, Volume 12, Issue 4, pp 574–589 | Cite as

Using Information Theory to Determine Optimum Pixel Size and Shape for Ecological Studies: Aggregating Land Surface Characteristics in Arctic Ecosystems

  • P. C. StoyEmail author
  • M. Williams
  • L. Spadavecchia
  • R. A. Bell
  • A. Prieto-Blanco
  • J. G. Evans
  • M. T. van Wijk


Quantifying vegetation structure and function is critical for modeling ecological processes, and an emerging challenge is to apply models at multiple spatial scales. Land surface heterogeneity is commonly characterized using rectangular pixels, whose length scale reflects that of remote sensing measurements or ecological models rather than the spatial scales at which vegetation structure and function varies. We investigated the ‘optimum’ pixel size and shape for averaging leaf area index (LAI) measurements in relatively large (85 m2 estimates on a 600 × 600-m2 grid) and small (0.04 m2 measurements on a 40 × 40-m2 grid) patches of sub-Arctic tundra near Abisko, Sweden. We define the optimum spatial averaging operator as that which preserves the information content (IC) of measured LAI, as quantified by the normalized Shannon entropy (E S,n) and Kullback–Leibler divergence (D KL), with the minimum number of pixels. Based on our criterion, networks of Voronoi polygons created from triangulated irregular networks conditioned on hydrologic and topographic indices are often superior to rectangular shapes for averaging LAI at some, frequently larger, spatial scales. In order to demonstrate the importance of information preservation when upscaling, we apply a simple, validated ecosystem carbon flux model at the landscape level before and after spatial averaging of land surface characteristics. Aggregation errors are minimal due to the approximately linear relationship between flux and LAI, but large errors of approximately 45% accrue if the normalized difference vegetation index (NDVI) is averaged without preserving IC before conversion to LAI due to the nonlinear NDVI-LAI transfer function.


information content Kullback–Liebler divergence leaf area index Shannon entropy spatial averaging triangulated irregular network tundra upscaling 



We acknowledge the funding from the US National Science Foundation (Grant numbers OPP-0096523, OPP-0352897, DEB-0087046, and DEB-00895825), from the University of Edinburgh, and from the Natural Environment Research Council. PS, MW, and AP-B were supported by the ABACUS project. LS was supported by a NERC studentship to the Centre for Terrestrial Carbon Dynamics. RB was supported by the University of Edinburgh research funding. Funding for the NERC ARSF flight that carried the ATM sensor used for DEM generation was provided by Bob Baxter and Brian Huntley at the University of Durham. We would like to thank Willem Bouten for use of the LAI-2000, Lorna Street and Sven Rasmussen for field assistance, Ben Poulter for ArcGIS assistance, Terry Callaghan and Gus Shaver for general support, and Mathias Disney for valuable comments on the manuscript.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • P. C. Stoy
    • 1
    Email author
  • M. Williams
    • 1
    • 2
  • L. Spadavecchia
    • 1
    • 2
  • R. A. Bell
    • 1
    • 3
  • A. Prieto-Blanco
    • 4
  • J. G. Evans
    • 5
  • M. T. van Wijk
    • 6
  1. 1.School of GeoSciencesUniversity of EdinburghEdinburghUK
  2. 2.NERC Centre for Terrestrial Carbon DynamicsUniversity of EdinburghEdinburghUK
  3. 3.Centre for Ecology, Evolution and ConservationUniversity of East AngliaNorwichUK
  4. 4.Department of GeographyUniversity College LondonLondonUK
  5. 5.Centre for Ecology and HydrologyOxfordshireUK
  6. 6.Plant Production SystemsWageningen UniversityWageningenThe Netherlands

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