A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring network. This paper presents a fractal-based criterion for the construction of coverage designs to optimize the location of sampling points. The algorithm does not depend on the covariance structure of the process and provides desirable results for situations in which a poor prior knowledge is available. The statistical characteristics of the method are explored by a simulation study while a design exercise concerning the Pescara area monitoring network is used to demonstrate potential designs under realistic assumptions.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Aarts, E. and Korst, J. (1990)Simulated Annealing and Boltzmann Machines-A stochastic Approach to Combinatorial Optimization and Neural Computing, Wiley, New York.
Di Battista, T. and Ippoliti, L. (1999)A spatial model building strategy. Journal of the Italian Statistical Society, 8, 2, 3.
Christakos, G. and Olea, R. A. (1992)Sampling design for spatially distributed hydrogeologic and environmental processes. Advances Water Resources, 15, 219-37.
Cressie, N. (1993). Statistics for Spatial Data, Wiley, New York.
Di Zio, S., Fontanella, L., and Ippoliti, L. (2002)Fractal Geometry For Optimal Spatial Sampling Designs. LASR Conference 2002. STATISTICS OF LARGE DATASETS. Functional and Image Data, Bioinformatics and Data Mining, University of Leeds, UK.
Gatrell, A. C., Bailey, C. T., Diggle, P. J., and Rowlingson, B. S. (1996)Spatial point pattern analysis and its application in geographical epidemiology. Trans. Inst. Br. Geogr. NS 21 256-274 1996, ISSN 0020-2754, Royal Geographical Society (with the Institute of British Geographers).
Gibson, L. and Lucas, D. (1982)Spatial data processing using balanced ternary. Proceedings of the IEEE Computer Society Conference on Pattern Recognition and Image Processing. IEEE Computer Society Press, Silver Springs, MD.
Goovaerts P. (2000)Estimation on simulation of soil properties?On optimisation problem with conflicting criteria. Geoderma, 97 (3), 165-186 (22).
Hastings, H. M. and Sugihara, G. (1993)Fractals:A user 's Guide for the Natural Sciences. Oxford University Press, Oxford, p. 235.
Jagadish, H. V. (1990)Linear clustering of objects with multiple attributes. SIGMOD Conference, 332-42.
Lark, R. M. (2002)Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood. Geoderma., 105, 49-80.
Mandelbrot, B. B. (1982)The Fractal Geometry of Nature, Freeman, New York
Mark, D. M. (1990)Neighbor-based properties of some orderings of two-dimensional space. Geographical Analysis, 2, 145-57
Martin, R. J., Di Battista, T., Ippoliti, L., and Nissi, E. (2000)A Point Source Model for Spatial Data. Technical Report STAT. 503/2000, Sheffield University.
Mate ´rn, B. (1960)Spatial variation. Meddelanden fran Statens Skogsforskningsinstitut, Stockholm, Sweden.
Matheron, G. (1963)Principles of geostatistics. Economic Geology, 58, 1246-66.
Mathworks (2000)Matlab, version 6. 1. Natick, Massachusetts.
Nychka, D., Yang, Q., and Royle, J. A. (1997)Constructing spatial designs using regression subset selection, in Statistics for the Environment Barnett V. and Turkman K. F. (eds. ), Vol. 3 Pollutation Assessment and Control. Wiley, New York.
Olea, R. A. (1984)Sampling design optimization for spatial functions. Mathematical Geology, 16, 369-92.
Stevens, Jr. D. L. and Olsen, A. R. (1999)Spatially restricted surveys over time for aquatic resources. Journal of Agricultural, Biological and Environmental Statistics, Vol. 4 (4), pp. 415-28.
Stevens, Jr. D. L. and Olsen, A. R. (2000)Spatially-restricted Random sampling Designs for Design-based and Model-based estimation. In Accuracy 2000:Proceedings of the 4th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Delft University Press, The Netherlands. pp. 609-16.
Stevens, Jr. D. L. and Olsen, A. R. (2004)Spatially balanced sampling of natural resources. Journal of the American Statistical Association, 99 (465), 262-278 (17).
Van Groenigen, J. W. (2000)The influence of variogram parameters on optimal sampling scheme for mapping by kriging. Geoderma, 97, 223-36.
Van Groenigen, J. W. and Stein, A. (1998)Spatial Simulated Annnealing for constrained optimization of spatial sampling schemes, Journal of Environmental Quality, 27, 1078-86.
Yamada, I. and Rogerson, P. (2003)An empirical comparison of edge effects correction methods applied to K-function analysis. Geographical Analaysis. 35, 2.
Yfantis, E. A., Flatman, G. T., and Behar, J. V. (1987)Effciency of kriging estimation for square, triangular, and hexagonal grids. Mathematical Geology, 19, 183-205.
About this article
Cite this article
Zio, S.D., Fontanella, L. & Ippoliti, L. Optimal spatial sampling schemes for environmental surveys. Environmental and Ecological Statistics 11, 397–414 (2004). https://doi.org/10.1007/s10651-004-4186-9