Section: New Results

Lumped hydrological models with infinite characteristic time transfer functions

Participant : Vincent Guinot.

Karst and mountainous catchments usually exhibit rainfall-runoff transfer functions involving multiple time scales. In most existing conceptual, hydrological models of such catchments, multiple time scale response is achieved by introducing several reservoirs and non-linear transfer functions. In [9] , multiple time scales are introduced by proposing a transfer function with an infinite characteristic time. The heavy-tailed transfer function behaves asymptotically as an inverse power of time. In the limit of long time scales, the governing equation for the system obeys a fractional differential equation. With a single reservoir, the proposed approach is shown to perform satisfactorily compared to other models of similar or more complex structure. The fractional differential equation is shown to be useless for usual time scales and should not be used in practice.