Threshold Vegetation Greenness under Water Balance in Different Desert Areas over the Silk Road Economic Belt

The sustainability of dryland vegetation growth over the Silk Road Economic Belt is under threat of water shortage, and the determination of water carrying capacity for vegetation is critically essential to balance water supply and water demand for the maintenance of existing ecosystems. To better understand how and why vegetation growth varies in different desert areas, this study first analyzed the spatiotemporal variation of the normalized difference vegetation index (NDVI). Then, we investigated the relationship between NDVI and climatic factors (precipitation, soil water content, air temperature, evapotranspiration), and estimated the threshold NDVI under water balance in different desert areas. Results showed that the higher NDVI was mainly distributed in Kazakhstan, Russia, and Azerbaijan, and it increased in approximately 53% of desert areas from 1982 to 2015 in the whole study region. The mean annual NDVI showed a simultaneous increasing trend in all desert areas from 1982 to 1994, and decreased significantly only in the cold arid desert area (p < 0.01, −0.0067 decade−1) or had no significant change in other desert areas after 1994 (p > 0.01). The climate condition generally appeared as a warming and drying trend in the past 34 years, with varied changing rates in different desert areas. NDVI presented a strong positive relationship with both precipitation and evapotranspiration in most desert areas. The threshold values of the mean annual NDVI under water balance between 1982 and 2015 were approximately 0.1041 (hot arid desert), 0.1337 (cold arid desert), 0.1346 (cold arid semi-desert), 0.0951 (hot arid desert semi-desert), 0.0776 (polar desert tundra), 0.1071 (hot arid desert shrub), 0.1377 (cold arid desert steppe), and 0.0701 (polar desert steppe), respectively. The responses of these threshold values to precipitation were all positive in different desert areas. These results provide an enhanced understanding of vegetation dynamics and ecological conservation, which are of great importance to implementing adaptation and mitigation measures for terrestrial ecosystems over the Silk Road Economic Belt.


Introduction
The Silk Road Economic Belt was proposed by the Chinese government in 2013, and aims to promote the development of an open world economic system by strengthening interregional cooperation [1]. It links China with central Asia, west Asia, southeast Asia, south Asia, Russia, and Europe [2], and contains lots of desert over the world, such as Arabian desert, Taklimakan

Study Region
The study region located in the Silk Road Economic Belt (https://en.tianditu.gov.cn/, "Layers"-"Silk Road"-"Land and Sea Silk Road"), which includes lots of desert areas (the area associated with desert ecosystem) in the northwest China, central Asia, Arabian Peninsula, and parts of North Africa. The desert areas were generated from a map of the global ecoregions, which was first produced by the World Wildlife Fund (https://www.worldwildlife.org/biomes) and further visualized by National Earth System Science Data Centre of China (http://www.geodata.cn/data/datadetails.html?dataguid=208109344688128&docId= 19421, in Chinese). The desert areas over the Silk Road Economic Belt included six desert ecosystems: Desert, semi-desert, desert semi-desert, desert tundra, desert·shrub, and desert steppe. According to the world maps of the Köppen-Geiger climate classification (http://koeppen-geiger.vu-wien.ac.at/shifts.htm), the main climates in these desert areas included hot arid, cold arid, and polar. The mean annual precipitation and air temperature were 157 mm and 14.81 • C between 1982 and 2015 in the whole study region, respectively. Based on the global ecoregions and climate classification, the study region was separated into eight subregions, including hot arid desert (HAdese), cold arid desert (CAdese), cold arid semi-desert (CAsmde), hot arid desert semi-desert (HAdesm), polar desert tundra (POdetu), hot arid desert shrub (HAdesh), cold arid desert steppe (CAdest), and polar desert steppe (POdest) (Figure 1). Their areas accounted for 20.5%, 22.0%, 21.3%, 9.0%, 1.1%, 16.6%, 6.1%, and 3.4% of the whole study region, respectively. The hot arid desert shrub area and hot arid desert semi-desert area were concentrated on the Arabian Peninsula and southwest Iran; the polar desert tundra only appeared in the border area of Tajikistan, Kyrgyzstan, and China; while the desert area, semi-desert area, and desert steppe area were distributed widely in the whole study region.

Study Region
The study region located in the Silk Road Economic Belt (https://en.tianditu.gov.cn/, "Layers" -"Silk Road" -"Land and Sea Silk Road"), which includes lots of desert areas (the area associated with desert ecosystem) in the northwest China, central Asia, Arabian Peninsula, and parts of North Africa. The desert areas were generated from a map of the global ecoregions, which was first produced by the World Wildlife Fund (https://www.worldwildlife.org/biomes) and further visualized by National Earth System Science Data Centre of China (http://www.geodata.cn/data/datadetails.html?dataguid=208109344688128&docId=19421, in Chinese). The desert areas over the Silk Road Economic Belt included six desert ecosystems: Desert, semi-desert, desert semi-desert, desert tundra, desert shrub, and desert steppe. According to the world maps of the Köppen-Geiger climate classification (http:// koeppen-geiger.vu-wien.ac.at/shifts.htm), the main climates in these desert areas included hot arid, cold arid, and polar. The mean annual precipitation and air temperature were 157 mm and 14.81 °C between 1982 and 2015 in the whole study region, respectively. Based on the global ecoregions and climate classification, the study region was separated into eight subregions, including hot arid desert (HAdese), cold arid desert (CAdese), cold arid semi-desert (CAsmde), hot arid desert semi-desert (HAdesm), polar desert tundra (POdetu), hot arid desert shrub (HAdesh), cold arid desert steppe (CAdest), and polar desert steppe (POdest) (Figure 1). Their areas accounted for 20.5%, 22.0%, 21.3%, 9.0%, 1.1%, 16.6%, 6.1%, and 3.4% of the whole study region, respectively. The hot arid desert shrub area and hot arid desert semi-desert area were concentrated on the Arabian Peninsula and southwest Iran; the polar desert tundra only appeared in the border area of Tajikistan, Kyrgyzstan, and China; while the desert area, semi-desert area, and desert steppe area were distributed widely in the whole study region.

Datasets
The vegetation growth between 1982 and 2015 was evaluated by the normalized difference vegetation index (NDVI), derived from the Advanced Very High Resolution Radiometer (AVHRR) observations produced by the Global Inventory Modeling and Mapping Studies (GIMMS) group (i.e., GIMMS NDVI3g v1, https://ecocast.arc.nasa.gov/data/pub/gimms/), with a spatial resolution of 1/12 degrees (8 km) and biweekly temporal resolution (two images in each month). It has been comprehensively corrected for atmospheric effects, sensor degradation, solar zenith angle, cloud contamination, and inter-sensor differences [31], and widely used to investigate spatiotemporal patterns in vegetation growth across diverse bioclimatic regions [32,33]. To match the climate grid

Datasets
The vegetation growth between 1982 and 2015 was evaluated by the normalized difference vegetation index (NDVI), derived from the Advanced Very High Resolution Radiometer (AVHRR) observations produced by the Global Inventory Modeling and Mapping Studies (GIMMS) group (i.e., GIMMS NDVI3g v1, https://ecocast.arc.nasa.gov/data/pub/gimms/), with a spatial resolution of 1/12 degrees (8 km) and biweekly temporal resolution (two images in each month). It has been comprehensively corrected for atmospheric effects, sensor degradation, solar zenith angle, cloud contamination, and inter-sensor differences [31], and widely used to investigate spatiotemporal patterns in vegetation growth across Remote Sens. 2020, 12, 2452 4 of 14 diverse bioclimatic regions [32,33]. To match the climate grid data, the raw NDVI data was resampled to a spatial resolution of 0.25 degrees and monthly temporal resolution. For spatially resampling, we averaged the data of nine grids with three rows and three columns to resample the 1/12 degrees to 0.25 degrees. For temporal resampling, we averaged the data of two images in each month to get the monthly dataset. Due to the different lengths of the growing season in the widespread region over the Silk Road Economic Belt [34], the mean annual NDVI was used in this study.
The monthly gridded air temperature (TEM), precipitation (PRE), and soil water content (SWC) with a spatial resolution of 0.25 degrees in period of 1982-2015 were obtained from the ERA5 (ECMWF Re-Analysis) dataset produced by European Centre for Medium-Range Weather Forecasts (ECMWF, https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels-monthlymeans?tab=overview). The soil water content in four layers was averaged to cover the region from surface to the root region with a depth of 2.89 m (https://confluence.ecmwf.int/display/CKB/ERA5%3A+ data+documentation). Compared with ERA-Interim, the biases in ERA5 have been greatly reduced [35].
The monthly gridded evapotranspiration (ET) with a spatial resolution of 0.25 degrees between 1982 and 2015 was obtained from the Global Land Evaporation Amsterdam Model (GLEAM, https: //www.gleam.eu/). GLEAM first calculates potential evaporation using the Priestley and Taylor equation based on observations of surface net radiation and near-surface air temperature, and further converted into actual evaporation using a multiplicative evaporative stress factor based on observations of microwave vegetation optical depth and estimates of root-zone soil moisture [36,37].

Data Analysis
Based on the PRE, ET, and SWC, the water balance equation for different desert areas can be expressed as follows: where R is the runoff, and is calculated by the water balance method (Equation (1)); a is the runoff coefficient; PRE t and PRE a are the total and available precipitation, respectively; and ∆SWC i and D i are the soil water content change and thickness in the i layer, respectively. According to the preliminary investigation of the raw data, we found one obvious turning point (i.e., the change rate before and after which has the maximum difference) of the mean annual NDVI. Therefore, two piecewise linear regression models were applied to assess the change trends of the mean annual NDVI, precipitation, soil water content, air temperature, and evapotranspiration in different desert areas, and the change rates were quantified by the slopes of the linear regressions [38].
Structural equation modeling is a statistical methodology that takes a confirmatory (i.e., hypothesis testing) approach to the analysis of a structural theory bearing on some phenomenon. It conveys two important aspects of the procedure: (a) The causal processes under study are represented by a series of structural (i.e., regression) equations, and (b) these structural relations can be modeled pictorially to enable a clearer conceptualization of the theory under study [39]. It has been widely used to visualize causal processes and quantify the influence degree of direct and indirect effects [40]. We used it to quantify the effect of climatic factors on NDVI in different desert areas, and the overall test of the model fit (chi-square), as well as tests of individual parameters (p value), were utilized to estimate the performance of the model. Structural equation model analyses were conducted using Amos 24 (IBM SPSS, http://www.spss.com.hk/amos/) [41].
Threshold NDVI was defined as "the NDVI under water balance, i.e., water supply (available precipitation) equals to water demand (evapotranspiration) for natural vegetation". For the calculation of this threshold value, single linear regression was first used to analyze the correlation between mean annual available precipitation and NDVI, and between mean annual evapotranspiration and NDVI, respectively. Then, the NDVI corresponding to the intersection of these two linear regressions was taken as the threshold NDVI.

Spatiotemporal Variation of NDVI
The mean annual NDVI between 1982 and 2015 in all desert areas over the Silk Road Economic Belt ranged from 0.0001 to 0.6361 (Figure 2a). It generally increased with the increase of latitude, i.e., the higher NDVI was mainly distributed in Kazakhstan, Russia, and Azerbaijan, with the lower values in North Africa, Arabian Peninsula, Iran, and northwest China. From 1982 to 2015, NDVI increased in approximately 53% of the desert areas and decreased in the other 47% of the desert areas, with an average change of 0.0007 in the whole study region (Figure 2b). The greening region accounted for 57%, 39%, 60%, 53%, 59%, 47%, 60%, and 81% of the area in the hot arid desert, cold arid desert, cold arid semi-desert, hot arid desert semi-desert, polar desert tundra, hot arid desert shrub, cold arid desert steppe, and polar desert steppe area, respectively. The regions of large increases in NDVI were distributed in the middle and east of Kazakhstan, the northwest of China, while the decreasing regions were mainly distributed around the Aral Sea and on the north of Caspian Sea. In other words, the pronounced change of mean annual NDVI was also concentrated on the high-latitude regions.
Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 14 calculation of this threshold value, single linear regression was first used to analyze the correlation between mean annual available precipitation and NDVI, and between mean annual evapotranspiration and NDVI, respectively. Then, the NDVI corresponding to the intersection of these two linear regressions was taken as the threshold NDVI.

Spatiotemporal Variation of NDVI
The mean annual NDVI between 1982 and 2015 in all desert areas over the Silk Road Economic Belt ranged from 0.0001 to 0.6361 (Figure 2a). It generally increased with the increase of latitude, i.e., the higher NDVI was mainly distributed in Kazakhstan, Russia, and Azerbaijan, with the lower values in North Africa, Arabian Peninsula, Iran, and northwest China. From 1982 to 2015, NDVI increased in approximately 53% of the desert areas and decreased in the other 47% of the desert areas, with an average change of 0.0007 in the whole study region (Figure 2b). The greening region accounted for 57%, 39%, 60%, 53%, 59%, 47%, 60%, and 81% of the area in the hot arid desert, cold arid desert, cold arid semi-desert, hot arid desert semi-desert, polar desert tundra, hot arid desert shrub, cold arid desert steppe, and polar desert steppe area, respectively. The regions of large increases in NDVI were distributed in the middle and east of Kazakhstan, the northwest of China, while the decreasing regions were mainly distributed around the Aral Sea and on the north of Caspian Sea. In other words, the pronounced change of mean annual NDVI was also concentrated on the high-latitude regions.  An obvious turning point of the mean annual NDVI in desert areas over the Silk Road Economic Belt was found around 1994 ( Figure 3). NDVI showed a simultaneous increasing trend from 1982 to 1994 in all desert areas, with the maximum rising rate of 0.0108 decade −1 in the cold arid desert steppe area. However, NDVI decreased significantly in the cold arid desert area with an average reduction rate −0.0067 decade −1 (p < 0.01), or had no significant change trend in other desert areas (p > 0.01) after 1994. Therefore, vegetation greening appeared in all desert areas between 1982 and 1994, while extensive vegetation browning mainly happened in the cold arid desert area after 1994.
Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 14 An obvious turning point of the mean annual NDVI in desert areas over the Silk Road Economic Belt was found around 1994 ( Figure 3). NDVI showed a simultaneous increasing trend from 1982 to 1994 in all desert areas, with the maximum rising rate of 0.0108 decade −1 in the cold arid desert steppe area. However, NDVI decreased significantly in the cold arid desert area with an average reduction rate −0.0067 decade −1 (p < 0.01), or had no significant change trend in other desert areas (p > 0.01) after 1994. Therefore, vegetation greening appeared in all desert areas between 1982 and 1994, while extensive vegetation browning mainly happened in the cold arid desert area after 1994.

Effect of Climatic Factors on NDVI
Four climatic factors in desert areas over the Silk Road Economic Belt presented marked variation patterns from 1982 to 2015 (Figure 4). The mean annual precipitation was higher than 600 mm in the polar desert tundra area, and less than 100 mm in all hot arid areas (desert, desert semidesert, and desert shrub). Precipitation generally decreased in the past 34 years for most of the desert areas, especially in the cold arid desert steppe area, with an average decreasing trend of 2.79 mm yr −1 between 1994 and 2015. In accordance with precipitation, the mean annual soil water content was

Effect of Climatic Factors on NDVI
Four climatic factors in desert areas over the Silk Road Economic Belt presented marked variation patterns from 1982 to 2015 (Figure 4). The mean annual precipitation was higher than 600 mm in the polar desert tundra area, and less than 100 mm in all hot arid areas (desert, desert semi-desert, and desert shrub). Precipitation generally decreased in the past 34 years for most of the desert areas, especially in the cold arid desert steppe area, with an average decreasing trend of 2.79 mm yr −1 between 1994 and 2015. In accordance with precipitation, the mean annual soil water content was higher than 0.2 m 3 /m 3 in the polar areas (desert tundra and desert steppe), between 0.1 and 0.2 m 3 /m 3 in all cold Remote Sens. 2020, 12, 2452 7 of 14 arid areas (desert, semi-desert, and desert steppe), and lower than 0.1 m 3 /m 3 in all hot arid areas. Soil water content decreased in all desert areas after 1994, especially in all cold arid areas, hot arid desert area, hot arid desert shrub area, and polar desert tundra area, with a significant downtrend (P < 0.01). The mean annual air temperature differs greatly between diverse desert areas, and the highest and lowest values distributed in the hot arid desert semi-desert area and the polar desert steppe area, respectively. Air temperature showed an increasing trend in all desert areas from 1994 to 2015, and the rising rate reached 0.036 • C yr −1 or larger in all hot arid areas. The mean annual evapotranspiration had the highest value in the cold arid desert steppe area, and the lowest value in the hot arid desert shrub area. It increased in all desert areas between 1994 and 2015, with a significant increasing rate 1.93 mm yr −1 in the cold arid desert steppe area (P < 0.01).
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 14 higher than 0.2 m 3 /m 3 in the polar areas (desert tundra and desert steppe), between 0.1 and 0.2 m 3 / m 3 in all cold arid areas (desert, semi-desert, and desert steppe), and lower than 0.1 m 3 /m 3 in all hot arid areas. Soil water content decreased in all desert areas after 1994, especially in all cold arid areas, hot arid desert area, hot arid desert shrub area, and polar desert tundra area, with a significant downtrend (P < 0.01). The mean annual air temperature differs greatly between diverse desert areas, and the highest and lowest values distributed in the hot arid desert semi-desert area and the polar desert steppe area, respectively. Air temperature showed an increasing trend in all desert areas from 1994 to 2015, and the rising rate reached 0.036 °C yr −1 or larger in all hot arid areas. The mean annual evapotranspiration had the highest value in the cold arid desert steppe area, and the lowest value in the hot arid desert shrub area. It increased in all desert areas between 1994 and 2015, with a significant increasing rate 1.93 mm yr −1 in the cold arid desert steppe area (P < 0.01).  of air temperature on NDVI was not significant in all cold arid areas (p > 0.01). Moreover, air temperature also showed a significant negative influence on evapotranspiration in the hot arid desert semi-desert area, hot arid desert shrub area, and cold arid desert steppe area (p < 0.01), indicating that temperature conditions may not be the limiting factors on vegetation growth and hydrological processes in these regions. NDVI presented a positive relationship with evapotranspiration in all desert areas, and this effect was significant in the hot arid desert area, cold arid desert area, cold arid semi-desert area, and hot arid desert semi-desert area (p < 0.01). Overall, one key action path might be that precipitation affected NDVI first and evapotranspiration further. Standardized total effects also certificated these interactions between water conditions (precipitation, soil water content), temperature condition, evapotranspiration, and NDVI. On the one hand, precipitation was the most important influencing factor on NDVI in all cold arid areas. On the other hand, NDVI showed a remarkably strong positive relationship with evapotranspiration in most desert areas. Generally, vegetation variation in desert areas was controlled by the water balance between precipitation and evapotranspiration. The structural equation model indicated complicated interactions between climatic factors and NDVI in different desert areas over the Silk Road Economic Belt ( Figure 5). Precipitation showed a significant positive effect on NDVI in all hot arid and cold arid areas (p < 0.01). In contrast, the influence of air temperature on NDVI was not significant in all cold arid areas (p > 0.01). Moreover, air temperature also showed a significant negative influence on evapotranspiration in the hot arid desert semi-desert area, hot arid desert shrub area, and cold arid desert steppe area (p < 0.01), indicating that temperature conditions may not be the limiting factors on vegetation growth and hydrological processes in these regions. NDVI presented a positive relationship with evapotranspiration in all desert areas, and this effect was significant in the hot arid desert area, cold arid desert area, cold arid semi-desert area, and hot arid desert semi-desert area (p < 0.01). Overall, one key action path might be that precipitation affected NDVI first and evapotranspiration further. Standardized total effects also certificated these interactions between water conditions (precipitation, soil water content), temperature condition, evapotranspiration, and NDVI. On the one hand, precipitation was the most important influencing factor on NDVI in all cold arid areas. On the other hand, NDVI showed a remarkably strong positive relationship with evapotranspiration in most desert areas. Generally, vegetation variation in desert areas was controlled by the water balance between precipitation and evapotranspiration.

Threshold NDVI under Water Balance
Both mean annual available precipitation and mean annual evapotranspiration showed a significant positive correlation with mean annual NDVI (p < 0.01), and the slope of the former one was smaller than the latter one ( Figure 6). The mean annual NDVI corresponding to the intersection point of these two fit lines was 0.1174. As the standard deviation of the mean annual NDVI between 1982 and 2015 was 0.0021, we infer that the threshold range of the mean annual NDVI under water balance in all desert areas over the Silk Road Economic Belt may be 0.1153~0.1195.

Threshold NDVI under Water Balance
Both mean annual available precipitation and mean annual evapotranspiration showed a significant positive correlation with mean annual NDVI (p < 0.01), and the slope of the former one was smaller than the latter one ( Figure 6). The mean annual NDVI corresponding to the intersection point of these two fit lines was 0.1174. As the standard deviation of the mean annual NDVI between 1982 and 2015 was 0.0021, we infer that the threshold range of the mean annual NDVI under water balance in all desert areas over the Silk Road Economic Belt may be 0.1153 ~ 0.1195. For the different desert areas, the threshold NDVI and its variation with precipitation change was obviously diverse (Figure 7, Table 1). The threshold value of the mean annual NDVI was generally higher in cold arid areas, followed by hot arid areas, and very low in polar areas. The response of the mean annual NDVI to precipitation was all positive in different desert areas, and generally represented the same order as the threshold NDVI. Though the polar desert tundra area had the highest precipitation, its threshold value of the mean annual NDVI was only 0.0776. This may be because the air temperature in the polar desert tundra area was very low, and the vegetation growth in this region was mainly limited by the temperature condition but not the water condition. For the different desert areas, the threshold NDVI and its variation with precipitation change was obviously diverse (Figure 7, Table 1). The threshold value of the mean annual NDVI was generally higher in cold arid areas, followed by hot arid areas, and very low in polar areas. The response of the mean annual NDVI to precipitation was all positive in different desert areas, and generally represented the same order as the threshold NDVI. Though the polar desert tundra area had the highest precipitation, its threshold value of the mean annual NDVI was only 0.0776. This may be because the air temperature in the polar desert tundra area was very low, and the vegetation growth in this region was mainly limited by the temperature condition but not the water condition.

Different Change Patterns of Vegetation Growth
Our results indicated remarkable spatial and temporal heterogeneity of vegetation growth in desert areas over the Silk Road Economic Belt. For the spatial pattern, both the high value and the pronounced change of the mean annual NDVI mainly appeared in the high-latitude region, especially in the cold arid desert area and cold arid semi-desert area in our study region. Jeganathan et al. demonstrated that high latitudes experienced the greatest changes in vegetation phenology [42] while de Beurs et al. also found the majority of land surface changes between 2001 and 2013 occurred in Kazakhstan and Uzbekistan [12]. For the temporal variation, we found an obvious turning point of the mean annual NDVI around 1994, which has been revealed by lots of previous studies, i.e., vegetation growth varied with a piecewise trend and the expansion of browning trends accelerated in 1990s [38,43,44]. Moreover, we found the browning region after 1994 was concentrated on the cold arid desert area, which was also consistent with Jeong et al., who declared that the vegetation growth decreased by 6.8% from 1998 to 2008 in the desert regions of Asia, and the bare soil areas inside the desert boundaries expanded by 8.7% per decade in the 2000s [45]. It should be noted that different remote sensing datasets often identify contrasting vegetation greenness trends [32,33], and extremely

Different Change Patterns of Vegetation Growth
Our results indicated remarkable spatial and temporal heterogeneity of vegetation growth in desert areas over the Silk Road Economic Belt. For the spatial pattern, both the high value and the pronounced change of the mean annual NDVI mainly appeared in the high-latitude region, especially in the cold arid desert area and cold arid semi-desert area in our study region. Jeganathan et al. demonstrated that high latitudes experienced the greatest changes in vegetation phenology [42] while de Beurs et al. also found the majority of land surface changes between 2001 and 2013 occurred in Kazakhstan and Uzbekistan [12]. For the temporal variation, we found an obvious turning point of the mean annual NDVI around 1994, which has been revealed by lots of previous studies, i.e., vegetation growth varied with a piecewise trend and the expansion of browning trends accelerated in 1990s [38,43,44]. Moreover, we found the browning region after 1994 was concentrated on the cold arid desert area, which was also consistent with Jeong et al., who declared that the vegetation growth decreased by 6.8% from 1998 to 2008 in the desert regions of Asia, and the bare soil areas inside the desert boundaries expanded by 8.7% per decade in the 2000s [45]. It should be noted that different remote sensing datasets often identify contrasting vegetation greenness trends [32,33], and extremely low NDVI values during the non-growing season may affect the calculation of the mean annual NDVI [46]; thus, more efforts are required to evaluate NDVI time series against field measurements of vegetation growth, primary productivity, and other biological processes in order to better understand ecosystem dynamics over the Silk Road Economic Belt.

Integrated Effect of Environmental Factors on Vegetation Growth
Among various climatic variables involving in vegetation-atmosphere interactions, precipitation variability is strongly related to vegetation change in arid and semi-arid regions due to the dominant role that it plays in water availability [17,19]. We found NDVI presented a strong positive relationship with both precipitation and evapotranspiration in most desert areas over the Silk Road Economic Belt. Moreover, both precipitation and soil water content decreased after 1994, while both air temperature and evapotranspiration increased in all desert areas after 1994. Therefore, water stress will be exacerbated, which may be one key reason for the "turning point" of the mean annual NDVI around 1994. Jeong et al. also revealed that increased precipitation in desert along 40 • N provided favorable conditions for vegetation growth (i.e., greening) in the 1990s but reduced precipitation and intensified warming, causing less moisture to be available for vegetation growth (i.e., browning) in the 2000s [45].
Particularly important, the region of west Asia will likely experience more drought events with climate warming [13], and the coupling between vegetation growth and precipitation will be stronger with the enhancement of drought [47,48]. Moreover, it has been demonstrated that vegetation growth has a 1-3-month lag response to precipitation anomalies [17,19], and winter precipitation can be an important component of the plant water budget during the following warm season [49]. Our study also found a temporal lag between precipitation anomalies and vegetation activity of 2 months but no significant lag at the annual scale (not included in this paper). Except for climate change, the vital relevance of anthropogenic activities on vegetation degradation has been proven by plenty of studies [9,12,45], indicating the necessity to combine climate change and human activities together for a deep understanding of the vegetation dynamics over the Silk Road Economic Belt.

Threshold Vegetation Greenness and Its Response to Precipitation
Determination of the water carrying capacity for vegetation could provide quantitative guidelines for the selection of plant species, density or biomass, and appropriate management for vegetative restoration [29]. Our study found that the threshold range of the mean annual NDVI was approximately 0.1153~0.1195 in the entire study region, and it was relatively higher in the cold arid areas, due to more precipitation. It is interesting that though the polar desert tundra had the maximum precipitation, the threshold NDVI was only about 0.0776, owing to the high elevation and dominant control by temperature conditions [14]. Though the research for a sustainable maximum vegetation density is necessary in arid and semi-arid areas, the quantification is not easy since it requires insightful understanding of the interactions between vegetation growth and environment change. Previous studies about the water carrying capacity for vegetation were mainly based on empirical methods, conceptual models, and physical models at the local scale [24,26,29]; however, all of them were difficult to use over the Silk Road Economic Belt, due to the lack of field experiments and sufficient data. Consequently, we tried to estimate the water carrying capacity for vegetation using a statistical model based on a remote sensing-derived vegetation index and climatic factors. However, because of the high spatiotemporal variability of vegetation growth and environmental conditions, both the scale issues and the uncertainly estimation are essential in future studies using higher resolution data (e.g., site observation, MODIS, Landsat, etc.) [50].

Conclusions
This research sought to show the spatiotemporal variation of vegetation growth and its influence by climatic factors in different desert areas over the Silk Road Economic Belt. Both the mean value and interannual change of NDVI between 1982 and 2015 increased with the increase of the latitude. It showed dramatic greening from 1982 to 1994 in all desert areas, while significant browning after 1994 was concentrated on the cold arid desert area. The climate condition generally appeared as a warming and drying trend in the past 34 years, and was dominated by warming in the hot arid desert area, and hot arid desert semi-desert area, and by drying in the cold arid desert steppe area. NDVI presented a strong positive relationship with both precipitation and evapotranspiration in most desert areas. The threshold range of the mean annual NDVI under the water balance between 1982 and 2015 was approximately 0.1153~0.1954 in the whole study region, and was the highest in the cold arid areas, followed by the hot arid areas and polar areas. The response of this threshold value to precipitation was all positive in different desert areas. These results provide an enhanced understanding of not only what areas are facing critical degradation under climate change and should be protected, but also what areas can be grazed by livestock more sustainably, or may support rainfed agriculture, which is critical for the regional eco-environmental management and sustainable socioeconomic development over the Silk Road Economic Belt.