Composite transfer functions for karst aquifers

Abstract

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.