Author(s): Alastair Barnett

Linked Author(s):

Keywords: Flood mapping; 3D model segments; Lidar ground survey; Map grid; Cross-sections; Segmented solution mesh; Warped surface interpolation; Hyperbolic paraboloids

Abstract: Mapping of a fixed 3D ground surface has long been achieved by the conventions of contour mapping on a 2D horizontal plan view. Here the third (height) dimension is represented by colour gradations, with a key provided to define the chosen contour ranges. Established surface mapping packages offer advanced facilities such as kriging, which usually provide the best reconstruction of incised channel bed shapes. However, the free surface of a 3D water body often has gradients far lower than ground slopes, so contour mapping of these at the same vertical scale as ground mapping will rarely provide useful resolution of water surface slopes. Therefore computational effort to prepare free surface solutions for mapping should be restricted to the tiny minority of time steps when the depth solution may need to be mapped. 3D scalar solutions can be set up along a channel at designated cross-sections and time steps to track only the mean water level across the section and the volumetric discharge rate through the section. Efficient double sweep methods can then be deployed in place of more computationally demanding matrix inversion technology. Any two cross-sections in a channel reach enclose a model segment, formally defined as the vertical projection of the quadrilateral joining the ends of two adjacent cross-sections. Each segment along the channel surface can usually then be characterized by longitudinal and lateral free surface slopes measured around this boundary quadrilateral. If a first attempt at segmentation does not provide adequate resolution of local areas, cross-sections should be moved closer together in appropriate places. The most accurate way of interpolating a surface defined by four such straight-line warped surface generators is by a hyperbolic paraboloid. Mathematical analysis suitable for software coding is introduced in the paper.

DOI: https://doi.org/10.64697/978-90-835589-7-4_41WC-P1948-cd

Year: 2025