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Marine Geophysical Research

, Volume 32, Issue 4, pp 493–501 | Cite as

Gridding heterogeneous bathymetric data sets with stacked continuous curvature splines in tension

  • Benjamin Hell
  • Martin Jakobsson
Original Research Paper

Abstract

Gridding heterogeneous bathymetric data sets for the compilation of Digital bathymetric models (DBMs), poses specific problems when there are extreme variations in source data density. This requires gridding routines capable of subsampling high-resolution source data while preserving as much as possible of the small details, at the same time as interpolating in areas with sparse data without generating gridding artifacts. A frequently used gridding method generalizes bicubic spline interpolation and is known as continuous curvature splines in tension. This method is further enhanced in this article in order to specifically handle heterogeneous bathymetric source data. Our method constructs the final grid through stacking several surfaces of different resolutions, each generated using the splines in tension algorithm. With this approach, the gridding resolution is locally adjusted to the density of the source data set: Areas with high-resolution data are gridded at higher resolution than areas with sparse source data. In comparison with some of the most widely used gridding methods, our approach yields superior DBMs based on heterogeneous bathymetric data sets with regard to preserving small bathymetric details in the high-resolution source data, while minimizing interpolation artifacts in the sparsely data constrained regions. Common problems such as artifacts from ship tracklines are suppressed. Even if our stacked continuous curvature splines in tension gridding algorithm has been specifically designed to construct DBMs from heterogeneous bathymetric source data, it may be used to compile regular grids from other geoscientific measurements.

Keywords

Gridding Interpolation Digital bathymetric model Seafloor topography Bicubic splines in tension 

Notes

Acknowledgements

David Sandwell provided the shell scripts for the remove-restore method. We are grateful for the valuable comments on the manuscript by Paul Wessel and another anonymous reviewer.

References

  1. Becker JJ, Sandwell DT, Smith WHF, Braud J, Binder B, Depner J, Fabre D, Factor J, Ingalls S, Kim SH, Ladner R, Marks K, Nelson S, Pharaoh A, Trimmer R, von Rosenberg J, Wallace G, Weatherall P (2009) Global bathymetry and elevation data at 30 arc seconds resolution: Srtm30_plus. Mar Geod 32:355–371. doi: 10.1080/01490410903297766 CrossRefGoogle Scholar
  2. Bell TH Jr (1979) Mesoscale seafloor roughness. Deep Sea Res A 26(1):65–76. doi: 10.1016/0198-0149(79)90086-4 CrossRefGoogle Scholar
  3. de Boor C (2001) A practical guide to splines, applied mathematical sciences, vol 27. Springer, New YorkGoogle Scholar
  4. Briggs IC (1974) Machine contouring using minimum curvature. Geophys 39:39–48CrossRefGoogle Scholar
  5. Burrough PA, McDonnel RA (1998) Principles of geographical information systems. Oxford University Press, OxfordGoogle Scholar
  6. Delaunay B (1934) Sur la sphère vide. Bull Acad Sci USSR Classe Sci Mat Nat VII:793–800Google Scholar
  7. Farr TG, Rosen PA, Caro E, Crippen R, Duren R, Hensley S, Kobrick M, Paller M, Rodriguez E, Roth L, Seal D, Shaffer S, Shimada J, Umland J, Werner M, Oskin M, Burbank D, Alsdorf D (2007) The shuttle radar topography mission. Rev Geophys 45(RG2004). doi: 10.1029/2005RG000183
  8. Forsberg R (1993) Modelling the fine-structure of the geoid: methods, data requirements and some results. Surv Geophys 14(4):403–418. doi: 10.1007/BF00690568 CrossRefGoogle Scholar
  9. Forsberg R, Tscherning C (1981) The use of height data in gravity field approximation by collocation. J Geophys Res 86(B9):7843–7854. doi: 10.1029/JB086iB09p07843 CrossRefGoogle Scholar
  10. Fox CG, Hayes DE (1985) Quantitative methods for analyzing the roughness of the seafloor. Rev Geophys 23(1):1–48. doi: 10.1029/RG023i001p00001 CrossRefGoogle Scholar
  11. Furrer R, Genton MG, Nychka D (2006) Covariance tapering for interpolation of large spatial datasets. J Comput Graph Stat 15(3):502–523. doi: 10.1198/106186006X132178 CrossRefGoogle Scholar
  12. Haining RP, Kerry R, Oliver MA (2010) Geography, spatial data analysis, and geostatistics: an overview. Geogr Anal 42(1):7–31. doi: 10.1111/j.1538-4632.2009.00780.x CrossRefGoogle Scholar
  13. Hall J (2006) GEBCO centennial special issue charting the secret world of the ocean floor: the GEBCO project 19032003. Mar Geophys Res 27(1):1–5. doi: 10.1007/s11001-006-8181-4 CrossRefGoogle Scholar
  14. Hartman L, Hössjer O (2008) Fast kriging of large data sets with gaussian markov random fields. Comput Stat Data Anal 52:2331–2349. doi: 10.1016/j.csda.2007.09.018 CrossRefGoogle Scholar
  15. Isaaks EH, Srivastava RM (1990) An introduction to applied geostatistics. Oxford University Press, OxfordGoogle Scholar
  16. Jakobsson M, Cherkis N, Woodward J, Macnab R, Coakley B (2000) New grid of Arctic bathymetry aids scientists and mapmakers. EOS Trans 81(9):89, 93 & 96Google Scholar
  17. Jakobsson M, Macnab R, Mayer L, Anderson R, Edwards M, Hatzky J, Schenke HW, Johnson P (2008) An improved bathymetric portrayal of the Arctic Ocean: implications for ocean modeling and geological, geophysical and oceanographic anlyses. Geophys Res Lett 35:L07,602. doi: 10.1029/2008GL033520 CrossRefGoogle Scholar
  18. Klenke M, Schenke HW (2002) A new bathymetric model for the central fram strait. Mar Geophys Res 23(4):367–378. doi: 10.1023/A:1025764206736 CrossRefGoogle Scholar
  19. Macnab R, Jakobsson M (2000) Something old, something new: compiling historic and contemporary data to construct regional bathymetric maps, with the Arctic Ocean as a case study. Int Hydrogr Rev 1(1):2–16Google Scholar
  20. Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266CrossRefGoogle Scholar
  21. Müller RD, Sdrolias M, Gaina C, Roest WR (2008) Age, spreading rates, and spreading asymmetry of the world’s ocean crust. Geochem Geophys Geosyst 9(4):Q04,006. doi: 10.1029/2007GC001743 CrossRefGoogle Scholar
  22. Pollard JM (1971) The fast fourier transform in a finite field. Math Comput 25(114):365–374CrossRefGoogle Scholar
  23. Reuter H, Nelson A, Jarvis A (2007) An evaluation of void filling interpolation methods for srtm data. Int J Geogr Inf Sci 21(9):983–1008CrossRefGoogle Scholar
  24. Sandwell DT, Smith WHF (1997) Marine gravity anomaly from Geosat and ERS 1 satellite altimetry. J Geophys Res 102:10039–10054CrossRefGoogle Scholar
  25. Smith WHF (1993) On the accuracy of digital bathymetric data. J Geophys Res 98(B6):9591–9603CrossRefGoogle Scholar
  26. Smith WHF, Sandwell DT (1997) Global sea floor topography from satellite altimetry and ship depth soundings. Science 277:1956–1962CrossRefGoogle Scholar
  27. Smith WHF, Wessel P (1990) Gridding with continuous curvature splines in tension. Geophys 55(3):293–305CrossRefGoogle Scholar
  28. Task group on gridding of the GEBCO SCDB (1997) On the preparation of a gridded data set from the GEBCO Digital Atlas contours. Tech. rep., GEBCO, version 9–16 June 1997Google Scholar
  29. Tobler W (1970) A computer movie simulating urban growth in the detroit region. Econ Geogr 46:234–240CrossRefGoogle Scholar
  30. Torge W (2001) Geodesy. De Gruyter, 281ffGoogle Scholar
  31. Vogt PR, Jung WY, Nagel DJ (2000) GOMaP: a matchless resolution to start the new millennium. EOS Trans 81(23):254, 258Google Scholar
  32. Ware C (1989) Fast note: fast hill shading with cast shadows. Comp Geosci 15(8):1327–1334CrossRefGoogle Scholar
  33. Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS Trans 79(47):579CrossRefGoogle Scholar
  34. Zhou Q, Liub X (2004) Analysis of errors of derived slope and aspect related to dem data properties. Comp Geosci 30(4):369–378. doi: 10.1016/j.cageo.2003.07.005 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Geological SciencesStockholm UniversityStockholmSweden

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