# Network Analysis for a Better Water Use Configuration in the Baiyangdian Basin, China

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Study Area

^{2}(39.4°N–40.4°N, 113.39°E–116.11°E). Its climate is characterized by continental monsoons and the average annual rainfall is 556 mm. The name of the basin comes from the largest Baiyangdian Lake of the northern China. Due to its important ecological and environmental role in the region, the lake was described as the “kidney” of the northern China. There are in total 3 municipalities (Baoding, Gaobeidian and Dingzhou) and 20 countries (Fuping, Quyang, Anguo, Boye, Tang, Wangdou, Shunping, Mancheng, Qingyuan, Li, Gaoyang, Anxin, Xiong, Rongcheng, Xushui, Laiyuan, Yi, Laishui, Dingxian and Zhuozhou) in the basin (Figure 1).

#### 2.2. Network Analysis for the Water Use System

#### 2.2.1. Network Model Description

**Figure 2.**The water use system (WUS) network model (1-Aquatic systems; 2-Primary industry; 3-Secondary industry; 4-Tertiary industry; 5-Resident consumption).

_{k}and y

_{k}represent boundary inputs (m

^{3}·year

^{−1}) and boundary output (m

^{3}·year

^{−1}) of the kth compartment, respectively. It is assumed that each component withdraws water from aquatic systems for consumption or production, and water will transfer between different sectors due to physical and virtual water trade transactions. The network model incorporates social-economic-ecological sectors into a whole system. The function of the system can be evaluated with ENA with a holistic perspective.

#### 2.2.2. Network Analysis Methods

No. | Name | Symbol | Algorithms |
---|---|---|---|

1 | Total System Throughput | TSTP | $={\displaystyle \sum _{i=1}^{n+2}{\displaystyle \sum _{j=1}^{n+2}{T}_{ij}}}$ |

2 | Average Mutual Information | AMI | $={\displaystyle \sum _{i,j}\frac{{T}_{ij}}{{T}_{\cdot \cdot}}}{\text{log}}_{2}\left[\frac{{T}_{ij}{T}_{\cdot \cdot}}{{T}_{i\cdot}{T}_{\cdot j}}\right]$ |

3 | Ascendency | A | $={\displaystyle \sum _{ij}{T}_{ij}}{\text{log}}_{2}\left[\frac{{T}_{ij}{T}_{\cdot \cdot}}{{T}_{i\cdot}{T}_{\cdot j}}\right]$ |

4 | Import Ascendency | A_{0} | $={\displaystyle \sum _{j=1}^{n}{T}_{n+1,j}}{\text{log}}_{2}\left[\frac{{T}_{n+1,j}{T}_{\cdot \cdot}}{{T}_{n+1\cdot}{T}_{\cdot j}}\right]$ |

5 | Internal Ascendency | A_{i} | $={\displaystyle \sum _{ij=1}^{n}{T}_{ij}}{\text{log}}_{2}\left[\frac{{T}_{ij}{T}_{\cdot \cdot}}{{T}_{i\cdot}{T}_{\cdot j}}\right]$ |

6 | Export Ascendency | A_{e} | $={\displaystyle \sum _{j=1}^{n}{T}_{j,n+2}}{\text{log}}_{2}\left[\frac{{T}_{j,n+2}{T}_{\cdot \cdot}}{{T}_{\cdot n+2}{T}_{j\cdot}}\right]$ |

7 | Development Capacity | C | $=-{\displaystyle \sum _{ij}{T}_{ij}}{\text{log}}_{2}\left[\frac{{T}_{ij}}{{T}_{\cdot \cdot}}\right]$ |

8 | Ratio ascendency | A/C, A_{0}/A, A_{i}/A, A_{e}/A |

_{ij}means total amount of flow from compartment j to compartment i.

_{0}, A

_{i}and A

_{e}) and ratio-based indicators (A/C, A

_{0}/A, A

_{i}/A and A

_{e}/A). Whole system indicators were used to describe the whole attribute of the WUS. TSTP reflects the system activity of the WUS and AMI represents the organization inherent in the WUS. Ascendency is the production of TSTP and AMI that quantifies both the level of system activity and the degree of the organization of the WUS. Capacity is functions as a mathematical upper bound on the ascendency. It represents the scope of the system for further development. A/C represents realized Ascendency under specific system structure. Component system indicators exhibit the characteristics of boundary input, output and interflows. For instance, A

_{0}may be used to describe the water withdrawal of each sector, and A

_{e}is associated with boundary output caused by each sector. The internal measures (A

_{i}) are generated by interflows, which affected mostly by water transfers among different sectors.

#### 2.3. Scenarios Analysis

_{i}− WUS

_{0})/WUS

_{0}× 100%.

No. | WS | Modification | Scenario |
---|---|---|---|

1 | WS_{1} | Increasing boundary input by 10% | Precipitation increase |

2 | WS_{2} | Decreasing boundary input by 10% | Precipitation decrease |

3 | WS_{3} | Increasing boundary output by 10% | Lower water use efficient |

4 | WS_{4} | Decreasing boundary output by 10% | Higher water use efficient |

5 | WS_{5} | Increasing interflows among component 2–5 by 10% | More water exchanges |

6 | WS_{6} | Decreasing interflows among component 2–5 by 10% | Less water exchanges |

7 | WS_{7} | Adding new pathways from 5–2, 5–3 and 5–4 | New water exchange mode |

8 | WS_{8} | Reducing pathways among component 2, 3 and 4 | Less water exchanges |

#### 2.4. Data Sources

^{3}·ton

^{−1}) of the commodity, P represents the sum of the volume of a single products’ production (ton) and VW is the virtual water quantity. The VWC of a specific crop or animal is taken as the raw material of the processed product [33]. Footprints of industrial sector were calculated with an average VWC per dollar added value in the industrial sector for simplicity [34]. Footprints of services sector were acquired by multiplying the VWC with the services output of 2008–2013 and the VWC of tertiary industry was provided by Zhao et al. (2009) [35].

## 3. Results and Discussion

#### 3.1. Fluctuations of Network Indicators from 2008–2013

_{0}, A

_{i}and A

_{e}) and ratio-based indicators (A/C, A

_{0}/A, A

_{i}/A and A

_{e}/A).

_{0}shares the largest growth with an annual growth rate of 14.6% and A

_{e}gets the least growth with an annual growth rate of 6.3%. The above results indicate that boundary outputs contribute more to the increases of system ascendency, which is corresponding to the increasing water withdrawals from aquatic systems. The above fact can be testified by the ratio-based indicators A

_{0}/A, A

_{i}/A and A

_{e}/A. The annual decrease rate of A

_{i}/A and A

_{e}/A are 0.9% and 2.3%, respectively, while the annual growth rate of A

_{0}/A reaches 2.7%.

#### 3.2. Results of Scenario Analysis

_{i}decreased most (4.6%) in all detected indicators. Decreased boundary output releases more interflows among different sectors of the WUS, resulting in a sharply decreased A

_{i}(7.5%) under scenario IV. Overall, indicator A

_{i}is robust most to the fluctuation of boundary outputs. In the same vein, increasing or decreasing the interflows will directly impacts the values of A

_{i}, and in a fierier way compared with that of scenario III and IV. An interesting phenomenon is the system organization measured by A and AMI became worse after adding additional links. For example, the percent change of TSTP is about −0.3% while A and AMI reduced more than 4.5%. Additions of new pathways may increase the ambiguity to the network. Oppositely, reducing inter-component-link will give rise to increases to all indicators except for index C.

#### 3.3. Suggested Water Use Strategies for the WUS

Industry | Measures | Goal Function |
---|---|---|

Aquatic systems | Environmental and ecological restoration | Higher TSTP, less damage to Aquatic systems |

Primary Industry | Using water-saving technology, reducing evapotranspiration and infiltration, planting low-water-consumption crop | Lower A_{e} and higher A_{i} |

Secondary Industry | Increasing water recycling rate both inside and outside the industry | Lower A_{e} and higher A_{i} and A/C |

Tertiary Industry | Water Saving and reclaimed water using | Lower A_{0} and A_{e} |

#### 3.4. Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Mao, X.; Yuan, D.; Wei, X.; Chen, Q.; Yan, C.; He, L.
Network Analysis for a Better Water Use Configuration in the Baiyangdian Basin, China. *Sustainability* **2015**, *7*, 1730-1741.
https://doi.org/10.3390/su7021730

**AMA Style**

Mao X, Yuan D, Wei X, Chen Q, Yan C, He L.
Network Analysis for a Better Water Use Configuration in the Baiyangdian Basin, China. *Sustainability*. 2015; 7(2):1730-1741.
https://doi.org/10.3390/su7021730

**Chicago/Turabian Style**

Mao, Xufeng, Donghai Yuan, Xiaoyan Wei, Qiong Chen, Chenling Yan, and Liansheng He.
2015. "Network Analysis for a Better Water Use Configuration in the Baiyangdian Basin, China" *Sustainability* 7, no. 2: 1730-1741.
https://doi.org/10.3390/su7021730