Reconstructing population density surfaces from areal data: A comparison of tobler's pycnophylactic interpolation method and area-to-point Kriging

Geographical Analysis

Volumn 42, Issue 1, 2010, Pages 78-98

  Yoo, Eun Hye ^a   Kyriakidis, Phaedon C ^b   Tobler, Waldo ^b  

^a UNIVERSITY AT BUFFALO   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITION; GEOSTATISTICS; GREEN FUNCTION; INTERPOLATION; KRIGING; LAPLACE TRANSFORM; NUMERICAL MODEL; POPULATION DENSITY; POPULATION ESTIMATION; SPATIAL ANALYSIS;

EID: 75249096350     PISSN: 00167363     EISSN: 15384632     Source Type: Journal    
DOI: 10.1111/j.1538-4632.2009.00783.x     Document Type: Article

References (34)

1. Barton G. Elements of Green's Functions and Propagation 1989, New York, Oxford University Press
2. Bracken I, Fotheringham S, Rogerson P. A Surface Model Approach to the Representation of Population-related Social Indicators. Spatial Analysis and GIS 1994, 247-59. In, edited by, London, Taylor and Francis
3. Briggs I C. Machine Contouring Using Minimum Curvature. Geophysics 1974, 34:39-48.
4. Chilès J P, Delfiner P. Geostatistics: Modeling Spatial Uncertainty 1999, New York, Wiley
5. Goodchild M F, Anselin L, Deichmann U. A Framework for the Areal Interpolation of Socioeconomic Data. Environment and Planning A 1993, 25:383-97.
6. Goovaerts P. Geostatistics for Natural Resources Evaluation 1997, New York, Oxford University Press
7. Goovaerts P. Geostatistical Analysis of Disease Data: Accounting for Spatial Support and Population Density in the Isopleth Mapping of Cancer Mortality Risk Using Area-to-Point Poisson Kriging. International Journal of Health Geographics 2006, 5((52)).
8. Goovaerts P. Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units. Mathematical Geosciences 2008, 40((1)):101-28.
9. Gotway C, Young L. Combining Incompatible Spatial Data. Journal of the American Statistical Association 2002, 97((458)):632-48.
10. Gotway C A, Young L J. A Geostatistical Approach to Linking Geographically Aggregated Data from Different Sources. Journal of Computational & Graphical Statistics 2007, 16((1)):115-35.
11. Greenberg M D. Application of Green's Functions in Science and Engineering 1971, Englewood Cliffs, NJ, Prentice Hall
12. Journel A G, Huijbregts C J. Mining Geostatistics 1978, New York, Academic Press
13. Kantorovich L V, Krylov V I. Approximate Methods of Higher Analysis 1958, New York, Interscience Publishers
14. Kitanidis P K. Introduction to Geostatistics: Applications in Hydrogeology 1997, New York, Cambridge University Press
15. Kitanidis P K. Generalized Covariance Functions Associated with the Laplace Equation and their Use in Interpolation and Inverse Problems. Water Resources Research 1999, 35:1361-67.
16. Krige D J. Lognormal-de Wijsian Geostatistics for Ore Evaluation, Series in Geostatistics No.1 1978, Johannesburg, South Africa, Southern African Institute of Mining and Metallurgy
17. Kyriakidis P C. A Geostatistical Framework for the Area-to-Point Spatial Interpolation. Geographical Analysis 2004, 36((3)):41-50.
18. Lam N S-N. Spatial Interpolation Methods: A Review. The American Cartographer 1983, 10:129-49.
19. Langford M, Unwin D J. Generating and Mapping Population Density Surfaces within a Geographical Information System. The Cartographic Journal 1994, 31:21-26.
20. Martin D. Mapping Population Data from Zone Centroid Locations. Transactions of the Institute of British Geographers NS 1989, 14((8)):90-97.
21. Martin D. An Assessment of Surface and Zonal Models of Population. International Journal of Geographical Information Systems 1996, 10:973-89.
22. Martin D, Tate N J, Langford M. Refining Population Surface Models: Experiments with Northern Ireland Census Data. Transactions in GIS 2000, 4:343-60.
23. Matheron G. 1971, The Theory of Regionalized Variables and its Applications, Centre de Géostatistique de l'Ecole des Mines de Paris, France. Fasc. 5, Ecole Nat. Sup. des Mines, Paris
24. Rendu J M. An Introduction to Geostatistical Methods of Mineral Evaluation, Series in Geostatistics No. 2 1981, Johannesburg, South Africa, South African Institute of Mining and Metallurgy
25. Roach G. Green's Functions 1970, London, Cambridge University Press
26. Ryan J, Maoh H, Kanaroglou P. Population Synthesis: Comparing the Major Techniques Using a Small, Complete Population of Firms. Geographical Analysis 2009, 41:181-203.
27. Selvadurai A P S. Partial Differential Equations in Mechanics I: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation 2001, Berlin, Germany, Springer Verlag
28. Thurstain-Goodwin M, Unwin D. Defining and Delineating the Central Areas of Towns for Statistical Monitoring Using Continuous Surface Representations. Transactions in GIS 2000, 4:305-17.
29. Tobler W R, Davis J, McCullagh M. Linear Operators Applied to Areal Data. Display and Analysis of Areal Data 1975, 14-38. In, edited by, London, Wiley
30. Tobler W R. Smooth Pychnophylactic Interpolation for Geographical Regions. Journal of the American Statistical Association 1979, 74((367)):519-30.
31. Wackernagel H. Multivariate Geostatistics: An Introduction with Applications 2003, Berlin, Germany, Springer
32. Wackernagel H, Thiery L, Grzebyk M, Gomez-Hernandez J, Soares A, Froidevaux R. The Larsen Model from a de Wijsian Perspective. GeoENV II: Geostatistics for Environmental Applications 1999, 125-35. In, edited by, Dordrecht, The Netherlands, Kluwer
33. Yoo E-H, Kyriakidis P C. Area-to-Point Kriging with Inequality-Type Data. Journal of Geographical Systems 2006, 8:357-90.
34. Yoo E-H, Kyriakidis P C. Area-to-Point Predictions under Boundary Conditions. Geographical Analysis 2008, 40:355-79.