Spatio-Temporal Coupling Analysis of Differences in Regional Grain–Economy–Population and Water Resources

Abstract

In the context of climate change and the intensification of population activities, differences in regional water resources are the main drivers leading to these resources’ unbalanced development. This problem can be addressed by exploring spatial differences and spatio-temporal patterns. Based on the spatio-temporal trends of grain production, social economy, population, and water resources in the Tarim River Basin from 2005 to 2020, this paper uses the barycenter model coupling situation model to analyze the evolutionary trend of the barycenter, spatial overlap and spatio-temporal coupling degree for each index. The results show the following: (1) The spatio-temporal distribution of grain production was larger in the east than in the west. Grain production increased by 18.10% across the basin, and the migration rate of the grain center of gravity (CG) was 16.61 km/a. (2) The spatio-temporal distribution of the economy was greater in the south than in the north, with a cumulative migration of 323.10 km to the southwest. During the study period, the population remained concentrated in the western portion of the basin, increasing 25.18% compared to the population prior to 2005. The spatial variation range of total water resources was small, showing a trend of slow increase from west to east. (3) The overlap between GDP and population was enhanced, with the coupling showing a slow rising trend. The overlap of water resources and grain space also increased and the consistency index was high. From 2011 to 2020, the average consistency index was 0.594 and the coupling degree of the two factors was enhanced. By combining grain production, economy, population, and water resources with the center of gravity model, this paper reveals the spatial differences of relevant factors in the Tarim River Basin, providing an important reference value for regional socio-economic development and the rational allocation of water resources.

1. Introduction

Global warming-induced climate change is having a significant impact on agricultural production in the nation [1,2], and it is also affecting the sustainability of China’s socio-economic development [3], population [4], and water resources [5]. Grain supply and demand, as a basic means and measure of production, is inextricably related to the national economy, people’s livelihoods, economic security, social stability, and other major strategic issues [6]. In grain production, natural conditions such as terrain, landform, climate, soil, and water are critically important. However, with the rapid pace of social and economic change in China, unbalanced development is bound to affect grain production [7].

Natural factors have established in influence over the years [8]. However, population growth and migration are now the primary drivers for the development of agriculture, leading to an increase in agricultural water intensity and a resetting of regional water resources distribution. The result has been an uneven distribution of water resources in time and space, causing difficulty in the development of grain production. At the same time, with the acceleration of industrialization and urbanization, people’s living standards have improved, sparking an increase in industrial and urban water demand. The outcome has been a grain water shortage and a rise in water conflicts [9].

In recent years, with rapid economic development and a decline in the status of grain production, the phenomenon of “economy driving away grain” has gradually emerged [10]. This in turn has caused a decline in the coordination between grain production and economic development. In [11], the authors found that rapid population growth is closely related to economic development and grain demand, while in [12], the researchers mainly focused on dynamic changes between population and the economy, and the authors explored possible driving mechanisms for these changes [13]. All of the above research concurs that socio-economic development and grain production depend on large but very limited water resources, and that the deterioration of the ecological environment and the low efficiency of agricultural water use make grain production increasingly restricted by water resources.

The uneven distribution and relative shortage of water resources between regions has also become the focus of current research. Some authors used the Gini coefficient [14] and the imbalance coefficient [15] to explore problems between water resources and grain production from various perspectives. Other researchers analyzed the coupling degree between water, energy, and grain [16]. Additionally, some scholars adopted the center of gravity approach from physics and applied it to geography to perform single-factor research, such as looking for the economic center of gravity [17], population center of gravity [18], grain center of gravity [19], and so on. Some researchers carried out comparison and correlation studies between double [20,21] or multiple [22] factors. The single-factor studies mainly focused on dynamic changes and driving mechanisms using different research scales. However, at the provincial scale, only a few studies investigate the coupling between multiple factors based on county and city, and there are few analyses of the coupling state of the gravity center of grain production and water resources based on the gravity center model.

Xinjiang covers a vast area of China’s arid northwest, and there are large gaps between its regions. These gaps are not only reflected in the ecological environment, but are also prominent in the development of Xinjiang as a whole. Compared with the eastern coastal area of China, which is famous for its dense interlocking settlements, the economic links between regions in northwest China are weaker. Therefore, revealing spatial differences and regional imbalances as a core issue affecting economic, social, and agricultural development is an important focus of geographical research [23].

The Tarim River Basin is located in the southern part of Xinjiang, with a complex ecosystem of “mountain-desert-oasis-city” [24]. Desert occupies one-third of the basin, whose unique geographical location and topographical features are the main reasons for the region’s unbalanced development [25]. This paper takes the Tarim River Basin as the research target area to analyze the degree of coupling or contradiction between grain output, the economy, and population at the basin and prefecture level. Additionally, the study analyzes data from the basin to examine the advantages of regional water resources and put forward suggestions for the grain production and economic development in the study area, in order to reasonably adjust the layout of grain production.

2. Data and Materials

2.1. Study Area

The Tarim River Basin is located in southern Xinjiang, China (73°10′–94°05′ E, 34°55′–43°08′ N). The landform in this region is extremely complex, with the terrain unit composed of mountain–plain–desert [26], a typical mountain–oasis–desert complex system (Figure 1). The basin, which has an extreme arid climate, covers about 103 × 10⁴ km² and accounts for 61.82% of the total area of Xinjiang, making it the largest inland river basin in China. The total amount of water resources in the basin is about 42.04 billion m³ [27,28].

There are 42 counties and cities in the Tarim River Basin, the main ones being Bayinggol Mongol Autonomous Prefecture, Aksu Prefecture, Kashgar Prefecture, Kizilsu Kirgiz Autonomous Prefecture, and Hotan Prefecture. In 2020, the population of the basin was around 12.30 million, accounting for nearly half (47.39%) of the total population of Xinjiang. The Kashgar area had the largest share (4.70 million) of the region’s population. The per capita GDP of the Tarim River Basin was CNY 417.05 billion [27,28], and the primary industry was CNY 91.55 billion, which was 46.21% of Xinjiang’s total GDP. The secondary industry accounted for 26.05% of the GDP, and the tertiary industry accounted for 40.24%.

2.2. Data Sources

The study looks at the spatial and property data of the construction corps of 42 counties and cities across five prefectures in the basin (Bayingol Mongolian Autonomous Prefecture, Aksu Prefecture, Kashgar Prefecture, Kizilsu Kirghiz Autonomous Prefecture and Hotan Prefecture). The spatial data also show the administrative divisions of the prefectures and counties and the barycenter coordinates of each county or municipal district. The data come from the National Center for Basic Geographic Information (http://www.webmap.cn, accessed on 7 June 2022).

Data on the grain yield, economy, and population of each county and city in the basin during the study period were obtained from the statistical bulletins of the Statistics Bureau of Xinjiang Uygur Autonomous Region, Statistics Bureau of Xinjiang Production and Construction Corps, and various counties and cities. The water resources data mainly include the total amount of water resources data in the basin, along with groundwater and surface water data.

The terrain data were obtained from the SRTM DEM data in the Geospatial Data Cloud (http://www.gscloud.cn, accessed on 16 October 2022).

2.3. Center of Gravity Model

The regional center of gravity (CG) is represented by the center of gravity model [29]. Assuming that a certain region is composed of n second-order regions, the coordinate expression of the CG of the study area is:

$$X_{ti}={\displaystyle \sum _{t=1}^n(C_t•X_i)}/{\displaystyle \sum _{t=1}^n{C}_t}$$

(1)

$$Y_{ti}={\displaystyle \sum _{t=1}^n(C_t•Y_i)}/{\displaystyle \sum _{t=1}^n{C}_t}$$

(2)

where X_ti and Y_ti represent the longitude and latitude coordinates of a certain population or the economic CG in year t, respectively; C_t represents the population or economy in the i-th small area; and X_i and Y_i represent the latitude and longitude coordinates of the geometric center of the i-th small area, respectively.

2.4. Center of Gravity Migration Distance

The calculation formula of the CG movement distance in the area may be expressed as:

$$C_{t-j}=R\ast \sqrt{{(y_t-y_j)}^2+{(x_t-x_j)}^2}$$

(3)

where the distance of the CG from year t to year j in the C_t–j study area unit is km, R is a constant, and the value of 111.111 is the coefficient for converting geographic coordinates into plane distance.

2.5. Coupling Situation Model

Coupling refers to a phenomenon whereby two or more motion forms affect each other through physical interaction. In geography, coupling refers to the deviation degree of the CG of two specific factors in the spatial distribution.

By calculating the spatial overlap and consistency of the CG of the two elements, the spatio-temporal coupling degree of the two elements was analyzed. The CG distance index (spatial overlap) represents the static perspective analysis of CG coupling, and the consistency of the CG directional change represents the dynamic perspective analysis of the CG coupling. Spatial overlap: The calculation formula of the CG distance index is as follows:

$$L=R\ast \sqrt{{\left(x_{ia}-x_{ib}\right)}^2+{\left(y_{ia}-y_{ib}\right)}^2}$$

(4)

where a and b represent different research factors, x_ia and x_ib represent the latitude of different factors in the same year, y_ia and y_ib represent the longitude of different factors in the same year, R is a constant, and the value is 111.111. The smaller the L is, the closer the spatial distance between the two elements, the higher the spatial overlap and the better the coupling. Conversely, the larger the L is, the weaker the overlap and the worse the coupling.

Consistency of change: Consistency of change refers to the displacement of two kinds of the CG relative to the time point of the vector angle θ. The greater the θ is, the more inconsistent the change. Since the value range of θ is 0° < θ < 180°, its cosine value A is used as the general index, −1 ≤ θ ≤ 1. When C = 1, the direction of the two is the same; when A is equal to negative 1, the two are going in opposite directions. Let the changes of longitude and latitude of the center of gravity from the previous time point be ∆x and ∆y, respectively. According to the law of cosine:

$$A=\cos \theta =\frac{\left(\Delta x_a^2+\Delta y_a^2\right)+\left(\Delta x_b^2+\Delta y_b^2\right)-\left[\left(\Delta x_a^2-\Delta y_a^2\right)+\left(\Delta x_b^2-\Delta y_b^2\right)\right]}{2\sqrt{\left(\Delta x_a^2+\Delta y_a^2\right)+\left(\Delta x_b^2+\Delta y_b^2\right)}}=\frac{\Delta x_a^2\Delta y_a^2+\Delta x_b^2\Delta y_b^2}{\sqrt{\left[\left(\Delta x_a^2+\Delta y_a^2\right)+\left(\Delta x_b^2+\Delta y_b^2\right)\right]}}$$

(5)

3. Results

3.1. Temporal and Spatial Distribution of “Grain-Economy-Population” and the Evolution of Gravity Center in the Tarim River Basin

3.1.1. Spatial Distribution of Grain and the Evolution of the CG in the Tarim River Basin

Spatial Distribution of Grain in the Tarim River Basin

The spatial distribution of grain yield in 2005, 2010, 2015, and 2020 in the Tarim River Basin (Figure 2) shows an overall increasing trend. In 2005, the higher yields were mainly concentrated in Aksu Prefecture, the Kashgar region and the Hotan region, with grain yield in the Tashkurgan Tajik Autonomous County in the Kashgar region being the highest. From the perspective of the spatial distribution of grain production, Bayingolin Mongolian Autonomous Prefecture was the lowest-yielding area in 2005. The main reason for the low yield is geography, as the area mainly consists of mountains, desert, and other geomorphic units. In fact, the Gobi desert, which grows no grain, accounts for 30.3% of the entire Bayingolin region. In 2010, the grain output of Jingxian County increased compared with that of 2005. In 2015, the grain output of more than half the counties and cities in Bayingolin Mongolian Autonomous Prefecture showed an increasing trend. By 2020, the grain output of Heshuo County was higher in this region, while other counties and cities were in the low-yield area.

However, in 2010, there were more counties and cities in the high-yield area. Most of these were north of Aksu. The elevation of Aksu is high in the north and low in the south, and the Gobi Desert dominates the Taklimakan Desert in the south. As a result, the grain output of the southern counties and cities was slightly lower than that of the northern ones. Meanwhile, the spatial distribution of grain yield in the Hotan region was relatively stable, with the low-yield area mainly distributed in the west. Minfeng County is in the middle of the study area and its wide distribution of desert resulted in a low yield for all four periods. Kashgar is located in the southwestern portion of the study area, where grain yield is typically high. In fact, the introduction of science and technology and the popularization of scientific farming allowed for the grain yield in Kashgar to reach the highest value for the whole basin. Kizilsu Kirgiz Autonomous Prefecture is located in the western part of the study area. Compared with other areas, grain output in this region was relatively small. Overall, the general pattern of grain yield in the Tarim River Basin during the study period was higher in the west and lower in the east. The areas with higher grain yield mainly have abundant water resources, while the other areas have limited water resources, which results in an uneven grain yield distribution.

Evolutionary Characteristics of the Grain CG in the Tarim River Basin

The migration track of the grain CG was plotted according to the total grain quantity of each administrative county and city in the Tarim River Basin from 2005 to 2020 (Figure 3 and

Table 1. Grain production, center of gravity coordinates and migration distance in the Tarim River Basin.

Years	Grain Production/×104 t	Longitude	Latitude	Migration Distance/km
2005	457.93	79.7925	38.8542	-
2006	444.34	79.5401	38.7836	29.12
2007	406.11	79.3261	38.6202	29.92
2008	478.25	79.5070	38.7184	22.88
2009	587.97	79.6902	38.8657	26.11
2010	589.59	79.5996	38.8069	12.00
2011	571.55	79.5723	38.8090	3.04
2012	598.23	79.5888	38.8425	4.14
2013	632.49	79.6675	38.8750	9.47
2014	637.87	79.7539	38.8766	9.60
2015	728.29	80.0460	38.9844	34.58
2016	752.49	79.7782	38.9519	29.97
2017	691.43	79.7118	38.9076	8.86
2018	515.22	79.8043	38.9580	11.70
2019	504.85	79.7812	39.0264	8.02
2020	540.80	79.7076	38.9199	9.67

). From the analysis of the spatial location of grain production CG and its cities and counties, the coordinates of the grain production center of the basin were 79.32–80.05 E and 38.02–38.63 N from 2005 to 2020. The CG is concentrated in Moyu County, with a cumulative migration distance of 249.08 km. The grain gravity center migrated from south to north across the basin and can be divided into four stages, as detailed below.

In the first stage (2005–2007), the grain CG migrated to the southwest. The longitude movement was 0.47 degrees and the latitude movement was 0.23 degrees, from Moyu County to Pishan County. Overall, the movement range of north–south was greater than that of east–west, the grain CG migration distance was 59.04 km, and the average annual transfer speed was 25.02 km/a. The main reason for the migration was that the ecological management of the Tarim River Basin made some achievements during this period, resulting in the water resources being more effectively utilized. Furthermore, the shortages in agricultural water were mitigated, which promoted the social stability of the region and achieved strong economic benefits.

In the second stage (2007–2015), the grain production center of the Tarim River Basin mainly moved in a northeasterly direction, from Pishan County to Moyu County. The east–west movement was larger than the north–south movement, with the whole grain production center migration distance estimated at 121.82 km. During this period, grain production in the basin first increased and then decreased. By the end of 2015, grain production had reached the maximum value for the entire study period (2005–2020).

In the third stage (2015–2017), national cultivated land protection measures began to be implemented. These were combined with the unified adjustment of agricultural industry structure and were oriented by green ecology, which meant the introduction of zero growth of fertilizers, pesticides, and other support policies. During this stage, the grain production CG migrated from east to west, at a distance of 38.82 km. The migration trend was not obvious, and the CG was located in Moyu County. Grain production in the Tarim River Basin was 752.5 × 10⁴ million tons at the end of 2015, which represented the highest grain output of the study period. As a turning point of the second and third stages, the state implemented policy subsidies that greatly encouraged farmers. These policies moved planting towards the current standardized and mechanized modern agriculture phase.

In the fourth stage (2017–2020), the change in the CG showed an obvious northeast migration trend, but the linear migration distance was relatively short (8.04 km). In 2017–2018, the CG moved to the northeast; in 2018–2019, it migrated to the north; and in 2019–2020, it migrated to the southwest. However, none of these migration trends were obvious and they resulted in a cumulative migration distance of only 29.39 km. In this stage, the grain yield in the study area showed a decreasing trend and a small decreasing range.

The grain production center of the whole basin was mainly distributed in Moyu County, Pishan County and Bachu County. In 2006–2008, the grain production center was located in Pishan County; in 2011–2012, it was located in Bachu County; and for the rest of the study period, it was located in Moyu County, meaning that the CG of grain production was mainly concentrated in Moyu County. The main reason for this is that the government implemented a series of price support policies in Moyu County, which motivated area farmers and led to larger harvests and higher yields.

At the regional level, the migration track of the grain production center moved through Bayingolin Mongolian Autonomous Prefecture from 2005 to 2020. According to the CG changes in longitude and latitude, grain production was concentrated in Korla City, showing a westward migration trend. Here, too, we can see stage characteristics. From 2005 to 2007, the grain CG moved to the southwest at a distance of 24.45 km. From 2007 to 2009, the CG moved southeast towards Yuli County at a rate of 9.07 km per year. It then moved from south to north during 2009–2010 and showed a reciprocating migration trend during 2010–2013, with a cumulative migration distance of 38.96 km. From 2013 to 2018, the migration trend in the latitude direction was significantly stronger than that in the longitude direction, and the migration distance was also longer than in other stages, reaching 10.49 km/a. In 2020, the CG moved to Yuli County.

Based on these data, we can see that during the study period, the grain output of Bayingolin Mongolian Autonomous Prefecture showed an increasing trend followed by a decreasing one. In 2011, the grain output reached its maximum level, increasing by 155.66% compared with 2005. After 2011, the grain output showed a decreasing trend, and the grain output in 2020 was 41.15 × 10⁴ million tons. The change in grain yield was somewhat related to the change in population.

From 2005 to 2020, the grain center of gravity in Aksu Prefecture exhibited obvious changes in latitude, but only slight changes in longitude. The main migration process occurred in Wensu County, with a cumulative migration of 110.68 km. In 2005, the grain CG was located in eastern Wensu County, but by 2007, it had moved to Baicheng County, with a minor longitude crossing distance and a shift of 0.048 degrees in latitude. From 2007 to 2009, the grain CG migrated to the southwest, showing a cumulative migration distance of 26.73 km. The CG then migrated from Baicheng County to Wensu County in 2008 and 2009, after which, from 2009 to 2015, the grain CG in Aksu Prefecture migrated to the northeast. For this move, the change of in the CG was relatively stable in latitude, with a migration distance of 40.34 km and a total of 0.22 degrees in longitude. The maximum rate of change was 6.72 km/a for the whole study period.

Meanwhile, from 2015 to 2020, the grain center of gravity mainly migrated to the west, with the most obvious changes being those in longitude. The cumulative migration distance reached a maximum of 32.74 km at a migration rate of 6.547 km/a. The grain CG in Aksu Prefecture showed a trend of fluctuating change. The most obvious increment was in Baicheng County, where the proportion of newly added grain was 103.04%, whereas the proportion of grain change in other counties and cities was relatively small. Among them, the grain yield in Shaya County showed a decreasing trend at a rate of 51.28%.

In the Hotan region, the grain CG from 2005 to 2020 was mainly distributed in Luopu County, and the CG distribution was disorderly. From 2005 to 2008, the CG mainly migrated to the southeast, with a cumulative migration distance of 7.05 km. From 2008 to 2016, it migrated back and forth, covering more distance than in 2005–2008. From 2016 to 2018, the CG migrated to the northwest, spanning a relatively long distance. The gravity center was located in Hotan City in 2008, but ten years later it had migrated to the northeast again, with a cumulative migration distance of 19.83 km.

It is worth noting that the migration distance from 2017 to 2020 was the longest during the study period. The main reason for this was the decreasing trend that had occurred from 2011 onward. In 2019, the migration distance reached a minimum of 70.34 × 10⁴ m tons. The grain output of all counties and cities began to decrease in 2017, with the grain output in Moyu County showing the most changes.

The grain CG in Kashgar was primarily concentrated in Yingjisha County during the study period. From there, it migrated from southwest to northeast. The Kashgar grain CG migrated 0.085 degrees in longitude, for a total of 66.376 km. It also shifted 0.060 degrees in latitude. Overall, Kashgar Prefecture showed a trend that demonstrated increasing fluctuation, reaching its maximum in 2016.

For Kizilsu Kirgiz Autonomous Prefecture, the grain CG from 2005 to 2020 had reciprocating characteristics, which can be divided into the following four stages. The first stage was from 2005 to 2008, when the CG migrated to the northwest with a small change range and a cumulative migration distance of 2.77 km. From 2008 to 2016, the CG migrated to the northeast, covering a cumulative distance of 19.13 km. The longest migration distance during this period occurred from 2008 to 2009. In 2008, the grain output was 1863 × 10⁴ million tons, while in 2009, it increased to 233,300 × 10⁴ million tons, for a total increase of 470 × 10⁴ million tons. The year 2017 saw the biggest change during the study period in Kizilsu Kirgiz. From 2017 to 2020, the center of gravity shifted to the north and east, with a stable migration trend and stable changes. After 2017, grain output also remained stable, reaching 2723 × 10⁴ million tons by 2020.

3.1.2. Spatial Distribution of the Economy and the Evolution of the CG in the Tarim River Basin

Spatial and Temporal Distribution of the Economy in the Tarim River Basin

From the perspective of spatial distribution in 2005, the majority of counties and cities had a gross domestic product (GDP) within the range of CNY 0–5 billion (Figure 4). Only two had a GDP of CNY 5–9 billion, while Korla’s GDP was within the CNY 9–20 billion range.

However, by 2020, the economic development of the northern basin area had significantly improved. For instance, the GDP of Alar City and Korla City were within the range of CNY 30–70 billion, showing a relatively rapid rise in the social economy. At the same time, the counties and cities in Aksu Prefecture and some in Bayingol Mongolian Autonomous Prefecture also experienced rapid economic development. There were 16 counties and cities with a GDP between CNY 5 billion and CNY 9 billion, six with a GDP between CNY 9 billion and CNY 20 billion, and three with a GDP between CNY 20 billion and CNY 30 billion.

Bayingol Mongolian Autonomous Prefecture is rich in natural resources and has good water and heat conditions. These factors led to the enlargement of the area’s industrial base, which plays an important role in the economic development of the Tarim River Basin. It also promotes social and economic recovery and development in the northern edge of the basin. As can be seen from the figure, Korla City is undergoing the fastest development process in the entire study area. Korla is situated in the core area of the Xinjiang Silk Road Economic Belt, giving it a strategic position of “north and south” in the region’s development. The cities surrounding Korla also benefit from its economic development opportunities. In addition, the secondary and tertiary industries have likewise gradually developed and now occupy an increasingly important position in the area’s industrial development.

Evolution of the Economic CG in the Tarim River Basin

Gross domestic product is a comprehensive data figure that reflects regional development. It is a collection of primary, secondary and tertiary industries that shows regional economic development in a relatively complete way. In order to better explain the evolutionary process of the regional economic CG in the Tarim River Basin, we decomposed it into different levels of industry (primary, secondary, and tertiary).

We calculated the longitude and latitude coordinates of GDP and the CG of the first and second industries for each year according to the industrial values and geographical locations of different states, counties, and cities in the Tarim River Basin from 2005 to 2020. To do so, we used the center of gravity calculation formula, in addition to the migration track of the GDP and the CG of the primary and secondary industries.

Analysis of the GDP CG migration track reveals an east-to-west movement with a cumulative migration distance of 323.10 km (Figure 5 and

Table 2. GDP, center of gravity coordinates, and migration distance in the Tarim River Basin.

Years	GDP/Billion	Longitude	Latitude	Migration Distance/km
2005	743.5795	81.9864	40.6236	-
2006	911.1095	82.4013	40.6976	46.8289
2007	1084.2815	82.2210	40.6500	20.7261
2008	1264.7730	82.3324	40.6253	12.6833
2009	1357.2718	81.8378	40.4891	56.9964
2010	1526.6751	82.1364	40.6006	35.4127
2011	2024.8725	82.0994	40.5835	4.5362
2012	2365.9208	81.9422	40.5320	18.3717
2013	2705.8339	81.8200	40.4879	14.4344
2014	2991.8713	81.8050	40.4732	2.3370
2015	3141.6891	81.4622	40.3482	40.5445
2016	3141.6891	81.3207	40.2856	17.1865
2017	2950.5990	81.4071	40.3068	9.8828
2018	3429.1245	81.3727	40.3148	3.93059
2019	3988.4774	81.3134	40.3042	6.6879
2020	4172.0684	81.0283	40.2375	32.5366

). This east-to-west change in GDP was greater than the south-to-north upward migration trend, indicating that the east–west economic development was more unbalance but had more potential. The GDP gravity center had a large spatial distribution span that involved two counties and two cities, namely Xayar County, Aral City, Aksu City and Awat County. From Xayar County to Awat County, the CG migration trend was uniform and only a short west-to-east migration occurred there during 2005–2008, 2009–2011 and 2016–2017. The cumulative migration distance was 187.07 km for all three stages. In other periods, the CG showed an east-to-west migration trend, with a cumulative migration distance of 136.03 km.

Thanks to the strong support of national policies, the GDP of the Tarim River Basin rose by 347% to CNY 323.955 billion during the study period. The GDP of the Kashgar region accounted for 27.90% of this increase. Most of the rest of the counties and cities in the basin saw unbalanced economic development. For example, the GDP of Bayingol Mongolian Autonomous Prefecture in the east was lower than that of the Kashgar region, which partly explains why the economic CG was mainly distributed in Xayar County, Aral City, Aksu City, and Awat County and gradually moved to the west.

Due to the basin’s northern geographical location, the population density there is higher than in the south, and is higher in the west than in the east. This is because the east is primarily desert, making it unsuitable for crop growth. At the same time, industry has been changing rapidly, developing new economic directions unrelated to agriculture. Scientific utilization and development have been gradually implemented, leading to the development of characteristic industries in accordance with local conditions. The decrease in the proportion of primary industry has left room for growth in secondary and tertiary industries, leading to a higher output value in those industries. Furthermore, the migration trend from west to east indicates that the eastern part of the study area is an emerging area of economic development, and that the secondary and tertiary industries located there play an important role in the region’s economic development. For example, the rich mineral resources have been developing rapidly since the 1990s, causing the economy of Bayingol Mongolian Autonomous Prefecture likewise to develop rapidly. Industrialization and urbanization are at high levels, which in turn impacts the social economy, the GDP, and the primary and secondary industries, all of which were in a growth state during 2005–2020.

As mentioned previously, GDP is composed of primary, secondary, and tertiary industries. However, this paper only analyzes the primary and secondary industries in the basin. The CG of the primary industry as a whole presents a north-to-south and east-to-west migration trend, with a linear migration distance of 20.92 km during the study period. The primary industry’s CG migration can be roughly divided into four stages. During the first stage (2005–2008), the cumulative CG migration to the southwest moved 30.57 km. During the second stage (2008–2013), it migrated 54.71 km west to east and saw a shift in longitude of 0.463 degrees. The east–west changes were also obvious in this stage. In the third stage (2013–2018), the CG migrated from east to west at a migration rate of 14.76 km/a. In the fourth stage (2018–2020), the CG migration trend shifted from the southwest to the northeast, covering a smaller distance and stabilizing. Overall, from 2005 to 2020, the cumulative migration distance of the center of gravity of GDP in the Tarim River Basin was 185.57 km, with a migration rate of 11.60 km/a.

The change law of the basin’s secondary industry gravity center shows a clear trend from east to west. Moreover, the CG transfer has a regularity similar to that of GDP, but with a few differences. The CG of the region’s secondary industry is mainly located in Luntai County, Kuqa County, and Xayar County, with the largest range of changes occurring in Xayar County. As with GDP, the secondary industry CG can be divided into several stages. The first stage (2005–2008) showed migration from west to east over a cumulative distance of 139.65 km. During 2006 to 2007, there was also a short trend (32.14 km) of westward migration. The second stage (2008–2016) saw a more stable migration, mostly from east to west, with a cumulative migration distance of 394.01 km. The third stage (2016–2019) found the gravity center to be mostly anchored in Shaya County and showed migration from west to east at 20.50 km/a, less than one-third the distance it had traveled during the second stage. Furthermore, the output value increased substantially, jumping from 10.66 × CNY 10⁴ million in 2016 to 13.13 × CNY 10⁴ million in 2019. The fourth stage (2019–2020) marked a return of the east-to-west migration trend, covering a distance of 64.90 km.

3.1.3. Population Spatial Distribution and Change in the CG in the Tarim River Basin

Temporal and Spatial Distribution of Population in the Tarim River Basin

In 2005, the population in the study area was greater in the west than in the east and was mainly concentrated in Kashgar, Hotan and Aksu regions (Figure 6). Over the course of the study period, the Kashgar region and Aksu Prefecture saw a rapid rise in population, with settlement spreading from the cities outward to surrounding counties. Kashgar, Shache County, Moyu County, and Aksu City experienced the greatest increase in population (from 450,000 to 900,000), while 19 other counties and cities boosted their median population of 200,000–300,000 to 300,000–450,000. Kashgar, which accounted for 39.53% of the total population in 2005, had a relatively slow growth rate, but still retained its position as the highest and most densely populated area of the basin, holding 40.22% of the region’s total population by 2020.

In contrast, Aksu Prefecture experienced the largest population increase ratio in the study area. This is not unexpected, since Aksu City is connected with the national Silk Road Economic Belt. Having the fastest economic development, Aksu Prefecture also drives population development. Bayingolin Mongolian Autonomous Prefecture likewise saw rapid economic development over the study period, but its population growth was slower than Aksu’s. The area that experienced the most pronounced population change is located in the southwestern portion of the Tarim River Basin. The superior natural conditions of the southwest, in conjunction with the economic incentives of the national population policy, were the main drivers of the population increase. The development of soil and water resources in the south also drew people and industry to the area.

Evolution of the Population CG in the Tarim River Basin

The present study draws the temporal and spatial evolutionary track of the population center of gravity in the Tarim River basin from 2002 to 2020 based on the statistical yearbook. As shown in Figure 7, the population CG migrated from northeast to southwest. This trend was particularly obvious during 2008–2018. The migration range in the north–south direction was smaller than that in the east–west direction. Moreover, the imbalance of population in the east–west direction was greater than that in the north–south direction, and the deviation degree in the longitude direction was greater than that in the latitude. This indicates that the imbalance of the population CG in the longitude direction was greater than that in the latitude.

More specifically, the center of gravity was mainly distributed in 79.49° E–79.72° E, 39.43° N–39.59° N, charting a westward course of 0.22° in longitude and a southward migration of 0.15° in latitude. During the study period, the population CG migrated 41.39 km in total, with some deviation in direction and speed. During 2005–2007, there was a temporary but slight trend of migration from northwest to southeast, while during 2012–2013, the moving distance was only 0.64 km (

Table 3. The number of populations, center of gravity coordinates, and migration distance in the Tarim River Basin.

Years	Populations/×104	Longitude	Latitude	Migration Distance/km
2005	980.53	79.6864	39.5729	-
2006	1009.33	79.6967	39.5827	1.5798
2007	999.81	79.7093	39.5603	2.8588
2008	1020.38	79.7097	39.5657	0.5964
2009	1045.37	79.7113	39.5674	0.2547
2010	1098.64	79.7014	39.5508	2.1404
2011	1099.78	79.7017	39.5514	0.0752
2012	1111.99	79.6959	39.5429	1.1479
2013	1134.84	79.6988	39.5479	0.6440
2014	1180.38	79.6414	39.5244	6.8889
2015	1172.17	79.6161	39.4981	4.0565
2016	1186.72	79.5341	39.4491	10.6132
2017	1219.19	79.5144	39.4393	2.4468
2018	1219.49	79.4926	39.4338	2.5029
2019	1085.91	79.5052	39.4310	1.4393
2020	1227.38	79.5416	39.4390	4.1432

). In 2018–2020, the change in population center mainly occurred in an east–west direction. The cumulative east–west migration distance was 8.09 km.

The population center of the entire basin, which is mainly distributed in Bachu County, showed a clear southwest migratory trend throughout the study period. The Kashgar region, which is located in the southwest, accounts for 38.14% of the total population of the entire basin. As mentioned, the Tarim River basin has various types of landforms, significant differences in natural conditions, and unbalanced economic development. In the process of economic migration, people are more inclined to head towards the region with better natural conditions and a better economic foundation. For these reasons, the population CG in the basin showed an overall trend of southwest migration.

Bayingolin Mongolian Autonomous Prefecture, on the other hand, showed a north-to-south migration trend, with the gravity center mainly distributed in and around Korla City. This prefecture also had an obvious change in latitude and a slight change in longitude, for a total linear migration distance of 16.00 km. The migration trend was most obvious in 2019–2020, when the migration distance was 12.39 km. However, there was a decrease in Korla’s population in 2020, bucking the trend of increasing population seen by most other counties and cities in the region. The cause was likely the choice of residents to shift from an urban to a rural lifestyle.

From 2005 to 2020, the migration of the population CG in Aksu Prefecture had major changes in longitude mainly in Wensu County and an overall migration trend from the northwest to the southeast. The disordered migration track indicates that the direction of annual population flow differs from the trend. The cumulative migration distance was 29.79 km, which is relatively short. Further, the migration process primarily occurred in the Aksu area, indicating that the movement of people was small and the change in population was relatively stable. In the Hotan region, the migration track of population showed a southeast-to-northwest trend. It occurred in the direction of Hotan City and was quite stable. The cumulative migration distance was 10.30 km, and the migration rate was 0.69 km/a. In the Kashgar area, the CG trended from east to west, with stable changes in latitude. The imbalance of population migration in longitude was greater than that in latitude. Further, the migration track from 2006 to 2007 was the maximum migration distance (7.24 km) during the study period, for one-third of the cumulative distance. Both the migration track and migration distance were concentrated after 2007, indicating that the population change in Hotan was stable and there was no large-scale movement.

Meanwhile, in Kizilsu Kirgiz Autonomous Prefecture, the migration direction of population center and grain center of gravity showed reciprocating characteristics, which can be roughly divided into two stages. From 2005 to 2008, the migration direction was from south to north, whereas from 2008 to 2020, the trend was from north to south. Linear migration mainly occurred in the longitude direction. The cumulative migration distance from 2005 to 2020 was 76.16 km, the migration rate was 5.08 km/a, and the linear migration distance was 0.40 km. Finally, although the changes in longitude were relatively stable, the imbalance in latitude was significant.

3.2. Analysis of the Spatial and Temporal Distribution of Water Resources and the Evolutionary Trend of CG in the Tarim River Basin

3.2.1. Temporal and Spatial Distribution of Water Resources in the Tarim River Basin

In looking at the spatial distribution of total water resources in the Tarim River Basin, we can see only slight variations, mainly within the range of 5.1 to 15.7 billion m³ (Figure 8). These show an increasing trend from west to east, with Kizilsu Kirgiz Autonomous Prefecture and Aksu Prefecture having the fewest water resources. In 2005, the total amount of water resources showed a phased distribution from west to east. However, by 2010, the resources in Aksu Prefecture had decreased, while those in other regions did not change. By 2015, an increasing trend was obvious in parts of the basin, mainly in Bayingolin Mongolian Autonomous Prefecture, the Hotan region, and the Kashgar region, which continued to the end of the study period. The sole exception was Kashgar Prefecture, which showed a decrease in water resources.

Surface water and groundwater are the main components of the basin’s total water resources, and the spatial distribution of surface water is similar to the change in these resources. From 2005 to 2020, the total surface water in Bayingolin Mongolian Autonomous Prefecture initially showed a decreasing trend, which then reversed. The variation range was between 7.1–9.1 billion m³ and 9.1–11.1 billion m³, with only a slight degree of change. The Hotan area showed the same trend of initial increase followed by a decrease, but on the whole had a greater increase. As well, Aksu Prefecture and the Kashgar region had an increase followed by a decrease, with the main distribution ranging between 5.1 and 7.1 billion m³, and 7.1 and 9.1 billion m³.

The spatial distribution of total groundwater is slightly different from that of total water resources. From 2005 to 2020, underground water volume and spatial distribution in Kizilsu Kirgiz Autonomous Prefecture and Aksu Prefecture did not change, ranging from 3.2–4.2 billion m³ to 6.2–8.2 billion m³. Any changes that occurred were relatively stable. In Kashgar region, the underground water volume exhibited an increasing trend which, by 2020, was distributed in the range of 6.2–8.2 billion m³. Meanwhile, in the Hetian area, underground water volume did not change significantly. The maximum amount of groundwater resources was in the range of 5.2–6.2 billion m³. Bayingolin Mongolian Autonomous Prefecture had the largest amount of groundwater resources, mainly distributed in the range of 6.2–8.2 billion m³.

The change and spatial distribution of water resources in the study region were affected by many factors during the study period, such as topographic and geomorphic features, climate, and the degree of exploitation and utilization. In 2000, an ecological water transmission project was launched in the lower reaches of the Tarim River, which saw 21 water transmission projects completed by 2020. The projects aimed to restore the basin’s ecological environment.

3.2.2. Analysis of the Evolutionary Trend of the CG of Water Resources in the Tarim River Basin

The change in the gravity center of water resources is shown in Figure 9. As can be seen, the barycenter is mainly distributed in Cele County, which is located between 81.18~81.86 E and 38.81~39.06 N. The overall migration trend is to the southwest, with a cumulative migration distance of 346.25 km and a migration rate of 23.08 km/a. In 2005–2006, the CG migrated to the southwest 37.05 km. In 2006–2007, it shifted to the southeast, while in 2007–2008, it moved to the northeast. In 2005–2008, the linear migration distance was 6.64 km and the cumulative migration distance was 79.81 km. In 2008–2012, the migration rate was 19.95 km/a and the CG of water resources showed a reciprocating migration trend. The change was especially obvious from 2010 to 2011. The cumulative migration distance in Cele County in 2008–2012 was 118.49 km.

From 2011 to 2020, the center of gravity migrated to the southeast across the basin. Furthermore, the east–west migration distance was greater than the south–north distance, but the south–north change was more stable. The ecological environment had improved to a certain extent by the ecological water transport, and the natural vegetation was gradually restored. The inter-annual fluctuation and uneven spatial distribution of precipitation contributed to the unstable change in water resources. There was a large amount of unused land in the basin, such as the Gobi desert, due to scant precipitation, long sunshine hours, and strong evaporation. The typical arid climate and unique natural geographical environment of the unused land resulted in glacial meltwater being its main water resource.

As mentioned earlier, the water resources across the Tarim River Basin mainly include surface water and groundwater. The spatial change chart of surface water and the groundwater CG was drawn according to the gravity center model (Figure 9). From 2005 to 2020, the surface water center of gravity was mainly distributed in Luopu and Cele counties, with a change in the CG in the range of 81.55~81.85 E, 38.92~39.06 N. The cumulative migration distance was 406.17 km. The migration trend of the surface water CG was roughly the same as that of the overall gravity center of water resources in the basin. Surface water is an important water source in the Tarim River Basin, so its developmental direction and trend are key factors for the development of the region’s water resources.

Groundwater is also an important component of water resources in the basin. Based on the migration trend of surface water, the spatial distribution and migration direction of the groundwater CG from 2005 to 2020 were studied. The results indicate that the spatial distribution was mainly concentrated in Luopu County, showing a north-to-south migration trend and a cumulative distance of 398.83 km. After 2000, the state and autonomous region implemented the aforementioned ecological water transport policy, which led to an increasing trend of fluctuation in the basin’s total water resources. After the implementation of the water transport policy, the fragile ecological environment and vegetation growth conditions were significantly improved.

The annual variation trend and track differ throughout the study period. From 2005 to 2010, the migration trend is from right to left, with a cumulative distance of 85.88 km and a shorter distance of 0.11 degrees in latitude. From 2010 to 2015, the change span of the gravity center was sizeable, and it constantly changed in the direction of longitude and latitude. The maximum migration change of longitude was 0.20 degrees, while that of latitude was 0.13 degrees. In 2013, the CG was located in Moyu County. During 2015–2020, the maximum migration distance occurred, with a large migration amplitude in the east–west direction and a cumulative distance of 193.97 km. Because groundwater is such an important water source for agricultural irrigation, industry, mining, and cities, its decrease leads to the occurrence of adverse natural phenomena. In 2018, the total value of groundwater was the lowest in five years.

3.3. Spatio-Temporal Coupling Analysis of Dual Elements

In order to further explore the spatial coupling of the gravity centers of “grain-economy-population” and water resources in the Tarim River Basin, this paper analyzes the spatial distance and the consistency of changes from the static and dynamic perspectives (Figure 10).

The CG of grain–economy–population and water resources in the Tarim River Basin is mainly distributed in the middle west of the study area. If we take the center of gravity of water resources as the standard, the CG of grain is always located to the west of the CG of water resources, the CG of GDP is always located to the north, and the CG of population is always located to the northwest.

From a static perspective (spatial overlap), the spatial distance between GDP and the population center of gravity decreased from 325.05 km to 187.50 km, and the coupling gradually increased. The migration trend of the two centers of gravity was the same as the direction. The economy and population in the study area were greatly affected by the natural factors of terrain, and with the development of society, the coupling between them gradually increased. To a certain extent, population agglomeration promotes urbanization, which then leads to cultural and economic exchange and cooperation. Economic development also plays a role in promoting population growth.

The spatial distance between population and grain CG is the lowest, with a small change range between 54.23 and 112.81 km. The two centers of gravity were relatively clustered, and the coupling was high. Because the central part of Tarim River Basin is the Taklimakan Desert, which is not suitable for planting or human habitation, the CG of grain and population shifted to the west, and the coupling increased.

The spatial distance curve of the CG of water resources and grain shows a fluctuation and slow growth trend. The spatial overlap decreased as a whole, reaching the minimum value of 179.46 in 2011 and the maximum value in 2007. However, the rising trend of the value in recent years has slowed and the fluctuation range has shrunk. The spatial overlap fluctuation of grain production and water resources, along with the instability of the water resources’ barycenter movement, are the main reasons for the increase in the spatial distance of the barycenter.

From 2005 to 2020, the change in distance of the GDP–grain center of gravity was the farthest apart, but the overall trend was downward and the spatial overlap was enhanced. Specifically, the farthest distance was 392.84 km and the nearest was 202.62 km. The gravity centers of these two factors were gradually nearing each other. However, the overall change in the gravity center of GDP and water resources was not as obvious, decreasing from 179.60 km in 2005 to 172.30 km in 2020 and charting a slow downward trend on the whole. These two factors’ gravity centers reached a maximum value in 2006 and a minimum one in 2015. After 2015, the spatial distance between GDP and the CG of water resources increased, the overlap weakened, and the coupling showed a slight downward trend. The CG of GDP migrated to the southwest, while the CG of water resources migrated to the southeast. The changes in the gravity centers confirmed the gradual increase in the spatial distance.

From a dynamic perspective, the consistency index of changes in the CG for GDP and population fluctuates between positive and negative values, and the coupling process presents multiple peaks and troughs (Figure 11). More specifically, changes in the consistency index were greater than 0 for 6 years, greater than 0.5 overall, and less than 0 for 9 years. The average matching degree was about −0.07 and the overall coupling was poor. However, from 2012 to 2020, the average matching degree was about 0.09 and there was an increase in the index. The results of the present study show that the GDP in recent years has shown an increasing trend due to the influence of science and technology and the support of national policies. The migration direction of GDP’s gravity center is consistent with that of population, enhancing the coupling of the gravity center of these two factors.

Over the total 15 years of the study period, there were 7 years in which the consistency of change in the CG of population and grain was greater than 0. The average matching degree was −1.21, showing an extremely mismatched state and poor overall coupling. From 2007 to 2017, the average matching degree was 0.11 and the consistency index increased slightly. This was followed by a downward trend in grain yield from 2017 to 2020, likely influenced by unevenness in the cultivated land area in each region and changes in economic structure. Moreover, the increase in the proportion of secondary industry led to the transfer of more population resources to economic development, gradually worsening the population and grain coupling.

The change consistency of the barycenter of water resources and grain fluctuated between positive and negative values, with an average matching degree of 0.34. Although the overall coupling degree showed an increasing trend, there were multiple peaks and troughs in the coupling process, and the movement direction of the barycenter of water resources and grain differed immensely. However, after 2013, the two factors showed a relatively high match. During the study period, the consistency index of the change in CG of the two factors was greater than 0 in 11 years and between 0.50 and 1 in 10 years. However, between 2011 and 2020, the average matching degree was 0.59, and the consistency index was at a high state. Research shows that with the development of agriculture under scientific management and irrigation in recent years, grain production and the rational allocation of water resources have advanced.

The study area’s extreme arid continental climate has caused a lack of uniformity in the spatial distribution of water resources. Furthermore, the movement of their CG has no obvious stage characteristics. The change in the CG of grain production and water resources is mainly due to the long migration distance of grain production in a northeasterly direction, while the fluctuation of the change consistency index is due to the irregular movement of the water resources’ gravity center.

4. Discussion

By exploring the spatial distribution and evolutionary law of “grain-economy-population” and water resources in the Tarim River Basin, this paper briefly summarized the grain production, economic development, and water resources of the basin’s prefectures and states. It also investigated the spatial distribution level of “grain-economy-population” and water resources, as well as the evolutionary law of the center of gravity, using the CG model. The aim in conducting this work is to provide a scientific research basis for the estimation of grain production and economic development across the region.

Based on the research results, this study shows that the population change and economic development in the Tarim River Basin experienced an increasing trend, which is consistent with the results of [30] and other studies. Furthermore, the population in the region is expected to increase in the future [31]. The research also shows that the GDP–population consistency index increased, the population and economic migration trends were the same, and the spatial distance between the two gradually decreased. Meanwhile, economic development showed great potential, and urbanization and industrialization were gradually dominated by secondary and tertiary industries. Population migration tended to drive positive economic changes, which in turn drove population migration: the two tended to be coupled. Without considering the influence of climate change on grain yield, we can assume that the demand for water resources in the study area will increase along with the population.

The report “The State of Grain and Agriculture 2020: Addressing Water Challenges in Agriculture” released by the FAO explains that the global population has grown rapidly over the past 20 years, while the availability of fresh water resources per capita has decreased by more than 20% during the same timeframe [32]. Grain and water resources are important issues that will profoundly affect sustainable development over the next decade [33,34]. Global water resources allocation is closely related to socio-economic development, land degradation, and desertification control. At present, most studies mainly focus on population–economy [35] and population–grain [36], while few look at the coupling relationship between the rational allocation of water resources and grain. Based on previous studies that discussed the coupling relationship between the population and economy [35], this study constructed the “grain-economy-population” framework for the Tarim River Basin, analyzed the regional differences in the study area combined with the distribution and configuration of water resources, and explored the coupling and matching between water resources and grain production under certain constraints. Considering that the Tarim River Basin is the core area of the “Silk Road Economic Belt” construction, the natural and economic conditions differ among the regions.

From the perspective of water resources supply, the water resources in the Tarim River Basin underwent stable changes. This is because the development of secondary and tertiary industries in the study area, the acceleration of urbanization, the emphasis on ecological environment, and the phenomenon of non-agricultural water resources were gradual occurrences. The increase in urban water consumption led to an increase in regional grain water pressure, but the coupling of grain–water resources was gradually enhanced, which also indicates that the future allocation of water resources is more inclined to agricultural production. Due to the unique geographical position and ecological environment of the Tarim River Basin and its unbalanced economic development [31], grain production was significantly affected by natural factors (terrain, climate, etc.) during the study period [37]. However, with the development of the economy, the effects of natural factors were gradually reduced, and the spatial distance between the economy and grain slowly decreased.

The current distribution of natural vegetation and cultivated land in the Tarim River Basin [38] shows that the shift of the grain center to the north is conducive to the development of cultivated land resources in the northern margin of the study area. Such a shift will also increase vegetation coverage in this area and lead to the improvement of the ecological environment. However, as this study mainly analyzed data for the Tarim River Basin as a whole rather than for the smaller basins within it, future investigations could explore spatial variations in the water resources of the region’s smaller basins, aiming to find the mechanisms driving the changes in those water resources.

5. Conclusions

This paper analyzed regional differences using a “grain-economy-population” framework for the Tarim River Basin. It also analyzed the spatio-temporal distribution of water resources and change trends in centers of gravity as well as the spatio-temporal coupling degree of the CG of these two factors. The following conclusions were drawn:

(1)

The grain yield in the Tarim River Basin was higher in the west and lower in the east. The migration of the grain center of gravity moved from south to north, and during the study period, the cumulative migration distance was 249.08 km. Economic development was slow in the south and rapid in the north, with Aksu Prefecture showing the fastest growth rate. The population center of gravity was distributed in Bachu County, showing greater instability in longitude and more balanced population development in latitude.

(2)

The spatial distribution of water resources was uneven, with total water resources showing an increasing trend from west to east. The western region was relatively short of water resources. The migration rate of total water resources was 23.08 km/a, charting a disorderly migration path mainly towards Qira County.

(3)

The spatial distance of the two factors of GDP–population and population–grain decreased, and the spatial overlap increased. The consistency index of the change in the CG of GDP–population fluctuated between positive and negative. After 2014, the average index increased to 0.11 and the coupling was slightly enhanced. The average matching degree between water resources and grain was 0.34, while the average matching degree was 0.594, indicating a good coupling.