Skip to main content

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

Marine Geophysical Research volume 32, pages 493–501 (2011)Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  • 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

    Article  Google Scholar 

  • Bell TH Jr (1979) Mesoscale seafloor roughness. Deep Sea Res A 26(1):65–76. doi:10.1016/0198-0149(79)90086-4

    Article  Google Scholar 

  • de Boor C (2001) A practical guide to splines, applied mathematical sciences, vol 27. Springer, New York

    Google Scholar 

  • Briggs IC (1974) Machine contouring using minimum curvature. Geophys 39:39–48

    Article  Google Scholar 

  • Burrough PA, McDonnel RA (1998) Principles of geographical information systems. Oxford University Press, Oxford

    Google Scholar 

  • Delaunay B (1934) Sur la sphère vide. Bull Acad Sci USSR Classe Sci Mat Nat VII:793–800

    Google Scholar 

  • 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

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Fox CG, Hayes DE (1985) Quantitative methods for analyzing the roughness of the seafloor. Rev Geophys 23(1):1–48. doi:10.1029/RG023i001p00001

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Isaaks EH, Srivastava RM (1990) An introduction to applied geostatistics. Oxford University Press, Oxford

    Google Scholar 

  • 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 & 96

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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):2–16

    Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Pollard JM (1971) The fast fourier transform in a finite field. Math Comput 25(114):365–374

    Article  Google Scholar 

  • Reuter H, Nelson A, Jarvis A (2007) An evaluation of void filling interpolation methods for srtm data. Int J Geogr Inf Sci 21(9):983–1008

    Article  Google Scholar 

  • Sandwell DT, Smith WHF (1997) Marine gravity anomaly from Geosat and ERS 1 satellite altimetry. J Geophys Res 102:10039–10054

    Article  Google Scholar 

  • Smith WHF (1993) On the accuracy of digital bathymetric data. J Geophys Res 98(B6):9591–9603

    Article  Google Scholar 

  • Smith WHF, Sandwell DT (1997) Global sea floor topography from satellite altimetry and ship depth soundings. Science 277:1956–1962

    Article  Google Scholar 

  • Smith WHF, Wessel P (1990) Gridding with continuous curvature splines in tension. Geophys 55(3):293–305

    Article  Google Scholar 

  • 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 1997

  • Tobler W (1970) A computer movie simulating urban growth in the detroit region. Econ Geogr 46:234–240

    Article  Google Scholar 

  • Torge W (2001) Geodesy. De Gruyter, 281ff

  • Vogt PR, Jung WY, Nagel DJ (2000) GOMaP: a matchless resolution to start the new millennium. EOS Trans 81(23):254, 258

    Google Scholar 

  • Ware C (1989) Fast note: fast hill shading with cast shadows. Comp Geosci 15(8):1327–1334

    Article  Google Scholar 

  • Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS Trans 79(47):579

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Geological Sciences, Stockholm University, 10691, Stockholm, Sweden

    Benjamin Hell & Martin Jakobsson

Authors
  1. Benjamin Hell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Jakobsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Benjamin Hell.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hell, B., Jakobsson, M. Gridding heterogeneous bathymetric data sets with stacked continuous curvature splines in tension. Mar Geophys Res 32, 493–501 (2011). https://doi.org/10.1007/s11001-011-9141-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11001-011-9141-1

Keywords

  • Gridding
  • Interpolation
  • Digital bathymetric model
  • Seafloor topography
  • Bicubic splines in tension