Abstract
The establishment of several large area monitoring networks over the past few decades has led to increased research into ways to spatially balance sample locations across the landscape. Many of these methods are well documented and have been used in the past with great success. In this paper, we present a method using geographic information systems (GIS) and fractals to create a sampling frame, superimpose a tessellation and draw a sample. We present a case study that illustrates the technique and compares results to those from other methods using data from Voyageurs National Park in Minnesota. Our method compares favorably with results from a popular plot selection method, Generalized Random Tessellation Stratified Design, and offers several additional advantages, including ease of implementation, intuitive appeal, and the ability to maintain spatial balance by adding new plots in the event of an inaccessible plot encountered in the field.
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Bartholdi, J. J., & Platzman, L. K. (1988). Heuristics based on spacefilling curves for combinatorial problems in Euclidean space. Management Science, 34(3), 291–305.
Cochran, W. G. (1977). Sampling techniques. New York: Wiley.
Cotter, J., & Nealon, J. (1987). Area frame design for agricultural surveys. National Agricultural Statistics Services, U. S. Department of Agriculture.
Fortin, M. J., Drapeau, P., & Legendre, P. (1989). Spatial autocorrelation and sampling design in plant ecology. Vegetatio, 83, 209–222.
Gillespie, A. (1999). Rationale for a national annual forest inventory program. Journal of Forestry, 97(12), 16–20.
Gregoire, T. G., & Scott, C. T. (2003). Altered selection probabilities caused by avoiding the edge in field surveys. Journal of Agricultural, Biological and Environmental Statistics, 8, 36–47.
Henderson, R. C., Archer, E. K., Bouwes, B. A., Coles-Ritchie, M. S., & Kershner, J. L. (2005). PACFISH/INFISH Biological Opinion (PIBO): effectiveness monitoring program seven-year status report, 1998 through 2004. Gen. Tech. Rep. RMRS-GTR-162, U.S. Department of Agriculture Forest Service, Rocky Mountain Research Station, Fort Collins, CO.
Jin, G., & Mellor-Crummey, J. (2005). Using space-filling curves for computation reordering. Proceedings of the Los Alamos Computer Science Institute Sixth Annual Symposium (published on CD). Los Alamos National Laboratory, Santa Fe, NM.
Johnson, W., Rhee, Y., & Shoemaker, O. (1993). Redesigning the consumer price index area sample. BLS Statistical Survey Papers, Bureau of Labor Statistics, Washington, DC.
Kincaid, T. (2006). User guide for spsurvey, version 1.4, probability survey design and analysis. Retrieved 12/5/2006, from http://www.epa.gov/nheerl/arm/analysispages/software.htm.
Lam, N., & Liu, N. (1996). Use of space-filling curves in generating a national rural sampling frame for HIV/AIDS research. The Professional Geographer, 48(3), 321–332.
Legendre, P. (1993). Spatial autocorrelation: trouble or new paradigm. Ecology, 74, 1659–1673.
Legendre, P., Dale, M. R. T., Fortin, M. J., Gurevitch, J., Hohn, M., & Myers, D. (2002). The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography, 25, 601–615.
Mandelbrot, B. (1982). The fractal geometry of nature. New York: Freeman.
McDonald, M. E., Paulsen, S., Blair, R., Dlugosz, J., Hale, S., Hedtke, S., et al. (2002). Environmental Monitoring and Assessment Program research strategy. EPA 620/R-02/002, US Environmental Protection Agency, Washington, D.C.
Olea, R. A. (1984). Sampling design optimization for spatial functions. Mathematical Geology, 16(4), 369–392.
Olsen, A. R., Sedransk, J., Edwards, D., Gotway, C. A., Liggett, W., Rathbun, S. L., et al. (1999). Statistical issues for monitoring ecological and natural resources in the United States. Environmental Monitoring and Assessment, 54(1), 1–45.
Olsen, A. R., Stevens, D. L., Jr., & White, D. (1998). Application of global grids in environmental sampling. Computing Science and Statistics, 30, 279–284.
Overton, W. S., & Stehman, S. V. (1996). Desirable design characteristics for long-term monitoring of ecological variables. Environmental and Ecological Statistics, 3, 349–361.
Palmer, C., Riitters, K., Strickland, T., Cassell, D., Byers, G., Papp, M., et al. (1992). Monitoring and research strategy for forests—Environmental Monitoring and Assessment Program (EMAP). EPA/600/4-91/012, U.S. Environmental Protection Agency, Office of Research and Development, Washington, DC.
Peano, G. (1890). Sur une courbe, qui remplit une aire plane. Mathematische Annalen, 36, 157–160.
Reams, G. A., Smith, W. D., Hansen, W. H., Bechtold, W. A., Roesch, F. A. & Moisen, G. G. (2005). The forest inventory and analysis sampling frame. In W. A. Bechtold & P. L. Patterson (Eds.), The enhanced forest inventory and analysis program—national sampling design and estimation procedures (pp. 11–26)). Asheville, NC: Gen. Tech. Rep. SRS-80, U.S. Department of Agriculture Forest Service, Southern Research Station.
Saalfeld, A. (1998). Sorting spatial data for sampling and other geographic applications. Geoinformatica, 2, 37–57.
Saalfeld, A., Zayatz, L., & Hoel, E. (1992). Contextual variables via geographic sorting: a moving averages approach. Proceedings of the section on survey research methods. Alexandria, VA: American Statistical Association.
Scott, C. T., Bechtold, W. A., Reams, G. A., Smith, W. D., Westfall, J. A., Hansen, W. H., et al. (2005). Sample-based estimators used by the Forest Inventory and Analysis National Information Management System.. In W. A. Bechtold & P. L. Patterson (Eds.), The enhanced forest inventory and analysis program—national sampling design and estimation procedures (pp. 43–67). Asheville, NC: Gen. Tech. Rep. SRS-80: U.S. Department of Agriculture Forest Service, Southern Research Station.
Shiver, B. D., & Borders, B. E. (1996). Sampling techniques for forest resource inventory. New York: Wiley.
Stevens, D. L., Jr. (1997). Variable density grid-based sampling designs for continuous spatial populations. Environmetrics, 8, 167–195.
Stevens, D. L., Jr., & Olsen, A. R. (1999). Spatially restricted surveys over time for aquatic resources. Journal of Agricultural, Biological, and Environmental Statistics, 4(4), 415–428.
Stevens, D. L., Jr., & Olsen, A. R. (2003). Variance estimation for spatially balanced samples of environmental resources. Environmetrics, 14, 593–610.
Stevens, D. L., Jr., & Olsen, A. R. (2004). Spatially balanced sampling of natural resources in the presence of frame imperfections. Journal of the American Statistical Association, 99, 262–278.
Theobald, D. M., Stevens, D. L., Jr., White, D., Urquhart, N. S., & Olsen, A. R. (2006). Using GIS to generate spatially-balanced random survey designs for natural resource applications. Retrieved 12/5/2006, from http://www.nrel.colostate.edu/projects/starmap/rrqrr_index.htm.
U.S. Forest Service (1992). Forest Service resource inventories: an overview. Washington, DC: U.S. Department of Agriculture, Forest Service, Forest Inventory, Economics, and Recreation Research.
U.S. Geological Survey. (2001). Vegetation spatial database coverage for the Voyageurs National Park Vegetation Mapping Project. USGS-NPS Vegetation Mapping Program, U.S. Geological Survey, Center for Biological Informatics, Denver, CO. Retrieved 1/17/2007, from http://biology.usgs.gov/npsveg/voya/metavoyaspatial.html.
West, Inc. (2006). S-Draw help file. Retrieved 12/5/2006, from http://www.west-inc.com/computer.php.
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Lister, A.J., Scott, C.T. Use of space-filling curves to select sample locations in natural resource monitoring studies. Environ Monit Assess 149, 71–80 (2009). https://doi.org/10.1007/s10661-008-0184-y
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DOI: https://doi.org/10.1007/s10661-008-0184-y