Quadtree flood simulations with sub-grid digital elevation models

Flooding is an increasing hazard to society and good governance now implies careful water management in terms of design, planning and control of urban and rural areas. This requires that rainstorms, extreme water levels and so on are taken into account with relevant precision. A great aid is the existence of graphical information systems with raster-based digital elevation models (DEMs). Modern technology such as Lidar means that DEMs are of ever-increasing resolution. This paper describes how, without adaptations, a DEM can be used efficiently for detailed 2D flooding simulations. The method is based on four components: the sub-grid method; bottom friction derived from the divided channel method; the finite-volume staggered grid method for shallow water equations with rapidly varying flows; and quadtrees.