Roger Moussa

Criteria for the choice of flood-routing methods in natural channels

Abstract The Saint-Venant equations are used to describe river waves. Generally, for flood routing in rivers, the Saint-Venant system is reduced to the diffusive wave equation which can be resolved using finite-difference algorithms. The choice of a numerical method, and of the space and time steps to be retained, depends essentially on the form of flood hydrographs and the hydraulic properties of the river. This paper investigates these areas; two sets of criteria are propossed, the first to define parameter ranges representing each wave type and then, in the particular case of the diffusive wave model, to define criteria for the choice of numerical algorithm and appropriate space and time steps. The first analysis was based on the concept that river wave behaviour is determined by the balance between friction and inertia. The conclusions relate to the magnitude of temporal characteristics of flood waves, expressed as a function of the Froude number of the steady uniform flow and a dimensionless wave number of the unsteady component of the motion. The second part discussed questions related to the diffusive wave problem and to numerical instabilities. A technique is proposed to guide the user in the choice of the computational algorithm and specifies the error introduced by numerical methods. The technique was applied to flood-routing simulation for the Loire river in France. In this case, two finite-difference algorithms were compared to the exact solution given by the analytical method. Comparisons between results show the efficiency of the technique to optimise the choice of the finite-difference method and the adequate space and time steps.

ANALYTICAL HAYAMI SOLUTION FOR THE DIFFUSIVE WAVE FLOOD ROUTING PROBLEM WITH LATERAL INFLOW

The diffusive wave equation is generally used in flood routing in rivers. The two parameters of the equation, celerity and diffusivity, are usually taken as functions of the discharge. If these two parameters can be assumed to be constant without lateral inflow, the diffusive wave equation may have an analytical solution: the Hayami model. A general analytical method, based on ‘Hayami’s hypothesis, is developed here which resolves the diffusive wave flood routing equation with lateral inflow or outflow uniformly distributed over a channel reach. Flood routing parameters are then identified using observed inflow and outflow and the Hayami model used to simulate outflow. Two examples are discussed. Firstly, the prediction of the hydrograph at a downstream section on the basis of a knowledge of the hydrograph at an upstream section and the lateral inflow. The second example concerns lateral inflow identification between an upstream and a downstream section on the basis of a knowledge of hydrographs at the upstream and downstream sections. The new general Hayami model was applied to flood routing simulation and for lateral inflow identification of the River Allier in France. The major advantages of the method relate to computer simulation, real-time forecasting and control applications in examples where numerical instabilities, in the solution of the partial differential equations must be avoided.

GEOMORPHOLOGICAL TRANSFER FUNCTION CALCULATED FROM DIGITAL ELEVATION MODELS FOR DISTRIBUTED HYDROLOGICAL MODELLING

Recently, several attempts have been made to relate the hydrological response of a catchment to its morphological and topographical features using different hypotheses to model the effect of the drainage network. Several transfer functions were developed and some of these are based on the theory of a linear model, the geomorphological unit hydrograph. The aim of this paper is to present a methodology to automatically identify the transfer function, using digital elevation models for applications in distributed hydrological modelling. The transfer function proposed herein is based on the Hayami approximation solution of the diffusive wave equation especially adapted for the routing hydrograph through a channel network. The Gardon d’Anduze basin, southern France, was retained for applications. Digital elevation models were used to extract the channel network and divide the basin into subcatchments. Each subcatchment produces, at its own outlet, an impulse response which is routed to the outlet of the whole catchment using the diffusive wave model described by two parameters: celerity and diffusivity functions of geometrical characteristics of the channel network. Firstly, a geomorphological unit hydrograph obtained by routing a homogeneous effective rainfall was compared with the unit hydrograph identified by a lumped model scheme, then the distributed model was applied to take into account the spatial variability of effective rainfall in the catchment. Results show that this new method seems to be adapted for distributed hydrological modelling; it enables identification of a transfer function response for each hydrological unit, here subcatchments, and then simulation of the contribution of each unit to the hydrograph at the outlet.

Fractal analyses of tree-like channel networks from digital elevation model data

Digital elevation models (DEMs) are generally used to automatically map the channel network and to delineate subbasins. The most common approach to extract a channel network from DEMs consists of specifying a threshold area S which is the minimum area required to drain to a point for a channel to form. This threshold area is usually specified arbitrarily, although it is recognized that different threshold areas will result in substantially different channel networks for the same basin. In this paper, we study the effect of S (that is also the scale of observation) on the morphometric properties (external and internal links, length of drainage paths, mainstream length) and scaling properties (such as Hortons and Strahlers laws, and fractal dimension). Three basins, located in southern France, were extensively studied. The results indicate that morphometric properties vary considerably with S, and thus values reported without their associated S should be used in hydrologic analysis with caution. Then, the fractal geometry is used to take into account the dependence of measured values on observation scales, which is not possible with classical hydrological indexes. The use of fractals allows, first, to point out self-similarity in the structure of channel networks and then to quantify the tree-like organization. New catchment shape indexes, independent of the observation scale S, are defined. These indexes are useful for comparing catchments and for measuring the irregularity level of the channel network.

Hydrological response characteristics of Mediterranean catchments at different time scales: a meta-analysis

ABSTRACT This work examines 140 hydrological studies conducted in the Mediterranean region. It identifies key characteristics of the hydrological responses of Mediterranean catchments at various time scales and compares different methods and modelling approaches used for individual-catchment studies. The study area is divided into the northwestern (NWM), eastern (EM) and southern (SM) Mediterranean. The analysis indicates regional discrepancies in which the NWM shows the most extreme rainfall regime. A tendency for reduced water resources driven by both anthropogenic and climatic pressures and a more extreme rainfall regime are also noticeable. Catchments show very heterogeneous responses over time and space, resulting in limitations in hydrological modelling and large uncertainties in predictions. However, few models have been developed to address these issues. Additional studies are necessary to improve the knowledge of Mediterranean hydrological features and to account for regional specificities. Editor D. Koutsoyiannis Associate editor A. Efstratiadis

Transport of a nematicide in surface and groundwaters in a tropical volcanic catchment

The aim of this article is to determine how the nematicide cadusafos [S,S-di-sec-butyl O-ethyl phosphorodithioate] contaminates water and soils at two scales, subcatchment and catchment. The study site was a small banana (Musa spp.)-growing catchment on the tropical volcanic island of Guadeloupe in the Caribbean. Two application campaigns were conducted, one in 2003 on 40% of the catchment and one in 2006 on 12%. The study involved monitoring for 100 d the surface water and groundwater flows and the cadusafos concentrations in the soil and in surface and groundwaters in a 2400 m(2) subcatchment and a 17.8 ha catchment. The results show that at the subcatchment scale the high retention in the A horizon of the soil limits the transport of cadusafos by runoff, whereas the lower retention of the molecule in the B horizon favors percolation toward the shallow groundwater. Comparing the losses of cadusafos at the subcatchment and at the catchment scales revealed that the nematicide re-infiltrated in the hydrographic network. Two successive phases of stream water contamination were observed, corresponding to two distinct contamination mechanisms: an event-dominated contamination phase (of <30 d) when transport was linked to overland flow during precipitation shortly after application, and a stabilized contamination phase when transport originated mainly from the drainage of the shallow aquifer. Lastly, comparing the losses of the two phases during 2003 and 2006 showed that shallow groundwater, which is promoted in such permeable soils under abundant tropical rainfalls, seems to be the main contributor to stream contamination.

Is the drainage network a fractal Sierpinski space

The most common approach to extract the channel network from digital elevation models is to specify a threshold area, S, which is the minimum area required to drain to a point within which a channel forms. This threshold area is usually specified arbitrarily, although it is recognized that different threshold areas will result in substantially different channel networks for the same basin. This paper studies the effects of S, which is also the scale of observation, on scaling and morphometric properties such as the number of sources and the areas of source basins and lateral basins. The Gardon basin, located in southern France, was extensively studied. The results indicate that morphometric properties vary considerably with S and that the spatial distribution of source basins can be considered as a fractal Sierpinski space. A simple model based on the procedure similar to the Sierpinski carpet construction is proposed to explain empirical relations between the number of source areas and the threshold, S. The model presents a new approach to estimate basin fractal properties and defines new indices to characterize the spatial distribution of first-order basins. This methodology is useful for hydrologists and geomorphologists dealing with river networks and spatial patterns of various basin properties such as vegetation, soil, soil moisture, and human activities.

Use of a flood-routing model to assess lateral flows in a karstic stream: implications to the hydrogeological functioning of the Grands Causses area (Tarn River, Southern France)

The aim of this study is to assess the spatio-temporal variability of lateral flows in the streams of a large karstic basin to construct a conceptual model of karst contributions to flood generation. The lateral flows of the Tarn River, which crosses the Grands Causses karst zone in Southern France, were investigated between several gauging stations along the river. First, through analysing the lateral flows on an event time scale of 30 floods, it was possible to identify the losing and gaining reaches, highlighting a highly variable attenuation/amplification role of karsts on flood generation. Second, the diffusive wave model was used to quantify the lateral flows on an hourly time step within a flood event. The simulations show a high variability of lateral outflows and inflows within a same reach according to the hydrometeorological conditions, with in some cases an inversion of the lateral flow direction during the flood. The results highlight complex surface/groundwater exchanges during a single flood event, with high river losses despite the concurrent flow of large springs feeding the stream. This spatio-temporal variability of the karst influence on flood generation was linked to the aquifer’s structure, which has improved the understanding of the hydro(geo)logical functioning of the Grands Causses massif. Finally, the new methodology proposed here opens challenging perspectives towards a framework for the analysis of surface–groundwater exchanges in karstic rivers.

Modeling of Floods—State of the Art and Research Challenges

This chapter presents a state of the art review and research challenges in modeling flood propagation and floodplain inundation. The challenges for flood inundation models are directly linked to the representation of flow processes, to the formulation of theoretical physical laws and to practical considerations. First, we review the various structures of coupled spatially distributed hydrological-hydraulic models and the corresponding spatial representation of flow processes. Second, we present the theoretical basis of 1-D and 2-D Saint-Venant “shallow water” equations with overbank flow, the approximation of Saint-Venant models such as the Diffusive Wave and the Kinematic Wave models and then discuss the domains and limits of applications of each type of models. Practical considerations linked to numerical solution schemes, boundary conditions and model parameterization, calibration, validation and uncertainty analysis were also considered. Finally, the discussion addresses the research challenges for guiding the modeler, according to the principle of parsimony, in seeking the simplest modeling strategy capable of (i) a realistic representation of the physical processes, (ii) matching the performances of more complex models and (iii) providing the right answers for the right reasons.

How Karst Areas Amplify or Attenuate River Flood Peaks? A Response Using a Diffusive Wave Model with Lateral Flows

This paper investigates the role of karst aquifers on flood generation and propagation using the Hayami Diffusive Wave (DW) model accounting for uniformly distributed lateral flows. The inverse model was applied on the main channel reaches of the Tarn basin at Millau (2,400 km2) in southern France to assess lateral inflows from karstic springs as well as lateral outflows from river losses. Results show that the DW model, which is simple, parsimonious, and easy-to-use, is able to quantify lateral flows avoiding difficult parameterisation. Surface/groundwater exchanges were characterised on several reaches along the stream, showing a highly variable attenuation/amplification influence of flood peak by karst units during a single flood event. We showed that the upstream part of the karst area have a dominant attenuation role by re-infiltrating part of runoff from the head-water basin in hard-rock areas, while the downstream part have a dominant amplification role due to high contributions of karst groundwater. These results improved the conceptual hydrogeological model of the Grands Causses region.