# Shallow Groundwater Responses to Rainfall Based on Correlation and Spectral Analyses in the Heilonggang Region, China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site

^{2}. The terrain in this region is gentle and inclines slightly from southwest to northeast with a topographic slope of 0.2~0.1‰. From west to east, the geomorphic type is dominated by the mountain alluvial-diluvial plain, the central alluvial-lacustrine plain and the coastal plain, respectively. Accordingly, from west to east, sediments change from gravel in front of the mountain, to medium coarse and medium fine sand in the middle, then to fine sand in the coastal area.

#### 2.2. Datasets

#### 2.3. Mann–Kendall Trend Analysis

#### 2.4. Auto-Correlation and Cross-Correlation Functions

_{xx}(k) is expressed as [12]:

_{x}and σ

_{y}are the standard deviations.

_{xy}values between rainfall and GWLs are computed, and the corresponding response time is identified. Then, a time series of response times is obtained for different windows. In this study, the window length is 6 months, and the sliding interval is 1.5 months. Note that the correlation coefficients should be not lower than the standard error of ~$2/\sqrt{N}$, where N is the sample size, and “2” is the critical value for the 0.95 probability of the normal distribution. That is, values for which the r

_{xy}peak was not significant at a 95% confidence level were left out.

#### 2.5. Wavelet Transform

_{t}(rainfall) at frequency scale s; and ${W}_{t}^{Y\ast}\left(s\right)$ is the complex conjugate of wavelet transform ${W}_{t}^{Y}\left(s\right)$ for y

_{t}(GWLs). The XWT can be represented using polar coordinates:

_{t}(s) is the phase angle, which denotes the delay between the two series at time t and scale s.

_{t}and y

_{t}; and Z

_{ν}(p) is the confidence level associated with the probability p, and $p={\int}_{0}^{{Z}_{\nu}\left(p\right)}{f}_{\nu}\left(z\right)dz$. The 5% significance level is determined using Z

_{2}(95%) = 3.999.

## 3. Results

#### 3.1. Observed Time Series and Trend Analysis

#### 3.2. Auto-Correlation and Cross-Correlation Analyses

^{−2}month

^{−1}at W2 to −5.0 × 10

^{−2}month

^{−1}at W4 (Table 3), and the time lag required for auto-correlation coefficients to reach 0.2 (k

_{0.2}values) also rises from W2 (5.7 months) to W4 (12.3 months). Note that without considering W2, there is an upward trend in persistence from upstream to downstream, which has also been identified by Duvert et al. [3] in a subtropical agricultural catchment dominated by alluvial aquifers in southeast Queensland, Australia.

_{xy}between precipitation and GWLs is the maximum of 0.52 at W2, followed by 0.45 at W1, 0.41 at W3, and 0.40 at W4. It is interesting that this order is consistent with the above ranking result from the auto-correlation functions of GWLs. That is, the shorter the memory time, the greater the correlation coefficient. The time lags corresponding to the peak values are 0.67 months at W2and W3, and 1.33 months at W1 and W4.

#### 3.3. Continuous Wavelet Spectra

#### 3.4. Cross Wavelet Spectral Analysis

## 4. Discussion

#### 4.1. Rainfall Intensity

#### 4.2. Pumping

#### 4.3. Humidity Index

#### 4.4. Comprehensive Analysis

_{y}is the specific yield; Σh is cumulative rise in water-level; and ΣP is the total precipitation in the period corresponding to the water level rise.

_{y}provided by [48] are also used. As a result, the recharge ratio we estimated as shown in Table 8 is larger than or close to the maximum value of the empirical values. As a whole, the recharge ratio decreases from upstream to downstream. Specially, it decreases from W2 to W4, which is in line with the inertia ranks as shown in Figure 4. Meanwhile, considering the smallest time lags indicated by the cross wavelet spectra, the site of W2 has a good potentiality for groundwater recharge.

#### 4.5. Limitations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Observed time series of rainfall and GWLs at (

**a**) W1, (

**b**) W2, (

**c**) W3, and (

**d**) W4. The blue and orange bands indicate the wet year and dry year, respectively.

**Figure 6.**Continuous wavelet spectra for both precipitation and GWLs at (

**a**) W1, (

**b**) W2, (

**c**) W3, and (

**d**) W4, with the global wavelet spectrum right side of each subplot. Zones surrounded by black lines have significant wavelet power at the 95% confidence level. White lines denote the cone of influence.

**Figure 7.**Cross wavelet spectra (left) with global wavelet spectra (right) between rainfall and GWLs at (

**a**) W1, (

**b**) W2, (

**c**) W3, and (

**d**) W4. Zones surrounded by black lines have significant wavelet power at the 95% confidence level. White lines denote the cone of influence. The phase angles are indicated by the black arrows.

**Figure 8.**Time series of rainfall intensity, response time, and 6-month moving average of GWLs at (

**a**) W1, (

**b**) W2, (

**c**) W3, and (

**d**) W4. The blue and orange bands indicate the wet and dry years, respectively.

**Table 1.**Detail information of the monitoring wells. The thickness of unsaturated zones was calculated as the average depth over the observation period.

Well Number | Surface Elevation (m a.s.l.) | Monitoring Depth (m) | Unsaturated Zone Thickness (m) | Observation Period (dd-mm-yyyy) | Frequency (Day^{−1}) |
---|---|---|---|---|---|

W1 | 34.44 | 11~48 | 5.6 | 5 February 2006—30 December 2020 | 5 |

W2 | 25.23 | 0~10 | 3.3 | 10 January 2005—30 October 2015 | 10 |

W3 | 8.51 | 0.5~4.33 | 2.2 | 5 January 2005—30 December 2020 | 5 |

W4 | 2.16 | 6.4~8.1 | 1.1 | 5 January 2005—30 December 2019 | 5 |

W1 | W2 | W3 | W4 | |
---|---|---|---|---|

S | −114,083 | −7903 | 124,953 | 127,118 |

Z | −9.7 | −3.1 | 9.6 | 10.7 |

W1 | W2 | W3 | W4 | |
---|---|---|---|---|

Slope (×10^{−2} month^{−1}) | −9.3 | −12.7 | −5.0 | −5.0 |

k_{0.2} (months) | 7.8 | 5.7 | 9.8 | 12.3 |

**Table 4.**Time lags from the cross wavelet spectra between rainfall and GWLs (period of 365 days band).

Title 1 | W1 | W2 | W3 | W4 |
---|---|---|---|---|

All significant periods Lags (days) | 2008–2020 | 2005–2014 | 2007–2020 | 2005–2019 |

139.14 ± 59.76 | 23.27 ± 12.03 | 145.01 ± 68.00 | 59.22 ± 26.14 | |

Wet years | 2009, 2013 | 2008–2009 | 2009–2010, 2012, 2015 | 2010 |

Lags (days) | 126.77 ± 11.07 | 39.07 ± 5.97 | 132.48 ± 20.30 | 49.40 ± 2.37 |

Years of pumping | 2009–2011, 2013–2017, 2020 | 2006, 2008–2009 2014 | 2007, 2010–2020 | 2008, 2014–2016, 2019 |

Lags (days) | 156.10 ± 38.79 | 39.07 ± 6.05 | 159.19 ± 74.44 | 88.74 ± 18.25 |

Years of no or little pumping | 2008, 2012, 2018–2019 | 2005, 2007, 2010–2013 | 2008, 2009 | 2005–2007, 2009–2013, 2017–2018 |

Lags (days) | 112.06 ± 50.74 | 23.31 ± 8.68 | 123.38 ± 23.85 | 44.46 ± 14.29 |

References | Study Sites | Study Periods | Depth(m) | Time Lags (Days) |
---|---|---|---|---|

Yu and Lin [22] | Pingtung Plain, Tainwan | 2005–2010 | - | 3.71–72.07 |

Zhang et al. [23] | Yellow River Delta | 2006–2010 | 1.2–2.2 | 35.51–178.36 |

Qi et al. [40] | Baiquan Spring Watershed, Jinan | 1990–2011 | ~20–70 | 80.8–185.37 |

Cai et al. [6] | Puyang area, Henan | 2006–2018 | 1–35.1 | 128–175 |

Feng et al. [41] | Xiongan New Area, China | 1991–2016 | 30–152 | 147.56–177.20 |

W1 | W2 | W3 | W4 | |
---|---|---|---|---|

All significant periods | 2009–2017 | 2005–2014 | 2008–2012, 2014–2018 | 2005–2007, 2014–2019 |

Lags (days) | 119.11 ± 39.41 | 14.85 ± 10.07 | 103.65 ± 40.20 | 47.60 ± 22.61 |

Factors | Variation | W1 | W2 | W3 | W4 |
---|---|---|---|---|---|

Wet years | Absolute changes (days) | −12.37 | −12.53 | −9.82 | |

Percentage change | −8.89% | −8.64% | −16.58% | ||

Pumping | Absolute changes (days) | 16.96 | 15.8 | 14.18 | 29.52 |

Percentage change | 12.19% | 67.90% | 9.78% | 49.85% | |

HI | Absolute changes (days) | −20.03 | −8.42 | −41.36 | −11.62 |

Percentage change | −14.40% | −36.18% | −28.52% | −19.62% |

W1 | W2 | W3 | W4 | |
---|---|---|---|---|

hydrologic year | 2018 | 2013 | 2009 | 2018 |

Vadose zone lithology | Silty clay | Silty clay | Silt | Silty clay |

S_{y} | 0.05 | 0.05 | 0.074 | 0.05 |

Recharge ratio α | 0.27 | 0.32 | 0.25 | 0.17 |

Empirical values of α | 0.18–0.26 | 0.15–0.26 | 0.20–0.28 | 0.12–0.19 |

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**MDPI and ACS Style**

Wang, C.; Dai, F.; Liu, Y.; Wang, Y.; Li, H.; Qu, W.
Shallow Groundwater Responses to Rainfall Based on Correlation and Spectral Analyses in the Heilonggang Region, China. *Water* **2023**, *15*, 1100.
https://doi.org/10.3390/w15061100

**AMA Style**

Wang C, Dai F, Liu Y, Wang Y, Li H, Qu W.
Shallow Groundwater Responses to Rainfall Based on Correlation and Spectral Analyses in the Heilonggang Region, China. *Water*. 2023; 15(6):1100.
https://doi.org/10.3390/w15061100

**Chicago/Turabian Style**

Wang, Chaoyue, Fenggang Dai, Yang Liu, Yunmeng Wang, Hui Li, and Wenjing Qu.
2023. "Shallow Groundwater Responses to Rainfall Based on Correlation and Spectral Analyses in the Heilonggang Region, China" *Water* 15, no. 6: 1100.
https://doi.org/10.3390/w15061100