Hybrid kriging methods for interpolating sparse river bathymetry point data

Abstract

Terrain models that represent riverbed topography are used for analyzing geomorphologic changes, calculating water storage capacity, and making hydrologic simulations. These models are generated by interpolating bathymetry points. River bathymetry is usually surveyed through cross-sections, which may lead to a sparse sampling pattern. Hybrid kriging methods, such as regression kriging (RK) and co-kriging (CK) employ the correlation with auxiliary predictors, as well as inter-variable correlation, to improve the predictions of the target variable. In this study, we use the orthogonal distance of a (x, y) point to the river centerline as a covariate for RK and CK. Given that riverbed elevation variability is abrupt transversely to the flow direction, it is expected that the greater the Euclidean distance of a point to the thalweg, the greater the bed elevation will be. The aim of this study was to evaluate if the use of the proposed covariate improves the spatial prediction of riverbed topography. In order to asses such premise, we perform an external validation. Transversal cross-sections are used to make the spatial predictions, and the point data surveyed between sections are used for testing. We compare the results from CK and RK to the ones obtained from ordinary kriging (OK). The validation indicates that RK yields the lowest RMSE among the interpolators. RK predictions represent the thalweg between cross-sections, whereas the other methods under-predict the river thalweg depth. Therefore, we conclude that RK provides a simple approach for enhancing the quality of the spatial prediction from sparse bathymetry data. Termos para indexação:Geoestatística; predição espacial; krigagem por regressão; morfologia fluvial. LEGLEITER, C. J.; KYRIAKIDIS, P. C. Spatial prediction of river channel topography by kriging. Earth Surface Processes and Landforms, 867:841-867, 2008. LOPES, H. L.; NETO, A. R.; CIRILO, J. A. Modelagem batimétrica no reservatório de Sobradinho: I -geração e avaliação de superfícies batimétricas utilizando interpoladores espaciais. Revista Brasileira de Cartografia, 65:907-922, 2013. MERWADE, V. Effect of spatial trends on interpolation of river bathymetry. Journal of Hydrology, 371:169-181, 2009. MERWADE, V.; COOK, A.; COONROD, J. GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation mapping. Environmental Modelling & Software, 23:1300-1311, 2008. MERWADE, V. M.; MAIDMENT, D. R.; GOFF, J. A. Anisotropic considerations while interpolating river channel bathymetry. Journal of Hydrology, 331:731-741, 2006. MERWADE, V. M.; MAIDMENT, D. R.; HODGES, B. R. Geospatial representation of river channels. Journal of Hydrologic Engineering, 10:243-251, 2005. MIRANDA, R. B.; SCARPINELA, G. A.; MAUAD, F. F. Influência do assoreamento na capacidade de armazenamento do reservatório da usina hidrelétrica de Três Irmãos (SP/BRASIL). Revista Brasileira de Recursos Hídricos, 34:69-79, 2013. ODEH, I. O. A.; MCBRATNEY, A. B.; CHITTLEBOROUGH, D. J. Spatial prediction of soil prop...