Advertisement

Ecosystems

, 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
Article

Abstract

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.

Keywords

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

Notes

Acknowledgments

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.

References

  1. Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19:716–723.CrossRefGoogle Scholar
  2. Anselin L. 1995. Local indicators of spatial association – LISA. Geographical Analysis 27: 93–115.Google Scholar
  3. Badiya Roy S, Avissar R. 2002. Impact of land use/land cover change on regional hydrometeorology in Amazonia. J Geophys Res 107. doi: 10.1029/2000JD000266
  4. Baldocchi DD. 2008. ‘Breathing’ of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurements systems, Turner Review. Australian Journal of Botany 56: 1–26.CrossRefGoogle Scholar
  5. Band LE, Peterson DL, Running SW, Coughlan JC, Lammers R. 1991. Forest ecosystem processes at the watershed scale: basis for distributed simulation. Ecological Modelling 56:171–196.CrossRefGoogle Scholar
  6. Beven KJ, Kirkby MJ. 1979. A physically-based variable contributing area model of basin hydrology. Hydrological Science Bulletin 24: 43–69.CrossRefGoogle Scholar
  7. Bliss LC. 1962. Adaptations of Arctic and alpine plants to environmental conditions. Arctic 15: 117–144.Google Scholar
  8. Boegh E, Soegaard H, Broge N, Hasager CB, Jensen NO, Schelde K. 2002. Airborne multispectral data for quantifying leaf area index, nitrogen concentration and photosynthetic efficiency in agriculture. Remote Sensing of Environment 81:179–193.CrossRefGoogle Scholar
  9. Brunsell NA, Ham JM, Owensby CE. 2008. Assessing the multi-resolution information content of remotely sensed variables and elevation for evapotranspiration in a tall-grass prairie environment. Remote Sensing of Environment 112: 2977–2987.CrossRefGoogle Scholar
  10. Brunsell NA, Young CB. 2007. Land surface response to precipitation events using MODIS and NEXRAD data. International Journal of Remote Sensing 29: 1965–1982.CrossRefGoogle Scholar
  11. Burnham KP, Anderson DR. 2002. Model selection and multimodel inference: a practical information-theoretic approach. Springer. 488p.Google Scholar
  12. Canadell JG, Le Quere C, Raupach MR, Field CB, Buitenhuis ET, Ciais P, Conway TJ, Gillett NP, Houghton RA, Marland G. 2007. Contributions to accelerating atmospheric CO2 growth from economic activity, carbon intensity, and efficiency of natural sinks. Proc. Natl. Acad. Sci. USA 104: 18353–18354.CrossRefGoogle Scholar
  13. Chen K, Blong R. 2002. Integrating remotely sensed images and areal census data for building new models across scales. Geoscience and Remote Sensing Symposium, 2002. IGARSS ′02. 2002 IEEE International, vol 4, pp 2385–7Google Scholar
  14. Christensen TR, Johansson T, Åkerman HJ, Mastepanov M, Malmer N, Friborg T, Crill P, Svensson BH. 2004. Thawing sub-Arctic permafrost: Effects on vegetation and methane emissions. Geophysical Research Letters 31: L04501.CrossRefGoogle Scholar
  15. Entekhabi D, Eagleson PS. 1989. Land surface hydrology parameterization for atmospheric general circulation models including subgrid scale spatial variability. Journal of Climate 2: 816–831.CrossRefGoogle Scholar
  16. Essery RLH, Best MJ, Betts RA, Cox PM, Taylor CM. 2003. Explicit representation of subgrid heterogeneity in a GCM land-surface scheme. Journal of Hydrometeorology 4: 530–543.CrossRefGoogle Scholar
  17. Fletcher BJ, Press MC, Baxter R, Phoenix GK. (unpublished data). Plant growth and photosynthesis across transition zones between Arctic vegetation patches: separation of ecological and physiological optima. Funct EcolGoogle Scholar
  18. Gold C, Angel P. 2006. Voronoi hierarchies. In: Raubal M, Miller HJ, Frank AU, Goochild MF, Eds. Geographic information science: 4th international conference, GIScience 2006. Münster, Germany: Springer. p 419Google Scholar
  19. Goodrich DC, Woolhiser DA, Keefer TO. 1991. Kinematic routing using finite elements on a triangular irregular network. Water Resour Res 38. doi: 10.1029/2001WR000854
  20. Gurney KR, Law RM, Denning AS, Rayner PJ, Pak BC, Baker D, Bousquet P, Bruhwiler L, Chen Y-H, Ciais P, Fung IY, Heimann M, John J. 2004. Transcom 3 inversion intercomparison: Model mean results for the estimation of seasonal carbon sources and sinks. Global Biogeochemical Cycles 18: GB1010.1011–GB1010.1018.CrossRefGoogle Scholar
  21. Haboudane D, Miller JR, Pattey E, Zerco-Tejada PJ, Strachan IB. 2004. Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture. Remote Sensing of Environment 90: 337–352.CrossRefGoogle Scholar
  22. Hancock GR. 2006. The impact of different gridding methods on catchment geomorphology and soil erosion over long timescales using a landscape evolution model. Earth Surface Processes and Landforms 31: 1035–1050.CrossRefGoogle Scholar
  23. Heinsch FA, Zhao M, Running SW, Kimball JS, Nemani RR, Davis KJ, Bolstad PV, Cook BD, Desai AR, Ricciuto DM, Law BE, Oechel WC, Kwon H, Luo H, Wofsy SC, Dunn AL, Munger JW, Baldocchi DD, Xu L, Hollinger DY, Richardson AD, Stoy PC, Siqueira MBS, Monson RK, Burns S, Flanagan LB. 2006. Evaluation of remote sensing based terrestrial productivity from MODIS using AmeriFlux tower eddy flux network observations. IEEE Transactions on Geoscience and Remote Sensing 44: 1908–1925.CrossRefGoogle Scholar
  24. Ivanov VY, Vivoni ER, Bras RL, Entekhabi D. 2004. Catchment hydrologic response with a fully distributed triangulated irregular network model. Water Resources Research 40: W11102, doi: 11110.11029/12004WR003218.CrossRefGoogle Scholar
  25. Jarvis PG, McNaughton KG. 1986. Stomatal control of transpiration: scaling up from leaf to region. Advances in Ecological Research 15: 1–49.CrossRefGoogle Scholar
  26. Jonasson S, Michelsen A, Schmidt IK, Nielsen EV. 1999. Responses in microbes and plants to changed temperature, nutrient and light regimes in the Arctic. Ecology 80: 1828–1843.Google Scholar
  27. Jørgensen SE, Marques JC, Müller F, Nielsen SN, Patten PC, Tiezzi E, Ulanowicz RE. 2007. A new ecology: systems perspective. Elsevier. p275.Google Scholar
  28. Katul GG, Lai C-T, Albertson JD, Vidakovic B, Schäfer KVR, Hsieh CI, Oren R. 2001. Quantifying the complexity in mapping energy inputs and hydrologic state variables into land-surface fluxes. Geophysical Research Letters 28: 3305–3307.CrossRefGoogle Scholar
  29. Kullback S. 1997. Information Theory and Statistics. Mineola, NY: Dover Publications. 416p.Google Scholar
  30. Kullback S, Leibler RA. 1951. On information and sufficiency. Annals of Mathematical Statistics 22: 79–86.CrossRefGoogle Scholar
  31. Kumler MP. 1994. An intensive comparison of triangulated irregular networks (TINs) and digital elevation models (DEMs). Cartographica 31: Monograph 45, 41–48Google Scholar
  32. Kustas WP, Norman JM. 2000. Evaluating the effects of subpixel heterogeneity on pixel average fluxes. Remote Sensing of Environment 74: 327–342.CrossRefGoogle Scholar
  33. Leuning R, Kelliher FM, DePury DG, Schulze E-D. 1995. Leaf nitrogen, photosynthesis, conductance and transpiration: scaling from leaves to canopies. Plant, Cell and Environment 18: 1183–1200.CrossRefGoogle Scholar
  34. Liu X, Kafatos M. 2005. Land-cover mixing and spectral vegetation indices. International Journal of Remote Sensing 26:3321–3327.CrossRefGoogle Scholar
  35. Mathiassen JR, Skavhaug A, Bø K. 2002. Texture similarity measure using Kullback-Leibler divergence between gamma distributions. Computer Vision — ECCV 2002. Berlin/Heidelberg: Springer. p19–49.Google Scholar
  36. Mauser W, Tenhunen JD, Schneider K, Ludwig R, Stolz R, Geyer R, Falge EM. 2001. Remote sensing, GIS and modelling: Assessing spatially distributed water, carbon and nutriend balances in the Ammer River catchment, in southern Bavaria. Tenhunen JD, Lenz R, Hantschel R, Hunter S, editors. Ecosystem approaches to landscape management in central Europe. Berlin: Springer.Google Scholar
  37. Monteith JL, Unsworth MH. 1990. Principles of environmental physics. London: Edward Arnold. 291p.Google Scholar
  38. Müller C, Lucht W. 2007. Robustness of terrestrial carbon and water cycle simulations against variations in spatial resolution. Journal of Geophysical Research 112: D06105, doi: 06110.01029/02006JD007875.CrossRefGoogle Scholar
  39. Myeni RB, Nemani RR, Running SW. 1997. Estimation of global leaf area index and absorbed PAR using radiative transfer models. IEEE Transactions on Geoscience and Remote Sensing 35: 1380–1393.CrossRefGoogle Scholar
  40. O’Neill RV, Rust B. 1979. Aggregation error in ecological models. Ecological Modelling 7: 91–105.CrossRefGoogle Scholar
  41. Pelgrum H. 2000. Aggregation of a nonlinear land surface model for heterogeneous terrain. Remote Sensing and Hydrology. Santa Fe, NM, USA: IAHS.Google Scholar
  42. Peuker TK, Fowler RJ, Little JJ, Mark DM. 1978. The triangulated irregular network. Proceedings of the DTM symposium. American Society of Photogrammetry—American Congress on Surveying and Mapping. Saint Lois, MO. pp 24–31Google Scholar
  43. Potter CS, Klooster SA, Nemani R, Genovese V, Hiatt S, Fladeland M, Gross P. 2006. Estimating carbon budgets for U.S. ecosystems. EOS, Transactions, American Geophysical Union 87: 85–96.CrossRefGoogle Scholar
  44. Quaife T, Lewis P, de Kauwe M, Williams M, Law BE, Disney M, Bowyer P. 2008. Assimilating canopy reflectance data into an ecosystem model with an ensemble Kalman filter. Remote Sensing of Environment 112: 1347–1364.CrossRefGoogle Scholar
  45. Rahman AF, Gamon JA, Sims DA, Schmidts M. 2003. Optimum pixel size for hyperspectral studies of ecosystem function in southern California chaparral and grassland. Remote Sensing of Environment 84: 192–207.CrossRefGoogle Scholar
  46. Rastetter EB, King AW, Cosby BJ, Hornberger GM, O’Neill RV, Hobbie JE. 1992. Aggregating fine-scale ecological knowledge to model coarser-scale attributes of ecosystems. Ecological Applications 2: 55–70.CrossRefGoogle Scholar
  47. Shannon CE. 1948. A mathematical theory of communication. Bell Syst Tech J 27: 379–423 and 623–656Google Scholar
  48. Shaver GR, Billings WD, Chapin FS, Giblin AE, Nadelhoffer KJ, Oechel WC, Rastetter EB. 1992. Global change and the carbon balance of Arctic ecosystems. BioScience 42: 433–441.CrossRefGoogle Scholar
  49. Shaver GR, Chapin FS, Gartner BL. 1986. Factors limiting growth and biomass accumulation in Eriophorum vaginatum L. in Alaskan tussock tundra. Journal of Ecology 74: 257–278.CrossRefGoogle Scholar
  50. Shaver GR, Street LE, Rastetter EB, van Wijk MT, Williams M. 2007. Functional convergence in regulation of net CO2 flux in heterogeneous tundra landscapes in Alaska and Sweden. Journal of Ecology 95: 802–817.CrossRefGoogle Scholar
  51. Spadavecchia L, Williams M, Bell R, Stoy PC, Huntley B, van Wijk MT. 2008. Topographic controls on the leaf area index of a Fennoscandian tundra ecosystem. J Ecol doi: 10.1111/j.1365-2745.2008.01424.x
  52. Stoy PC, Katul GG, Siqueira MBS, Juang J-Y, Novick KA, Oren R. 2006. An evaluation of methods for partitioning eddy covariance-measured net ecosystem exchange into photosynthesis and respiration. Agricultural and Forest Meteorology 141: 2–18.CrossRefGoogle Scholar
  53. Street LE, Shaver GR, Williams M, van Wijk MT. 2007. What is the relationship between changes in canopy leaf area and changes in photosynthetic CO2 flux in Arctic ecosystems? Journal of Ecology 95: 139–150.CrossRefGoogle Scholar
  54. Sullivan PF, Arens SJT, Chimner RA, Welker JM. 2008. Temperature and microtopography interact to control carbon cycling in a high Arctic fen. Ecosystems 11: 61–76.CrossRefGoogle Scholar
  55. Tenhunen JD, Geyer R, Valentini R, Mauser W, Cernusca A. 1999. Ecosystem studies, land-use change, and resource management. Tenhunen J, Kabat P, editors. Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. West Sussex, UK: John Wiley and Sons. p1–19.Google Scholar
  56. Ulanowicz RE. 2001. Information theory in ecology. Computers and Chemistry 25: 393–399.PubMedCrossRefGoogle Scholar
  57. van Wijk MT, Williams M. 2005. Optical instruments for measuring leaf area index in low vegetation: application in Arctic ecosystems. Ecological Applications 15: 1462–1470.CrossRefGoogle Scholar
  58. van Wijk MT, Williams M, Shaver GR. 2005. Tight coupling between leaf area index and foliage N content in Arctic plant communities. Oecologia 142: 421–427.PubMedCrossRefGoogle Scholar
  59. Vivoni ER, Ivanov VY, Bras RL, Entekhabi D. 2004. Generation of triangulated irregular networks based on hydrological similarity. Journal of Hydrologic Engineering 9: 288–302.CrossRefGoogle Scholar
  60. Vivoni ER, Ivanov VY, Bras RL, Entekhabi D. 2005a. On the effects of triangulated terrain resolution on distributed hydrologic model response. Hydrological Processes 19: 2101–2122.CrossRefGoogle Scholar
  61. Vivoni ER, Teles V, Ivanov VY, Bras RL, Entekhabi D. 2005b. Embedding landscape processes into triangulated terrain models. International Journal of Geographic Information Science 19: 429–457.CrossRefGoogle Scholar
  62. Walker DA, Auerbach NA, Lewis BE, Shippert MM. 1995. NDVI, biomass, and landscape evolution of glaciated terrain in northern Alaska. Polar Record 31: 169–178.CrossRefGoogle Scholar
  63. Walko RL, Avissar R. 2006. The ocean-land-atmosphere model (OLAM): a new generation of earth system model. EOS Trans. AGU 87 Fall Meeting Suppl., Abstract A33F-05Google Scholar
  64. Wesson KH, Katul GG, Siqueira MBS. 2003. Quantifying organization of atmospheric turbulent eddy motion using nonlinear time series analysis. Boundary-Layer Meteorology 106: 507–525.CrossRefGoogle Scholar
  65. Wilby RL, Wigley TML. 1997. Downscaling general circulation model output: a review of methods and limitations. Progress in Physical Geography 21: 530–548.CrossRefGoogle Scholar
  66. Williams M, Bell R, Spadavecchia L, Street LE, van Wijk MT. 2008. Upscaling leaf area index in an Arctic landscape through multi-scale observations. Glob Chang Biol 14. doi: 10.1111/j.1365-2486.2008.01590.x
  67. Williams M, Rastetter EB. 1999. Vegetation characteristics and primary productivity along an Arctic transect: implications for scaling-up. Journal of Ecology 87: 885–898.CrossRefGoogle Scholar
  68. Williams M, Rastetter EB, Shaver GR, Hobbie JE, Carpino E, Kwiatkowski BL. 2001. Primary production of an Arctic watershed: an uncertainty analysis. Ecological Applications 11: 1800–1816.CrossRefGoogle Scholar
  69. Williams M, Schwarz PA, Law B, Irvine J, Kurpius MR. 2005. An improved analysis of forest carbon dynamics using data assimilation. Global Change Biology 11: 89–105.CrossRefGoogle Scholar

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

Personalised recommendations