Multi-objective optimal allocation of water resources based on ‘three red lines’ in Qinzhou, China

With improvements in living standards, people's requirements for water quantity and water quality have increased. Water shortages and deterioration of water quality have caused conflicts in the supply and demand of regional water resources. There are also problems such as low water use efficiency and the fact that water ecology continues to be negatively impacted by human activities (Mei, 2010; Liu et al., 2013). Under the combined effects of these factors, the economic, social, and environmental benefits of water resources are difficult to optimize, which restricts regional economic development and social stability.

The optimal allocation of water resources is an important means to alleviate supply–demand conflicts in different regions. By distributing limited water resources to different sectors scientifically and reasonably, the maximum benefits of water use can be obtained (Habibi Davijani et al., 2016a, 2016b). Thus, particular development theories have been put forward which approach water resources allocation based on balance development (Liu et al., 2015), sustainable development (Niu et al., 2016), and evaporation transpiration (ET) development (Zhou et al., 2009).

The methods above pay more attention to water quantity allocation, with less emphasis on water quality. Other theories such as ecology development (Naiman & Bilby, 1998; Myers & Bazely, 2003), green development (Adam, 1995), and low carbon use (Kanakoudis et al., 2012; Kanakoudis & Papadopoulou, 2014; Kanakoudis, 2015) comprehensively consider regional water quantity and water quality factors but neglect water use efficiency when considering the allocation of water resources. This can lead to problematic policy recommendations to resolve the contradiction between supply and demand, such as building new water supply facilities rather than optimizing the use of existing options.

In 2011, the No. 1 Document of the Central Committee of the Communist Party of China clearly articulated ‘China's Most Stringent Water Resources Management’ (CMSWRM) (CPC Central Committee and State Council, 2010). The three red lines (TRL) constraint is the core of CMSWRM. They consist of the total water use red line (TWURL), the water use efficiency red line (WUERL), and the controlling pollution red line (CPRL) (Global Water Partnership, 2013).

The purpose of establishing the TWURL is to strictly limit the rapid growth of total water use and to control the development of water resources within the scope of carrying capacity. The purpose of re-establishing the WUERL is to enhance the efficiency of water use, thus saving water. Controlling agricultural and industrial water use efficiency is crucial in this respect. ‘Irrigation efficiency’ (IE) is an important indicator to measure the efficiency of the agriculture sector in regions which are less influenced by climate conditions (Jensen, 2007) and plant structure (Liu & Song, 2019). ‘Water used per CNY10,000 industrial added value’ (WUPCIAV) can reflect the technology of industrial water use, the level of water-saving reforms, and enterprise management (Zang et al., 2016) and can thus be a suitable indicator for evaluating industrial water use efficiency. The purpose of establishing the CPRL is to strengthen water pollution prevention and water resources protection, so that the total amount of allowed pollutant discharge (TAOAPD) into rivers can be controlled considering the carrying capacity in water environments (Yi et al., 2017).

At present, the essence of Chinese water resources management (WRM) involves combining the TRL with regional water resources allocation (WRA). Optimal models connecting the TRL constraint are necessary to solve WRA problems (Wang et al., 2012). Wang & Zhang (2014) presents a multi-source joint regulation model based on the TRL by considering the objective of socio-economic benefits. Related studies have also been conducted by Liang & Zuo (2013), Tursunmo (2015), and Zhao (2015). However, they only considered quota constraints. Ignoring the WUPCIVA index will lead to increasing water demand in the secondary sector, which further aggravates the imbalance between supply and demand.

Different researchers have constructed WRM models to support local implementations of the national CMSWRM initiative: in Yangquan city (Ren, 2015); Weihe basin (Wang et al., 2015); Taiyuan city (Jiang et al., 2016); and Yuhuan city (Zhong et al., 2018), However, they all use sectoral pollutant discharge concentrations in status years instead of planning years, which would likely cause excessive total sewage discharge into rivers in planning years.

Further, reviewing the literature it appears that extant studies have focused on areas experiencing water shortages due to a lack of water resources. However, Qinzhou is located on the southwest coast of Guangxi and has a subtropical marine monsoon climate with an average annual rainfall of 2,026.3 m³. Due to the lack of large-scale water storage projects in the upper reaches, Qinzhou can be characterized as a water shortage area from an engineering perspective which is obviously different from those water shortage areas which experience a lack of water resources (Chen et al., 2018a).

This paper seeks to address the issue of regional water resources allocation given the CMSWRM context. The objective of the paper is to present a systematic framework of water resources allocation considering TRL constraints to support CMSWRM, and establish a multi-objective non-linear programming model to allocate domestic and cross-basin water to different sectors in Qinzhou.

Allocating water given the TRL means adhering to the constraints of water supply, water demand, and total sewage discharge in the model. The system framework of water resources allocation based on the TRL is shown in Figure 1 and the principles of water resource allocation are as follows:

1. The TWURL controls total water withdrawal by calculating the rate of water resource development and utilization. Either domestic water sources (surface water, groundwater, and reuse water) or water from cross-basin diversion projects (CBDP) can be used to allocate water to each sector. The sum of the water supplied by the two types of water sources must not exceed the regional TWURL constraint.

2. Water used per CNY 10,000 industrial added value (WUPCIAV) and irrigation efficiency (IE) are important indicators for quantifying the WUERL; these indicators are respectively applied to industrial and agricultural water demand forecasts in each planning year, which can then limit the increasing water demand in these sectors and allow the total volume of water allocated to be restrained. The results of water demand forecasts are used as water demand constraints in the allocation model.

3. It would be prudent to convert the CPRL into an index of the total amount of allowed pollutant discharge (TAOAPD) including many pollutant indicators as a constraint in the model. However, current monitoring capabilities do not cover all these pollutants, so, chemical oxygen demand (COD) which is monitored by a governmental entity in China can be used as a representative indicator to proxy for a broader array of pollutants. The TAOAPD for COD is thus the water quality constraint in the model, and the total amount of COD discharged by each sector using domestic and CBDP water sources must not exceed the regional TAOAPD for COD.

4. Domestic water sources should be prioritized for supplying water in view of the higher cost of CBDP. When domestic water sources are fully utilized, sectors still lacking water could consider using CBDP water sources.

• (1)

  Social benefits target

• (2)

  Economic benefits target

• (3)

  Environment benefits target

• (1)

  Water supply capacity constraints

• (2)

  Users' water demand constraint under the WUERL

• (3)

  Guaranteed municipal water supply rate

• (4)
  TWURL constraint

  

  (8)

  where is the upper limit of the TWURL constraint in sub-area k.
• (5)
  CPRL constraint

  

  (9)

  where is the TAOAPD for COD.
• (6)
  Non-negative constraints

  

  (10)

  

  (11)

NSGA-II (Deb et al., 2002) is an evolutionary algorithm for solving multi-objective optimization problems. The algorithm assigns fitness values to chromosomes based on a non-dominated sorting approach. Non-dominated solutions are equally valued solutions to a Pareto front. The non-dominated sorting approach aims to preserve diversity among the non-dominated solutions, making use of crowding distance. The crowding distance is a measure of solution density that is used in the selection operator: the less close a solution is to another solution, the higher the chance of selection. In the process of optimization, all objectives are considered to be equally important. When the algorithm finishes searching for a set of optimal solutions, relevant decision-makers analyze and select their preferred solution from this set. If a decision-maker does not have enough target information in advance, or needs to change the expectation value based on developments in their understanding or experience of the problem, interactive use can improve the search efficiency of the algorithm. Importantly, this has proven to be an appropriate algorithm for solving water resource management problems (Bazargan-Lari et al., 2009; Shokri et al., 2014; Ahmadi et al. 2015).

Qinzhou is divided into five administrative divisions (Figure 2): Qinnan, Qinbei, Qingang, Lingshan, and Pubei. There are 388 water storage projects with a total storage capacity of 80,002 × 10⁴ m³, in which the total annual designed water supply capacity is 80,829 × 10⁴ m³ (Chen et al., 2018a). In 2014, Qinzhou consumed 15.16 × 10⁸ m³ water in total, WUPCIAV was 65 m³, IE was 0.456, and the water qualification rate of the water function zone was 66% (Qinzhou Water Conservancy Bureau, 2014). It is anticipated that Qinzhou will operate the Yujiang CBDP in 2030, which will increase the water supply to 3.229 × 10⁸ m³ to address water shortages (Qinzhou Water Resources and Hydropower Survey and Design Institute, 2008).

Planning years are set as 2020 and 2030. To implement stringent water resources management in Qinzhou, the target for total water use will be set at 16.53 × 10⁹ m³ in 2020 and 16.95 × 10⁹ m³ in 2030 (Guangxi Water Resources Department, 2011). The WUPCIAV indicator will decrease to 50 m³ in 2020 and 40 m³ in 2030; and the IE will reach 0.53 in 2020 and 0.6 in 2030. According to the quantified capacity of the water function area of small and medium-sized rivers in Qinzhou and the control plan for total pollutant discharge (Guangxi Water Resources and Hydropower Survey and Design Institute, 2015), TAOAPD for COD will be limited to 44,275.8 ton in 2020 and 44,211.4 ton in 2030.

Results are presented in Table 1 using the quota method to forecast the five sectors' water demand in the region under a guaranteed rate of p= 75% 2020 and 2030. The quotas are determined with reference to Guangxi urban water consumption quota DB45/T 679-2017 (Guangxi Water Resources Department, 2017a), Guangxi main industrial products water consumption quota DB45/T 678-2017 (Guangxi Water Resources Department, 2017b), and Guangxi agriculture, forestry, fishery, and rural water consumption quota DB45/T 804-2012 (Guangxi Water Resources Department, 2012). The relevant social and economic data were obtained from the Qinzhou City Master Plan (2012–2030) (People's Government Office of Qinzhou, 2013).

The method proposed by Chen et al. (2018b) is used to forecast the available water supply in Qinzhou in the planning years. As noted, the Yujiang CBDP will be operational in 2030, augmenting the water supply to Qinzhou. Relevant data concerning this additional supply are taken from the Yujiang Cross-basin Diversion Project Water Resources Argument Report (Qinzhou Water Resources and Hydropower Survey and Design Institute, 2008). In addition, according to the report requirements, the CBDP water will only supply the municipal, secondary, tertiary, and agricultural sectors in Qinbei, Qingang, and Lingshan. Water supply predictions under a guaranteed rate of p = 75% in Qinzhou in 2020 and 2030 are shown in Table 2.

• (1)

  Sector weight coefficient

According to the characteristics of water use sectors in Qinzhou, and with reference to the principle of ‘First live, then production’ (Zeng, 2008), the sectoral supply sequence is municipal, tertiary, secondary, ecology, and agriculture with sector weights (Equation 12) of 0.33, 0.27, 0.20, 0.13, and 0.07, respectively.

• (2)

  Water use output coefficient

• (3)

  Sewage discharge coefficient

The sewage discharge coefficient measures the ratio of wastewater generation in the process of water use.

According to the code for urban wastewater and storm water engineering planning GB 50318-2017 (Ministry of Housing and Urban-Rural Development of the People's Republic of China, 2017), the coefficients of sewage discharge in the municipal, tertiary, and secondary sectors are 0.8, 0.8, and 0.6, respectively. Sewage discharge in agriculture is mostly related to the loss of fertilizer, so the rate of fertilizer use can be used to determine the sewage discharge coefficient in that sector. Thus, based on Ma et al. (2012), the coefficient of sewage discharge in agriculture is 0.6.

• (4)

  COD concentrations

According to the Qinzhou Environmental Bulletin (Qinzhou Ecology and Environment Bureau, 2014) and Qinzhou Water Resources Bulletin (Qinzhou Water Conservancy Bureau, 2014), in 2014, total COD emissions from the municipal, secondary, and agricultural sectors in Qinzhou were 23,730.64 ton, 6,636.61 ton, and 12,970.24 ton, respectively, and the total water consumption in these three sectors was 22,775 × 10⁴m³, 18,289 × 10⁴ m³, and 110,123 × 10⁴ m³, respectively.

Using Equation (14), the status-quo concentrations of COD for each sector were = = 130.25 g/m³, = 57.96 g/m³, and = 19.63 g/m³.

Because it is complex to forecast COD concentrations in the planning years, two scenarios were developed by setting different COD concentrations for each sector to give ample scope for local decision-makers to appreciate the consequences of plausible alternative futures.

In scenario 1, for 2020 we used the status-quo concentrations of COD in each sector. Sewage treatment facilities will be constructed to reduce the amount of pollutants discharged from the municipal, secondary, and tertiary sectors in Qinzhou. Therefore, the primary sewage discharge standard (GB 18918-200; Ministry of Housing and Urban-Rural Development of the People's Republic of China, 2002) was used to determine the COD concentrations for the municipal and tertiary sectors in 2030 i.e., 50 g/m³.

In scenario 2, for 2020 we used the secondary sewage discharge standard (GB 18918-200; Ministry of Housing and Urban-Rural Development of the People's Republic of China, 2002) to determine COD concentrations i.e., 100 g/m³. By 2030, with the gradual improvement of sewage treatment facilities in Qinzhou, the COD concentrations of the municipal, secondary, and tertiary sectors align with the primary discharge standard. As the total amount of COD discharge from the agricultural sector tends to be stable, the COD concentrations of the agricultural sector in the two scenarios are taken as 19.63 g/m³ in 2020 and 2030.

Since groundwater only supplies the municipal sector in Qinzhou and all of the reuse water is generated from industrial water treatment, reuse water can only be allocated to the secondary sector. Because the water supply volume from these two water sources is small, different domestic water sources will not be distinguished to simplify the model solution. In other words, the study only considered the water supply sequence coefficient between domestic and CBDP water sources. Water allocated to each sector from the two water sources in each sub-area was used as the model decision variables i.e., X₁, X₂, …, X₂₅, …, X₃₇.

The function gamultiobj based on the NSGA-II algorithm was employed to solve the optimization model. Genetic parameters were set as follows: the Pareto Fraction is 0.3, the population size is 200, there are 10,000 generations, StallGenLimit is 10,000, the crossover fraction is 0.8, and TolFun is 1 × 10⁻¹⁰⁰. The result of the model operation is the Pareto solution to water allocation for the two scenarios under a guaranteed rate of p = 75% in 2020 and 2030. Then, a set of solutions is selected that best meet the relevant socio-economic and environmental objectives.

The target results concerning the optimal allocation of water resources in the two scenarios for the planning years 2020 and 2030 in Qinzhou are shown in Table 4. If COD concentrations are not reduced, the water shortage in Qinzhou in 2020 and 2030 will amount to 29,278.6 × 10⁴ m³ and 58,612.8 × 10⁴m³, respectively, and total GDP will be 1,434.1 × 10⁸ CHY and 2,326 × 10⁸ CHY, respectively. The total amount of COD pollutants discharged will be 44,275.8 tons and 44,211.4 tons in 2020 and 2030, respectively, which reaches the upper limit of the TAOAPD for COD in both planning years. After reducing the COD concentration of pollutants, the water shortage in Qinzhou decreases to 29,064.9 × 10⁴ m³ and 35,886.4 × 10⁴ m³, in 2020 and 2030, respectively; the total GDP increases to 1,509.9 × 10⁸ CHY and 4,194.1 × 10⁸ CHY, respectively; and the total amount of COD pollutants discharged reduces to 37,892.2 tons and 40,947.3 tons, respectively.

The water volume allocation results for 2020 are shown in Figure 3. In scenario 1, the overall total allocated volume in the region is 134,953.61 × 10⁴ m³, and the disaggregated water volume allocations in Qinnan, Qinbei, Qingang, Lingshan, and Pubei are 27,283.82 × 10⁴m³, 25,989.7 × 10⁴ m³, 15,436.84 × 10⁴ m³, 44,091.08 × 10⁴ m³, and 22,152.17 × 10⁴ m³, respectively. As the total amount of COD generated by water consumption in each sector is 44,275.8 tons, and it just reaches the upper limit of the TAOAPD for COD in 2020, to ensure the total amount of COD does not exceed the upper limit, Qinzhou has 231.8 × 10⁴ m³ volume of water which cannot be used. In Qinnan, the allocated volume not only meets the water demand itself, but surplus water can even be distributed to the other four water scarce sub-areas at volumes of 2,149.51 × 10⁴ m³, 7,660.72 × 10⁴ m³, 2,114.98 × 10⁴ m³, and 356.93 × 10⁴ m³, respectively.

In scenario 2, the total allocated water volume is 135,167.4 × 10⁴ m³, all of which is utilized. The water volume allocation in the five sub-areas is 27,283.82 × 10⁴m³, 24,249.54 × 10⁴ m³, 15,569.51 × 10⁴ m³, 44,553.96 × 10⁴ m³, and 23,510.57 × 10⁴ m³, respectively. In Qinnan, the allocated volume still meets the water demand, and surplus water is distributed to the other four water scarce sub-areas at volumes of 409.34 × 10⁴ m³, 7,793.41 × 10⁴m³, 2,577.86 × 10⁴ m³, and 1,715.37 × 10⁴ m³, respectively.

The water volume allocation results for 2030 are shown in Figure 4. In scenario 1, the total allocated volume is 146,774.08 × 10⁴ m³, and the volumes allocated in Qinnan, Qinbei, Qingang, Lingshan, and Pubei are 31,984.94 × 10⁴, 30,079.29 × 10⁴, 12,880.48 × 10⁴, 44,464.76 × 10⁴, and 28,454.67 × 10⁴ m³, respectively. Due to the COD concentration of pollutants not being reduced, the total amount of COD generated by all sectors just using domestic water sources will have reached the upper limit of the TAOAPD for COD in 2030, so that water cannot be sourced from the Yujiang CBDP. At the same time, 6,435.43 × 10⁴ m³ of domestically sourced water cannot be used. Qinnan can distribute its surplus water to the other four water scarce sub-areas at volumes of 301.12 × 10⁴, 1,848.43 × 10⁴, 215.03 × 10⁴, and 248.41 × 10⁴ m³, respectively.

In scenario 2, the allocated volume by domestic water and Yujiang CBDP is 153,209.51 × 10⁴ and 16,290.49 × 10⁴, respectively. The domestic water volume allocation in the five sub-areas is 31,984 × 10⁴, 29,111.22 × 10⁴, 15,505.07 × 10⁴, 44,310.8 × 10⁴, and 32,387.6 × 10⁴ m³, respectively, and the Yujiang CBDP supplies water in the three of these sub-areas – Qinbei, Qingang, and Lingshan, at volumes of 8,917.59 × 10⁴, 6,179.18 × 10⁴, and 1,207.08 × 10⁴m³, respectively(shown in Figure 5). Due to the total allocated volume in Qinzhou being 169,500 × 10⁴ m³, which will have met the upper limit of TWURL in 2030, there is 15,999.51 × 10⁴ m³ of Yujiang CBDP water that cannot be used. Qinnan can distribute its surplus water to the other four water scarce sub-areas at volumes of 423.12 × 10⁴, 4,473.02 × 10⁴, 61.07 × 10⁴, and 4,181.34 × 10⁴ m³, respectively.

Assuming the COD concentration of pollutants is not reduced, the water shortage rates in each water use sector in 2020 and 2030 are shown in Figures 6 and 7, respectively. The excessive COD concentrations in the municipal sector, and no benefit from water use, will directly cause water scarcity; therefore, the water shortage rates in this sector in Qinbei, Qingang, Lingshan, and Pubei will be 2.38%, 0.24%, 2.3%, and 0.95%, respectively, in 2020, and 3.49%, 3.71%, 3.72%, and 0.58%, respectively, in 2030. The water shortage rates in the tertiary sector in the four water scarce sub-areas will be 18.92%, 14.02%, 6.25%, and 4.55%, respectively, in 2020, and 71.36%, 78.59%, 75.4%, and 79.36%, respectively, in 2030. Although the COD concentrations produced by the tertiary sector are the same as those from the municipal sector, there is no water supply guarantee rate, resulting in a high water shortage rate in that sector.

Due to the rapid growth of water consumption in the secondary sector in the two planning years, and the lower weight set by the model, the water shortage rate of the sector is also large: 12.13%, 14.02%, 6.25%, and 4.55%, respectively, in 2020, and 47.87%, 70.56%, 76.72%, and 33.56%, respectively, in 2030. Moreover, because of the lower COD concentrations discharged by the secondary sector, the water shortage rate of the sector is significantly smaller than that of the tertiary industry.

In both 2020 and 2030, the water shortage rate of the ecology sector will be 0. This is because water consumption in this sector does not lead to COD pollutant discharges. Therefore, to meet the overall objectives of model, and the TAOAPD for COD, the volume allocated to other sectors, especially the tertiary sector, will be largely transferred to the ecology sector.

The huge amount of water used in the agricultural sector (which is greater than any other sector in the region) coupled with the lower economic benefits of water use, and the minimum weight given by the model result in a large water volume shortage in this sector. The water shortage rates in the agricultural sector in the four water scarce sub-areas will be 27.98%, 67.89%, 34.27%, and 25.48%, respectively, in 2020, and 23.11%, 34.7%, 22.6%, and 11.53%, respectively, in 2030.

When the COD concentration of pollutants is reduced, the water shortage rates in each water use sector in Qinzhou in 2020 and 2030 are shown in Figures 8 and 9, respectively. Domestic water sources in Qinzhou in 2020 and 2030 can be fully utilized. Although part of the volume from the Yujiang CBDP source cannot be used in 2030, the water shortage in Qinzhou in the two planning years will be significantly decreased. The water shortage rates in the municipal sector in the four water scarce sub-areas will be 1.77%, 0.58%, 4.15%, and 3.33%, respectively, in 2020, which has a slight upward trend compared with scenario 1; because the Yujiang CBDP will operate in 2030, only two sub-areas – Qingang and Pubei – will be short of water, at rates of 0.26% and 0.88%, respectively.

Since using water in the secondary and tertiary sectors can produce large economic benefits and small COD concentrations, water volumes tend to be allocated to these two sectors. Therefore, they can meet their water demands in 2020. Although the secondary sector will still meet demand in 2030, a 1.36% water shortage rate occurs in the tertiary sector in Pubei in that year because this sub-area cannot use the CBDP water sources.

As water use in the ecology sector does not produce marked economic benefits and the sector weight is too low, the volume allocated to it originally will be largely transferred to other sectors, resulting in a large water shortage rate in the sector. The water shortage rates in the ecology sector in the four water scarce sub-areas will be 61.31%, 78.63%, 92.11%, and 36.87%, respectively, in 2020, and 25.73%, 54.58%, 22.77%, and 3.06%, respectively, in 2030.

The agricultural sector benefits from increased water volume allocation compared to scenario 1, so the water shortage rates will be significantly reduced, being 37.69%, 0.03%, 32.07%, and 16.45%, respectively, in 2020, and 15.88%, 44.22%, and 22.95%, respectively, in Qinbei, Lingshan, and Pubei in 2030.

To address the issue of regional water resource allocation under CMSWRM, the paper presents a systematic allocation framework considering TRL constraints to support CMSWRM. A multi-objective linear programming model is configured in MATLAB to allocate domestic and CBDP water across sectors in Qinzhou. The gamultiobj function based on the NSGA-II algorithm was used to solve the model. It can be discerned from the solution that when the COD concentrations in each sector are not reduced, a proportion of the domestic water sources cannot be utilized, both in 2020 and 2030. Moreover, Yujiang CBDP projects were also unable to operate, which further aggravates the contradiction between supply and demand in Qinzhou owing to the TAOAPD for COD. However, if the COD concentrations in each sector are reduced, Qinzhou can obtain comprehensive benefits, in which water shortages in the region will amount to 29,064.9 × 10⁴ and 35,886.4 × 10⁴ m³ in 2020 and 2030, respectively; total GDP will be 1,509.9 × 10⁸ CHY and 4,194.1 × 10⁸ CHY, respectively; and the total amount of COD pollutants discharged will be 37,892.2 and 40,947.3 tons, respectively.

It is necessary to speed up the improvement of sewage treatment facilities in Qinzhou to reduce the concentration of pollutants discharged from various sectors for the sake of solving the contradiction between supply and demand in Qinzhou under CMSWRM in the two planning years. While the secondary and agricultural sectors have already met the WUERL, they still experience water shortages. Therefore, water use efficiency in Qinzhou should be improved by increasing water conservation intensity in each sector, as well as interventions to better optimize industrial structure.

As agriculture consumes more water than any other sector, it is a particularly critical focus from management and sustainability perspectives. Thus the optimization of crop planting structures in irrigation areas represents fruitful terrain for future research, pursuant of increasing water use efficiency and decreasing total water consumption in Qinzhou. Finally, it is problematic and erroneous to overly rely on GDP as a comprehensive benefit indicator. Future research should seek to design and operationalize a composite economic benefit index which accounts for a broader array of pertinent metrics covering health, wellbeing, water security, and economic stability as well as accounting for the non-market economic values of ecosystems as estimated by different expressed and revealed preference techniques.

This research was supported by National Natural Science Foundation of China (Grant Nos. 51469002 and 51669003).