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.

[1]  I. A. Nalder,et al.  Spatial interpolation of climatic Normals: test of a new method in the Canadian boreal forest , 1998 .

[2]  R. Franke.  Smooth Interpolation of Scattered Data by Local Thin Plate Splines , 1982 .

[3]  Philippe J. J. Desmet,et al.  Effects of Interpolation Errors on the Analysis of DEMs , 1997 .

[4]  Shoji Fukuoka,et al.  Longitudinal Dispersion in Sinuous Channels , 1973 .

[5]  Chieh-Li Chen,et al.  Application of Taylor transformation to nonlinear predictive control problem , 1996 .

[6]  Panayiotis Diplas,et al.  Using two-dimensional hydrodynamic models at scales of ecological importance , 2000 .

[7]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[8]  M. Tomczak,et al.  Spatial Interpolation and its Uncertainty Using Automated Anisotropic Inverse Distance Weighting (IDW) - Cross-Validation/Jackknife Approach , 1998 .

[9]  Glenn S. Carter,et al.  Creating rectangular bathymetry grids for environmental numerical modelling of gravel-bed rivers , 1997 .

[10]  R. Sibson,et al.  A brief description of natural neighbor interpolation , 1981 .

[11]  John A. Goff,et al.  Interpolation of Fluvial Morphology Using Channel-Oriented Coordinate Transformation: A Case Study from the New Jersey Shelf , 2004 .

[12]  Marian Eriksson,et al.  Understanding Anisotropy Computations , 2000 .

[13]  David R. Maidment,et al.  Geospatial Representation of River Channels , 2005 .

[14]  James E Ball,et al.  MODELING SPATIAL VARIABILITY OF RAINFALL OVER A CATCHMENT , 1998 .

[15]  G. Jirka,et al.  Mixing in rivers , 1986 .

[16]  Serge Massicotte,et al.  Determination of the drainage structure of a watershed using a digital elevation model and a digital river and lake network , 2001 .

[17]  R. Webster,et al.  Kriging: a method of interpolation for geographical information systems , 1990, Int. J. Geogr. Inf. Sci..

[18]  H. Mitásová,et al.  General variational approach to the interpolation problem , 1988 .

[19]  Norbert Silvera,et al.  Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density , 2006 .

[20]  A. D. Gordon,et al.  Interpreting multivariate data , 1982 .

[21]  M. Goodchild,et al.  Environmental Modeling with GIS , 1994 .

[22]  D. F. Watson,et al.  A PRECISE METHOD FOR DETERMINING CONTOURED SURFACES , 1982 .

[23]  S. Sorooshian,et al.  Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system , 2004, Journal of Hydrology.

[24]  S. Naoum,et al.  A Hydroinformatic Approach to Assess Interpolation Techniques in High Spatial and Temporal Resolution , 2004 .

[25]  Fred C. Collins,et al.  A comparison of spatial interpolation techniques in temperature estimation , 1995 .

[26]  J. Hay,et al.  High-resolution studies of rainfall on Norfolk Island: Part II: Interpolation of rainfall data , 1998 .

[27]  Dafer Ali Algarni,et al.  Comparison of thin plate spline, polynomial, CI—function and Shepard's interpolation techniques with GPS-derived DEM , 2001 .

[28]  M. Hutchinson.  A new procedure for gridding elevation and stream line data with automatic removal of spurious pits , 1989 .

[29]  J. R. French,et al.  Hydrodynamic modelling as a basis for explaining estuarine environmental dynamics: some computational and methodological issues , 2000 .