Anisotropic considerations while interpolating river channel bathymetry

Numerical modeling of flow dynamics in river channels may require the spatial interpolation of scattered measurements of bathymetry elevation to obtain elevations at computational mesh nodes. This paper examines the various spatial interpolation methods used in interpolating river channel bathymetry. Commonly used interpolation methods, namely inverse distance weighting, spline (tension and regularized), natural neighbor, TopoGrid, and ordinary kriging (isotropic and anisotropic) are evaluated within the ArcGIS environment by using root mean square error (RMSE) criteria. To study the anisotropic effects, the interpolation methods are evaluated in two different coordinate systems: a Cartesian ( x, y) coordinate system and a flow-oriented ( s, n) coordinate system. Using the data from the Brazos River in Texas, it is shown that TopoGrid, natural neighbor and ordinary kriging, which do not account of anisotropy in the data, performed better than anisotropic kriging in the Cartesian coordinate system. In the flow-oriented coordinate system, the performance of anisotropic spatial interpolation methods is significantly better (40% reduction in RMSE) compared to the isotropic interpolation methods. A modified version of inverse distance weighting method, called elliptical inverse distance weighting (EIDW), is developed to account for river anisotropy. The RMSE results from application of EIDW are close to that from anisotropic kriging, thus providing a simple and computationally faster alternative to complex kriging methods.