# An Application of Correlation and Spectral Analysis in Hydrological Study of Neighboring Karst Springs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}[48]. It is a typical example of the river in deep karst region with topographically complex landscape, where the surface and subsurface catchment boundary do not coincide, so a precise delineation of catchment is very difficult. The Cetina River catchment mostly lies in the mountain region with peaks over 1500 m a.s.l., while the rest of it morphologically belongs to the areas of karst poljes (Kupreško Polje, Duvanjsko Polje, Glamočko Polje and Livanjsko Polje in Figure 1. Livanjsko Polje is considered as the world’s largest karst polje, which together with the area of Buško Blato covers 433 km

^{2}. Climatologically, the north-eastern (Bosnian) part of the catchment has a continental climate with hot and dry summers and mild and wet winters, while the south-western (Croatian) part is under strong influence of the Adriatic Sea and the Mediterranean climate [53,54,55,56]. Consequently, the precipitation regime on the Cetina River catchment is complex and variable. The amount of average annual rainfall varies and hypsometrically differs from 1100 to 2700 mm with an average of about 1380 mm. The catchment area dominantly consists of permeable carbonate layers from Paleogene period. Quaternary formations of alluvial and marsh deposits are situated in larger flat areas like karst poljes and valleys [52]. The catchment is placed in the karst terrain formed of very thick layers of limestones and dolomites with intensive karstification and complex hydrogeological conditions. The whole area represents a typical karst terrain with specific karst forms like ponors and other speleological sites, so water from rainfall rather easily infiltrates. Consequently, the catchment is characterized by high, rapid infiltration with fast underground flows and by almost total absence of surface flow. The exceptions are the areas of the karst poljes, where intermittent and permanent surficial watercourses are formed on impermeable alluvial deposits and marls. Most of the groundwater flow occurs within limestones, in fissures, fractures and conduits of different and irregular shapes and varying sizes. The values of apparent groundwater flow velocities vary in a wide range between 0.5 and 24 cm/s [46], depending on the hydrological period and water table position. The slow movement of water is related with the dry season.

^{3}/s, but flow during the summer ranges from 4 to 6 m

^{3}/s [48]. Morphologically, the Cetina River has a valley composed of narrow canyons incised in carbonate rocks and zones of lateral valley widening. The upper course of this river includes the Cetina springs zone, the Peruča Lake, a 1.5 km long narrow carbonate canyon, and the section through the Sinjsko Polje where the river has a morphology of a typical plain river. Several permanent and intermittent karst springs are located along the left side of the Peruča Lake and the riverbed through the Sinjsko Polje, which get their water from the carbonate rocks at contacts with the impermeable marl rocks. The most important are presented in Figure 1. The springs Rumin Mali and Rumin Veliki are among them. The distance between these two springs is 640 m. The spring Rumin Mali is located at higher altitude (326.8 m a.s.l.) in comparison with the Rumin Veliki (307.6 m a.s.l.). The results of tracing tests that were performed long time ago (between 1957 and 1961, [46]) show that all these springs are fed by water from the Livanjsko Polje through underground drainage systems of Dinara and Kamešnica Mountains. Concerning the Rumin Springs, the tracing tests of the ponor in Čaprazlije (697 m a.s.l.) revealed that the largest part of water from this area goes to the spring Dabar. Tracer appeared also on the springs Dragović, Peruča, Rumin Veliki, Rumin Mali and Cetina Springs. The tracing tests of Veliki Ponor (693 m a.s.l.) and Opaki Ponor (703 m a.s.l.) reveled that practically all water from this part of Livanjsko Polje goes to the spring Rumin Veliki. More than 94% of the injected tracer appeared at this spring. The remaining small quantities of tracer were observed on the springs Dabar, Peruča, Rumin Mali, Kosinac, Ruda Velika and Grab. The karst springs Ruda Velika, Grab and Kosinac drain dominantly the area of Buško Blato (696–703 m a.s.l.).

#### 2.2. Available Data

_{S}, P

_{L}), air temperature (T

_{S}, T

_{L}) and relative humidity (RH

_{S}, RH

_{L}). Daily rainfall also was measured in the village of Bitelić Donji (P

_{B}), at a rain gauge situated at the foot of Dinara Mountain (RG Bitelić Donji), but only during the period 1999–2008. The measurement of daily discharge from the spring Rumin Veliki (Q

_{RV}) has been carried out since 1948 and from the spring Rumin Mali (Q

_{RM}) since 1950. However, the analyzed time series are from the periods 1950–1972 and 1996–2018, where all data are complete. The basic statistical characteristics of the daily time series for three analyzed periods, 1950–1972, 1996–2018 and 1999–2008, are presented in Table 1.

^{3}/s before 1973. After the construction of HPP Orlovac, mean annual discharge is only 6.91 m

^{3}/s, or 36% of the previous. The intermittent karst spring Rumin Mali had mean annual discharge of 2.74 m

^{3}/s. After 1973, it amounts 1.61 m

^{3}/s, which is 59% of the previous. For both springs, the maximum measured discharge belongs to the period of natural conditions of flow in the Cetina River. It is 106 m

^{3}/s for the spring Rumin Veliki, and 16.5 m

^{3}/s for the spring Rumin Mali. The air temperature during period 1996–2018 ranged between −7.2 and 30.4 °C, at MS Sinj, and between −15.6 and 29.1 °C, at MS Livno. The mean air temperature for the entire period is 13.1 and 10.2 °C, respectively. The mean relative humidity at MS Sinj and MS Livno during the analyzed period was 69 and 74%, respectively. Although the altitudes of MS Sinj and MS Livno are different, these two stations have a similar rainfall regime. Specifically, the mean daily rainfall for MS Sinj and MS Livno for the period 1996–2018 are 3.18 and 3.21 mm, which corresponds to the mean annual rainfall of 1162 and 1172 mm, respectively. A more detailed hydrological analysis reveals that, during the same period, the annual rainfall ranged from 831 to 1686 mm at MS Sinj, and from 808 to 1796 mm at MS Livno. Correlation coefficient between daily rainfall at these two stations was 0.85. However, daily maximums observed in each year were not correlated. The rainfall observed at RG Bitelić Donji during the period 1999–2008 had a slightly different regime. The mean value and the maximum value are higher in Table 1, as well as the standard deviation, which show that the rainfall at this location is more abundant.

#### 2.3. Methods

_{x}and μ

_{y}are the means of x and y, respectively. The truncation point m determinates the domain of this function, i.e., the time interval in which the analysis is carried out. It is recommended that $m=n/3$ [14,15]. The cross-correlation function (CCF) between time series x and y is

_{x}and σ

_{y}are the standard deviations of x and y, respectively. It should be noted that the correlation coefficient (CC) between time series x and y can be obtained as ${r}_{xy}={r}_{xy}\left(0\right)$. For completely random time series, 95% confidence limits are approximately $\pm 2/\sqrt{n}$ [14]. The autocorrelation function (ACF) of these two series can be obtained from Equation (2) as

- no effect—input time series x is an antecedent cause of output time series y and there is no relationship between series z and y,
- explanation effect (control effect)—control series z is an antecedent cause of output series y and there is no relationship between series x and y,
- partial explanation effect—input series x is an antecedent cause of output series y, but control series z is also either antecedent or intervening cause,
- suppression effect—control series z has a positive effect through one path and a negative effect through another path, or when control series z is weakly correlated with one of the original series.

## 3. Results

_{RM}and Q

_{RV}for periods 1950–1972 and 1996–2018 are presented in Figure 3. Generally, ACF quantifies the linear dependency of successive values over a time and outlines a system memory. In karst hydrology, ACF of spring discharge provides the information about the storage capacity of karst system. The storage capacity depends on the degree of karstification, but also on the surface ponds, soil cover and epikarst properties. To compare functions of various aquifers, the so-called memory effect is defined as the time lag where ACF becomes less than 0.2 [15]. An undeveloped karst system, with a large storage, has a high memory effect where ACF shows a slightly decreasing slope. On the contrary, a developed karst network, without important storage, corresponds to a low memory effect where ACF has a much steeper slope. In Figure 3, it can be noted that ACF(Q

_{RM}) and ACF(Q

_{RV}) for the first period 1950–1972 have very similar forms and the memory effect of approximately 63 days. Concerning the second period 1996–2018, the form of ACF(Q

_{RM}) is only slightly changed, as well as the memory effect that is reduced for only 1 day, and it amounts 62 days. It shows that, despite an evident change in hydrological regime after construction of HPP Orlovac in 1973, the storage capacity of the spring Rumin Mali apparently remains the same. It is not the case with the spring Rumin Veliki. The values of ACF(Q

_{RV}) obtained for the period 1996–2018 are significantly lower, and the memory effect is reduced to approximately 40 days. Concurrently, a bimodal behavior of this spring has become more evident. It should be emphasized that the time series of karst spring discharge contain a seasonal oscillation, so ACF(Q

_{RM}) and ACF(Q

_{RV}) in Figure 3 exhibit an evident periodicity with a period of approximately 365 days. The seasonal oscillation of discharge in Dinaric karst is dominantly the consequence of a similar oscillation in evapotranspiration rate during a year, which is manifested in groundwater recharge.

_{RM}and Q

_{RV}for the period 1950–1972 and 1996–2018 are presented in Figure 4a–d. SDF shows how the variance of analyzed time series is distributed over the range of frequencies. The peaks in SDF at various frequencies lead to the identification of periodicity in series. In system analyses, SDF of output time series also contains information about the filtering effect of analyzed system. It implies that there is a possibility to identify a change in the filtering effect during a time by comparing SDF of output time series obtained for two periods. In this study, SDF is used to analyze the change in short period and long period oscillations of discharge from two analyzed springs. In this context, the term long period implies the oscillations with the periods larger than 10 days, which corresponds to the frequency range below 0.1 1/day (Figure 4a,b). Truncation point is $m=2556\mathrm{days}$ (approximately 7 years). It can be noted that the seasonal oscillation of karst spring discharge is manifested in both SDF(Q

_{RM}) in Figure 4a, and both SDF(Q

_{RV}) in Figure 4b, as a periodicity at frequency 0.00274 1/day corresponding to the period of 365 days. The comparing SDF(Q

_{RM}) for two periods in Figure 4a reveals that the variance associated to the seasonal periodicity in discharge Q

_{RM}is only slightly attenuated for the second period. The attenuation of the seasonal periodicity is more evident for discharge Q

_{RV}(Figure 4b), which also indicates that the storage capacity of the aquifer of Rumin Veliki is significantly lower after the human intervention in 1973. Concerning the short period oscillations of discharge with the periods less than 10 days, which corresponds to the frequency range above 0.1 1/day, the obtained results are presented in Figure 4c,d. The truncation point is $m=365\mathrm{days}$. This range mostly describes oscillations in peak discharge. It can be noted that the values of SDF(Q

_{RM}) for the period 1950–1972 and 1996–2018 are similar (Figure 4c). Two functions have only small differences in shape, which means that the distribution of variance for the discharge from Rumin Mali has not been significantly changed at high frequencies. Concerning the discharge from Rumin Veliki (Figure 4d), the distribution of variance for two periods is evidently different. The values of SDF(Q

_{RV}) for the period 1996–2018 are higher, which shows that the filtering effect of aquifer is reduced. In fact, a redistribution of variance from the low to high frequency range occurred after 1973, so the relative importance of the oscillations in peak discharge increased.

_{L}and P

_{S}obtained for the period 1996–2018 are compared in Figure 5a. It is evident that MS Livno and MS Sinj have a very similar regime of daily rainfall. They both have similar periodicities and a seasonal component revealing that time series P

_{L}and P

_{S}cannot be considered as a white noise. A similar result is obtained also for RG Bitelić Donji for the period 1999–2008 (Figure 5b). The seasonal periodicity in rainfall is a climatological characteristic of study area.

_{L}, P

_{S}) and discharge (Q

_{RM}, Q

_{RV}) for the period 1996–2018 are presented in Figure 6, as well as a confidence interval. CCF is an indicator of linear dependency between two time series as a function of time lag k. If CCF shows statistically significant values and it is not symmetrical, a causal relationship between two series exists. In a system analysis, if the input time series is a white noise, CCF represents the impulse response function. If the input time series contains a periodicity, CCF may exhibit an oscillation depending on the filtering effect of the system. Considering a karst hydrological system, CCF between the input time series of rainfall and the output time series of discharge provides the information about the system response including significance, duration, and time delay. The duration of the system response represents the range of positive lags from the origin where CCF has statistically significant values. The time delay (time to peak or response time) gives an estimate of the pressure pulse transfer times through the karst system. It also indicates the degree of karstification. Consequently, several details require attention in Figure 6:

- The seasonal periodicity observed in rainfall (Figure 5a) is manifested in all functions, especially at negative lags where statistically significant values exist. This periodicity is more evident for the discharge from Rumin Mali (CCF(P
_{S},Q_{RM}) and CCF(P_{L},Q_{RM}) in Figure 6) than for the Rumin Veliki (CCF(P_{S},Q_{RV}) and CCF(P_{L},Q_{RV}) in Figure 6). This result is in accordance with the results of spectral analyses, where the spectral density function for the Rumin Mali in Figure 4a obtained for the period 1996–2018 has larger values at frequency 0.00274 1/day than the spectral density function for the Rumin Veliki in Figure 4b for the same period. - Differences between CCF(P
_{S},Q_{RM}) and CCF(P_{L},Q_{RM}) and between CCF(P_{S},Q_{RV}) and CCF(P_{L},Q_{RV}) are small, which shows that the rainfall from MS Sinj and MS Livno produce similar cross-correlation functions. The same result is obtained also for RG Bitelić Donji for the period 1999–2008, which means that the entire catchment probably has a similar variation of daily rainfall, considering a long period. - The time delay is the same for all functions. It amounts 1 day, so the pressure pulse is quickly transferred towards both springs after rainfall.
- CCF(P
_{S},Q_{RV}) and CCF(P_{L},Q_{RV}) have larger values at lags below 10 days than CCF(P_{S},Q_{RM}) and CCF(P_{L},Q_{RM}), which means that the discharge from Rumin Veliki is better correlated with rainfall during the period of quick flow. On the other hand, the discharge from Rumin Mali is better correlated with rainfall during the period of baseflow. The spring Rumin Mali also has evidently longer duration of response. Specifically, CCF(P_{S},Q_{RM}) and CCF(P_{L},Q_{RM}) become statistically insignificant at legs above approximately 135 days, whereas CCF(P_{S},Q_{RV}) and CCF(P_{L},Q_{RV}) become insignificant at legs above 92 days. These results show that a difference in the degree of karstification between the aquifers of two springs exist.

_{L}and the output time series of discharge Q

_{RM}and Q

_{RV}, where the control time series are rainfall P

_{S}and P

_{B}, are compared in Figure 7a,b. The main aim of this analyses is to characterize groundwater connections between the Livanjsko polje and the Rumin Springs. It should be emphasized that RG Bitelić Donji is situated at the foot of Dinara Mountain, immediately next to the catchment boundary of Rumin Mali (Figure 1). On the other hand, MS Sinj is in Sinjsko Polje, almost 10 km away from the catchment of Rumin Springs. It means that the control time series P

_{S}theoretically has no effect (Figure 2). In practice it is not the case, because of the spurious correlation that always exists between rainfall observed at neighboring locations. The rainfall time series P

_{S}evidently has a similarity with rainfall on the Dinara Mountain, so the effect of this similarity is removed from cross-correlation functions in Figure 6 by using P

_{S}as the control series. The obtained results show that the seasonal periodicity is not present in PCCF(P

_{L},Q

_{RV}|P

_{S}), PCCF(P

_{L},Q

_{RM}|P

_{S}), PCCF(P

_{L},Q

_{RV}|P

_{B}) and PCCF(P

_{L},Q

_{RM}|P

_{B}). It is completely removed by using the control time series P

_{S}and P

_{B}, which reveals that the origin of this periodicity in cross-correlation functions is not the rainfall P

_{L}. This result indicates that a relationship between the rainfall from Livanjsko Polje and the baseflow components of Rumin Springs does not exist. At lags corresponding to the first 10 days of spring response, PCCF(P

_{L},Q

_{RV}|P

_{S}) and PCCF(P

_{L},Q

_{RV}|P

_{B}), have evidently larger values than PCCF(P

_{L},Q

_{RM}|P

_{S}) and PCCF(P

_{L},Q

_{RM}|P

_{B}). In addition, control time series P

_{B}explains almost completely the existing correlation between P

_{L}and Q

_{RM}, so PCCF(P

_{L},Q

_{RM}|P

_{B}) in Figure 7b fluctuates at upper boundary of confidence interval. It shows that the relationship between time series P

_{L}and Q

_{RV}is relatively strong, whereas the relationship between P

_{L}and Q

_{RM}hardly exists. This result indicates that the part of catchment in Livanjsko Polje has an important role in generation of the quick flow component of discharge from the spring Rumin Veliki. It is not the case with the spring Rumin Mali. Concerning lags larger than 10 days, the functions obtained for two springs have similar behavior. Statistically significant effects are registered approximately during first 60 days. Figure 7c,d compare the partial cross-correlation functions between the input time series of rainfall P

_{S}and P

_{B}and the output time series of discharge Q

_{RM}and Q

_{RV}where the control time series is rainfall P

_{L}. The main aim of this analysis is to estimate the relative importance of the part of catchment located on the west side of Dinara Mountain. It can be noted that the partial effects in Figure 7c,d are more significant than the effects in Figure 7c,d, especially during the first 10 days corresponding to the quick flow. The strongest relationship at these lags is obtained for the rainfall from MS Bitelić (Figure 7d), which is in accordance with the present knowledge that the origin of quick flow components of both springs is the catchment on Dinara Mountain. The shapes of PCCF(P

_{B},Q

_{RV}|P

_{L}) and PCCF(P

_{B},Q

_{RM}|P

_{L}) are similar, which means that the responses of two springs are rather synchronized during the first 10 days after intensive rainfall. Concerning the partial effects located on other lags, results show that PCCF(P

_{S},Q

_{RV}|P

_{L}) and PCCF(P

_{S},Q

_{RM}|P

_{L}) in Figure 7c as well as PCCF(P

_{B},Q

_{RV}|P

_{L}) and PCCF(P

_{B},Q

_{RM}|P

_{L}) in Figure 7d consist the seasonal periodicity that was noted in CCF(P

_{S},Q

_{RV}) and CCF(P

_{S},Q

_{RM}) (Figure 6). The control time series P

_{L}practically has no effect on this periodicity, which confirms that the catchment located on Dinara Mountain is mainly responsible for the generation of the baseflow components of both springs.

_{L}, air temperature T

_{L}and relative humidity RH

_{L}observed at MS Livno, on the form of ACF(Q

_{RM}) and ACF(Q

_{RV}). The obtained results are presented in Figure 8a,b. It can be noted that the control time series of rainfall P

_{L}practically has no effects on the form of autocorrelation functions. The effects of control time series of relative humidity RH

_{L}are observable, but they also do not play any important role. The largest effect is produced by the control time series of air temperature T

_{L}. It should be noted that very similar results are obtained by using the meteorological data from MS Sinj, so they are not presented here. The resulting function for the spring Rumin Veliki (PACF(Q

_{RV}|T

_{L}) in Figure 8a) can be divided in two segments. First segment comprises lags below 60 days, where PACF(Q

_{RV}|T

_{L}) has statistically significant values. It shows that the actual memory effect of this spring is 60 days, which is 20 days longer than the estimation obtained from ACF(Q

_{RV}) using classical method [15]. The second segment includes lags above 60 days where PACF(Q

_{RV}|T

_{L}) is rather flat, and it variates around the interval of confidence. This result shows that the time series T

_{L}removes almost completely the effect of seasonal periodicity from ACF(Q

_{RV}), which means that the air temperature has very important role in generation of the baseflow component of Rumin Veliki. Concerning the spring Rumin Mali, two segments also can be recognized in PACF(Q

_{RM}|T

_{L}) in Figure 8b. First segment covers lags below 63 days where PACF(Q

_{RM}|T

_{L}) has statistically significant values. The second segment includes lags above 63 days where, differently from the spring Rumin Veliki, time series T

_{L}cannot remove periodicity. The existence of a seasonal periodicity in PACF(Q

_{RM}|T

_{L}) and the absence in PACF(Q

_{RV}|T

_{L}), as well as the evident differences between PACF(Q

_{RM}|T

_{L}) and PACF(Q

_{RV}|T

_{L}) at lags below 60 days, indicate that the springs Rumin Mali and Rumin Veliki have significantly different hydrological functioning.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Location map of the Cetina River catchment with groundwater connections determined by tracing tests.

**Figure 2.**Schematic presentation of effects for a hydrological system with two input time series of correlated rainfall, x and z, and an output time series of discharge y: (

**a**) there is no relationship between series z and y, (

**b**) there is no relationship between series x and y, (

**c**) series x and z are antecedent cause of output series y.

**Figure 3.**Autocorrelation function (ACF) of discharge for the springs Rumin Mali (Q

_{RM}) and Rumin Veliki (Q

_{RV}) for periods 1950–1972 and 1996–2018. CI—confidence interval.

**Figure 4.**Spectral density function (SDF) of discharge for periods 1950–1972 and 1996–2018 for the springs Rumin Mali and Rumin Veliki for: (

**a**,

**b**) low frequency range and truncation point of m = 2556 days, and (

**c**,

**d**) high frequency range and truncation point of m = 365 days.

**Figure 5.**Spectral density function (SDF) of rainfall for: (

**a**) MS Sinj (P

_{S}) and MS Livno (P

_{L}) for period 1996–2018 for truncation point m = 2556 days, and (

**b**) RG Bitelić Donji (P

_{B}) for period 1999–2008 for truncation point m = 1220 days.

**Figure 6.**Cross-correlation function (CCF) between rainfall and discharge, where the input time series is rainfall from MS Sinj (P

_{S}) and MS Livno (P

_{L}) and the output time series is discharge from the spring Rumin Mali (Q

_{RM}) and Rumin Veliki (Q

_{RV}), for period 1996–2018. CI—confidence interval.

**Figure 7.**Partial cross-correlation function (PCCF) for the input time series of rainfall from MS Livno (P

_{L}), where the control time series is: (

**a**) rainfall from MS Sinj (P

_{S}) and (

**b**) rainfall from RG Bitelić Donji (P

_{B}). PCCF for the control time series of rainfall P

_{L}, where the input time series is: (

**c**) rainfall P

_{S}, and (

**d**) rainfall P

_{B}. The output time series is discharge from the springs Rumin Mali (Q

_{RM}) and Rumin Veliki (Q

_{RV}). CI—confidence interval.

**Figure 8.**Partial autocorrelation function (PACF) of discharge for the spring: (

**a**) Rumin Veliki (Q

_{RV}), and (

**b**) Rumin Mali (Q

_{RM}), where the control series is rainfall (P

_{L}), air temperature (T

_{L}) and relative humidity (RH

_{L}) from MS Livno, for period 1996–2018. CI—confidence interval.

1950–1972 | 1996–2018 | 1999–2008 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Rumin Mali | Rumin Veliki | Livno | Sinj | Rumin Mali | Rumin Veliki | Bitelić Donji | |||||

Q_{RM}(m ^{3}/s) | Q_{RV}(m ^{3}/s) | P_{L}(mm) | T_{L}(°C) | RH_{L}(%) | P_{S}(mm) | T_{S}(°C) | RH_{S}(%) | Q_{RM}(m ^{3}/s) | Q_{RV}(m ^{3}/s) | P_{B}(mm) | |

Min. | 0 | 0.26 | 0 | −15.6 | 15 | 0 | −7.2 | 22 | 0 | 0.04 | 0 |

Mean | 2.74 | 19.2 | 3.21 | 10.2 | 74 | 3.18 | 13.1 | 69 | 1.61 | 6.91 | 3.47 |

Max. | 16.5 | 106 | 125.1 | 29.1 | 100 | 153.4 | 30.4 | 100 | 9.38 | 87.6 | 187.7 |

S. D. | 3.09 | 20.1 | 8.06 | 12.1 | 8.03 | 8.53 | 19.7 | 7.63 | 2.19 | 12.0 | 9.40 |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/w12123570

**AMA Style**

Denić-Jukić V, Lozić A, Jukić D.
An Application of Correlation and Spectral Analysis in Hydrological Study of Neighboring Karst Springs. *Water*. 2020; 12(12):3570.
https://doi.org/10.3390/w12123570

**Chicago/Turabian Style**

Denić-Jukić, Vesna, Ana Lozić, and Damir Jukić.
2020. "An Application of Correlation and Spectral Analysis in Hydrological Study of Neighboring Karst Springs" *Water* 12, no. 12: 3570.
https://doi.org/10.3390/w12123570