IWRA World Water Congress 2008 Montpellier France
1. Water availability, use and management
storm events, small catchments, numerical model, 2D shallow water equations.
AbstractShallow water models are
extensively used to compute the flow field and flood regions in rivers. The input data required in such models are the
topography, the bed roughness coefficient, and the water discharge flowing through the reach under study. The water
discharge is usually obtained using simple hydrologic models based on empirical formula, which relate the water
discharge with the precipitation intensity, the catchment surface, mean slope and soil. Usually such models contain
simplified representations of surface runoff, evapotranspiration, and channel flow. In addition, the water discharge is
introduced at one specific cross section in the hydraulic model, while in reality there is a continuous spatially
distributed contribution of runoff to the river discharge.
Recent advances in the numerical schemes for solving
the two-dimensional shallow water equations permit modelling water flow over complex topography with extremely
small water depths, including the propagation of wet-dry fronts. This fact, together with the continuous increase in
computational efficiency, opens up the possibility of computing the surface runoff due to precipitation in a whole
watershed. Precipitation surface runoff is actually a very shallow water flow, and therefore it should be well
represented by the two-dimensional shallow water equations.
This paper presents a two-dimensional shallow
water model which computes at the same time the precipitation runoff, flow velocity and water surface levels in the
entire watershed, including the all the river reaches. The depth averaged mass and momentum conservation equations
are solved, considering the effects of bed friction, bed slope, precipitation and infiltration. Hence, the model has a
conceptual and mathematical ground much stronger than classic hydrologic models. The numerical problems which
arise from the small water depths, the presence of wet-dry fronts and the large bed friction forces, are successfully
solved in the present model.
The only parameters of the model which need calibration are the bed friction
coefficient and the infiltration properties of the soil. The effects of small scale microtopography which is not resolved
by the model, must be included via the bed friction coefficient, in the same way as the effects of ripples and dunes in
rivers are included in the bed friction stress. The sensitivity of the model to bed friction and infiltration parameters has
been studied. When the bed friction coefficient and infiltration can be accurately identified, and the topography is well
defined, the predictions of the model are very satisfactory, and this is shown in the validation results presented in this
paper. In order to avoid the uncertainty in the parameter determination of a real catchment, experimental validation
of the model is presented in simple 1D and 2D geometries. Several experiments are modelled, with different
topography, surface roughness, and rainfall intensities and durations. The agreement with experimental results is very
The model presented can be used in the forecasting of flood regions in catchments due to storm
events, as well as in the design of hydraulic structures to mitigate and control flood risks.