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Water 2014, 6(6), 1581-1600; doi:10.3390/w6061581

Article
Identifying Major Factors Affecting Groundwater Change in the North China Plain with Grey Relational Analysis
Xue Li 1,2, Guomin Li 1,* and Yuan Zhang 3,4,5
1
Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; E-Mail: lixue@mail.iggcas.ac.cn
2
University of Chinese Academy of Sciences, Beijing 100049, China
3
National Engineering Research Center of Urban Environmental Pollution Control (The Ministry of Science and Technology of the People’s Republic of China), Beijing 100037, China; E-Mail: zhangyuan@mail.iggcas.ac.cn
4
State Environmental Protection Engineering (Beijing) Center for Industrial Wastewater Pollution Control (Ministry of Environmental Protection of the People’s Republic of China), Beijing 100037, China
5
Beijing Municipal Research Institute of Environmental Protection, Beijing 100037, China
*
Author to whom correspondence should be addressed; E-Mail: guominli@mail.iggcas.ac.cn; Tel.: +86-10-8299-8620; Fax: +86-10-8202-1292.
Received: 4 December 2013; in revised form: 9 May 2014 / Accepted: 12 May 2014 /
Published: 3 June 2014

Abstract

: The North China Plain (NCP) is facing a water crisis under the dual impact of natural and anthropogenic factors. Groundwater levels have declined continuously since 1960, causing a series of environmental problems that have restricted sustainable development in the region. In the present study, we first utilized a previously developed 3D groundwater model to determine changes in groundwater level in the region over the past 50 years (1961–2010). We then applied grey relational analysis (GRA) to identify and ordinate major factors that have contributed to these changes. The results show an overall decreasing trend in groundwater levels in this region over the past 50 years and an increase in the water table depth at a rate of approximately 0.36 m/a. Groundwater exploitation showed the most significant correlation with the groundwater table decline, when compared with other factors including precipitation and river leakage. Therefore, human activities should be considered the primary force driving the groundwater level down. The results of this study have implications for developing criteria that consider changes in both climate and socio-economics. Furthermore, since the NCP is one of the most water-scarce and densely populated regions in the world, the analytical approach used in and the insights gained from this study are of international interest.
Keywords:
grey relational analysis; groundwater change; North China Plain

1. Introduction

Groundwater is directly related to human existence and to the sustainable development of a society, because it plays an important role as a water resource. More than two billion people worldwide depend on groundwater for their daily water supply, and a large proportion of the world’s agricultural and industrial water requirements are supplied by groundwater [1]. Due to an increasing demand for groundwater in response to rapidly growing urban, industrial, and agricultural water requirements, several countries, especially those in arid and semi-arid zones, are experiencing water shortages resulting from the imbalance between demand and supply [2].

Groundwater resources are influenced by both climate change and human activities [3,4]. For example, climate change has resulted in increasing global atmospheric temperatures, and has led to a modified precipitation pattern, which may have a direct impact on groundwater levels [5]. Previous studies investigating the response of groundwater systems to climate change have achieved considerable success [6,7,8]. It has been shown that groundwater systems have undergone changes due to human activities, including groundwater abstraction and reservoir construction. Since 1960, access to pumped wells has caused a rapid worldwide increase in groundwater development for municipal, industrial, and agricultural purposes [9]. The global use of groundwater was estimated to be 750–800 km3/a [10,11].

The combination of climate change and indiscriminate groundwater development has caused a general decline in groundwater levels, resulting in the depletion of groundwater, land subsidence, and saltwater intrusion in deltaic areas [12]. Lower groundwater levels are a threat to the environment and hinder economic development. Excessive groundwater depletion has affected vast regions, including Northwest India, North China, and the Central USA [13]. Thus, it is important to understand the evolution of groundwater systems, and the dual effects of climate change and anthropogenic activities.

The North China Plain (NCP) is an example of an area where groundwater levels have declined continuously since 1960. It is one of the most densely populated regions in the world, with a population of approximately 130 million in an area of about 140,000 km2 [14]. As one of the most important social, economic, and agricultural regions in China, the NCP contributes approximately 25% of the total grain yield of China, and groundwater provides 70% of the water supply for this region [15]. As water demand has exceeded the natural renewable supply, many urban and irrigated areas in the NCP have come to experience regular water shortages. The indiscriminate exploitation of groundwater and decreasing precipitation over recent years has caused groundwater levels to continue to decline [16,17] with adverse environmental effects [18,19]. Therefore, it is particularly important to study the change of groundwater in the NCP and to analyze the factors influencing groundwater dynamics.

Groundwater is a complex system from recharge to discharge, and its analysis is often subject to large uncertainty owing to insufficient data. Groundwater can therefore be regarded as a grey system, i.e., one with insufficient information [20]. In the early 1980s, Deng [21] formally introduced the grey system theory to handle uncertainties in small data samples with imprecise information, and this field has expanded to include grey relational analysis (GRA), grey modeling (GM), and prediction theory [20,22]. To date, grey system theory has been applied extensively in many fields, including hydrology, manufacturing, and financial analyses [23,24,25]. For groundwater, Gau et al. [26] used GRA to identify factors for the selection of suitable groundwater recharge sites, using hydrogeological data obtained with a groundwater flow model. Similarly, Du et al. [27] adopted GRA to infer that surface water irrigation and groundwater mining are the main factors driving change in groundwater levels in both highland and lowland areas in the Baojixia Irrigation District. Yeh et al. [28] used grey theory to predict variations in the water level in observation wells on the Pingtung Plain. However, no study to date has used GRA to identify the major factors influencing groundwater levels in the NCP, which faces a water crisis.

In this study, we first apply a previously established 3D groundwater model based on MODFLOW to understand groundwater change since 1960 in the over-exploited area of the NCP. Then, we analyze variations in factors influencing groundwater levels and identify the major factors based on GRA.

2. Study Area and Hydrogeologic Setting

Our study region spans 114.2°–118.1° E and 36.0°–40.6° N, and includes two municipalities (Beijing and Tianjin) and one province (Hebei). We consider Beijing, Tianjin, and Hebei plains as three typical areas with depleted groundwater levels. The study region has an area of 80,592 km2 and is bordered by the Taihang and Yan mountains, Bohai Bay, and the Zhang River to the west, north, east, and south, respectively (Figure 1). The landforms are typical of a plain landscape, with elevation less than 100 m. From west to east, the region can be divided into three principal zones: the piedmont, central, and coastal plains. This region experiences a semi-arid continental monsoon climate, with annual average precipitation of approximately 500–600 mm, 75% of which occurs in the summer (i.e., from July to September). Annual water surface evaporation ranges from 1100 to 2000 mm.

Water 06 01581 g001 1024
Figure 1. Location and topography of study area

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Figure 1. Location and topography of study area
Water 06 01581 g001 1024

The stratigraphy of the study area consists mainly of unconsolidated Quaternary sediments. Based on this stratigraphy, the groundwater system is divided into four aquifer groups [29]; aquifers I and II are combined as shallow aquifers, whereas III and IV are deep aquifers (Figure 2).

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Figure 2. Hydrogeological section of the study area [29].

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Figure 2. Hydrogeological section of the study area [29].
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The recharge, runoff, and discharge of the system have changed over the past 50 years influenced by natural climate and human activities (Figure 3). Under natural conditions, recharge resulted primarily from precipitation infiltration, mountainous lateral flow, and river leakage, and discharge was primarily through phreatic evaporation. Groundwater flowed from west to east, and the deep water flowed into the shallow aquifers at the center and east of the plain. At present, irrigation return flow forms an additional recharge source, and exploitation has replaced phreatic evaporation as the main discharge. Groundwater now flows into the center of the cone, with shallow water flowing into the deep aquifers in the center and east of the plain.

Water 06 01581 g003 1024
Figure 3. Changes in groundwater recharge, runoff, and discharge in the study area (a) in the natural state; and (b) under natural climate and anthropogenic influence.

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Figure 3. Changes in groundwater recharge, runoff, and discharge in the study area (a) in the natural state; and (b) under natural climate and anthropogenic influence.
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3. Methods

3.1. Groundwater Flow Model

The groundwater flow model is based on MODFLOW (Modular Three-dimensional Finite-difference Ground-water Flow Model) [30], which incorporates a set of stress packages that enable the simulation of external flow stresses, such as those imposed by wells, areal recharge, evapotranspiration, drains, and rivers [31,32]. To apply a groundwater model to a specific site, the conceptual model must be identified [33,34]. Here, we generalized the groundwater flow in the study area as a heterogeneous, anisotropic, transient, and three-dimensional flow system.

The numerical model had 188706 active cells and each grid cell was 2 km × 2 km, based on the hydrogeological conditions and data obtained from the porous aquifers at the study site. The model included three layers: aquifer groups I and II (layer 1); group III (2); and group IV (3). The simulation was run from 1961 to 2010 at a temporal interval of 1 year. The observed field of groundwater in 1959 was taken as the initial flow field in the model. The model was calibrated using observations from historic water level contour maps for 1975, 1984, 1992, 2003, and 2005 [19,35], and observation wells between 2003 and 2008. Further information on the model is provided in a separate study [36].

3.2. Grey Relational Analysis

3.2.1. Basic Idea

GRA is a calculation of the geometric proximity between different discrete sequences, a reference sequence, and at least one comparison sequence within a system. The proximity is described by the grey relational grade, which is a measure of the similarities of discrete data that can be arranged in sequential order. Further information on this concept and examples of its application are available in the literature [23].

The basic concept of the technique is illustrated with sample time series in Figure 4. The function X0(k) denotes the reference series, and X1(k) and X2(k) denote the comparison series. The similarity between X0(k) and X1(k) is “greater” than that between X0(k) and X2(k). Thus, the relational grade between X0(k) and X1(k) can be regarded as higher and that between X0(k) and X2(k) as lower. This geometric consideration is effectively an analysis of the geometric proximity between different discrete series.

Water 06 01581 g004 1024
Figure 4. Similarity and difference of sequences.

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Figure 4. Similarity and difference of sequences.
Water 06 01581 g004 1024

3.2.2. Basic Approach

The GRA method involves the following steps:

(1) Determining the reference and comparison series

The time series X0 is referred to as the reference series, which represents the characteristics of the system. The m time series Xi is a comparison series of factors influencing the characteristics of the system.

Water 06 01581 i001
Water 06 01581 i002

Here, k and i represent the period and evaluating factors, respectively.

(2) Data pre-processing

Pre-processing is typically required, because the range and units of one data sequence often differ from those of others. This processing is a way of transferring the original X0, Xi to comparable sequences X0, Xi. Various methods have been proposed for processing of data for grey relational analysis [25], the most basic forms are listed below:

Water 06 01581 i003
Water 06 01581 i004
Water 06 01581 i005
where, Xi denotes the original sequences; and Xi the sequences after data processing; Xi’ is the average value of sequence Xi.

(3) Determining the deviation sequences Δ0i

We determine the deviation sequences Δ0i between the corresponding values in the reference and comparison series, and the maximum and minimum values, which are denoted by maxΔ0i(k) and minΔ0i(k), respectively.

Δ0i(k) = |x0(k) − xi(k)|

(4) Calculation of the grey relational coefficient ξi(k) of each series

Water 06 01581 i006

Here, ρ ∈(0, 1] is the distinguishing coefficient, which differentiates the degree of proximity of X0 and Xi, such that ξi(k)∈[0,1]. This value can be adjusted based on the actual system requirements. Generally, ρ is taken as 0.5 based on the minimum information [37].

(5) Calculation of the grey relational grade γi

Water 06 01581 i007

4. Results and Discussion

4.1. Groundwater Flow Dynamics

The simulated results were used to illustrate the groundwater change in the study area during the 50-year period. We selected the shallow groundwater levels in 1965, 1975, 1985, 1995, and 2005 as representative of their respective decades; these are presented in Figure 5.

In 1965, groundwater flow extended from the mountains to Bohai Bay, with groundwater levels of 70 m near Shijiazhuang (at the mountain) and 0 m near Tianjin (coastal area). The average water table depth was 10 m. Conversely, in 1975, cones of depression were observed in parts of Beijing and Baoding. The natural flow fields changed as the groundwater began to flow into the center of the cones. The groundwater level decreased to approximately 60 m near Shijiazhuang, whereas groundwater levels of 30 m expanded to the west, with an average water table depth of 11 m.

Overall groundwater levels had declined and additional cones of depression had formed by 1985. Regions with groundwater levels below 30 m continued expanding to the west, with an average water table depth of 16 m.

Further decline in groundwater levels was observed by 1995. In addition to the enhanced cones of depression in Beijing, Ning-Bo-Longin, and Xingtai, new cones formed in other locations (e.g., Handan). The groundwater levels below 30 m continued to expand westward, reaching the mountain front, with an average water table depth of 24 m.

By 2005, the overall decline of groundwater levels had stopped, and groundwater levels rose in the cone at Beijing. However, the cones of depression at Baoding, Lixian, and Bazhou merged, and the cone at Ning-Bo-Long expanded into the central plain. These results are in agreement with field investigations [16]. The region with groundwater levels below 30 m continued to shift westward, and the average water table depth was 22 m.

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Figure 5. Simulated groundwater levels: (a) 1965; (b) 1975; (c) 1985; (d) 1995; (e) 2005.

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Figure 5. Simulated groundwater levels: (a) 1965; (b) 1975; (c) 1985; (d) 1995; (e) 2005.
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Based on these results, we conclude that the simulated groundwater table depths increased at an average rate of 0.36 m/a over the 50-year period studied (Figure 6). Similar results were obtained in the work of Cao [38], in which a rate of 0.3 m/a was determined for the NCP.

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Figure 6. Change of annual average water table depth during 1961–2010.

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Figure 6. Change of annual average water table depth during 1961–2010.
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4.2. Factors Influencing Groundwater Levels

The flow fields in the study area have changed dramatically because of changes in climate and human activities: the former affects groundwater primarily via precipitation and evaporation, whereas the latter affect groundwater largely through exploitation and the construction of reservoirs.

4.2.1. Climate Change

In arid (and semi-arid) landscapes, climate change has a great impact on water resources. In particular, groundwater dynamics are affected by precipitation infiltration and phreatic evaporation, which result from changes in precipitation and temperature that affect evaporation indirectly. Over the past 50–100 years, the climate of the NCP has undergone obvious changes, with an increasing trend in temperature and decreasing trend in precipitation [39]. We measured these long-term trends in mean annual precipitation and temperature in the study area using a nonparametric technique (the Mann–Kendall test [40,41,42]).

Based on the precipitation data series from the China Meteorological Data Sharing Service system, annual average precipitation in the study area was 531.39 mm in 1961–2010. We observed a clear inter-annual variation in precipitation, and what appears to be a 12-year trend (Figure 7a). Ip [43] found an inter-annual 4–7 year component and inter-decadal 19-year periodicity in North China, whereas Kuang [44] calculated periodicities of 6–7, 21–22, and 35–36 years. These different results could be caused by the length of the time series applied. The long-term trend for the precipitation series showed that the nonparametric Mann–Kendall test supported H0 at the 5% significance level (Table 1), which means that precipitation had a decreasing trend that was not significant.

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Figure 7. (a) Annual average precipitation and (b) annual average temperature in the study area in 1961–2010.

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Figure 7. (a) Annual average precipitation and (b) annual average temperature in the study area in 1961–2010.
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Table Table 1. Monotonic trend tests for the precipitation and temperature time series.

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Table 1. Monotonic trend tests for the precipitation and temperature time series.
ItemMann–Kendall test
Z0βH0
Precipitation−1.58−1.78S
Temperature4.480.028C

Notes: C Contradict; S Support; Significance level p=5%; Z0 is statistics of Mann–Kendall test.

Based on the temperature data series from the China Meteorological Data Sharing Service system, annual average temperature in the study area was 12.6 °C in 1961–2010 (Figure 7b). The Mann–Kendall test for temperature change contradicts hypothesis H0 (Table 1); that is, an increasing trend for the temperature series was found to be significant at the 5% level. Temperature increased at a rate of 0.28 °C/10 a, similar to results in previous studies [39,45]. This increasing trend in mean annual temperature resulted in an increase in water vapor capacity. Increased evaporation caused by the rise in temperature would have exacerbated the loss of groundwater through evaporation in the study area during the past five decades. Groundwater table depths declined over the study period, suggesting that climate change may have accelerated the decrease in groundwater levels.

4.2.2. Human Activities

Groundwater exploitation increases the discharge of groundwater, changing the natural flow field, and has become the most important discharge route for groundwater. Construction of reservoirs in the upstream areas has reduced groundwater recharge by surface water in the plain.

We obtained groundwater exploitation data from the Hydrological Bureau of each municipality and from previous field research [19,35,36,46,47,48]. During the study period, groundwater abstraction has progressed from a random and disorderly activity to a systematic process. Increasing volumes of water have been pumped from greater depths [29], especially since the 1970s (Figure 8a). In the study area, the total recharge was 14.4 billion m3/a from 1991 to 2003, whereas the total discharge was 16.6 billion m3/a; that is, groundwater was over-exploited with a net abstraction of 2.2 billion m3/a [19]. The annual average abstraction in the study area was estimated at 11.2 billion m3/a from 1961 to 2010 with agriculture accounting for an estimated 73%–84% of the total exploitation [49].

Water 06 01581 g008 1024
Figure 8. (a) Groundwater exploitation and (b) irrigation in the study area during 1961–2010.

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Figure 8. (a) Groundwater exploitation and (b) irrigation in the study area during 1961–2010.
Water 06 01581 g008 1024

River leakage in the plains is one of the primary recharge sources for groundwater, and old channels with good permeability allow the passage of surface water to the groundwater system. However, many water projects built since the 1960s in the upstream regions of rivers retain runoff, reducing groundwater recharge by surface water in the plains. According to Zhang et al. [19], the total water released from the reservoirs was 53.0 billion m3/a from 1960 to 2002, 2.2 billion m3/a in the 1960s, and only 0.63 billion in the 1980s. The reasons for this are twofold: upstream water use increased with the development of society and economy; combined with changes in climate including decreasing precipitation (i.e., decreasing runoff) and increasing temperature. Groundwater levels were reduced further when the decreased runoff resulted in less groundwater recharge.

Irrigation return flow, following exploitation for agriculture and water release from reservoirs, has become a new source of groundwater recharge. Groundwater is the primacy source for irrigation, accounting for 81%–93% of total irrigation water in the NCP [50]. The total amount of groundwater used for irrigation in the study area was estimated based on the volume of groundwater abstracted for agriculture and the ratio above, giving an estimate of 10.5 billion m3/a from 1961 to 2010. The estimated volume exhibited a trend similar to that of groundwater exploitation (Figure 8b).

4.3. GRA between Water Table Depth and Influencing Factors

Declining groundwater levels pose many environmental and geological problems. Therefore, it is important to understand which of the several factors affecting groundwater levels are the true driving forces. Based on the simulated groundwater levels and the factors described above, we used GRA to rank the influence of the factors.

(1) Calculation of the reference and comparison series

X0 is the reference series, representing water table depth, and Xi is the comparison series, considered to be factors that influence water table depth. The study period was 50 years, and the series were as follows:

X0′ = {x0′(1),x0′(2),…x0′(50)} -----Water table depth
X1′ = {x1′(1),x1′(2),…x1′(50)} -----Precipitation infiltration
X2′ = {x2′(1),x2′(2),…x2′(50)} -----Phreatic evaporation
X3′ = {x3′(1),x3′(2),…x3′(50)} -----Groundwater exploitation
X4′ = {x4′(1),x4′(2),…x4′(50)} -----River leakage
X5′ = {x5′(1),x5′(2),…x5′(50)} -----Irrigation return flow

(2) Data pre-processing

The results of the sequences are presented in Table 2.

Table Table 2. The sequences after data pre-processing.

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Table 2. The sequences after data pre-processing.
nX0X1X2X3X4X5
10.3970.8631.5150.2771.8860.551
20.4440.6901.5110.3371.8860.670
30.5330.9471.3860.3471.8860.689
40.5321.2241.0390.3571.8860.709
50.6010.4471.4830.3781.8860.753
60.5560.7761.2610.3771.8860.750
70.5550.7871.2480.4131.8860.822
80.5590.4781.5130.4501.8860.895
90.5970.9441.2030.4871.8860.969
100.6580.7271.2270.5241.8861.076
110.5640.9631.6230.5881.2520.643
120.5990.6091.8730.6471.2520.711
130.5931.2071.5190.7201.2520.791
140.6790.9031.6010.7961.2520.871
150.7830.6951.5720.8321.2520.909
160.7840.9981.4490.8741.2520.961
170.7341.3221.4750.9291.2521.015
180.7720.9191.5250.9701.2521.061
190.8150.9051.3851.0181.2521.101
200.8020.7351.4081.1091.2521.191
210.8760.8510.8431.0880.5140.913
220.9130.9380.8401.1120.5140.933
230.9710.8490.7901.1380.5140.955
240.9880.9660.7611.1680.5140.980
250.9951.1090.6491.1840.5140.993
261.0380.7820.8051.1960.5141.005
271.0651.1080.7071.1930.5140.999
281.0991.1080.7521.2080.5141.005
291.1890.7870.8111.2340.5141.026
301.2101.3130.6541.2320.5141.001
311.1971.2930.6291.2350.7371.143
321.2150.8680.7071.2490.7371.155
331.3021.1540.7051.2510.7371.158
341.3671.4480.7051.2530.7371.161
351.4591.4930.6901.2650.7371.171
361.4271.3350.6711.2870.7371.191
371.5190.7520.7401.2940.7371.119
381.3791.2010.6351.3080.7371.127
391.3700.8010.7051.3290.7371.136
401.3551.1460.7011.3360.7371.130
411.3770.9800.8331.3880.7371.234
421.4590.8400.8341.3820.5961.228
431.2981.4180.6881.3560.5961.205
441.2991.2470.7261.3350.5961.187
451.3531.1250.7291.3150.5961.169
461.3070.9670.6411.3140.5961.168
471.3991.1490.6561.2870.5961.144
481.3201.3610.5251.2280.5961.092
491.3131.3430.5231.1950.5961.063
501.3831.1320.5251.2090.5961.074

(3) Calculation of the deviation sequences Δ0i

The deviation sequences were calculated using Equation 6: Δ01(1) = |x0(1)−x1(1)| = |0.397–0.863| = 0.466, Δ01(2) = |x0(2)−x1(2)| = |0.397–1.515| = 1.118. The same method was adopted for i = 1–5 and the results for all Δ0i are presented in Table 3. Based on these results, maxΔ0i(k) = 1.442 and minΔ0i(k) = 0.002.

Table Table 3. The deviation sequences.

Click here to display table

Table 3. The deviation sequences.
nΔ01Δ02Δ03Δ04Δ05
10.4661.1180.1201.4890.154
20.2461.0680.1071.4420.226
30.4150.8540.1861.3540.157
40.6920.5070.1751.3540.177
50.1540.8830.2221.2860.152
60.2200.7050.1791.3300.194
70.2310.6920.1421.3310.267
80.0810.9540.1091.3270.336
90.3470.6070.1101.2890.372
100.0690.5690.1341.2280.418
110.3991.0590.0240.6880.079
120.0091.2740.0480.6520.112
130.6140.9260.1270.6590.198
140.2240.9220.1170.5730.192
150.0880.7890.0480.4690.126
160.2140.6650.0900.4680.177
170.5880.7410.1940.5170.281
180.1480.7530.1990.4800.290
190.0910.5710.2030.4370.287
200.0680.6060.3070.4490.389
210.0260.0330.2120.3620.037
220.0250.0740.1990.3990.020
230.1220.1810.1670.4560.016
240.0220.2270.1800.4730.008
250.1140.3460.1880.4810.002
260.2570.2330.1580.5240.034
270.0440.3580.1280.5500.066
280.0080.3470.1090.5850.094
290.4030.3790.0440.6750.164
300.1030.5560.0220.6960.209
310.0960.5670.0390.4590.054
320.3470.5080.0340.4770.060
330.1480.5970.0500.5640.144
340.0800.6620.1140.6300.206
350.0340.7690.1940.7220.288
360.0920.7560.1400.6900.236
370.7670.7790.2250.7820.400
380.1780.7440.0710.6420.252
390.5700.6650.0410.6330.234
400.2090.6540.0190.6170.224
410.3970.5440.0110.6400.143
420.6190.6250.0770.8630.231
430.1200.6100.0580.7020.093
440.0520.5730.0360.7030.112
450.2280.6240.0380.7570.184
460.3400.6660.0080.7100.139
470.2500.7430.1120.8030.256
480.0410.7950.0920.7240.228
490.0300.7900.1180.7170.251
500.2510.8580.1750.7870.309

(4) Calculation of the grey relational coefficient ξi(k)

The parameters were calculated using Equation 7 and the results are presented in Table 4.

(5) Calculation of the grey relational grade γi of each series

The parameters were calculated using Equation 8, and the results are presented in Table 4.

Table Table 4. The calculated grey relational coefficient and grey relational grade for five comparison sequences

Click here to display table

Table 4. The calculated grey relational coefficient and grey relational grade for five comparison sequences
nξ1ξ2ξ3ξ4ξ5
10.6090.3930.8600.3270.827
20.7480.4050.8740.3340.764
30.6370.4600.7980.3490.824
40.5120.5890.8070.3490.806
50.8270.4510.7670.3610.829
60.7690.5080.8030.3530.791
70.7600.5120.8380.3530.732
80.9020.4320.8720.3530.685
90.6770.5450.8710.3600.662
100.9150.5610.8460.3710.635
110.6460.4060.9720.5140.905
120.9900.3630.9410.5270.868
130.5420.4390.8530.5240.788
140.7650.4400.8630.5590.792
150.8940.4790.9400.6080.854
160.7740.5220.8920.6090.805
170.5530.4950.7910.5840.722
180.8330.4910.7870.6020.716
190.8910.5600.7830.6250.718
200.9170.5450.7040.6180.652
210.9690.9590.7760.6680.955
220.9700.9100.7860.6460.977
230.8580.8020.8140.6140.982
240.9740.7640.8030.6060.993
250.8670.6780.7960.6021.000
260.7400.7580.8230.5810.959
270.9460.6710.8520.5690.919
280.9920.6770.8720.5540.888
290.6440.6580.9450.5180.818
300.8780.5670.9740.5110.778
310.8850.5620.9520.6130.934
320.6770.5890.9580.6040.926
330.8330.5490.9380.5630.836
340.9030.5230.8670.5360.781
350.9580.4860.7910.5010.717
360.8900.4900.8400.5130.756
370.4860.4820.7650.4820.645
380.8050.4940.9140.5310.743
390.5610.5220.9490.5340.757
400.7780.5260.9780.5410.765
410.6470.5720.9880.5320.837
420.5400.5380.9060.4570.760
430.8610.5440.9290.5090.888
440.9350.5590.9550.5080.868
450.7620.5380.9530.4900.800
460.6820.5220.9930.5050.841
470.7450.4940.8680.4750.741
480.9490.4770.8900.5010.762
490.9640.4790.8620.5030.744
500.7440.4580.8080.4800.702
γi0.7920.5490.8680.5110.809
Grey relational order34152

The factors that control water table depth, in order of decreasing importance, are X3 (groundwater exploitation), X5 (irrigation return flow), X1 (precipitation infiltration), X2 (phreatic evaporation), and X4 (river leakage) (i.e., γ3 > γ5 > γ1 > γ2 > γ4). Exploitation and irrigation return flow represent human influence, whereas precipitation infiltration represents climate change. Therefore, human activities are the major factors responsible for declining groundwater levels in the study area. The correlation between river leakage and water table depth was the weakest of all factors studied, which could be caused by the small contribution of river leakage to groundwater recharge since the 1980s.

It was noted that data pre-processing caused some fluctuations of the grey relational grade. We therefore used two additional methods Equations (4) and (5) for data pre-processing to obtain grey relational grades. The three methods obtained the same grey relational order, indicating that the results are robust.

The GRA results, suggesting human activities (particularly exploitation) are the primary driving forces of groundwater change, are consistent with previous estimates using the projection pursuit regression (PPR) technique [51]. These analyses of historical groundwater level changes since 1960 have generally shown that groundwater is in a state of imbalance. The large cones of depression that have formed in the study area (likely caused by human activities) are representative of unsustainable groundwater exploitation.

The principle of sustainability, defined by the United Nations Commission on Sustainable Development in 1987, calls for satisfying current needs without compromising the needs of future generations, and has been adopted for the management of groundwater resources development. Sophocleous [52] noted that the sustainable yield of an aquifer must be considerably less than recharge if adequate amounts of water are to be available to sustain both the quantity and quality of streams, springs, wetlands, and groundwater-dependent ecosystems. In this context, sustainable exploitation involves compromise to ensure that resources can be maintained for an infinite time without causing serious environmental, economic, or social consequences. To maintain groundwater equilibrium, groundwater abstraction should not exceed the recharge rate minus other conditions.

Many previous studies have investigated ways to achieve groundwater sustainability, including liming groundwater abstraction, increasing groundwater recharge, conjunctive use of surface and groundwater, and better use of groundwater storage [53,54]. Several effective approaches have been attempted in the NCP [55]. The South-to-North Water Diversion Project (SNWDP) is proposed as a significant method to manage and prevent the continued shortage of groundwater resources in northern China. This route conveys water from Danjiangkou, which is located in a branch of Yangzi River, to Beijing and Tianjin in the north via a 1241.2 km long main canal [56]. The first phase of the project will be completed after the flood season in 2014, supplying the NCP with 5.7 billion m3/a of water [57]. This approach should remediate the groundwater cone to some extent; however, considerable time will be required to recover the groundwater environment [58].

5. Conclusions

We used a groundwater flow model to determine groundwater change in the NCP. Over the past 50 years, groundwater conditions have changed dramatically, with declining levels and the development of cones of depression. The primary factors influencing groundwater levels are precipitation, temperature, groundwater exploitation, and the construction of reservoirs. Both climate change and human activities contribute to the changes, although groundwater exploitation was found to be the major driving factor.

GRA was able to separate the influence of different factors associated with groundwater dynamics, calculate the grey relational order, and produce reasonable results. It is therefore suitable and sensitive enough to identify major and minor driving forces.

Many different sustainable development strategies will be required to stop the decline in groundwater levels. At present, the implementation of the SNWDP will significantly reduce water shortages and the deterioration of the groundwater ecological environment in the NCP. The project will also provide valuable information for groundwater sustainable development strategies in other hotspots facing water shortages.

Although the concept underpinning groundwater sustainability is clear, the criteria for developing current sustainability projects cannot yet be evaluated, because both climate and socio-economic patterns are changing. We describe a method that offers promise in identifying those criteria. In particular, the combination of numerical simulation and grey system theory will be useful in developing criteria to achieve sustainable development. The results presented here may be applicable for similar areas of water scarcity.

The scope of this study was restricted by the limited data available on climate change and human activities. We were not able to completely separate their respective influences on groundwater. Therefore, further study of the impact of human activities on climate change in the context of groundwater will be important in future.

Acknowledgements

We are grateful to the Major State Basic Research Development Program of China (973 Program NO. 2010CB428801) for supporting this research. We appreciate our collaborators in this program for providing access to data information. We would also like to thank the peer reviewers for their care and attention in providing comments on the manuscript.

Authors Contributions

Xue Li conceived the subject of the article and wrote it. Yuan Zhang established the groundwater flow model and gathered information. Guomin Li revised paper, recommended and directed this research. All the authors are involved in preparing the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Kemper, K. Groundwater—From development to management. Hydrogeol. J. 2004, 12, 3–5. [Google Scholar] [CrossRef]
  2. De Vries, J.; Simmers, I. Groundwater recharge: An overview of processes and challenges. Hydrogeol. J. 2002, 10, 5–17. [Google Scholar] [CrossRef]
  3. Chen, H.; Wang, S.; Gao, Z.; Hu, Y. Artificial Neural Network Approach for Quantifying Climate Change and Human Activities Impacts on Shallow Groundwater Level—A Case Study of Wuqiao in North China Plain; IEEE: New York, NY, USA, 2010. [Google Scholar]
  4. Hsu, K.-C.; Yeh, H.-F.; Chen, Y.-C.; Lee, C.-H.; Wang, C.-H.; Chiu, F.-S. Basin-scale groundwater response to precipitation variation and anthropogenic pumping in Chih-ben watershed, Taiwan. Hydrogeol. J. 2012, 20, 499–517. [Google Scholar] [CrossRef]
  5. Hao, X.; Chen, Y.; Xu, C.; Li, W. Impacts of climate change and human activities on the surface runoff in the Tarim river basin over the last fifty years. Water Resour. Manag. 2008, 22, 1159–1171. [Google Scholar] [CrossRef]
  6. Bloomfield, J.P.; Gaus, I.; Wade, S.D. A method for investigating the potential impacts of climate-change scenarios on annual minimum groundwater levels. Water Environ. J. 2003, 17, 86–91. [Google Scholar] [CrossRef]
  7. Scibek, J.; Allen, D.M. Modeled impacts of predicted climate change on recharge and groundwater levels. Water Resour. Res. 2006, 42, W11405. [Google Scholar]
  8. Waibel, M.S.; Gannett, M.W.; Chang, H.; Hulbe, C.L. Spatial variability of the response to climate change in regional groundwater systems—Examples from simulations in the deschutes basin, oregon. J. Hydrol. 2013, 486, 187–201. [Google Scholar] [CrossRef]
  9. Konikow, L.; Kendy, E. Groundwater depletion: A global problem. Hydrogeol. J. 2005, 13, 317–320. [Google Scholar] [CrossRef]
  10. Shah, T.; Molden, D.; Sakthivadivel, R.; Seckler, D. Global groundwater situation: Opportunities and challenges. Eco. Polit. Wkly. 2001, 36, 4142–4150. [Google Scholar]
  11. Wada, Y.; van Beek, L.P.H.; van Kempen, C.M.; Reckman, J.W.T.M.; Vasak, S.; Bierkens, M.F.P. Global depletion of groundwater resources. Geophys. Res. Lett. 2010, 37, L20402. [Google Scholar]
  12. Manca, F.; Capelli, G.; La Vigna, F.; Mazza, R.; Pascarella, A. Wind-induced salt-wedge intrusion in the Tiber river mouth (Rome–Central Italy). Environ. Earth Sci. 2014. [Google Scholar] [CrossRef]
  13. Custodio, E. Aquifer overexploitation: What does it mean? Hydrogeol. J. 2002, 10, 254–277. [Google Scholar] [CrossRef]
  14. Zheng, C.; Liu, J.; Cao, G.; Kendy, E.; Wang, H.; Jia, Y. Can China cope with its water crisis?—Perspectives from the North China Plain. Ground Water 2010, 48, 350–354. [Google Scholar] [CrossRef]
  15. Liu, C.; Yu, J.; Kendy, E. Groundwater exploitation and its impact on the environment in the North China Plain. Water Int. 2001, 26, 265–272. [Google Scholar] [CrossRef]
  16. Fei, Y.; Zhang, Z.; Zhang, F.E.; Wang, Z.; Chen, Z.; Chen, J.; Qian, Y.; Li, Y. An analysis of the influence of human activity and climate change on water resources of the North China Plain. Acta Geosci. Sin. 2007, 28, 567–571.(In Chinese). [Google Scholar]
  17. Fei, Y.; Miao, J.; Zhang, Z.; Chen, Z.; Song, H.; Yang, M. Analysis on evolution of groundwater depression cones and its leading factors in North China Plain. Resour. Sci. 2009, 31, 394–399.(In Chinese). [Google Scholar]
  18. Zhu, L.; Gong, H.; Li, X.; Li, Y.; Su, X.; Guo, G. Comprehensive analysis and artificial intelligent simulation of land subsidence of Beijing, China. Chin. Geogr. Sci. 2013, 23, 237–248. [Google Scholar] [CrossRef]
  19. Zhang, Z.; Fei, Y.; Chen, Z.; Zhao, Z.; Xie, Z.; Wang, Y.; Miao, J.; Yang, L.; Shao, J.; Jin, M.; et al. Investigation and Assessment of Sustainable Utilization of Groundwater Resources in the North China Plain; Geological Publishing House: Beijing, China, 2009. [Google Scholar]
  20. Yo-Ping, H.; Chi-Chang, H. The integration and application of fuzzy and grey modeling methods. Fuzzy Sets Syst. 1996, 78, 107–119. [Google Scholar] [CrossRef]
  21. Ju-Long, D. Control problems of grey systems. Syst. Control Letters 1982, 1, 288–294. [Google Scholar] [CrossRef]
  22. Deng, J. The theory and method of socioeconomic grey systems. Soc. Sci. China 1984, 6, 47–60.(In Chinese). [Google Scholar]
  23. Wong, H.; Hu, B.; Ip, W.; Xia, J. Change-point analysis of hydrological time series using grey relational method. J. hydrol. 2006, 324, 323–338. [Google Scholar] [CrossRef]
  24. Lin, J.; Lin, C. The use of the orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics. Int. J. Mach. Tools Manuf. 2002, 42, 237–244. [Google Scholar] [CrossRef]
  25. Kung, C.-Y.; Wen, K.-L. Applying grey relational analysis and grey decision-making to evaluate the relationship between company attributes and its financial performance—A case study of venture capital enterprises in taiwan. Decis. Support. Syst. 2007, 43, 842–852. [Google Scholar] [CrossRef]
  26. Gau, H.S.; Hsieh, C.Y.; Liu, C.W. Application of grey correlation method to evaluate potential groundwater recharge sites. Stoch. Environ. Res. Risk Assess. 2006, 20, 407–421. [Google Scholar] [CrossRef]
  27. Du, W.; Wei, X.; Li, P.; Li, P.; Han, Y. Dynamic evolutionary tendency of groundwater in irrigationdistrict in changing environment and its driving factors. J. Drain. Irrig. Mach. Eng. 2013, 31, 993–999.(In Chinese). [Google Scholar]
  28. Yeh, Y.; Su, M.; Tsou, I. Forecasting of groundwater level using grey modeling. J. Taiwan Water Conserv. 1995, 43, 66–73. [Google Scholar]
  29. Chen, W. Groundwater in Hebei Province; Earthquake Publishing House: Beijing, China, 1999. [Google Scholar]
  30. McDonald, M.G.; Harbaugh, A.W. A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model; Scientific Publications Company: Reston, VA, USA, 1984. [Google Scholar]
  31. Harbaugh, A.W.; Banta, E.R.; Hill, M.C.; McDonald, M.G. Modflow-2000, the US Geological Survey Modular Ground-Water Model: User Guide to Modularization Concepts and the Ground-Water Flow Process; US Geological Survey: Reston, VA, USA, 2000.
  32. Harbaugh, A.W. Modflow-2005, the US Geological Survey Modular Ground-Water Model: The Ground-Water Flow Process; US Department of the Interior, US Geological Survey: Reston, VA, USA, 2005.
  33. La Vigna, F.; Demiray, Z.; Mazza, R. Exploring the use of alternative groundwater models to understand the hydrogeological flow processes in an alluvial context (Tiber river, Rome, Italy). Environ. Earth Sci. 2014, 71, 1115–1121. [Google Scholar] [CrossRef]
  34. La Vigna, F.; Mazza, R.; Capelli, G. Detecting the flow relationships between deep and shallow aquifers in an exploited groundwater system, using long-term monitoring data and quantitative hydrogeology: The Acque Albule basin case (Rome, Italy). Hydrol. Process. 2013, 27, 3159–3173. [Google Scholar]
  35. Zhang, Z.; Shen, Z.; Xue, Y. Groundwater Environment Evolution in the North China Plain; Geological Publishing House: Beijing, China, 2000. [Google Scholar]
  36. Zhang, Y.; Li, G. Long-term evolution of cones of depression in shallow aquifers in the North China Plain. Water 2013, 5, 677–697. [Google Scholar] [CrossRef]
  37. Deng, J. The Primary Methods of Grey System Theory; Hua Zhong University of Science and Technology Press: Wuhan, China, 2005. [Google Scholar]
  38. Cao, G.; Zheng, C.; Scanlon, B.R.; Liu, J.; Li, W. Use of flow modeling to assess sustainability of groundwater resources in the North China Plain. Water Resour. Res. 2013, 49, 159–175. [Google Scholar] [CrossRef]
  39. Xia, J.; Liu, C.; Ding, Y.; Jia, S.; Lin, C. Water Issues Vision in China; Science Publishing House: Beijing, China, 2011. [Google Scholar]
  40. Mann, H.B. Nonparametric tests against trend. Econometrica 1945, 13, 245–259. [Google Scholar] [CrossRef]
  41. Kendall, M.G. Rank Correlation Methods; Oxford: Griffin, UK, 1955. [Google Scholar]
  42. Partal, T.; Kahya, E. Trend analysis in turkish precipitation data. Hydrol. Process. 2006, 20, 2011–2026. [Google Scholar] [CrossRef]
  43. Ip, W.C.; Zhang, L.; Wong, H.; Xia, J. Multi-scale variability and trends of precipitation in North China. Water Resour. 2011, 38, 18–28. [Google Scholar] [CrossRef]
  44. Kuang, Z.; Ji, Z.; Lin, Y. Wavelet analysis of rainfall data in North China. Clim. Environ. Res. 2000, 5, 312–317.(In Chinese). [Google Scholar]
  45. Tan, F.; Wang, J.; Song, Y. Characteristic of cliamte change in the North China Plain for recent 45 years. Meteorol. Mon. 2010, 36, 40–45.(In Chinese). [Google Scholar]
  46. Fei, Y. Evolution and Conservation of Groundwater in Hebei Plain to the South of Beijing and Tianjin; Hohai University: Nanjing, China, 2006. [Google Scholar]
  47. Xu, X. A Study of Numerical Simulation for Groundwater Flow in the Beijing Plain; China University of Geosciences (Beijing): Beijing, China, 2006. [Google Scholar]
  48. Yang, Y.; Li, X.; Wang, L.; Li, C.; Liu, Z. Characteristics of the groundwater level regime and effect factors in the plain region of Tianjin city. Geol. Surv. Res. 2011, 34, 313–320.(In Chinese). [Google Scholar]
  49. Zhang, G.; Fei, Y.; Wang, J.; Yan, M.; Yu, C.; Wang, G.; Wang, H.; Feng, H.; Liu, Z.; Liu, K.; et al. Adaptation between Irrigation Agriculture and Groundwater in North China Plain; Science Press: Beijing, China, 2012. [Google Scholar]
  50. Zhang, G.; Fei, Y.; Liu, C.; Yan, M.; Wang, J. Adaptation between irrigation intensity and groundwater carrying capacity in North China Plain. Trans. Chin. Soc. Agric. Eng. 2013, 29, 1–10.(In Chinese). [Google Scholar]
  51. Xu, Y. Evaluation of groundwater level drawdown driving forces in the Hebei plain to the south of Beijing and Tianjin. Prog. Geogr. 2003, 22, 490–498.(In Chinese). [Google Scholar]
  52. Sophocleous, M. From safe yield to sustainable development of water resources—The Kansas experience. J. Hydrol. 2000, 235, 27–43. [Google Scholar] [CrossRef]
  53. Alley, W.M.; Reilly, T.E.; Franke, O.L. Sustainability of Ground-Water Resources; US Department of the Interior, US Geological Survey: Reston, VA, USA, 1999.
  54. Galloway, D.L. Evolving Issues and Practices in Managing Ground-Water Resources. US Department of the Interior, US Geological Survey: Reston, VA, USA, 2003. [Google Scholar]
  55. Liu, J.; Zheng, C.M.; Zheng, L.; Lei, Y.P. Ground water sustainability: Methodology and application to the North China Plain. Ground Water 2008, 46, 897–909. [Google Scholar]
  56. Wang, L.; Ma, C. A study on the environmental geology of the Middle Route Project of the South–North water transfer. Eng. Geol. 1999, 51, 153–165. [Google Scholar] [CrossRef]
  57. Changjiang Water Resources Commission of the Ministry of Water Resources. The south-to-north water transfer project planning (2001 revision). Chin. Water Resour. 2003, 1, 48–55.(In Chinese). [Google Scholar]
  58. Zhang, Y.; Li, G.-M. Influence of South-to-North Water Diversion on major cones of depression in North China Plain. Environ. Earth Sci. 2014, 71, 3845–3853. [Google Scholar] [CrossRef]
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