# A New Perspective to Explore the Hydraulic Connectivity of Karst Aquifer System in Jinan Spring Catchment, China

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area and Hydrogeological Conditions

^{2}. The southern edge of Jinan is close to Mount Tai, and the northern boundary is the Yellow River. Jinan is located in the intersection between the north-west alluvial plains and the south-central low mountains and hills in Shandong Province. Thus, Jinan’s terrain distribution has characteristics of high in the south and low in the north. There are many springs in Jinan, thereby leading to its nickname of “Spring City” [53,54]. The main recharge source of karst groundwater in Jinan is rainfall. The average annual rainfall is 647.9 mm, and rainfall is concentrated in June to September each year, which accounts for 70% of the total annual rainfall [55]. Jinan has many springs because of its unique topographic features and geological structure. The karst aquifer system of Jinan is a gentle monoclinic structure with an elevation difference of over 500 m from south to north. This topography is conducive to the surface water and groundwater in southern sections flowing into the northern urban areas [56]. The abundant karst groundwater in Mount Tai flows into the Jinan urban area from south to north, and a large amount of karst groundwater is blocked by impermeable Mesozoic igneous rocks in Northern Jinan and is collected in the contact zone. Under the influence of strong water pressure, karst groundwater flows out forming typical ascending springs through many underground pores, caves, and fractures. Then, many springs outflow perennially in the Jinan urban area and ultimately form Jinan spring groups (Figure 1 and Figure 2). Among many springs in Jinan, Baotu Spring and Black Tiger Spring are the most well-known. However, in recent years, the free outflow rate of both springs has been significantly reduced, and karst groundwater quality deterioration has occurred in the Jinan spring groups due to the over-exploitation of karst groundwater and rapid urbanization [57,58]. Meanwhile, the karst groundwater table in Jinan spring groups has progressively lowered, and some springs have even dried up. In Baotu Spring, the drying-up phenomenon appeared in 1972–2002 (Figure 3). After 2002, a series of spring preservation measures were implemented, which narrowly maintained the continuous outflow of spring water, whereas the outflow rate of springs remained relatively small. Therefore, a potential drying-up crisis occurred during the dry months (from May to June) each year.

#### 2.2. Analysis of Fluctuant Law and Influence Factor in Karst Groundwater Table

## 3. Methods

#### 3.1. Basic Thinking in the Improved Grey Amplitude Relation Model

#### 3.2. Development of the Improved Grey Amplitude Relation Model

#### 3.2.1. Data Preprocessing

#### 3.2.2. Creation of the Polyline

#### 3.2.3. Calculation of the Fluctuation Amplitude Values

#### 3.2.4. Calculation of the Water Table Fluctuation Relation Coefficient

#### 3.2.5. Calculation of WTFRD

#### 3.2.6. Property of WTFRD

- (i)
- Water table fluctuation relation coefficient (${R}_{1,j}(i)$) and WTFRD (${\gamma}_{1,j}$) are only subjected to magnitude and direction of the fluctuations amplitude, which are unaffected by other factors, such as sequence abscissa $X$. They are highly suited to investigate the relationship between two sequences with obvious fluctuation trends in complex systems.
- (ii)
- The existence of a complete positive correlation between two waves (${R}_{1,j}(i)=1$) when the magnitude and direction of the amplitude between the two waves are equal.$$\begin{array}{c}{R}_{1,j}(i)=\mathrm{sgn}({A}_{1}(i,i+1),{A}_{j}(i,i+1))\ast \frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|+\left|\left|{A}_{1}(i,i+1)\right|-\left|{A}_{j}(i,i+1)\right|\right|}\\ =\frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|+\left|\left|{A}_{1}(i,i+1)\right|-\left|{A}_{j}(i,i+1)\right|\right|}\\ =\frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}\\ =1\text{}\end{array}$$
- (iii)
- A complete negative correlation occurs between two waves (${R}_{1,j}(i)=-1$) when the equal magnitude and the opposite direction occur within amplitudes.$$\begin{array}{c}{R}_{1,j}(i)=\mathrm{sgn}({A}_{1}(i,i+1),{A}_{j}(i,i+1))\ast \frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|+\left|\left|{A}_{1}(i,i+1)\right|-\left|{A}_{j}(i,i+1)\right|\right|}\\ =(-1)*\frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|+\left|\left|{A}_{1}(i,i+1)\right|-\left|{A}_{j}(i,i+1)\right|\right|}\\ =(-1)*\frac{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}{1+\left|{A}_{1}(i,i+1)\right|+\left|{A}_{j}(i,i+1)\right|}\\ =-1\text{}\end{array}$$
- (iv)
- If and only if ${A}_{1}(i,i+1)={A}_{j}(i,i+1)$, then ${R}_{1,j}(i)=\pm 1$; and ${A}_{1}(i,i+1)={A}_{j}(i,i+1)=0$, ${\gamma}_{1,j}=1$. Furthermore, the numerator of ${R}_{1,j}(i)$ is not greater than the denominator, that is, $(1+|{A}_{1}(i,i+1)|+|{A}_{j}(i,i+1)|\le 1+|{A}_{1}(i,i+1)|+|{A}_{j}(i,i+1)|+||{A}_{1}(i,i+1)|-|{A}_{j}(i,i+1)||)$; thus, $-1\le {R}_{1,j}(i)\le 1$ and $-1\le {\gamma}_{1,j}\le 1$.
- (v)
- A high absolute value of WTFRD indicates a strong correlation. If $\left|{\gamma}_{0,1}\right|>\left|{\gamma}_{0,j}\right|$, then the correlation between ${L}_{0}$ and ${L}_{1}$ is stronger than that of ${L}_{0}$ and ${L}_{j}$.

#### 3.2.7. Grading WTFRD

## 4. Results

#### 4.1. Analysis of Whole-Year WTFRD

#### 4.2. Analysis of WTFRD in Different Periods

#### 4.2.1. Rainfall and Karst Groundwater Recharge during Different Periods

#### 4.2.2. WTFRD Analysis from April to July Each Year

#### 4.2.3. WTFRD Analysis from August to November Each Year

^{4}m

^{3}is the maximal over the past four years) that reduces the annual average WTFRD during this period. Accordingly, artificial recharge is the main influence factor for piecewise WTFRD from August to November, followed by rainfall and winter wheat irrigation.

#### 4.2.4. WTFRD Analysis from December to March of Next Year

^{4}m

^{3}) from December 2016 to March of next year is larger than that of other years (Table 5). The annual average WTFRD from December to March of next year is reduced by the artificial recharge due to the hysteretic nature of karst groundwater movement. Hence, the piecewise WTFRD from December to March of next year is mainly affected by artificial recharge, while the influence of rainfall and exploitation on piecewise WTFRD is smaller.

#### 4.3. Analysis of Total WTFRD

#### 4.4. Case Verification

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location map of Jinan spring catchment shows 1—Cuima Village, 2—Yinjialin Village, 3—Dujiamiao Village, 4—Zhuzhuang Village, 5—Nanbali Village, 6—Kuangli Village, 7—Baotu Spring, 8—Black Tiger Spring.

**Figure 2.**Geological longitudinal section of Jinan spring catchment shows 1—Soil (Q

_{4}), 2—Dolomitic limestone (O

_{1}), 3—Limestone and shale (€

_{3}), 4—Oolitic limestone (€

_{2}), 5—Limestone and shale (€

_{1}), 6—Flow direction, 7—Granitic gneiss (Ar

_{3}), 8—Diorite (M

_{Z}), 9—Fault, 10—Jinan spring groups; (Q

_{4}is Quaternary sediment, O

_{1}is Lower Ordovician, €

_{1}is Lower Cambrian, €

_{2}is Middle Cambrian, €

_{3}is Upper Cambrian, Ar

_{3}is Archean, M

_{Z}is Mesozoic).

Statistics | Baoto Spring | Black Tiger Spring | Dujiamiao Village | Zhuzhuang Village | Nanbali Village | Kuangli Village | |
---|---|---|---|---|---|---|---|

Missing value | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

Mean | 28.141 | 28.084 | 29.114 | 29.289 | 29.043 | 28.885 | |

Median | 28.050 | 27.989 | 29.157 | 29.305 | 28.955 | 28.800 | |

Mode | 27.989 ^{a} | 27.367 ^{a} | 27.563 ^{a} | 28.108 ^{a} | 27.553 ^{a} | 27.385 ^{a} | |

Minimum | 27.427 | 27.367 | 27.563 | 28.108 | 27.553 | 27.385 | |

Maximum | 29.185 | 29.211 | 30.859 | 30.692 | 30.745 | 30.590 | |

Range | 1.758 | 1.844 | 3.296 | 2.584 | 3.192 | 3.205 | |

Standard error of Mean | 0.063 | 0.065 | 0.126 | 0.096 | 0.113 | 0.116 | |

Variance | 0.184 | 0.199 | 0.744 | 0.430 | 0.600 | 0.627 | |

Standard deviation | 0.429 | 0.446 | 0.863 | 0.656 | 0.775 | 0.792 | |

Skewness | 0.523 | 0.657 | 0.079 | 0.134 | 0.231 | 0.165 | |

Standard error of Skewness | 0.347 | 0.347 | 0.347 | 0.347 | 0.347 | 0.347 | |

Kurtosis | 0.043 | 0.189 | −0.680 | −0.522 | −0.289 | −0.449 | |

Standard error of Kurtosis | 0.681 | 0.681 | 0.681 | 0.681 | 0.681 | 0.681 | |

Percentiles | 10 | 27.488 | 27.429 | 27.769 | 28.411 | 27.958 | 27.819 |

50 | 28.050 | 27.989 | 29.157 | 29.305 | 28.955 | 28.800 | |

90 | 28.809 | 28.778 | 30.349 | 30.220 | 30.251 | 30.038 |

^{a}indicates the minimum value of the Mode when multiple Modes present.

Year | Total Rainfall in Jinan (mm) | Abundance or Shortage of Rainfall | Artificial Recharge Quantity in Western Jinan (10^{4} m^{3}) |
---|---|---|---|

2014 | 444 | Extremely dry year | 2439.3 |

2015 | 572.8 | Dry year | 2608.4 |

2016 | 710.8 | Normal precipitation year | 3372.85 |

2017 | 520.5 | Dry year | 3024.06 |

WTFRD | Grade Division | Evaluative Meaning |
---|---|---|

0–0.3 | Low relation degree | Study sequence deviates greatly from the reference sequence |

0.3–0.6 | Medium relation degree | Certain deviation exists between study sequence and reference sequence |

0.6–0.8 | Relatively strong relation degree | Study sequence is close to the reference sequence |

0.8–1.0 | High relation degree | Study sequence is extremely close to the reference sequence |

Site | Dujiamiao Village | Zhuzhuang Village | Nanbali Village | Kuangli Village | Whole-Year WTFRD |
---|---|---|---|---|---|

Baotu Spring | 0.710 | 0.694 | 0.673 | 0.711 | 0.697 |

Black Tiger Spring | 0.669 | 0.650 | 0.675 | 0.713 | 0.677 |

Year | Rainfall in Jinan (mm) | Artificial Recharge Quantity in Western Jinan (10^{4} m^{3}) | Exploitation in Western Jinan | ||||
---|---|---|---|---|---|---|---|

April toJuly | August to November | December to March | April to July | August to November | December to March | ||

2014 | 153.6 | 290.4 | 0 | 1310 | 977 | 32.6 | Mainly concentrated in April to July and October to November each year (the specific data were not announced) |

2015 | 340.2 | 232.6 | 0 | 1800.2 | 701 | 49.2 | |

2016 | 358 | 352.8 | 0 | 2001.1 | 1220.09 | 209.67 | |

2017 | 186.9 | 330.6 | 4.5 | 2118.7 | 678.46 | 104.53 |

Site | Year | Dujiamiao Village | Zhuzhuang Village | Nanbali Village | Kuangli Village | Annual Average WTFRD | Piecewise WTFRD |
---|---|---|---|---|---|---|---|

Baotu Spring | 2014 | 0.393 | 0.364 | 0.088 | 0.098 | 0.236 | 0.419 |

2015 | 0.641 | 0.664 | 0.918 | 0.661 | 0.721 | ||

2016 | 0.929 | 0.936 | 0.121 | 0.386 | 0.593 | ||

2017 | 0.129 | 0.161 | 0.130 | 0.085 | 0.126 | ||

Black Tiger Spring | 2014 | 0.112 | 0.336 | 0.091 | 0.096 | 0.159 | 0.388 |

2015 | 0.639 | 0.596 | 0.917 | 0.659 | 0.703 | ||

2016 | 0.924 | 0.845 | 0.124 | 0.382 | 0.569 | ||

2017 | 0.130 | 0.143 | 0.130 | 0.087 | 0.122 |

Site | Year | Dujiamiao Village | Zhuzhuang Village | Nanbali Village | Kuangli Village | Annual Average WTFRD | Piecewise WTFRD |
---|---|---|---|---|---|---|---|

Baotu Spring | 2014 | 0.677 | 0.968 | 0.685 | 0.948 | 0.820 | 0.820 |

2015 | 0.917 | 0.937 | 0.918 | 0.926 | 0.925 | ||

2016 | 0.661 | 0.654 | 0.641 | 0.646 | 0.650 | ||

2017 | 0.960 | 0.673 | 0.959 | 0.956 | 0.887 | ||

Black Tiger Spring | 2014 | 0.680 | 0.618 | 0.689 | 0.952 | 0.735 | 0.772 |

2015 | 0.915 | 0.853 | 0.917 | 0.925 | 0.902 | ||

2016 | 0.668 | 0.588 | 0.645 | 0.650 | 0.638 | ||

2017 | 0.680 | 0.663 | 0.960 | 0.957 | 0.815 |

Site | Year | Dujiamiao Village | Zhuzhuang Village | Nanbali Village | Kuangli Village | Annual Average WTFRD | Piecewise WTFRD |
---|---|---|---|---|---|---|---|

Baotu Spring | 2014 | 0.949 | 0.943 | 0.938 | 0.940 | 0.943 | 0.846 |

2015 | 0.623 | 0.919 | 0.933 | 0.953 | 0.857 | ||

2016 | 0.624 | 0.909 | 0.648 | 0.932 | 0.778 | ||

2017 | 0.662 | 0.938 | 0.946 | 0.678 | 0.806 | ||

Black Tiger Spring | 2014 | 0.957 | 0.934 | 0.951 | 0.959 | 0.950 | 0.861 |

2015 | 0.903 | 0.899 | 0.930 | 0.950 | 0.920 | ||

2016 | 0.626 | 0.898 | 0.646 | 0.931 | 0.775 | ||

2017 | 0.666 | 0.900 | 0.949 | 0.681 | 0.799 |

Period | Influence Factors of WTFRD | Major Factor | Total WTFRD | Grade Division |
---|---|---|---|---|

April to July | Rainfall, exploitation, artificial recharge | Exploitation | 0.404 | Medium relation degree |

August to November | Rainfall, exploitation, artificial recharge | Artificial recharge | 0.796 | Relatively strong relation degree |

December to March of next year | Rainfall, artificial recharge | Artificial recharge | 0.854 | High relation degree |

Entire year | Rainfall, exploitation, artificial recharge | Exploitation | 0.687 | Relatively strong relation degree |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Wang, W.; Qu, S.; Huang, Q.; Liu, S.; Xu, Q.; Ni, L.
A New Perspective to Explore the Hydraulic Connectivity of Karst Aquifer System in Jinan Spring Catchment, China. *Water* **2018**, *10*, 1368.
https://doi.org/10.3390/w10101368

**AMA Style**

Zhang Z, Wang W, Qu S, Huang Q, Liu S, Xu Q, Ni L.
A New Perspective to Explore the Hydraulic Connectivity of Karst Aquifer System in Jinan Spring Catchment, China. *Water*. 2018; 10(10):1368.
https://doi.org/10.3390/w10101368

**Chicago/Turabian Style**

Zhang, Zhengxian, Weiping Wang, Shisong Qu, Qiang Huang, Shuai Liu, Qiaoyi Xu, and Ludong Ni.
2018. "A New Perspective to Explore the Hydraulic Connectivity of Karst Aquifer System in Jinan Spring Catchment, China" *Water* 10, no. 10: 1368.
https://doi.org/10.3390/w10101368