Warming enhanced the climate temporal effects on vegetation across Siberia

: Widespread climate warming and growing season greening have been observed across most of the Northern Hemisphere in recent decades. However, the response of greening to amplified warming remains unclear with regard to the temporal effects (cumulative and time-lag effects) in cold regions of the Northern Hemisphere. We therefore provide a comprehensive analysis of the relationship between the enhanced vegetation index (EVI) and climate factors (e.g., land surface temperature (LST), precipitation, and solar radiation) across Siberia, which is experiencing rapid warming and greening, during 2000-2016 by using a random forest regression model. We found that solar radiation was the dominant driving factor of vegetation greening in 55.95% of the study area (concentrated in southwest Siberia), followed by temperature (41.28%, concentrated in northeast Siberia) and precipitation (2.78%). Furthermore, the cumulative and time-lag effects increased the explanation of vegetation variation by climate factors, from 0.71 to 0.78, and were observed in more than 80% of the area of Siberia. The average cumulative duration was 3.61 ± 1.97 months, and the time-lag period was 1.51 ± 1.20 months, with the longest term found in deciduous broadleaf forests and the shortest term found in shrublands. Our results indicated that the vegetation activities were influenced by cumulative effects combined with time-lag effects. The temporal effects varied with land cover categories, and the complex ecosystem generally corresponded to long-term temporal effects, and vice versa. Hence, the tundra shrub converted to boreal forest caused by warming in Siberia enhanced the climate temporal effects.


Introduction:
The global climate system has been experiencing a dramatic change characterized by warming over the past century (Qin 2004;Pecl et al. 2017), and climate change has profound effects on the functioning of terrestrial ecosystems. Vegetation is a crucial component of terrestrial ecosystems, as it combines the energy, water and carbon exchanges between the land surface and atmosphere (Law et al. 2002). The identification of the persistence and resilience of terrestrial ecosystems under climate change has been a global research priority (McMahon et al. 2011;Garcia et al. 2014;Piao et al. 2019).
The response of vegetation to climate change has been a general indicator used to evaluate terrestrial ecosystem conditions (Deng et al. 2019). The impact of climate change on vegetation has been well documented by previous studies through direct or indirect perspectives (Nemani et al. 2003;Buitenwerf, Rose & Higgins 2015).
Vegetation activities are directly affected by external climate forcing (Seddon et al. 3 2016). For instance, temperature is closely related to vegetation photosynthesis and respiration (Hu et al. 2016). It has been shown that increasing temperature improves vegetation productivity and prolongs the growing season in high-latitude and highaltitude areas . Precipitation (PRE) is an indispensable source of moisture for terrestrial ecosystems and is associated with the processes of various vegetation activities, especially in arid and semiarid areas where PRE is the primary factor restricting vegetation growth (Vicente-Serrano et al. 2013). Solar radiation (SR) reflects the potential heat available for vegetation activities and significantly influences metabolic processes. Additionally, SR is related to environmental light intensity, which is considered a major factor regulating vegetation growth . which has greatly impacted the global ecosystem (Walsh et al. 2020).
In addition to studies focused on the vegetation response to climate change based on simultaneous climate factors, an increasing number of studies have demonstrated that the impact of climate change on vegetation has certain temporal effects, including cumulative and time-lag effects (Penuelas & Filella 2001;Bertrand et al. 2011;Mulder, Iles & Rockwell 2017;Kong et al. 2020). Cumulative effects represent that climate factors are continuously dynamic, and their impact on vegetation is cumulative and 4 chronic over a period of time (Xu et al. 2013). Time-lag effects refer to the vegetation response to previous rather than current climate factors, as terrestrial ecosystems are resilient to external factors (Willis, Jeffers & Tovar Ingar 2018). Once cumulative and time-lag effects are considered, the analysis of the impact on climate factors on vegetation activities can be assessed in greater detail (Wu et al. 2015;Wen et al. 2019).
The accomplishment of vegetation life-stage transitions requires the cumulated temperature to reach a certain threshold, and this threshold affects leaf onset, offset and flowering (Piao et al. 2015;Gonzalez-Suarez, Walker & Bennett 2020). Moreover, the impact of temperature on vegetation generally lags, and the phenological characteristics of vegetation in spring are mainly determined by the temperature of the last winter, as heat penetration into the soil takes time (Xu et al. 2013;Ettinger et al. 2020).
Cumulative PRE also greatly affects vegetation activities, and correlations between vegetation and cumulated PRE are strongly reflected in the distribution of plant biomes and ecosystem complexes, especially in arid regions (Guerschman et al. 2020). Zeng et al. (Zeng et al. 2013) indicated that more than 80% of vegetation variation could be explained by cumulative PRE in some arid regions. The time-lag effects of PRE mostly represent vegetation in semiarid and semi-humid regions, as the vegetation in those regions has the ability to adapt to variations in moisture and is unable to respond quickly (Vicente-Serrano et al. 2013). Cumulative SR is closely associated with vegetation distribution patterns and plant biomes at the global scale and is the main reason for the vegetation latitudinal gradient. It has been reported that a reduction in SR contributes to the primary negative effects of climate change on vegetation (Chen et al. 2021).

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Notably, cumulative SR is the dominant climate driving force affecting vegetation activities in cold ecosystems (Wu et al. 2015).
Siberia is located in the arctic and sub-arctic; it has a typical cold ecosystem and features vegetation structure and species composition gradients (Montesano et al. 2016).
As the main plant biomes across Siberia, taiga and tundra are among the most valuable and sensitive environmental zones on Earth (Callaghan et al. 2002;Walther et al. 2019 To address the abovementioned issues, we explore the relationships between vegetation and climate factors in the context of cumulative and time-lag effects, seeking to 1) determine whether the cumulative and time-lag effects combine to impact vegetation growth and 2) evaluate the sensitivity of vegetation to climate factors at different time scales. Therefore, we chose LST, PRE and SR to represent the climate driving force and the (EVI) to represent the vegetation activities. Random forest regression was fitted to 6 evaluate the relationship between climate factors and vegetation under four scenarios: based on simultaneous climate factors, considering cumulative effects, or/and considering time-lag effects of climate factors. Finally, the relative importance of climate factors on vegetation growth was obtained.

Vegetation index data
In recent decades, remote sensing has emerged as an effective tool in the dynamic monitoring of vegetation over larger areas, making it possible to indicate the health and density of vegetation through the measurement of solar-induced chlorophyll fluorescence (Guanter et al. 2012). Based on satellite land observation data, many vegetation indices have been proposed, such as the normalized vegetation difference index (NDVI) (Deering, Eck & Banerjee 1999), vegetation condition index (VCI) (Kogan 1995a), vegetation health index (VHI) (Kogan 1995b), and temperature and vegetation dryness index (TVDI) (Sandholt, Rasmussen & Andersen 2002). Among those indices, the NDVI, as the most widely used, is a normalized ratio of the nearinfrared and red visible bands and is calculated directly without any assumptions regarding environmental conditions. The major disadvantage of the NDVI is the influence of additive noise effects, such as those caused by aerosols (Huete et al. 2002).
Considering the wavelength dependency of aerosol effects, Huete et al.(2002) proposed the EVI, which uses the more atmosphere-sensitive blue band to correct the red band to eliminate the aerosol influence. The EVI is a normalized vegetation index with a value ranging from 0 to 1, calculated by the following equation: where , and are the near-infrared, red band and blue band reflectance, respectively. These three factors have been atmospherically corrected or partially atmosphere corrected; G is the gain factor and equals 2.5; L is the canopy background adjustment and equals 1; and 1 and 2 are the coefficients of the aerosol influences in the red band, which uses the blue band to correct and is equal to 6 and 7.5, respectively.
The EVI is significantly correlated with photosynthetic activities and chlorophyll contents and has been widely used in research on biophysical and structural vegetation properties and spatial/temporal variations (Seddon et al. 2016;Li & Xiao 2020). In this study, we used the MOD13C2 version 6 product, which provides the monthly global distribution of the EVI at a 0.05° spatial resolution. Moreover, any pixels with an EVI below 0 were removed because there was no vegetation cover there. The growing season lasts from April to September since the mean temperature in these months is above 0°C.

Meteorological data
Vegetation activities are limited by both energy conditions and water availability (Beer et al. 2010). LST indicates the combined results of surface-atmosphere interactions and energy fluxes, and it is a considerable surface parameter in terms of driving boundary layer processes (Good et al. 2017). In this paper, we used the MOD11C3 version 6 product, which provides the monthly global land surface temperature at a 0.05°C 8 resolution. The product has been verified by 42 carefully selected sites around the world and is more accurate than the previous version (Wan 2008 2018). In this work, SR was derived from the Watch Forcing Data methodology applied to the ERA-Interim (WFDEI) reanalysis dataset (Weedon et al. 2018). Based on the three-hour SR provided by the dataset, we calculated the daily SR of each month.
Moreover, PRE and SR data were resampled from 0.1° and 0.5° to 0.05° by bilinear interpolation, respectively, the same as the spatial resolution of other data.

Land cover data
Land cover represents the ecosystem surface canopy and vegetation communities, and different vegetation communities have diversified biophysical and biochemical processes. The land cover data used here were obtained from the MODIS land cover product (MCD12C1) (Friedl et al. 2010). The product contains 13 classification schemes of global land cover maps at a 0.05° resolution. We adopted the classification schemes of the leaf area index (LAI), as our work is mainly related to vegetation. The LAI classification contains 10 land cover categories: 7 categories of natural vegetation, water body, non-vegetated land and built-up land. The land cover categories that occupied more than 1% of the total area were retained (Table 1). Furthermore, the pixels with changed land cover were discarded. Siberia is mainly occupied by savannas and grasslands, which account for 50.33% and 21.53% of the total area, respectively.
Savannas are distributed primarily in north-eastern Siberia, while grasslands are distributed in southwestern Siberia. Forests are mainly needleleaf, covering 15.05% of the area (Figure 1).

Analysis
The EVI, LST, PRE and SR were linearly detrended before analysis to reduce the impacts of temporal autocorrelation between vegetation and climate factors. The cumulative effects were analysed under 1-, 3-, 6-and 12-month time scales, and the time-lag effects were analysed under 0-, 1-, 2-and 3-month time scales according to other studies (Wu et al. 2015;Wen et al. 2019;Ding, Li & Peng 2020). In this study, the climate variables were computed by the following equations: Random forest regression was applied to fit the relationship between the vegetation and climate factors. As one machine learning algorithm, random forest is based on regression tree analysis and has many properties: the ability to fit models with various types of data, the ability to fit nonlinear relationships, the ability to ignore the interaction or collinearity between variables, and even the ability to ignore missing values. Random forest regression creates a set of regression trees, and the output of the model is the average of the predictions of all regression trees. In this study, a random forest regression model of each pixel was built through the Randomforest package of the R project, and the number of regression trees was 500. Furthermore, the coefficient of determination (R 2 ) and relative importance (RI) of each climate factor in each pixel were analysed to capture the key time scale (KTS) and key relative importance (KRI).
Based on the results, the response of vegetation to climate variables was evaluated. and land cover category (d).
Note: the mean EVI is provided above each bar.
The mean EVI in the growing season was 0.29 in Siberia, and its spatial distribution

Cumulative and time-lag effects
A random forest regression model was applied to fit the relationship between vegetation The distribution of R 2 performance was divergent when the EVI was small and tended to be gradually flatten with increasing EVI, which indicated that the random forest 16 regression model was more suitable in areas with good vegetation (Fig. 6-b). Fig. 6 shows the spatial distribution of R 2 and the corresponding time scale of the four scenarios. The 0.71 variation in vegetation across Siberia could be explained by simultaneous climate factors, and the weak performance of the model was mainly concentrated in the southwestern Ob basin, indicating that the vegetation in this area was greatly affected by factors other than climate factors ( Fig. 6-a). The consideration of cumulative effects of climate factors increased the R 2 to 0.73, and no cumulative effects were observed in 68.39% of the area, followed by A3T0 (A3T0 means cumulative duration is three months and time-lag period is zero month, same as the rest, 15.46%) and A6T0 (15.90%); additionally, A12T0 accounted for only 0.25% of the area ( Fig. 6-b, c). The consideration of the time-lag effects of climate factors increased the ability to explain the vegetation variation to 0.74, and no time-lag effects were observed in 65.63% of the area, followed by A1T3 (39.45%), A1T1 and A1T2, which occupied 6.03% and 1.29%, respectively ( Fig. 6-d, e). When considering both cumulative and time-lag effects, we obtained a mean R 2 of 0.77, A1T0 was observed in 19.42% of the area, and 80.58% showed cumulative and/or time-lag effects ( Fig. 6-f, g). Note: A1T0 in figure b means cumulative duration is one month and the time-lag period is zero months, same as the rest.

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Further results were obtained based on the scenarios of considering both cumulative and time-lag effects. The spatial distribution of R 2 increased from west to east, with an overall average of 0.72 ± 0.13 in the Ob basin, 0.79 ± 0.08 in the Yenisei basin and 0.80 ± 0.07 in the Lena basin. The R 2 also varied with land cover categories, performing well in deciduous needleleaf forests (0.84 ± 0.04) and deciduous broadleaf forests (0.82 ± 0.04), followed by that in evergreen needleleaf forests (0.81 ± 0.06), savannas (0.79 ± 0.08), shrublands (0.79 ± 0.06); the weakest value was found in grasslands (0.68 ± 0.13). and 6-month (36.64%) cumulative durations of climate factors and less sensitive to 12 months (0.28%); furthermore, no cumulative effects were observed in 22.86% of the area (cumulative duration is 1 month), which indicated that vegetation hardly responded to cumulative climate factors with a duration greater than 6 months. The time-lag effects were mainly manifested in a period of 3 months (33.28%), followed by 1 month (28.46%) and 2 months (11.61%), and 26.65% of the area exhibited no time-lag effects (time-lag effects period was 0 months). The duration of the time lag generally varied with different cumulative durations: the no time lag effect area mainly corresponded to 1-month cumulative effects (A1T0), which indicated that the response of vegetation to climate was immediate in those pixels; additionally, 1-month time lag effects 19 corresponded to 6-month cumulative effects (A6T1), and 2-and 3-month time lag effects corresponded to 3-month cumulative effects (A3T2 and A3T3).  Note: the bounds of the boxes in c-f indicate the mean and mean ± standard deviation.

Relative importance of climate factors
According to the key time scale of each pixel, the relative importance of LST, PRE and SR were extracted. Across Siberia, SR was the leading climate driver, followed by LST, and PRE was the least important. The mean SR relative importance was 28.84, and SR was the dominant climate factor (SR relative importance was the highest among the pixels) in 55.95% of the area, mainly distributed in the Ob basin and in the south of Yenisei basin. The mean relative importance of LST was 27.86, and LST was observed as the dominant climate factor in 41.28% of the area, concentrated in the Lena basin and in the north of the Yenisei basin. The mean relative importance of PRE was 11.83, and the pixels dominated by PRE occupied only 2.78% of the area ( Fig. 8-a, Fig. 8-c). The order of relative importance of climate factors in different land cover categories was similar, which showed that SR was the most 22 important and PRE was the least important. Only in shrublands was LST more important than SR and became the main climate driving factor (Fig. 8-d).

Discussion
Vegetation greenness in Siberia has been observed to increase with climate warming, especially in regions primarily characterized by tundra shrubs, where considerable greening has been reported (Forbes, Fauria & Zetterberg 2010;Berner et al. 2020). In 23 the boreal forests and grasslands, the greening trend was relatively small (Fig. 3-1 d).
Since entering the 21 st century, a slowing or reversal of apparent greening has been widely reported across Siberia (Bhatt et al. 2013). The ratio of the greening to browning transition from 2000 to 2016 was 5.9:1 in our research, and another study based on 1982-2014 GIMMS NDVI suggested that the ratio was 16.8:1 across boreal and arctic ecosystems (Park et al. 2016). Moreover, the trends of vegetation growth had large spatial heterogeneity (Miles, Miles & Esau 2019). In northern Siberia, greening was dominant, and its ratio declined with decreasing latitude (Fig. 3-1 b). Such characteristics have also been documented by Mile's research (Miles & Esau 2016). Loranty et al. (2016) indicated that the variation in vegetation was closely related to the distribution of permafrost, with greening in areas of continuous permafrost and browning in areas of discontinuous permafrost.
Climate change was the primary driving force for vegetation variation in Siberia , and the explanation of climate factors increased when cumulative and timelag effects were considered (Fig. 6). In previous studies, Ding et al. (2020) confirmed that the explanation of vegetation growth by climate change would increase from 54% to 63% by factoring in the consideration of cumulative and time-lag effects. Wen et al.
(2019) compared the results from scenarios considering time-lag effects only and considering both cumulative and time-lag effects and found that the latter would increase the explanation of the model in 77% of the global area. Moreover, in arctic and north temperate regions, the calculated R 2 increased from 0.76 to 0.78 and from 0.74 to 0.77, respectively (Wen et al. 2019). These results indicated that vegetation growth was 24 affected by both cumulative and time-lag effects, which improves our understanding of the interaction between vegetation and climate. Furthermore, overcoming many limitations and problems of the linear regression model (Breiman 2001), the random forest regression model is the most commonly used model and has good performance, especially in regions with a high EVI (Fig. 3-A). The model will provide us with new inspiration for the application of machine learning algorithms in geographical research.
The cumulative duration and time-lag period reflect the persistence and resilience of an ecosystem. Our research showed that the short-term cumulative effects generally corresponded to the short-term time-lag effects in each land cover category and vice versa. Moreover, the temporal effects of short time scales corresponded to ecosystems with less function and diversity, such as tundra shrubs. In contrast, the temporal effects at the long-term scale corresponded to complex ecosystems, such as boreal forests (Figs. 3-4). Complex ecosystems always exhibit high climate tolerance due to the collaboration and complementarity of biodiversity (Ehbrecht et al. 2021). Moreover, long-term temporal effects occurred in regions with better climate conditions ( Fig. 2-2). Because the function and diversity of ecosystems are mainly determined by climate, complex ecosystems are generally supported by warm and humid climates (Harrison, Spasojevic & Li 2020). Our result was not observed in Ding's research, which was explicable, as Ding assumed that the temporal effects of climate on vegetation growth were less than three months, thus ignoring the long-term effects (Ding, Li & Peng 2020).
However, the temporal effects in many semiarid and semi-humid regions have exceeded 3 months, or even 12 months or more (Vicente-Serrano et al. 2013;Büntgen et al. 2015).

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The impact of different climate factors on vegetation varies greatly. Across Siberia, vegetation activities were strongly restricted by SR and temperature and less affected by PRE. Based on the random forest regression model, the mean relative importance of SR was 28.84, and it was the dominant climate factor in 55.95% of the area. Regional SR mainly depends on latitude, but the actual incoming radiation on the land surface is determined by sunshine duration, atmospheric aerosol, topography and cloudiness.
Some studies chose the cloudiness index to characterize incoming photosynthetically active solar radiation (de Jong et al. 2013;Seddon et al. 2016). In high-latitude regions, vegetation activities are driven by a combination of SR and temperature (Seddon et al. 2016;Wen et al. 2019). In our research, SR was slightly more important than temperature. A possible explanation is that vegetation in cold ecosystems has the ability to adapt to low temperatures and the ability to complete photosynthesis processes at lower optimum temperatures. For example, mosses can photosynthesize at temperatures near -10°C and exhibit negative net ecosystem exchange fluxes (He, He & Hyvönen 2016). However, SR is closely associated with light intensity, and when the light intensity is insufficient to reach the light compensation point, the rate of photosynthesis is less than that of respiration, resulting in positive net ecosystem exchange fluxes (Kutzbach, Wille & Pfeiffer 2007).
Temperature was a key climate factor that restricted vegetation activities in Siberia. The relative importance of temperature was 27.86, and it was the dominant climate factor in 41.28% of the area. Previous studies based on remote sensing data or field simulation experiments have provided strong evidence that greening across Siberia is mainly 26 driven by warming (Elmendorf et al. 2012;Phoenix & Bjerke 2016). However, some studies have also indicated that the effect of warming on vegetation depends on soil moisture, with more positive effects in humid regions . In other cases, changes in surface albedo, permafrost and soil nutrients could also influence the vegetation response to warming and even affect the key environmental constraints that limit vegetation activities . The greening speed of Siberia has slowed in recent years , which may be due to the negative effect of warming, as warming enhances soil moisture consumption, especially in the middle of the growing season. The reduced leaf water potential caused by low soil moisture leads to stomatal constraints on photosynthesis, and finally, the benefit of ameliorating low temperature limitation on photosynthesis by warming decreases (Comiso & Hall 2014;Reich et al. 2018). Furthermore, the slowing of warming in the past decade has been regarded as an important reason for the phenomenon (Fyfe et al. 2016;Hedemann et al. 2017).
PRE seems to be less important to vegetation growth in Siberia, with a mean relative importance of only 11.83, although the annual PRE is low across Siberia, especially in the Yenisei basin and Lena basin. However, vegetation in Siberia is seldom restricted by water availability, and the low vapor pressure deficit as the temperature decreases reduces water stress; moreover, the thawing of permafrost in the growing season provides necessary soil moisture for vegetation growth (Anderson et al. 2019).
Furthermore, the sensitivity of vegetation to precipitation was different among each plant species. The grasslands of Siberia are concentrated in the north-western region, 27 far from the coastline and at lower altitudes. Compared with other land cover categories, vegetation on grasslands was more sensitive to precipitation for high temperatures and low precipitation (Chen et al. 2020). Other land cover categories generally have strong resistance and resilience to water stress, especially in tundra. The vegetation biome is dominated by mosses and lichens, which have the ability to tolerate extreme drying, as they can lose cell water without dying and resume when they obtain appropriate moisture (Robinson et al. 2018). The importance of water availability to vegetation is complex in Siberia, as increasing temperatures would increase the saturated water vapor pressure at a rate of 7%/K, which will exacerbate the water deficit of vegetation (Yuan et al. 2019), and warming would cause earlier snowmelt, which often results in the drying of surface soils and adversely affects vegetation (Gamon et al. 2013). In contrast, the increasing summer precipitation across most of the arctic region and substantial permafrost thawing would reduce the water deficit that affects vegetation (Douglas, Turetsky & Koven 2020). During the study period, the major land cover changes in Siberia were the mutual conversions of grasslands and woodlands and the transfer of shrubland to woodlands (Fig. 9). These phenomena have been verified by previous studies, and ongoing warming was considered the dominant factor for dramatic change (Pearson et al. 2013;Miles, Miles & Esau 2019). Vegetation activities were constrained by both energy conditions and water availability. In the southern boreal forest, warming enhanced the water stress on vegetation and resulted in woodland degradation to grasslands (12.86×10 4 km 2 ), while in the northern boreal forest, warming improved the energy limitation, with suitable moisture conditions, and the shrublands gradually succeeded in woodlands (15.64×10 4 km 2 ) (Berner et al. 2013;Myers-Smith et al. 2015). Moreover, in the northern Ob basin and southern Yenisei basin (high altitude), which are also energy-limited ecosystems, a larger area (15.34×10 4 km 2 ) of grasslands was converted into woodlands as warming occurred (Aakala et al. 2014;Arekhi et al. 2018). Overall, the forest treeline sharply contracted in the south and expanded in the north, but the total area increased by approximately 12.13×10 4 km 2 . Woodlands showed more obvious climate temporal effects than shrublands due to their high ecosystem resilience; hence, the change in land cover across Siberia as warming continues would enhance the climate temporal effects on vegetation.
Notably, only 17a meteorological data points were used in this research. Therefore, the 29 results of our research are possibly biased, as the stable result was generally analysed using meteorological data that were more than 30a. The MODIS EVI was used to characterize the vegetation activity in our research. The most common datasets of the vegetation index include the Advanced Very-High-Resolution Radiometer (AVHRR, 1982-present); SPOT Vegetation (SPOT-VEG, 1998-present); Landsat sensors (1972present) and MODIS (2000-present (Nemani et al. 2003;Seddon et al. 2016), and the temporal effects should also be analysed separately to reveal more details of the vegetation response to climate factors.

Conclusion
In this paper, the cumulative and time-lag effects of climate factors on vegetation in Siberia from 2000-2016were analysed through a random forest regression model.
Furthermore, the differences in cumulative and time-lag effects were compared among each basin and land cover category, and the underlying mechanisms were discussed.
This study revealed more details of the temporal effects of climate factors, enriched our understanding of the interaction between vegetation and climate change, and highlighted that the duration of temporal effects corresponded to regional climate 30 conditions and ecosystem complexity: long-term temporal effects occurred in relatively warm and humid regions, such as boreal forests, and short-term temporal effects occurred in relatively cold regions, such as tundra shrubs. Moreover, the land cover change caused by warming would enhance the temporal effects.

Declarations：
• Ethics approval and consent to participate Not applicable • Consent for publication Not applicable • Availability of data and material All datasets analysed during the current study have listed in Table 1. The datasets generated during the current study are available from the corresponding author on reasonable request.