Effect of spatial trends on interpolation of river bathymetry

Abstract

Continuous surface of river bathymetry (bed topography) is typically produced by spatial interpolation of discrete point or cross-section data. Several interpolation methods that do not account for spatial trend in river bathymetry produce inaccurate surfaces, thus requiring complex interpolation methods such as anisotropic kriging. Although isotropic methods are unsuitable for interpolating river bathymetry, issues that limit their use remain unaddressed. This paper addresses the issue of effect of spatial trend in river bathymetry on isotropic interpolation methods. It is hypothesized that if the trend is removed from the data before interpolation, the results from isotropic methods should be comparable with anisotropic methods. Data from six river reaches in the United States are used to: (i) interpolate bathymetry data using seven spatial interpolation methods; (ii) separate trend from bathymetry; (iii) interpolate residuals (bathymetry minus trend) by using all seven interpolation methods to get residual surfaces, (iv) add the trend back to residual surfaces; and (v) compare resulting surfaces from (iv) with surfaces created in (i). Quantitative and qualitative comparison of results through root mean square error (RMSE), semi-variograms, and cross-section profiles show that significant improvement (as much as 60% in RMSE) can be accomplished in spatial interpolation of river bathymetry by separating trend from the data. Although this paper provides a new simple way for interpolating river bathymetry by using (otherwise deemed inappropriate) isotropic methods, the choice of trend function and spatial arrangement of discrete bathymetry data play a vital role in successful implementation of the proposed approach.