Fractional Process with Jumps for Karstic Spring Discharge

Fractal dimensions for the daily discharge data series of several karstic springs in Northeast Hungary have recently been computed and analyzed. We model four of those series, having similar fractal dimensions, using a superposition of a fractional Ornstein-Uhlenbeck process and a jump process of renewal-reward type. Beyond some usual goodness-of-fit measures, simulations of the model show an appealing visual fit. When the fractal dimension is not taken into account in the modeling, the simulated accumulated discharges tend to significantly exceed the realistic one.