Channel network critical nodes, E-GIUH and space-time dynamics of flood events

Abstract

The space-time dynamics of floods are mainly controlled by the spatial distribution of rainfall, the channel network topological structure, the soil hydrodynamic properties and initial water content conditions. In this complex setting, it remains unclear what is the relative contribution of each of these factors. The scope of this work is to report where and how changes in the space-time dynamics of rainfall, land use, morphology of streams, are shaping flood hydrograph. The methodology assesses the impact of the spatial subdivision of the catchment into subcatchments on the output of a hydrological/hydraulic model (MHYDAS) when applied as lumped, semi-distributed or spatially distributed. Based on the graph theory, a new deterministic iterative model to describe the channel network structure is proposed on the basis of a conceptualization of the topology of the channel network, and exploiting the morphometric characteristics of internal nodes. For each flood event, internal nodes are classified by order of importance depending on the drained area and its corresponding rainfall and soil properties. This enables to identify the “critical nodes” of the channel network which may vary from one event to another. We test different spatial catchment subdivision schemes using 1, 2, 3, … n critical nodes of the channel network. Then, for each catchment subdivision we run the spatially distributed hydrological model MHYDAS to simulate hydrographs at the outlet. Applications were conducted on twelve French Mediterranean catchments with an area ranging between 1 and 1000 km², characterized by high variability of rainfall and soil hydrodynamic characteristics. Simulations were conducted on observed rainfall/runoff events but also on virtual rainfall events (20 events) in order to study a large range of spatiotemporal rainfall variability. Results show that the spatial catchment subdivision on the basis of respectively one, two or three critical nodes are sufficient to simulate the hydrograph at the outlet with respectively a Nash-Sutcliffe criteria of 0.43, 0.59 and 0.78. Then, for each flood event, we calculate the Geomorphological Instantaneous Unit Hydrograph (GIUH) which is central to describe the catchment response. Finally, we compare the GIUH and the E-GIUH (Andrieu et al., 2021) which is specific to each flood event and which is derived from rainfall/runoff data and formulated as an inverse problem with parameters such as the E-GIUH velocity and coefficient of dispersion, as well as the hyetograph of rainfall excess. The results show the agreement between the GIUH obtained from 3 critical nodes and the E-GIUH.  The characteristics of the critical nodes such as the drained area, the distance to the outlet, and the position on the channel network are useful descriptors for modeling the GIUH function and for representing the scaling properties of a channel network. They are sufficient descriptors to reproduce the main shape of the GIUH, the peak, the time to peak, and the main properties such as non-negativity, non-stationarity, and power law decay of the spectrum. They may be used to establish catchment typology, to compare catchments, and to classify flood events for catchment regionalization.