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

Abstract

Various methods of time series analysis have been used in studies of karst hydrological systems. Among these methods, correlation and spectral analysis have had an important role. The correlation analysis most often has been based on determination of correlation coefficients and correlation functions. Partial correlation functions (PCF) are a mathematical tool of the correlation analysis which practical applicability in karst hydrology is insufficiently explored. In this study, the correlation and spectral analysis are applied on the catchment of Rumin Springs located in the Dinaric karst area between Croatia and Bosnia and Herzegovina. The available daily data are the rainfall, air temperature and relative humidity from three locations, as well as the discharge from two springs. The periods before and after the construction of HPP Orlovac in 1973 are analyzed. The basic hypothesis is that a difference between PCF obtained for two neighboring karst springs describe a difference in their functioning. The results of application show that PCF can resolve some ambiguities concerning the effects included in correlation functions and can provide the additional information that cannot be obtained by other methods of time series analysis. The obtained results are mostly in accordance with the present knowledge, and they support the existing hypotheses about the functioning of Rumin Springs.

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

“…The autocorrelation function measures the correlation of two observed series with different time lags and indicates the similarity of the observed data series with the same lagged series. Below is a brief overview of the autocorrelation function with the corresponding expressions [38][39][40].…”

“…where C (k) is the autocovariance and σ is the standard deviation. According to Denić-Jukić et al [38], the truncation point m represents the domain of the function or the range of the time interval in which the analysis is performed. The recommendation is that the value of the variable m does not exceed the value of n/3, because for values in the range between n/3 and n/2 the results start to change, while after n/2 they are no longer accurate [40].…”

“…where C 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.…”

“…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]:…”

Modeling Probabilistic-Based Reliability Analysis for Irrigation Water Supply Due to Uncertainties in Hydrological and Irrigation Factors

“…As mentioned in the above sections, the hydrological and irrigation factors are needed to irrigate the crops at all canals in the irrigation zones. Since the hydrological variables (e.g., surface runoff and precipitation) are commonly treated as correlated in time and space [26], the hydrological factors concerning the surface runoff should be temporally and spatially correlated variates. Moreover, the offtakes and intakes of several hydraulic structures are mainly delivered to the irrigation zone; in addition, they significantly change with the demands of the livelihood and industry.…”