# Karst Lake’s Dynamics Analysis as a Tool for Aquifer Characterisation at Field Scale, Example of Cryptodepression—Red Lake in Croatia

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}, there are 601 dolines identified, with an average density of 22 dolines/km

^{2}. According to Pahernik [24], who determined doline density for Croatia, this is a low-density value. The area NE of Imotski (Rudine) is an area of high density (70–90 dolines/km

^{2}) with a high impact of precipitation infiltration and importance for karst water quality. The most spacious surface karst features are collapsed dolines with Red Lake and Blue Lake as the largest ones. According to the topo map and Croatian Cave Cadastre [25], there is known 15 caves, mostly vertical shafts (up to 100 m deep) in the vadose zone. The Polje has a flat bottom filled and flattened by younger, mostly Holocene, deposits (alluvium, marl, sand, and clay) [12,15] with prevalent fluvio-accumulational and fluvio-denudational relief forms. The Polje is important as a local base level with the occurrence of springs at the contact along the base of the karst plateau with Opačac Spring as one of the biggest springs.

## 3. Materials and Methods

#### 3.1. Data Used

_{r}). The transformed values of integral volume changes are shown in Figure 3.

#### 3.2. Method Used

#### 3.2.1. Recession Curve Analysis

^{2}). The second recession segment, the one with the second-highest initial value, is translated to its proper position according to the corresponding time shift. The next step is to test the composite curve of the first and second recession segments with regression models. The most appropriate regression model is selected and the next recession segment is translated to the corresponding position on the previously defined curve. The procedure is repeated for all recession segments and the result is MRC.

_{0}and the recession coefficient α:

_{1}, and the intersection with the y-axis is Q

_{01}. By subtracting the remaining values of the empirical curve from the values of the straight line, the empirical values of the second segment are obtained. Then, the second segment is approximated by the straight line with slope α

_{2}and y-axis intercept Q

_{02}. The procedure is repeated for n segments of the recession curve, which are merged into a single curve according to the principle of superposition:

#### 3.2.2. Correlation and Spectral Analysis

_{xy}and C

_{yx}are covariances and σ

_{x}and σ

_{y}are the standard deviations of the two observed series [38,39,41]. Spectral analysis, unlike correlation analysis, analyses signals in the frequency domain. Therefore, the spectral density function represents a Fourier transform of the autocorrelation function. Both functions describe a stationary stochastic process containing the same information but in a different domain. The identification of periodic phenomena, expressed in terms of the detection of different peaks, is defined by the spectral density function as follows [38,39]:

_{xy}(f) and the co-spectrum Λ

_{xy}(f) [39,41].

_{xy}and the gain function G

_{xy}may be defined using the known values of the spectral density functions S

_{x}and S

_{y}, as well as the cross-spectral density function S

_{xy}[42]:

_{xy}, expresses the linearity of the input–output relationship between signals. It ranges from 0 to 1, with 0 denoting no correlation and 1 denoting the strongest correlation between two signals at frequency f. The gain function represents the output signal’s amplification (>1) or attenuation (<1) in contrast to the input signal.

_{xy}as a complex number, the amplitude α

_{xy}and phase ϕ

_{xy}functions may be constructed using the complex number’s trigonometric form.

## 4. Results and Discussion

#### 4.1. Analysis of Lake’s Dynamics and Recession Periods

_{1}denotes quick emptying of channels and cracks in karst and a more permeable aquifer, whereas α

_{2}denotes slower emptying of subsurface reserves. As a result, recession coefficients are used to describe the predominant flow mechanisms in the karst aquifer. The average value of the quasi-recession coefficient α

_{1}is 0.1103, while α

_{2}is 0.082. A shift in the slope of the master recession curve indicates a change in the value of quasi-recession coefficients. Looking at the quasi-recession coefficients, the dominance of base flow over direct flow is undeniable. This can be explained by the dominance of the rock matrix in the karst, which causes slow drainage of water from smaller pores and cracks. It is obvious that groundwater plays an important role in the formation of integral volume changes in Red Lake, which is why the lake never dries up. As previously stated, the shift in the quasi-recession coefficient occurs around the level of Opačac Spring. To better understand the functioning of the lake, but also its connection with the spring, the signals were analysed in the time and frequency domain.

#### 4.2. Analysis in Spatial and Frequency Domain

_{xy}. The values of G

_{xy}> 1 indicate amplification of the input signal, while the values of G

_{xy}< 1 indicate attenuation of the input signal. The input signal is attenuated at high frequencies and amplified at low frequencies. Analysis of integral volume changes in Red Lake showed attenuation of the input signal at frequencies above 0.036 and in Opačac discharges at frequencies above 0.0038.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bonacci, O. Karst Hydrology With Special Reference to the Dinaric Karst; Springer: Berlin/Heidelberg, Germany, 1987. [Google Scholar]
- Stevanović, Z. Karst Waters in Potable Water Supply: A Global Scale Overview. Environ. Earth Sci.
**2019**, 78, 662. [Google Scholar] [CrossRef] - Bonacci, O. Preliminary Analysis of the Decrease in Water Level of Vrana Lake on the Small Carbonate Island of Cres (Dinaric Karst, Croatia). Geol. Soc. Spec. Publ.
**2018**, 466, 307–317. [Google Scholar] [CrossRef] - Ožanić, N.; Rubinić, J. Hidraulic Limitation of Exploitation Vrana Lake for Water Supply (Croatia). In Proceedings of the XXIX IAHR Congress—21st Century: The New Era for Hydraulic Research and its Applications, Beijing, China, 16–21 September 2001; pp. 100–106. [Google Scholar]
- Garašić, M. New Speleohydrogeological Research of Crveno Jezero (Red Lake) near Imotski in Dinaric Karst Area (Croatia, Europe)—International Speleodiving Expedition “Crveno Jezero 98”. In Proceedings of the 13th International Congress of Speleology, Brasilia, Brazil, 15–22 July 2001; pp. 457–460. [Google Scholar]
- Gavazzi, A. Die Seen Des Karstes (Karst Lakes). In Abhandlungen der K. K. Geographischen Gesellschaft; Lechner: Vienna, Austria, 1903; Volume 5, p. 136. [Google Scholar]
- Cvijić, J. Geomorfologija 2 (Geomorphology 2); Srpska Akademija Nauka i Umetnosti: Beograd, Serbia, 1926. [Google Scholar]
- Andrić, I.; Jukić, B.; Bonacci, O. Pregled Recentnih Znanstvenih Istraživanja Vezanih Za Crveno i Modro Jezero u Imotskom. In Zavičajna Baština—Problemi i Perspektive u Upravljanju Baštinom; Parlov, M., Kolovrat, I., Biočić, M., Eds.; Crkva u Svijetu: Split, Croatia, 2018; pp. 31–41. [Google Scholar]
- Roglić, J. Imotsko Polje—Fizičko-Geografske Osobine. (Physical-Geographic Characteristics of Imotski Polje). Poseb. Izd. Geogr. Druš.
**1938**, 21, 125. [Google Scholar] - Bonacci, O. Crveno i Modro Jezero Kod Imotskog. Hrvat. Vode
**2006**, 14, 45–54. [Google Scholar] - Petrik, M. Hidrografska Mjerenja u Okolici Imotskog (Hydrographic Measurements near Imotski). Ljetop. JAZU
**1960**, 64, 266–286. [Google Scholar] - Bojanić, L.; Ivičić, D.; Batić, V. Hidrogeologija Imotskog Polja s Osvrtom Na Značaj u Regionalnom Smislu. Geol. Vjesn.
**1981**, 34, 127–135. [Google Scholar] - Milanović, P.T. Karst Hydrogeology; Water Resources Publications: Littleton, CO, USA, 1981; p. 434. [Google Scholar]
- Bahun, S. O Postanku Crvenog i Modrog Jezera Kod Imotskog. Geol. Vjesn.
**1991**, 44, 275–280. [Google Scholar] - Bonacci, O.; Andrić, I. Morphological Study of Red Lake in Dinaric Karst Based on Terrestrial Laser Scaning and Sonar System. Acta Carsolog.
**2014**, 43, 229. [Google Scholar] [CrossRef][Green Version] - Bonacci, O.; Roje-Bonacci, T. Interpretation of Groundwater Level Monitoring Results in Karst Aquifers: Examples from the Dinaric Karst. Hydrol. Processes
**2000**, 14, 2423–2438. [Google Scholar] [CrossRef] - Andrić, I.; Bonacci, O.; Jukić, B. Rezultati Najnovijih Hidroloških i Geomorfoloških Istraživanja Crvenog Jezera Kod Imotskog. Hrvat. Vode
**2013**, 21, 344–348. [Google Scholar] - Andrić, I.; Bonacci, O.; Jukić, B. Hidrološka Mjerenja Na Crvenom Jezeru u Razdoblju Od 28. Rujna 2013. Do 10. Rujna 2015. Hrvat. Vode
**2017**, 25, 253–258. [Google Scholar] - Pérez-Bielsa, C.; Lambán, L.J.; Plata, J.L.; Rubio, F.M.; Soto, R. Characterization of a Karstic Aquifer Using Magnetic Resonance Sounding and Electrical Resistivity Tomography: A Case-Study of Estaña Lakes (Northern Spain). Hydrogeol. J.
**2012**, 20, 1045–1059. [Google Scholar] [CrossRef] - Tallaksen, L.M. A Review of Baseflow Recession Analysis. J. Hydrol.
**1995**, 165, 349–370. [Google Scholar] [CrossRef] - Basha, H.A. Flow Recession Equations for Karst Systems. Water Resour. Res.
**2020**, 56, e2020WR027384. [Google Scholar] [CrossRef] - Zdilar, S. Reljef Zavale Imotskog Polja i Njegovo Geoekološko Vrednovanje; Augustini: Zagreb, Croatia, 2001. [Google Scholar]
- Dragicevic, I.; Prelogovic, E.; Vlado, K.U.K.; Buljan, R. Recent Tectonic Activity in the Imotsko Polje Area. Geol. Croat.
**1999**, 52, 191–196. [Google Scholar] [CrossRef] - Pahernik, M. Prostorna Gustoća Ponikava Na Području Republike Hrvatske. Hrvat. Geogr. Glas.
**2012**, 74, 5–26. [Google Scholar] [CrossRef][Green Version] - Katastar Speleoloških Objekata Republike Hrvatske. Available online: https://crospeleo.mingor.hr (accessed on 1 December 2021).
- Šegota, T.; Filipčić, A. Köppenova Podjela Klima i Hrvatsko Nazivlje. Geoadria
**2003**, 8, 17–37. [Google Scholar] [CrossRef][Green Version] - Bonacci, O.; Roje-Bonacci, T. Water Losses from the Ričice Reservoir Built in the Dinaric Karst. Eng. Geol.
**2008**, 99, 121–127. [Google Scholar] [CrossRef] - The MathWorks, Inc. About Identified Nonlinear Models. Available online: https://www.mathworks.com/help/ident/ug/about-nonlinear-model-identification.html (accessed on 1 December 2021).
- Ojha, A.K.; Mallick, D.; Mallick, C. Existence and Global Logarithmic Stability of Impulsive Neural Networks with Time Delay. arXiv
**2010**, arXiv:1002.1164. [Google Scholar] - Burden, F.; Winkler, D. Bayesian Regularization of Neural Networks. In Artificial Neural Networks; Springer: Berlin/Heidelberg, Germany, 2008; pp. 23–42. [Google Scholar]
- Nathan, R.J.; McMahon, T.A. Evaluation of Automated Techniques for Base Flow and Recession Analyses. Water Resour. Res.
**1990**, 26, 1465–1473. [Google Scholar] [CrossRef] - Fiorotto, V.; Caroni, E. A New Approach to Master Recession Curve Analysis. Hydrol. Sci. J.
**2013**, 58, 966–975. [Google Scholar] [CrossRef][Green Version] - Toebes, C.; Morrissey, W.B.; Shorter, R.; Hendy, M. Base-Flow-Recession Curves. Handbook of Hydrological Procedures: Procedure No 8; A.R. Shearer, Government Printer: Wellington, New Zeland, 1969. [Google Scholar]
- Sujono, J.; Shikasho, S.; Hiramatsu, K. A Comparison of Techniques for Hydrograph Recession Analysis. Hydrol. Processes
**2004**, 18, 403–413. [Google Scholar] [CrossRef] - Posavec, K.; Parlov, J.; Nakić, Z. Fully Automated Objective-Based Method for Master Recession Curve Separation. Ground Water
**2010**, 48, 598–603. [Google Scholar] [CrossRef] [PubMed] - Posavec, K.; Bacani, A.; Nakic, Z. A Visual Basic Spreadsheet Macro for Recession Curve Analysis. Ground Water
**2006**, 44, 764–767. [Google Scholar] [CrossRef] - Petras, I. An Approach to the Mathematical Expression of Recession Curves. Water SA
**1986**, 12, 145–149. [Google Scholar] - Denić-Jukić, V.; Lozić, A.; Jukić, D. An Application of Correlation and Spectral Analysis in Hydrological Study of Neighboring Karst Springs. Water
**2020**, 12, 3570. [Google Scholar] [CrossRef] - Larocque, M.; Mangin, A.; Razack, M.; Banton, O. Contribution of Correlation and Spectral Analyses to the Regional Study of a Large Karst Aquifer (Charente, France). J. Hydrol.
**1998**, 205, 217–231. [Google Scholar] [CrossRef] - Mangin, A. Pour Une Meilleure Connaissance Des Systèmes Hydrologiques à Partir Des Analyses Corrélatoire et Spectrale. J. Hydrol.
**1984**, 67, 25–43. [Google Scholar] [CrossRef] - Padilla, A.; Pulido-Bosch, A. Study of Hydrographs of Karstic Aquifers by Means of Correlation and Cross-Spectral Analysis. J. Hydrol.
**1995**, 168, 73–89. [Google Scholar] [CrossRef] - Chatfield, C. The Analysis of Time Series: An Introduction, 6th ed.; Chapman and Hall/CRC: New York, NY, USA, 2016. [Google Scholar]

**Figure 2.**Geological map of the study area (

**A**), the cross-section a-a combined with the volume curve of Red Lake as a function of water level (

**B**) and doline density map (

**C**).

**Figure 3.**Integral volume changes of Red Lake with imputed missing values obtained using neural networks. The transformed values of the integral volume changes.

**Figure 4.**Comparison of precipitation at the Imotski gauging station with Red Lake integral volume changes (IVC), related water levels (H), and Opačac Spring discharges.

**Figure 5.**Master recession curve obtained by Adapted matching strip method, Tabulation and Petras method.

**Figure 7.**Cross correlation functions of discharges at Opačac Spring with integral volume changes in Red Lake and their combination with precipitation.

**Figure 8.**Spectral density functions of integral volume changes in Red Lake and discharges at Opačac.

**Figure 9.**Coherence, phase and gain function of integral volume changes in Red Lake and discharges at Opačac Spring.

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**MDPI and ACS Style**

Vrsalović, A.; Andrić, I.; Buzjak, N.; Bonacci, O. Karst Lake’s Dynamics Analysis as a Tool for Aquifer Characterisation at Field Scale, Example of Cryptodepression—Red Lake in Croatia. *Water* **2022**, *14*, 830.
https://doi.org/10.3390/w14050830

**AMA Style**

Vrsalović A, Andrić I, Buzjak N, Bonacci O. Karst Lake’s Dynamics Analysis as a Tool for Aquifer Characterisation at Field Scale, Example of Cryptodepression—Red Lake in Croatia. *Water*. 2022; 14(5):830.
https://doi.org/10.3390/w14050830

**Chicago/Turabian Style**

Vrsalović, Adrijana, Ivo Andrić, Nenad Buzjak, and Ognjen Bonacci. 2022. "Karst Lake’s Dynamics Analysis as a Tool for Aquifer Characterisation at Field Scale, Example of Cryptodepression—Red Lake in Croatia" *Water* 14, no. 5: 830.
https://doi.org/10.3390/w14050830