# Groundwater Level Fluctuation Analysis in a Semi-Urban Area Using Statistical Methods and Data Mining Techniques—A Case Study in Wrocław, Poland

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Current Situation

## 3. Experiment and Data Description

## 4. Methods and Preliminary Analysis

## 5. Discussion

## 6. Future Work

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Shiklomanov, I.A. The World’s Water Resources; Water in Crisis: A Guide to the World’s Fresh Water Resources; Oxford University Press: Oxford, UK, 1993; pp. 13–23. [Google Scholar]
- Margat, J.; Van der Gun, J. Groundwater around the World: A Geographic Synopsis; CRC Press: Boca Raton, FL, USA, 2013. [Google Scholar]
- The United Nations World Water Development Report 2020: Water and Climate Change; UNESCO: Paris, France, 2020.
- Howard, K.W.F.; Israfilov, R.G. (Eds.) Current Problems of Hydrogeology in Urban Areas, Urban Agglomerates and Industrial Centres; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Taylor, C.J.; Alley, W.M. Ground-Water-Level Monitoring and the Importance of Long-Term Water-Level Data; Number 1217-2002; US Geological Survey: Reston, VA, USA, 2002.
- Jacobi, J. Das Grundwasser von Breslau [The Groundwater of Breslau]; Morgenstern: Breslau, Poland, 1876. [Google Scholar]
- Worsa-Kozak, M.; Kotowski, A.; Wartalski, A. Monitoring of groundwater table levels in the neighborhood of Midtown Water Node in Wrocław City. Prz. Geol.
**2008**, 56, 302–307. [Google Scholar] - Moon, S.K.; Woo, N.C.; Lee, K.S. Statistical analysis of hydrographs and water-table fluctuation to estimate groundwater recharge. J. Hydrol.
**2004**, 292, 198–209. [Google Scholar] [CrossRef] - Tasker, G.D.; Guswa, J.H. Application of a Mathematical Model to Estimate Water Levels. Groundwater
**1978**, 16, 18–21. [Google Scholar] [CrossRef] - Anderson, M.P.; Woessner, W.W.; Hunt, R.J. Applied Groundwater Modeling: Simulation of Flow and Advective Transport; Academic Press: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Shiri, J.; Kisi, O.; Yoon, H.; Lee, K.K.; Nazemi, A.H. Predicting groundwater level fluctuations with meteorological effect implications—A comparative study among soft computing techniques. Comput. Geosci.
**2013**, 56, 32–44. [Google Scholar] [CrossRef] - Jeong, J.; Park, E.; Han, W.S.; Kim, K.Y.; Suk, H.; Jo, S.B. A generalized groundwater fluctuation model based on precipitation for estimating water table levels of deep unconfined aquifers. J. Hydrol.
**2018**, 562, 749–757. [Google Scholar] [CrossRef] - Szymanowski, M.; Wieczorek, M.; Namyślak, M.; Kryza, M.; Migała, K. Spatio-temporal changes in atmospheric precipitation over south-western Poland between the periods 1891–1930 and 1981–2010. Theor. Appl. Climatol.
**2019**, 135, 505–518. [Google Scholar] [CrossRef] [Green Version] - Oh, Y.Y.; Yun, S.T.; Yu, S.; Hamm, S.Y. The combined use of dynamic factor analysis and wavelet analysis to evaluate latent factors controlling complex groundwater level fluctuations in a riverside alluvial aquifer. J. Hydrol.
**2017**, 555, 938–955. [Google Scholar] [CrossRef] - Barzegar, R.; Fijani, E.; Moghaddam, A.A.; Tziritis, E. Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network-based models. Sci. Total Environ.
**2017**, 599, 20–31. [Google Scholar] [CrossRef] - Rakhshandehroo, G.R.; Amiri, S.M. Evaluating fractal behavior in groundwater level fluctuations time series. J. Hydrol.
**2012**, 464, 550–556. [Google Scholar] [CrossRef] - Joelson, M.; Golder, J.; Beltrame, P.; Néel, M.C.; Di Pietro, L. On fractal nature of groundwater level fluctuations due to rainfall process. Chaos Solitons Fractals
**2016**, 82, 103–115. [Google Scholar] [CrossRef] [Green Version] - Kostić, S.; Stojković, M.; Guranov, I.; Vasović, N. Revealing the background of groundwater level dynamics: Contributing factors, complex modeling and engineering applications. Chaos Solitons Fractals
**2019**, 127, 408–421. [Google Scholar] [CrossRef] - Yoon, H.; Jun, S.C.; Hyun, Y.; Bae, G.O.; Lee, K.K. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J. Hydrol.
**2011**, 396, 128–138. [Google Scholar] [CrossRef] - Du Bui, D.; Kawamura, A.; Tong, T.N.; Amaguchi, H.; Nakagawa, N. Spatio-temporal analysis of recent groundwater-level trends in the Red River Delta, Vietnam. Hydrogeol. J.
**2012**, 20, 1635–1650. [Google Scholar] [CrossRef] - Sahoo, S.; Jha, M.K. On the statistical forecasting of groundwater levels in unconfined aquifer systems. Environ. Earth Sci.
**2015**, 73, 3119–3136. [Google Scholar] [CrossRef] - Chiaudani, A.; Di Curzio, D.; Palmucci, W.; Pasculli, A.; Polemio, M.; Rusi, S. Statistical and fractal approaches on long time-series to surface-water/groundwater relationship assessment: A central Italy alluvial plain case study. Water
**2017**, 9, 850. [Google Scholar] [CrossRef] [Green Version] - Yan, S.F.; Yu, S.E.; Wu, Y.B.; Pan, D.F.; Dong, J.G. Understanding groundwater table using a statistical model. Water Sci. Eng.
**2018**, 11, 1–7. [Google Scholar] [CrossRef] - Habib, A.; Sorensen, J.P.; Bloomfield, J.P.; Muchan, K.; Newell, A.J.; Butler, A.P. Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis. J. Hydrol.
**2017**, 549, 715–730. [Google Scholar] [CrossRef] - Nguyen, P.T.; Ha, D.H.; Avand, M.; Jaafari, A.; Nguyen, H.D.; Al-Ansari, N.; Phong, T.V.; Sharma, R.; Kumar, R.; Le, H.V.; et al. Soft Computing Ensemble Models Based on Logistic Regression for Groundwater Potential Mapping. Appl. Sci.
**2020**, 10, 2469. [Google Scholar] [CrossRef] [Green Version] - Górka, M.; Skrzypek, G.; Hałas, S.; Jędrysek, M.O.; Strąpoć, D. Multi-seasonal pattern in 5-year record of stable H, O and S isotope compositions of precipitation (Wrocław, SW Poland). Atmos. Environ.
**2017**, 158, 197–210. [Google Scholar] [CrossRef] [Green Version] - Jabłoński, A.; Barszcz, T.; Bielecka, M. Automatic validation of vibration signals in wind farm distributed monitoring systems. Measurement
**2011**, 44, 1954–1967. [Google Scholar] [CrossRef] - Wyłomańska, A.; Zimroz, R. Signal segmentation for operational regimes detection of heavy duty mining mobile machines—A statistical approach. Diagnostyka
**2014**, 15/2, 33–42. [Google Scholar] - Zimroz, R.; Madziarz, M.; Żak, G.; Wyłomańska, A.; Obuchowski, J. Seismic signal segmentation procedure using time-frequency decomposition and statistical modelling. J. Vibroeng.
**2015**, 17, 3111–3121. [Google Scholar] - Wodecki, J.; Stefaniak, P.; Michalak, A.; Wyłomańska, A.; Zimroz, R. Technical condition change detection using Anderson–Darling statistic approach for LHD machines—Engine overheating problem. Int. J. Min. Reclam. Environ.
**2018**, 32, 392–400. [Google Scholar] [CrossRef] - Polak, M.; Obuchowski, J.; Wyłomańska, A.; Zimroz, R. Seismic signal enhancement via AR filtering and spatial time-frequency denoising. In Cyclostationarity: Theory and Methods III; Springer: Berlin/Heidelberg, Germany, 2017; pp. 51–68. [Google Scholar]
- Kruczek, P.; Polak, M.; Wyłomańska, A.; Kawalec, W.; Zimroz, R. Application of compound Poisson process for modelling of ore flow in a belt conveyor system with cyclic loading. Int. J. Min. Reclam. Environ.
**2018**, 32, 376–391. [Google Scholar] [CrossRef] - Przylibski, T.A.; Wyłomańska, A.; Zimroz, R.; Fijałkowska-Lichwa, L. Application of spectral decomposition of
^{222}Rn activity concentration signal series measured in Niedźwiedzia Cave to identification of mechanisms responsible for different time-period variations. Appl. Radiat. Isot.**2015**, 104, 74–86. [Google Scholar] [CrossRef] - Szczurek, A.; Maciejewska, M.; Wyłomańska, A.; Zimroz, R.; Żak, G.; Dolega, A. Detection of occupancy profile based on carbon dioxide concentration pattern matching. Measurement
**2016**, 93, 265–271. [Google Scholar] [CrossRef] - Bartkowiak, A.; Zimroz, R. Dimensionality reduction via variables selection—Linear and nonlinear approaches with application to vibration-based condition monitoring of planetary gearbox. Appl. Acoust.
**2014**, 77, 169–177. [Google Scholar] [CrossRef] - Belkhiri, L.; Mouni, L. Geochemical characterization of surface water and groundwater in Soummam Basin, Algeria. Nat. Resour. Res.
**2014**, 23, 393–407. [Google Scholar] [CrossRef] - Pathak, A.A.; Dodamani, B. Trend analysis of groundwater levels and assessment of regional groundwater drought: Ghataprabha River Basin, India. Nat. Resour. Res.
**2019**, 28, 631–643. [Google Scholar] [CrossRef] - Chiaudani, A.; Curzio, D.D.; Rusi, S. The snow and rainfall impact on the Verde spring behavior: A statistical approach on hydrodynamic and hydrochemical daily time-series. Sci. Total Environ.
**2019**, 689, 481–493. [Google Scholar] [CrossRef] - Bhakar, P.; Singh, A.P. Groundwater quality assessment in a hyper-arid region of Rajasthan, India. Nat. Resour. Res.
**2019**, 28, 505–522. [Google Scholar] [CrossRef] - Daughney, C.J.; Raiber, M.; Moreau-Fournier, M.; Morgenstern, U.; van der Raaij, R. Use of hierarchical cluster analysis to assess the representativeness of a baseline groundwater quality monitoring network: Comparison of New Zealand’s national and regional groundwater monitoring programs. Hydrogeol. J.
**2012**, 20, 185–200. [Google Scholar] [CrossRef] - Helstrup, T.; Jørgensen, N.O.; Banoeng-Yakubo, B. Investigation of hydrochemical characteristics of groundwater from the Cretaceous-Eocene limestone aquifer in southern Ghana and southern Togo using hierarchical cluster analysis. Hydrogeol. J.
**2007**, 15, 977–989. [Google Scholar] [CrossRef] - Qi, P.; Zhang, G.; Xu, Y.J.; Wang, L.; Ding, C.; Cheng, C. Assessing the influence of precipitation on shallow groundwater table response using a combination of singular value decomposition and cross-wavelet approaches. Water
**2018**, 10, 598. [Google Scholar] [CrossRef] [Green Version] - Lorentz, S.A.; Hughes, G.; Schulze, R.E. Techniques for Estimating Groundwater Recharge at Different Scales in Southern Africa. In Groundwater Recharge Estimation in Southern Africa; Xu, Y., Beekman, H.E., Eds.; UNESCO: Paris, France, 2003; Volume 64, pp. 149–155. [Google Scholar]
- Hiscock, K.M.; Bense, V.F. Hydrogeology: Principles and Practice, 2nd ed.; Wiley Blackwell: Hoboken, NJ, USA, 2014. [Google Scholar]
- Wojewoda, J.; Kowalski, A.; Gotowała, R.; Sobczyk, A. Budowa geologiczna terenów wodonośnych ujęcia infiltracyjnego we Wrocławiu. Biul. Państwowego Inst. Geol.
**2016**, 466, 323–341. [Google Scholar] - Szponar, A.; Szponar, A.M. Geologia i Paleogeografia Wrocławia [Geology and Paleogeography of Wrocław]; Wydawnictwo KGHM CUPRUM Centrum Badawczo-Rozwojowe: Wrocław, Poland, 2008. [Google Scholar]
- Książek, S.; Suszczewicz, M. City profile: Wrocław. Cities
**2017**, 65, 51–65. [Google Scholar] [CrossRef] - Gmochowska, W.; Pietranik, A.; Tyszka, R.; Ettler, V.; Mihaljevič, M.; Długosz, M.; Walenczak, K. Sources of pollution and distribution of Pb, Cd and Hg in Wrocław soils: Insight from chemical and Pb isotope composition. Geochemistry
**2019**, 79, 434–445. [Google Scholar] [CrossRef] - Kasprzak, M.; Traczyk, A. LiDAR and 2D electrical resistivity tomography as a supplement of geomorphological investigations in urban areas: A case study from the city of Wrocław (SW Poland). Pure Appl. Geophys.
**2014**, 171, 835–855. [Google Scholar] [CrossRef] [Green Version] - Worsa-Kozak, M. Wahania zwierciadła wód podziemnych na terenach zurbanizowanych (miastoWrocław)[Groundwater table fluctuations in urban areas (City of Wrocław)]. Ph.D. Thesis, University of Wrocław, Wrocław, Poland, 2007. [Google Scholar]
- Worsa-Kozak, M. Groundwater table fluctuations types in urban area, Wroclaw, SW Poland. In XXXVIII IAH Congress Groundwater Quality Sustainability; Zuber, A., Kania, J., Kmiecik, E., Eds.; University of Silesia Press: Katowice, Poland, 2010; pp. 313–319. [Google Scholar]
- Pearson, K. VII. Note on regression and inheritance in the case of two parents. Proc. R. Soc. Lond.
**1895**, 58, 240–242. [Google Scholar] - Pozzi, F.; Di Matteo, T.; Aste, T. Exponential smoothing weighted correlations. Eur. Phys. J. B
**2012**, 85, 175. [Google Scholar] [CrossRef] - Maimon, O.; Rokach, L. Data Mining and Knowledge Discovery Handbook; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
- Ward, J.H., Jr. Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc.
**1963**, 58, 236–244. [Google Scholar] [CrossRef] - Tibshirani, R.; Walther, G.; Hastie, T. Estimating the number of clusters in a data set via the gap statistic. J. R. Stat. Soc. B
**2001**, 63, 411–423. [Google Scholar] [CrossRef] - Kendall, M.G. A new measure of rank correlation. Biometrika
**1938**, 30, 81–93. [Google Scholar] [CrossRef] - Spearman, C. The proof and measurement of association between two things. Am. J. Psychol.
**1987**, 100, 441–471. [Google Scholar] [CrossRef] [PubMed] - Pleczyński, J. Odnawialność zasobów wód podziemnych [Renewability of Groundwater Resources]; Wydawnictwa Geologiczne: Warsaw, Poland, 1981. [Google Scholar]
- Thomas, B.; Behrangi, A.; Famiglietti, J. Precipitation Intensity Effects on Groundwater Recharge in the Southwestern United States. Water
**2016**, 8, 90. [Google Scholar] [CrossRef] [Green Version] - Bayer, F.M.; Bayer, D.M.; Pumi, G. Kumaraswamy autoregressive moving average models for double bounded environmental data. J. Hydrol.
**2017**, 555, 385–396. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Cross-section of a typical groundwater flow system (modified from: [5]).

**Figure 2.**Location of the experiment’s area. (latitude: 51${}^{\circ}$6${}^{\prime}$19.3${}^{\u2033}$ N longitude: 17${}^{\circ}$5${}^{\prime}$20.7${}^{\u2033}$ E altitude: $116.3$ m a.s.l.).

**Figure 5.**Time series of measured data; (

**a**) groundwater level, (

**b**) precipitation, (

**c**) temperature, (

**d**) relative humidity, (

**e**) air pressure, (

**f**) insolation.

**Figure 6.**Time series of the groundwater level. The hydrological year is marked by the black line. Additionally, the summer/winter seasons are indicated with red broken lines.

**Figure 7.**The detrended groundwater level fluctuation. The hydrological year is marked by the black line. Additionally, the summer/winter seasons are indicated with red broken lines.

**Figure 8.**Pearson correlation matrix for time series of detrended groundwater levels corresponding to the hydrological years (HYs).

**Figure 9.**Pearson correlation matrix for time series of detrended groundwater levels corresponding to the winter seasons of the HYs.

**Figure 10.**Pearson correlation matrix for time series of detrended groundwater levels corresponding to the summer seasons of the HYs.

**Figure 11.**Dendrogram for time series of detrended groundwater levels corresponding to the HYs from applying the AHP clustering.

**Figure 12.**Clustering of the time series of detrended groundwater levels corresponding to the HYs by applying the AHP method. The years presented in the legend correspond to the years in the dendrogram (Figure 11).

**Figure 13.**Dendrogram for time series of detrended groundwater level corresponding to winter seasons from applying the AHP clustering.

**Figure 14.**Clustering of the time series of detrended groundwater levels corresponding to the winter seasons by applying the AHP method. The years in the legend are corresponding to the years in the dendrogram (Figure 13).

**Figure 15.**Dendrogram for time series of detrended groundwater levels corresponding to the summer seasons from applying the AHP clustering.

**Figure 16.**The clustering of the time series of detrended groundwater levels corresponding to the summer seasons by applying the AHP method. The years in legend are corresponding to the years in the dendrogram (Figure 15).

**Figure 17.**The Pearson ($\rho $), Kendall ($\tau $) tau and Spearman rho (r) correlation coefficient between time series of detrended groundwater level and precipitation. W: winter season, S: summer season.

**Figure 18.**Time series of daily precipitation and detrended groundwater level for the selected years (the same cluster, i.e., data with similar behavior).

**Figure 19.**Cumulative sum of precipitation calculated for each season. The winter seasons (left panel) and the summer seasons (right panel).

**Figure 20.**The Pearson ($\rho $), Kendall ($\tau $) tau and Spearman rho (r) correlation coefficient between time series of detrended groundwater level and the cumulative sum of precipitation. W: winter season, S: summer season.

**Figure 21.**Scatterplots for the winter seasons. On the OY axis, the detrended groundwater levels and on the OX axis the cumulative sums of precipitation are presented. The bottom right plot presents the winter season with the highest correlation: 2005, 2006, 2009, 2013, 2016.

**Figure 22.**Scatterplots for the summer seasons. On the OY axis, the detrended groundwater levels and on the OX axis the cumulative sums of precipitation are presented. The bottom right plot presents the summer seasons with the highest correlation: 2004, 2005, 2008, 2012, 2018.

© 2020 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**

Worsa-Kozak, M.; Zimroz, R.; Michalak, A.; Wolkersdorfer, C.; Wyłomańska, A.; Kowalczyk, M.
Groundwater Level Fluctuation Analysis in a Semi-Urban Area Using Statistical Methods and Data Mining Techniques—A Case Study in Wrocław, Poland. *Appl. Sci.* **2020**, *10*, 3553.
https://doi.org/10.3390/app10103553

**AMA Style**

Worsa-Kozak M, Zimroz R, Michalak A, Wolkersdorfer C, Wyłomańska A, Kowalczyk M.
Groundwater Level Fluctuation Analysis in a Semi-Urban Area Using Statistical Methods and Data Mining Techniques—A Case Study in Wrocław, Poland. *Applied Sciences*. 2020; 10(10):3553.
https://doi.org/10.3390/app10103553

**Chicago/Turabian Style**

Worsa-Kozak, Magdalena, Radosław Zimroz, Anna Michalak, Christian Wolkersdorfer, Agnieszka Wyłomańska, and Marek Kowalczyk.
2020. "Groundwater Level Fluctuation Analysis in a Semi-Urban Area Using Statistical Methods and Data Mining Techniques—A Case Study in Wrocław, Poland" *Applied Sciences* 10, no. 10: 3553.
https://doi.org/10.3390/app10103553