in the high-altitude areas showed a slower warming trend (approximately 0.2-0.3 ℃ 10a -1 ) than that in the low-altitude areas in Zone 3 (Fig. 7b). A slight EDW phenomenon was observed in the Tolm 340 Mountains in Zone 1. However, Zone 2 showed remarkable EDW in September compared to that in the other zones. Similar to March, areas above 3000 m warmed faster than the lowlands, especially in the Ili Valley (Fig. 7b). In summary, Zone 2 was found to have a significant EDW area at the maximum temperature for March and September. Figures 5 to 7 show the general features of EDW in four typical areas. Taking Zone 2 as an example, Fig. S31 showed the warming rate of Tmin in December was amplified with elevation in some certain transects (the grids in the red rectangles). that altitude is not the only factor that affects temperature changes. The slope and aspect are other important factors responsible for the temperature changes due to the widespread valleys in the Zone 2. The local micro-terrains directly affect the absorption of solar radiation which would change the land surface processes such as latent heat, sensible heat and evapotranspiration. Thus, the EDW should be further detected on a finer spatial scale in some specific areas. 350

Discussion
Our analysis shows that the EDW phenomenon is very complicated for a large mountain system. It is difficult to arbitrarily judge the prevalence of EDW in mountain systems. Based on a comprehensive quantitative analysis, we believe that significant EDW signals exist in the CTM on local scales with respect to different temperature metrics. Although previous studies have mainly focused on the EDW of annual and seasonal temperatures, the monthly scale has not received sufficient 355 attention. However, seasonal temperatures do not clearly reflect the EDW characteristics. In complex terrain, monthly temperature changes are more significant, especially during seasonal transitions. For example, rapid warming in March would accelerate the melting of ice and snow, affecting glaciers and regional water resources in the mountains.
The air temperature changes were mainly affected by two aspects: one is the vertical energy exchange between the ground and atmosphere, which leads to periodic changes on the daily and annual scales; and the other is the temperature advection 360 caused by movement of cooling and heating masses, which leads to non-periodic changes. Numerous studies have shown that atmospheric circulation not only affects the latitude and zonality of climate via the zonal distribution of circulation but also expands the influence range of sea-land and topography via energy and water transportation (Dickinson, 1983;Harding et al., 2001). It is worth noting that the temperature trend is always positive at an altitude of 4500 m or higher in the CTM.
However, the minimum temperature has a cooling trend in January and December below 4000 m ( Fig. 2a and 2d). The 365 significant altitude warming amplification phenomenon could be observed above 4500 m for the Tmean in June and August ( Fig. 3 and Table 6). The significant EDW of Tmax could be observed above elevation of 4000 m in April. The air at high altitudes is similar to that in the free atmosphere and the dry adiabatic process is dominant. The absorption and reflection of solar radiation by the surface mainly determine the temperature change. In low-altitude areas, the impact of the underlying surface characteristics (e.g. terrain and land cover) is more significant. The CTM has a complex terrain with many mountain 370 basins and canyons. Because of the "Cold Lake" effect in winter, the lapse rate is even positive. A temperature inversion layer often occurs in deep canyons at night. Meanwhile, in low-altitude areas, the more surface soil moisture results in an increase in the latent heat fluxes, which further causes more absorbed solar radiation and then temperature warming in winter (Rangwala et al., 2012). This mechanism is closely related to snowlines and treelines because the migration of snowlines and treelines changes the surface albedo (Pepin et al., 2015). and January, a relatively significant correlation (p < 0.05) was found between Tmean/Tmax and snow depth. Figure 9 shows the scatter plots of the comparison of Tmin and Tmean in March with the snow depth. A negative correlation was perspicuous and visible. In general, there was a negative correlation between temperature and snow cover/snow depth (Figs. 8 and 9), which implies that temperature warming promotes the accelerated melting of snow. Meanwhile, the accelerated melting of snow may affect temperature warming. The detailed feedback mechanism between snow and temperature needs to 415 be further verified and explored using advanced technology and models. In summary, although many hypothetical mechanisms of EDW have received widespread attention, most of them are limited to phenomenon description and qualitative analysis. The present study attempted to conduct preliminary explorations of the mechanism based on limited snow cover and snow depth data. There is a lack of quantitative investigations on the core processes, dominant factors, and spatio-temporal differences of EDW. 420

Conclusions
Compared with the warming trend over the national land surface (WCC) and the low-altitude areas (LCC), the CTM is warming faster (0.633 and 0.640 ℃ 10a -1 for Tmin and Tmax, respectively) in spring (Table 3). However, on a monthly scale, warming rates are more complicated. The warming trends of the three temperature indicators (Tmin, Tmax, and Tmean) in March (0.835 and 1.339 ℃ 10a -1 for Tmin and Tmax, respectively) and June (0.752 and 0.422 ℃ 10a -1 for Tmin 425 and Tmax, respectively) in the CTM were higher than those over the entire national land surface on an average (Table 4). In addition, Tmax in February, Tmax and Tmean in April, and Tmin in May were also higher than the national average. Therefore, EDW detection based on a monthly scale was more reasonable.
It cannot be simply concluded that the high-altitude areas are warming faster than the low-altitude areas. Quantitative analysis is required to provide solid evidence for the EDW phenomenon. Using altitude grouping and a linear regression 430 model, we quantitatively determined the significance of EDW along with the detailed performance of the warming trends with respect to Tmin, Tmean and Tmax at different altitudes. In general, the altitude thresholds for EDW phenomenon are different for three temperatures in twelve months. In the case of Tmin, January, February, April, and December showed significant EDW trends (p < 0.01). The most significant EDW phenomenon was found in December (Table 5, Fig. 2d). In general, Tmin was associated with a strong EDW in winter. The warming rates of Tmin above 5000 m were always positive, 435 which could lead to faster melting of snow. March, April, August, and September showed different elevation-based sensitivities with respect to Tmax (Table 7). The most significant EDW phenomenon can be found at altitudes above 4000 m in April and August as well as above 4500 m in September (Fig. 4). Almost all Tmax warming trends in March and April were positive in the CTM. The significant EDW phenomena were identified above 4500 m for Tmax in June and August. 3000 m ( Table 6).
The CTM is a large mountain system comprising many mountains. Therefore, EDW characteristics are diverse in different mountains. The EDW of Tmin in January was significant in the Bogda and Balikun Mountains, whereas it was significant in December in the Tolm Mountains (Fig. 5). For Tmax in March, all typical mountains exhibited EDW characteristics, especially the central CTM and Bogda Mountains (Fig. 6). A significant EDW signal of Tmax was observed in September in 445 central CTM (eastern part of the Borokoonu Mountains). The most significant EDW signal of Tmean was observed in the Tolm and Balikun Mountains in January. The Bogda and Balikun Mountains exhibited significant EDW features in February.
After preliminary research, a significant negative correlation (p<0.01) between minimum/mean temperature and snow depth was observed in March and June (Fig. 9). However, the specific feedback mechanism between snow and temperature remains unclear. Even in the same mountainous area, significantly different mechanisms of EDW were observed for 450 different topographies, altitudes, and seasons. Future studies should focus on conducting in-depth quantitative research on the mechanism of EDW based on regional climate models and field surveys, especially in Zones 1 and 2 with accelerating snow melting.

Data availability
The dataset is released at https://doi.org/10.1594/PANGAEA.887700 in the Network Common Data Form (NetCDF) format. 455 The coverage of the dataset is 41.1814-45.9945 °N, 77.3484-96.9989 °E. The spatial resolution is 1km and the total number of grid points is 818126 for the larger Chinese Tianshan Mountain region, which includes more surrounding areas. This study used 356133 grids. The time step was 6-hourly at 00, 06, 12, and 18 UTC. The dataset contains 288 NetCDF files and one user guidance file. The monthly temperature data set at the 0.5° latitude-longitude grid (CMA05) over continental China was provided by the China Meteorological Data Sharing Service System of the National Meteorological Information Center 460 (http://data.cma.cn/data/cdcdetail/dataCode/SURF_CLI_CHN_TEM_MON_GRID_0.5.html, last access: 05 January 2021).