Nonlinear kernel functions for karst aquifers

This paper presents a form of kernel function for karst aquifers derived from the time-invariant and non-anticipatory Volterra series. The shape of the kernel function depends on the current value of an index of antecedent recharge that is considered as an indicator of groundwater levels and vadose zone saturation. The proposed nonlinear form preserves specific characteristics of instantaneous unit hydrographs. By using analogies with the conceptual model of nonlinear reservoir, it is shown that the second component of the kernel function characterizes the prevailing type of groundwater flow. If the second component is positive, the free-surface flow is dominant, whereas the negative value indicates that the flow under pressure prevails. Groundwater recharge rates are calculated by using a groundwater recharge model based on the Palmer’s soil-moisture balance method. The values of parameters of the groundwater recharge model are estimated by the spectral method which is modified to avoid the assumption about exponential forms of autocorrelation functions of input and output time series. This paper analyzes also the practical applicability of nonlinear kernels for the preliminary characterization of karst aquifers and the karst springs discharge modeling. The results of applications on the springs zones of the rivers Krka and Krčić are in accordance with previous assumptions that the Main Krka Spring is an ascending karst spring which aquifer is situated deeply inside the karst underground, whereas the Main Krčić Spring function as a descending karst spring.