Extending the concept of unit hydrograph to dynamic river networks

This thesis investigates the influence of the temporal variability of the active flowing network on the hydrologic response of a catchment exploiting the concept of unit hydrograph. The Instantaneous Unit Hydrograph (IUH) is a consolidated hydrological tool that formalizes the transformation of effective rainfall into discharge at the catchment outlet. While classical hydrological theories treat the IUH as a time-invariant probability density function of response times, identified from a fixed network configuration, recent research has highlighted the dynamical nature of river networks as a fundamental, yet partially unexplored, driver of catchment functioning. To address this, a generalized, time-variant unit hydrograph model is developed, formulated conceptually, and implemented numerically to represent the effect of variable length on the IUH and the catchment discharge. This formulation introduces a time-dependent convolution that relates effective rainfall to discharge, integrating the temporal evolution of the network length. Comparison with static benchmarks demonstrates that static formulations fail to capture peak discharge magnitude and recession shape. In particular, theoretical and numerical results show that the hydrograph crest is governed by the transient activation of the flowing network. Channel network expansion triggers a rapid mobilization of pre-stored soil water, amplifying the hydrologic response of river basins as opposed to stationary configurations. The asymmetry between rapid network expansion and slow contraction dictates a long-lasting effect of network dynamics on the catchment drainage efficiency between rain events. Dynamic recession time scales and the emergence of non-linear storage dynamics are jointly modulated by rainfall intensity and the network-dependent saturation state. The effect of network dynamics on the catchment discharge is particularly evident in erratic regimes, where the frequency of events is relatively lower. This thesis bridges classical IUH theory with network dynamics, providing a parsimonious framework to characterize catchment hydrologic response accounting for the time-varying network configurations.