Damir Jukić

Composite transfer functions for karst aquifers

Linear transfer functions have been extensively used in hydrological studies. Generally, we support this conclusion: rainfall-runoff models based on the convolution between rainfall rates and a nonparametric transfer function (NTF) are not successful at simulating karst spring discharges during long recession periods. The tails of identified transfer functions have irregular shapes and they are not accurate physical representation of the transport through a karst system. Irregularities are the result of unavoidable errors in input and output time series and simplifications made by considering the system as linear and time invariant. This paper deals with a new form of the transfer functions for karst aquifers, the so-called composite transfer function (CTF). The CTF simulates discharges by two transfer functions adapted for the quick flow and the slow flow hydrograph component modeling. NTF is responsible for the quick flow component. The slow flow component is modeled by a parametric transfer function that is an instantaneous unit hydrograph mathematically formulated and defined from a conceptual model. By using the CTF, the irregular shape of the tail of the identified transfer function can be avoided, and the simulation of long recession periods as well as the simulation of a complete hydrograph becomes more successful. The NTF, the Nash model, the Zoch model and other similar conceptual models can be considered separately as simplified forms of the CTF. The rainfall-runoff model based on the convolution between rainfall rates and the CTF was tested on the Jadro Spring in Croatia. The results of the application are compared with the results obtained by applying NTFs independently.

HIGHER-ORDER PARTIAL CROSS-CORRELATION FUNCTION AS A TOOL FOR INVESTIGATING HYDROLOGICAL RELATIONS IN KARST

This paper demonstrates the practical applicability of higher-order partial cross-correlation function in hydrological system analysis. The study area is the karst hydrological system of two adjacent karst springs Jadro and Žrnovnica situated in the Dinaric karst of Croatia. The subject of interest is the hydrological relation between these two springs and three basins located in the central part of Jadro Spring catchment. The relation is investigated by the higher-order partial cross-correlation function between rainfall and spring discharge using various sets of control signals. The available hourly time series are the discharges from two springs as well as the rainfall rates, air temperature and relative humidity from the meteorological stations Dugopolje, Konjsko and Vucevica. Depending on analysis goals, the sets of control signals consist of one or several time series including the air temperature, relative humidity, rainfall rates and the discharge from adjacent spring. The results of practical application show that the effects of hydrological processes can be recognized in the higher-order partial cross-correlation function. The clear distinction can be made between the causal relationship and spurious correlations that always exist in hydrological time series. Consequently, the drawbacks of classical cross-correlation analysis can be overcome and the form of cross-correlation function can be completely explained. Generally, the higher-order partial cross-correlation function can give valuable information about spatial and temporal characteristics of groundwater flow through karst underground that cannot be obtained by the classical cross-correlation analysis. The inferences presented in this paper about the spatial and temporal distribution of water between the central part of Jadro Spring catchment and the Žrnovnica Spring are generally in accordance to the existing hypothesis about functioning of this karst hydrological system.