Rectilinear Inverse Distance Weighting Methodology for Bathymetric Cross-Section Interpolation along the Mississippi River
Publication: Journal of Hydrologic Engineering
Volume 22, Issue 7
Abstract
In frequently monitored fluvial systems, such as the middle Mississippi River, large databases of hundreds of cross-section surveys are often needed for assessment of long-term morphologic change and contributing hydraulic parameters. Developing customized interpolation schemes with optimized coefficients for each survey in such large databases is impractical. Using a database of 158 cross-section bathymetric surveys of the middle Mississippi River, automated surface generation of commonly available interpolation algorithms, [i.e., triangulated irregular networks (TIN), inverse distance weighting (IDW), spline with tension, and ordinary kriging] were evaluated and compared with an interpolation algorithm developed for this database, termed rectilinear IDW (RIDW). TIN and RIDW interpolation algorithms had the lowest root-mean square error (RMSE) among all methods evaluated, with the largest difference between them occurring along the perimeter of the interpolated surfaces. TIN interpolation resulted in sharp, geometric edges along the boundaries of the interpolated surfaces requiring postprocessing, whereas RIDW interpolation produced smoother edges that sometimes elongated scour holes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was funded by the Saint Louis University, Graduate Programs Presidential Fellowship. The authors acknowledge the assistance and collaborative efforts of Donald Duncan, Dave Gordon, John Vest and Edward Brauer, all of whom are employees of the U.S. Army Corps of Engineers.
References
ArcGIS 10.2 [Computer software]. Environmental Systems Research Institute, Redlands, CA.
Burroughes, J., George, K., and Abbott, V. (2001). “Interpolation of hydrographic survey data.” Hydrogr. J., 99, 21–29.
Caviedes-Voullieme, D., Morales-Hernandez, M., Lopez-Marijuan, I., and Garcia-Navarro, P. (2014). “Reconstruction of 2D river beds by appropriate interpolation of 1D cross sectional information for flood simulation.” Environ. Model. Software, 61, 206–228.
Chaplot, V., Darboux, F., Bourennane, H., Leguedois, S., Silvera, N., and Phachomphon, K. (2006). “Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density.” Geomorphology, 77(1–2), 126–141.
Conner, J. T., and Tonina, D. (2014). “Effect of cross section interpolated bathymetry on 2D hydrodynamic model results in a large river.” Earth Surf. Processes Landforms, 39(4), 463–475.
Costabile, P., and Macchione, F. (2015). “Enhancing river model set-up for 2-D dynamic flood modelling.” Environ. Model. Software, 67, 89–107.
El-Hattab, A. I. (2014). “Single beam bathymetric data modelling techniques for accurate maintenance dredging.” Egypt. J. Remote Sens. Space Sci., 17(2), 189–195.
Flanagin, M., Grenotton, A., Ratcliff, J., Shaw, K. B., Sample, J., and Abdelguerfi, M. (2007). “Hydraulic splines: A hybrid approach to modeling river channel geometries.” Comput. Sci. Eng., 9(5), 4–15.
Fukuoka, S., and Sayre, W. W. (1973). “Longitudinal dispersion in sinuous channels.” J. Hydraul. Div., 99(1), 195–217.
Goff, J. A., and Nordfjord, S. (2004). “Interpolation of fluvial morphology using channel-oriented coordinate transformation: A case study from the New Jersey shelf.” Math. Geol., 36(6), 643–658.
Holley, E. R., and Jirka, G. H. (1986). “Mixing in rivers, United States army engineer waterways experiment station.”. Vicksburg, MI.
Legleiter, C. J., and Kyriakidis, P. C. (2007). “Forward and inverse transformations between cartesian and channel-fitted coordinate systems for meandering rivers.” Math. Geol., 38(8), 927–958.
Legleiter, C. J., and Kyriakidis, P. C. (2008). “Spatial prediction of river channel topography by kriging.” Earth Surf. Processes Landforms, 33(6), 841–867.
Legleiter, C. J., Kyriakidis, P. C., McDonald, R. R., and Nelson, J. M. (2011). “Effects of uncertain topographic input data on two-dimensional flow modeling in a gravel-bed river.” Water Resour. Res., 47(3), W03518.
Li, J., and Heap, A. D. (2008). “A review of spatial interpolation methods for environmental scientists.” Geoscience Australia, Symonston, Canberra.
MATLAB [Computer software]. MathWorks, Natick, MA.
Merwade, V. (2009). “Effect of spatial trends on interpolation of river bathymetry.” J. Hydrol., 371(1–4), 169–181.
Merwade, V., Cook, A., and Coonrod, J. (2008). “GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation mapping.” Environ. Model. Software, 23(10–11), 1300–1311.
Merwade, V. M., Maidment, D. R., and Goff, J. A. (2006). “Anisotropic considerations while interpolating river channel bathymetry.” J. Hydrol., 331(3–4), 731–741.
Merwade, V. M., Maidment, D. R., and Hodges, B. R. (2005). “Geospatial representation of river channels.” J. Hydrol. Eng., 243–251.
Pasternack, G. B., Gilbert, A. T., Wheaton, J. M., and Buckland, E. M. (2006). “Error propagation for velocity and shear stress prediction using 2D models for environmental management.” J. Hydrol., 328(1–2), 227–241.
Schäppi, B., Perona, P., Schneider, P., and Burlando, P. (2010). “Integrating river cross section measurements with digital terrain models for improved flow modelling applications.” Comput. Geosci., 36(6), 707–716.
Tate, E. C., Maidment, D. R., Olivera, F., and Anderson, D. J. (2002). “Creating a terrain model for floodplain mapping.” J. Hydrol. Eng., 100–108.
Tomczak, M. (1998). “Spatial interpolation and its uncertainty using automated anisotropic inverse distance weighting (IDW): Cross-validation/jackknife approach.” J. Geogr. Inform. Decis. Anal., 2(2), 18–30.
U.S. Army Corps of Engineers Saint Louis District. (2014). “Inland electronic navigation charts.” ⟨⟩ (Feb. 21, 2015).
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 28, 2016
Accepted: Dec 9, 2016
Published online: Mar 27, 2017
Published in print: Jul 1, 2017
Discussion open until: Aug 27, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.