The arid region of NWC (Figure 1), including the entire Xinjiang Uygur Autonomous Region, the Hexi Corridor in Gansu Province, the western Helan Mountains in the Inner Mongolia Autonomous Region, and parts of Qinghai Province and the Ningxia Hui Autonomous Region, covers an area of 2.27 million km² (Chen, 2010; Zhang et al., 2011; Qin et al., 2018). The topography of this region is very complex. The defining morphological features of the entire region are mountains, which generally run east to west, with interspersed basins. The Tianshan Mountains extend across the center of Xinjiang and divide it into two regions, commonly known as southern Xinjiang and northern Xinjiang (Chen et al., 2012; Zhang et al., 2012). The Altay Mountains extend along the northern edge of the study area, and the Karakoram Mountains run along its southern edge. Between the Altay and Tianshan Mountains lies the Junggar Basin, whereas the Tarim Basin lies between the Tianshan and Kunlun Mountains. The elevation of this region ranges from -154.31 m asl (Aydingkol Lake) to 8611 m asl (Mount Qogir), as reported by the National Bureau of Surveying, Mapping, and Geoinformation of the People's Republic of China; 16.4% of the study area is located above 3510 m asl, where rain gauges are rarely installed. According to Chen (2010), the elevation demarcation points between mountainous areas and plains are 1000 m for the Altay Mountains and the northern slope of the Tianshan Mountains, 1500 m for the Qilian Mountains and the southern slope of the Tianshan Mountains, and 2000 m for the Kunlun Mountains (Figure 1).

The study area has a broad scope, and its climate, topography, and land cover are all complex. To enable better description of relevant spatial patterns, this area was divided into nine sub-regions reflecting the impact of topography on the local climate, following Mu (2010) and Zhao (2011), as shown in Figure 1 and Table 1. The regionalization was based on the relationship between elevation and precipitation from rain gauge data according to Zhao (2011). The precipitation is highly correlated with elevation in each sub-region. The choice of divisions was informed primarily by the presence of mountains, the slope aspect of the mountains, and the further division of the Tianshan Mountains into three sections (the western, central, and eastern portions). The nine sub-regions are numbered sequentially from north to south and from west to east. For example, sub-region 1 consists mainly of the southern slope of the Altay Mountains and the northern part of the Junggar Basin, which are located in northern Xinjiang. The Tianshan Mountains are divided into the northern slope (windward slope) and southern slope (leeward slope). Sub-regions 2, 3, and 4 contain the western, central, and eastern portions of the northern slope of the Tianshan Mountains, and sub-regions 5, 6, and 7 contain the western, central, and eastern portions of the southern slope of the Tianshan Mountains. Sub-region 8 is the northern slopes of the Karakoram and Kunlun mountains and the southern Tarim Basin. Sub-region 9 is the northern slope of the Qilian Mountains. The areas of these sub-regions range from 4.5 × 10⁴ km² to 6.7 × 10⁵ km², of which mountainous areas account for 22%-68.4%. Precipitation-elevation profiles were derived to show relevant vertical distribution patterns, which are discussed with respect to each region.

The remote-sensing-based precipitation products mentioned above [TRMM 3B42, TRMM 3B43 (Huffman et al., 2010), CMORPH, and PERSIANN] were evaluated in our previous work (Yang and Luo, 2014a). The results showed that TRMM 3B43 performed best, whereas CMORPH and PERSIANN overestimated the precipitation to a greater extent. A back-propagation neural network approach was later proposed and used to correct the bias of TRMM 3B43, and acceptable biases and accuracy were obtained (Yang and Luo, 2014b). Thus, the bias-corrected version of TRMM 3B43 was used in this study. The data have a spatial resolution of 0.25° and a temporal resolution of one month; they cover January 1998 to December 2010.

In addition, CHN, a gridded daily precipitation dataset based on interpolation from rain gauge data that covers only China, was also used in this study. CHN is open-source and is published by the China Meteorological Data Service Centre (http://http://data.cma.cn/). It is generated by thin-plate spline interpolation of data from 2474 rain gauges spanning 1961 to the present. The spatial resolution is 0.5°. This dataset has good quality, as demonstrated by cross-validation and error analysis. CHN was resampled to a spatial resolution of 0.25° using ArcGIS software before the analysis so that it has the same resolution as TRMM 3B43. According to Yang and Luo (2014b), who analyzed the representative range of precipitation and topography in detail, a 0.25° grid is sufficient to represent the complexity of the terrain.

The Advanced Spaceborne Thermal Emission and Reflection Radiometer digital elevation model (DEM) data, with coverage from 83°N to 83°S and a resolution of 1 arcsec (30 m horizontal spacing at the equator), were used to extract an elevation value for each grid cell. These data are available via the National Aeronautics and Space Administration Warehouse Inventory Search Tool.

The spatial and temporal distribution patterns of precipitation in the arid region of NWC are the main topic of this study. On the temporal scale, TRMM 3B43 and CHN data were used to analyze the variability of seasonal precipitation and the interannual variation in the mountainous areas, plains, and each of the nine sub-regions. For the horizontal dimension, precipitation contour maps based on these two precipitation products were drawn and analyzed. For each sub-region, the areal precipitation was calculated and compared to previous studies. The precipitation concentration index (PCI) was used to represent the concentration degree of precipitation. It was proposed by Oliver (1980) and developed by De Luis et al. (1997). The PCI has a more intuitive physical meaning and simpler calculation than other indices (Zhang et al., 2021). The seasonal time scale is defined as follows:

where P_i is the monthly precipitation in the ith month for each gauge or grid. PCI values of less than 10 indicate a uniform precipitation distribution (low precipitation concentration), and values between 10 and 15 indicate moderate precipitation concentration. Values between 15 and 20 represent an irregular precipitation distribution, and values above 20 represent strong irregularity in the precipitation distribution.

The distribution of precipitation in each sub-region across the vertical profiles was calculated. The precipitation for each grid cell was represented separately by the means of the TRMM 3B43 and CHN data for that cell, and the mean value for the corresponding grid cell from the DEM data was extracted to represent elevation. This enabled one-to-one matching of precipitation and elevation for each dataset. Next, the precipitation and elevation were averaged in each 300 m elevation band for each sub-region, which allowed us to construct a set of vertical profiles for each dataset. The confidence bands (CBs) of the two datasets were both determined by Equation (2) at the 95% confidence level.

where CB is bounds of the confidence band, $\bar{X}$is the average value of the dataset, $\delta $is the standard deviation, and n is the sample size. The precipitation–elevation profiles generated by the two datasets were compared, and the distribution features in each sub-region are discussed with reference to other reports in the literature. Analysis over all three dimensions thus yields an overall picture of the spatial distribution patterns of precipitation in the arid region of NWC.

The temporal variability of precipitation was analyzed in terms of seasonal distribution and interannual variation using both TRMM 3B43 and CHN data (separately) for mountainous areas, plains, and each of the nine sub-regions. Seasonal differences in precipitation were evident, as shown in Table 2.

Owing to the monsoon, the precipitation in NWC and its sub-regions was concentrated mainly in summer, which accounted for 36.4% to 69.8% of the average annual precipitation, whereas winter precipitation accounted for only 2.5% to 14%. The precipitation was more concentrated in summer in southern Xinjiang than in northern Xinjiang, accounting for 48.7%-69.8% and 36.4%-51.4% of the annual precipitation, respectively. In winter, however, the opposite trend appeared; the proportion of precipitation in southern Xinjiang was 2.8%-8.7%, whereas that in northern Xinjiang was 6%-14%.

Seasonal differences in precipitation also appeared between mountainous areas and plains because of differences in elevation, available moisture, and dynamic conditions. The most notable difference was that precipitation was higher in mountainous areas than in plains. The largest difference appeared in summer, where mountain areas received 57-204 mm of precipitation, whereas plains received much less (17-86 mm).

The interannual variation of precipitation can be characterized by variation coefficients, where larger values indicate more unstable annual precipitation, whereas smaller ones indicate little interannual variation in precipitation. Table 3 shows that the variation coefficients ranged from 0.08 to 0.19 for TRMM 3B43 and from 0.14 to 0.23 for CHN on the sub-region scale. The variation coefficients for mountainous areas were higher by 0.01-0.16 than those for plains for TRMM 3B43 and higher by 0.02-0.17 for CHN. This result indicates that the interannual variation of precipitation was smaller in mountainous areas than in plains. High-altitudes areas, which receive more precipitation, exhibited more interannual stability in precipitation.

The precipitation in mountainous areas is reportedly several times, or even dozens of times, greater than that in basins. Northern Xinjiang receives more precipitation than southern Xinjiang (Xie et al., 2017). In the Tianshan Mountains, the northern slope (windward side) receives more precipitation than the southern slope (leeward side), and the precipitation gradually decreases from west to east (Chen, 2010). The Ili Valley of the western Tianshan Mountains, which is affected by the westerly current and plentiful of water vapor, receives the most precipitation in the study area (Shi et al., 2008). The Altay Mountains are affected mainly by the Arctic current, which carries only one-third or one-fourth the water vapor of the westerly current; consequently, the Altay Mountains receive less precipitation than the Tianshan Mountains (Su et al., 2007). The eastern and western parts of the Qilian Mountains are affected by the southeast monsoon and westerly current, respectively. Moisture is more plentiful in the eastern part than in the western part, and the eastern part thus receives more precipitation (Zhang et al., 2008; Chen, 2010). The Junggar and Tarim basins, however, which are located in the hinterland of the Eurasian continent and far from the ocean, receive the least precipitation (Zhang and Yuan, 2002; Li, 2003; Chen, 2010).

Judging visually from the contour maps of precipitation (Figure 2), the spatial precipitation distributions presented by CHN and TRMM 3B43 were consistent with the characteristics described above. The maps showed that precipitation was concentrated mainly in the mountainous areas, whereas the plains received much less precipitation than the mountains. Table 4 lists the annual precipitation estimated from the two grid datasets for each of the nine sub-regions for reference.

Table 5 lists the estimated annual precipitation in different parts of the study area from the two datasets; literature values are also given for comparison. The latter were derived from rain gauge observations for each specific region using an arithmetic method. Comparison analysis may reveal the performance of the two grid datasets in different sections. Zhang et al. (2011) indicated that the annual precipitation over the entire study area is at most 200 mm, whereas Chen (2010) estimated it at 151 mm, and Guo et al. (2020) indicated that it is approximately 130 mm and decreases from east to west. TRMM 3B43 and CHN gave values of 137 and 143 mm, respectively, which were similar to the results of Chen (2010) and Guo et al. (2020). Northern and southern Xinjiang reportedly receive 254-278 mm and 116 mm, respectively, of precipitation annually (Su et al., 2007; Chen, 2010). The TRMM 3B43 and CHN datasets gave estimations of 259 and 273 mm for northern Xinjiang, and 100 and 98 mm for southern Xinjiang, respectively. These estimates are reasonable for northern Xinjiang and slightly (16-18 mm) lower than the literature values for southern Xinjiang. In Gansu and Inner Mongolia, the annual precipitation estimates from TRMM 3B43 and CHN were 115 and 136 mm, respectively; these values are 15 mm lower and 6 mm higher than the value of 130 mm obtained by Chen (2010).

The spatial distribution of the PCI in summer (Figure 3) showed values of 8.8-10.8 for the gauge data, 8.3-10.2 for the CHN data, and 8.3-11 for the TRMM data, respectively. The mean values were 8.3, 8.7, and 8.9 for the gauge, CHN, and TRMM data, respectively. The PCI from the TRMM data was slightly higher than those from the gauge and CHN data. On the spatial scale, the three datasets consistently indicated moderate precipitation concentration (10 ≤ PCI < 15) in a few areas of the northern slopes of the Karakoram and Kunlun mountains (sub-region 8), whereas the precipitation was uniformly distributed in the other sub-regions.

The grid cells for each sub-region were grouped in elevation bands of 300 m, and the elevation in each range is given as the average value. In each elevation band, the grid cell precipitation was statistically analyzed. The average values with the CBs at P = 95% were then plotted against elevation, showing the precipitation distribution pattern in the vertical dimension for each sub-region (Figure 4).

The TRMM 3B43 and CHN data showed that precipitation generally increased with elevation, although it may begin to decrease at some elevations in some sub-regions. Quantitatively, however, the CHN dataset gave higher precipitation than TRMM 3B43 except in the western part of the northern slope of the Tianshan Mountains and the northern slopes of the Karakoram and Kunlun mountains (sub-regions 2 and 8).

The most complicated profile was found on the southern slope of the Altay Mountains (sub-region 1), where the precipitation began to decrease with elevation between approximately 2560 and 3100 m and then increased above 3100 m. Some previous studies have found that precipitation increased with elevation and decreased at approximately 2000 m asl (Zhang and Deng, 1987; Su et al., 2007). Ning et al. (2020) indicated that the first and second precipitation peaks appeared at approximately 2400 and 3200 m, respectively; these values are similar to our results.

For the northern slope of the Tianshan Mountains (sub-regions 2, 3, and 4), studies based on limited rain gauge data have indicated that the only maximum relative humidity layer resulted in the unique zone of maximum precipitation (Zhang and Deng, 1987); however, the location of the zone varied, for example, 1600-2100 m asl by Lin (1995), 2000 m asl by Lin (1985), 2160 m asl by Zhang and Deng (1987), and 2400 m asl by Weng (1985), probably because of differences in data source. Some studies reported that there were two peaks in the precipitation profile in the northern Tianshan Mountains. The first peak is reportedly located at 1600-2000 m asl (Chen, 2010) or 2000 m asl (Su et al., 2007); the second reportedly lies at 3500 m (Su et al., 2007) or 4000 m (Han et al., 2004). Li et al. (2018) indicated that two large precipitation zones in the central part of the northern Tianshan Mountains are located at approximately 1900 and 3500 m and that precipitation decreases nonlinearly with decreasing altitude, but fluctuates according to a certain law. The results of previous studies contained significant uncertainties. The scarcity of data in high-elevation areas has been a problem to date. Most previous studies were based on rain gauge data from various sources, and thus reached different conclusions (Zhao et al., 2011). In this study, the CHN and TRMM 3B43 data showed decreases above 3460 and 2870 m, respectively, indicating that there is only one zone of maximum precipitation. For the sub-regions, the CHN grid datasets generally showed monotonically increasing precipitation with increasing elevation in the northern Tianshan Mountains, except in their western and central parts (sub-regions 2 and 3). In these two sub-regions, CHN showed that precipitation decreases with increasing elevation starting at 4300 and 3700 m asl, respectively.

Figure 4 shows that for the southern Tianshan Mountains, the precipitation estimated from TRMM 3B43 increased with elevation, with a slight decrease between 4900 and 5200 m; the values ranged from 47 to 356 mm. The precipitation estimated from CHN decreased slightly above 5200 m and was higher in general than that estimated from TRMM 3B43, with values between 84 and 555 mm. Nonetheless, maxima appeared in the high-altitude (above 5200 m) region for both datasets, which is consistent with the finding of Lin (1985) that the maximum precipitation appeared above 3000 m in this region. However, other studies indicated that the precipitation first increased and then decreased with elevation, with a maximum at 2500 m (Li, 2006; Su et al., 2007; Chen, 2010) or approximately 3500 m (Zhou and Chen, 1998), indicating that the precipitation was lower at high altitudes than in mid-mountain regions.

In the western part (sub-region 5) of the southern Tianshan Mountains, the precipitation above 4600 m was the same as that of the entire southern Tianshan area, because these high areas appeared only in sub-region 5. For the central part (sub-region 6) of the southern Tianshan Mountains, the precipitation estimates from TRMM 3B43 increased monotonically with elevation, and the maximum appeared at the highest elevation (3900-4200 m), whereas the precipitation estimates from CHN decreased slightly above 3700 m, where the maximum precipitation appeared, as shown in Figure 4. Zhao et al. (2011) reported that the maximum appeared at 3332 m and that precipitation then began to decrease in sub-region 5. They also indicated that the precipitation increased monotonically with elevation and that the maximum appeared at the highest rain gauge (2458 m) in sub-region 6; however, the vertical distribution above that elevation was unclear. The precipitation profiles from CHN and TRMM 3B43 below 3332 m in sub-region 5 and below 2458 m in sub-region 6 were clearly consistent with the result of Zhao et al. (2011). However, the precipitation continued to increase with elevation above those elevations in this study. In the eastern part of the southern Tianshan Mountains (sub-region 7), Luo et al. (2000) found that the annual precipitation in the Hami region (belongs to sub-region 7) increased by 13 mm for every 100 m increase in elevation, and the annual precipitation above 4000 m asl in Yushugou Valley (which is also in sub-region 7) was 400-500 mm. Liu et al. (2017) reported that precipitation increased with increasing altitude from 34.5 to 1677.2 m. TRMM 3B43 data showed that precipitation first increased and then decreased slightly at 3700 m. By contrast, CHN data showed a decrease-increase-decrease pattern, with a maximum value at 2600-2900 m (Figure 4). The trend from TRMM 3B43 was similar to that reported in the above studies, but the precipitation values from TRMM 3B43 and CHN were both smaller than the reported values.

Figure 4 also shows that for the northern slopes of the Karakoram and Kunlun mountains (sub-region 8), the precipitation estimated from TRMM 3B43 first increased and then decreased with elevation; the maximum value appeared at 4800-5100 m. By contrast, the precipitation estimated from CHN increased with elevation, and the maximum value appeared at the highest elevation. Zhao et al. (2011) showed that a quadratic polynomial could fit the relationship between precipitation and elevation in this region; a maximum of 106.8 mm appeared at 3840 m, which indicated that the mid-mountain region received more precipitation than higher elevations. The zone of maximum precipitation was at least 1000 m lower than the estimate from the gridded data.

Previous studies of the vertical precipitation pattern in Gansu and Inner Mongolia (sub-region 9) showed that precipitation increased nonlinearly with elevation (Zhu and Wang, 1996) or that the relationship could be described by a sigmoid curve with the maximum at the highest elevation (Tang, 1985). Chang et al. (2002) and Chen and Zeng (2011) found that precipitation first increased and then decreased, with maximum at 3650 m or 2600-2700 m, respectively. Sun et al. (2019) indicated that the maximum precipitation zones in the eastern, central, and western sections of the Qilian Mountains were 4100, 4500, and 4700 m, respectively. In this study, both gridded datasets showed that precipitation first increased and then decreased with elevation, with a maximum at 4300 m (as shown in Figure 4). This trend was consistent with the results of Chang et al. (2002) and Chen and Zeng (2011), and the maximum precipitation zones were similar to the result of Sun et al. (2019).

The precipitation distribution in the arid region of NWC exhibits high spatiotemporal variability because of the complex topography. Topographical factors such as elevation, relative relief, slope, and aspect strongly affect the precipitation distribution. Our previous study indicated that elevation factors have the greatest effect on precipitation, followed by slope and aspect (Yang and Luo, 2014a; Yang and Luo, 2014b). In this study, the study area was divided into nine sub-regions according to the locations and aspects of the mountains, and this partition indirectly accounted for the differences between the windward and leeward sides of mountain ranges. For this reason, the elevation-precipitation relationship was analyzed, but the effects of slope and aspect were not considered in this study.

Differences in elevation over short distances can result in significant changes in the distribution of precipitation due to interactions between topography and atmospheric flow in mountainous areas (Guo et al., 2014). The study area has complex topography and large variation in elevation, which ranges from -154.31 to 8611 m asl. However, more than 90% of the rain gauges are located below 2000 m asl. Because of the sparsity of rain gauges in high-altitude areas, it is very difficult to derive precipitation-elevation relationships. The vertical distribution of precipitation has long been under debate. The results reported by previous studies also differed, and the precipitation-elevation profiles at high altitudes remained unclear because of the large uncertainty resulting from insufficient observations. Gridded precipitation datasets such as TRMM 3B43 and CHN cover the entire study area, including high-elevation zones, and thus the precipitation-elevation relationship can be derived. However, uncertainties remain. They may lie in the extreme sensitivity of microwave (MW) signals from clouds over complex topography and the highly variable surface in mountainous regions; the use of indirect measurement and precipitation retrieval algorithms (Rozante and Cavalcanti, 2008; Zhao and Garrett, 2008); and the misclassification of seasonal or perennial snow-ice cover as rain clouds by passive MW (Hirpa et al., 2010). However, these quantitative uncertainties still cannot be addressed, because very few observational data can be used for reference at high elevations.

Finally, many previous studies have analyzed precipitation frequency, intensity, and diurnal cycles using subdaily or daily datasets (Zhou et al., 2008; Shen et al., 2010; Guo et al., 2015; Guo et al., 2016). However, because of the limited temporal resolution of the corrected monthly TRMM 3B43 data, analyses at these scales could not be performed in this study.