Temporal scaling of groundwater discharge in dual and multicontinuum catchment models

This paper presents a multicontinuum approach to model fractal temporal scaling of catchment response in hydrological systems. The temporal scaling of discharge is quantified in frequency domain by the transfer function HðxÞ, which is defined as the ratio between the spectra of catchment response and recharge time series. The transfer function may scale with frequency x as HðxÞ x2b. While the classical linear and Dupuit models predict exponents of b52 and b51, observations indicate scalings with noninteger exponents b. Such behaviors have been described by multifractal models, which, however, often lack a relation to the medium characteristics. We revisit and extend the classical linear Dupuit aquifer models and discuss their physical meanings in the light of the resulting aquifer dynamics. On the basis of these classical models, we derive a multicontinuum approach that provides physical recharge models which are able to explain fractal behaviors with exponents 1=2 < b < 2. Furthermore, this approach allows to link the fractal dynamics of the discharge process to the physical aquifer characteristics as reflected in the distribution of storage time scales. We systematically analyze the catchment responses in the proposed multicontinuum models, and identify and quantify the time scales which characterize the dynamics of the catchment response to recharge.