A THEORETICAL BASIS FOR APPLICATION OF PARTIAL CORRELATION FUNCTIONS IN HYDROLOGICAL SYSTEM ANALYSIS WITH REFERENCE TO KARST

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This paper investigates a theoretical aspect of application of partial correlation functions in hydrological system analysis. The functioning of hydrological system is simulated with the conceptual mathematical model consisting of series of linear reservoirs where the inputs are synthetic time series representing rainfall on catchment and the resulting output time series represents the discharge from spring. The partial correlation functions are calculated for the input and output time series describing specific hydrological situations that may occur in karst. Three major issues causing difficulties in interpreting results of correlation analysis of time series of rainfall and karst spring discharge are in focus: the spatial variability of retention characteristics of karst, the spatial and temporal variability of rainfall on catchment, and the existence of unobserved inflows or outflows. The results show that the effects of space-time-variant hydrological processes and nonstationary components can be detected in the correlation functions, and the clear distinction can be made between the causal relationship and spurious correlations. Consequently, the internal structure of linear and time-invariant hydrological system can be determined from the input and output time series even if the input time series are spuriously correlated, so the contribution of each part of system to the output can be evaluated. Practically, it means that partial correlation functions can provide information about the spatial variability of groundwater recharge including the recognition of areas of dominant supply and the detection of areas located outside of a karst hydrological system by using only time series of rainfall and spring discharge. Generally, the obtained results confirm that the partial correlation functions are capable to provide valuable information about the spatial and temporal characteristics of hydrological system that cannot be obtained by the classical correlation analysis. The main contribution of this paper is a theoretical basis for interpretation of forms of partial correlation functions.