In geostatistics, spatial autocorrelation is utilized to estimate optimally local values from data sampled elsewhere. The powerful synergy between geostatistics and remote sensing went unrealized until the 1980s. Today geostatistics are used to explore and describe spatial variation in remotely sensed and ground data; to design optimum sampling schemes for image data and ground data; and to increase the accuracy with which remotely sensed data can be used to classify land cover or estimate continuous variables. This article introduces these applications and uses two examples to highlight characteristics that are common to them all. The article concludes with a discussion of conditional simulation as a novel geostatistical technique for use in remote sensing.
Armstrong, M., editor, 1989: Geostatistics 1 and 2. Dordrecht: Kluwer Academic.
2.
Atkinson, P. M.1991: Optimal ground-based sampling for remote sensing investigations: estimating the regional mean. International Journal of Remote Sensing12, 559-567.
3.
Atkinson, P. M.1993: The effect of spatial resolution on the experimental variogram of airborne MSS imagery. International Journal of Remote Sensing14, 1005-1011.
4.
Atkinson, P. M.1995: A method for describing quantitatively the information, redundancy and error in digital spatial data. In Fisher, P., editor, Innovations in GIS II, London: Taylor & Francis, 85-96.
5.
Atkinson, P. M.1996: Modelling the negative cross-correlation between locational error and underlying variation in field-based measurements of reflectance. In RSS96: Remote sensing science and industry, Nottingham: Remote Sensing Society, 559-566.
6.
Atkinson, P. M.1997: Scale and spatial dependence. In van Gardingen, P. R., Foody, G. M. and Curran, P. J., editors, Scaling-up, Cambridge: Cambridge University Press, 35-60.
7.
Atkinson, P. M. and Curran, P. J. 1994: The effects of the support on the precision of cokriging from remotely sensed data. In Proceedings of the annual conference of the International Association of Mathematical Geology, Québec: International Association for Mathematical Geology Press, 9-14.
8.
Atkinson, P. M. and Curran, P. J.1995: Defining an optimal size of support for remote sensing investigations. IEEE Transactions on Geoscience and Remote Sensing33, 768-776.
9.
Atkinson, P. M. and Curran, P. J.1997: Choosing an appropriate spatial resolution for remote sensing. Photogrammetric Engineering and Remote Sensing63, 1345-1351.
10.
Atkinson, P. M., Curran, P. J. and Webster, R.1990: Sampling remotely sensed imagery for storage, retrieval and reconstruction. The Professional Geographer42, 345-353.
11.
Atkinson, P. M., Curran, P. J. and Webster, R., Curran, P. J. and Webster, R.1992: Cokriging with ground-based radiometry. Remote Sensing of Environment41, 45-60.
12.
Atkinson, P. M. and Danson, F. M. 1988: Spatial resolution for remote sensing of forest plantations. In Proceedings, IGARSS ’88 symposium, Noordwijk: ESA Publications Division, ESTEC, 221-223.
13.
Atkinson, P. M., Dunn, R. and Harrison, A. R.1996: Measurement error in reflectance data and its implications for regularizing the variogram. International Journal of Remote Sensing17, 3735-3750.
14.
Atkinson, P. M. and Harrison, A. R.1995: An improved method of estimating measurement error in remotely sensed images. In Askne, J., editor, Sensors and environmental applications of remote sensing, Rotterdam: A.M. Balkema, 399-406.
15.
Atkinson, P. M. and Kelly, R. E. J.1997: Scaling-up snow depth in the UK for comparison with SSM/I imagery. International Journal of Remote Sensing18, 437-443.
16.
Atkinson, P. M., Webster, R. and Curran, P. J.1994: Cokriging with airborne MSS imagery. Remote Sensing of Environment50, 335-345.
17.
Bhatti, A. V., Mulla, D. and Frazier, B.1991: Estimation of soil properties and wheat yields on complex eroded hills using geostatistics and Thematic Mapper images. Remote Sensing of Environment37, 181-191.
18.
Brown, D. G. and Bara, T. J.1994: Recognition and reduction of systematic error in elevation and derivative surfaces from 712 minute DEMs. Photogrammetric Engineering and Remote Sensing60, 189-194.
19.
Burgess, T. M. and Webster, R.1980a: Optimal interpolation and isarithmic mapping of soil properties. I. The semi-variogram and punctual kriging. Journal of Soil Science311, 315-331.
20.
Burgess, T. M. and Webster, R.1980b: Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging. Journal of Soil Science31, 333-341.
21.
Burgess, T. M., Webster, R. and McBratney, A. B.1981: Optimal interpolation and isarithmic mapping of soil properties. IV. Sampling strategy. Journal of Soil Science32, 643-659.
22.
Carr, J. R.1995: Numerical analysis for the geological sciences. Englewood-Cliffs, NJ: Prentice-Hall.
23.
Carr, J. R.1996: Spectral and textural classification of single and multiple band digital images. Computers and Geosciences22, 849-865.
24.
Carr, J. R. and Myers, D. E. 1984: Application of the theory of regionalised variables to the spatial analysis of Landsat data. In Proceedings, ninth Pecora symposium, Silver Spring, IEEE, 55-61.
25.
Chavez, P. S.1988: An improved dark-object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment24, 459-479.
26.
Chavez, P. S.1992: Comparison of spatial variability in visible and near-infrared spectral images. Photogrammetric Engineering and Remote Sensing58, 957-964.
Cohen, W. B., Spies, T. A. and Bradshaw, G. A.1990: Semivariograms of digital imagery for analysis of conifer canopy structure. Remote Sensing of Environment34, 167-178.
29.
Congalton, R.1988: Using spatial analysis to explore the errors in maps generated from remotely sensed data. Photogrammetric Engineering and Remote Sensing54, 587-592.
30.
Cressie, N.1990: The origins of kriging. Mathematical Geology22, 239-253.
31.
Cressie, N.1991: Statistics for spatial data. New York: Wiley.
32.
Csillag, F. 1987: A cartographer’s approach to quantitative mapping of spatial variability from ground sampling to remotely sensed data. In Chrisman, N. R., editor, Proceedings, eighth international symposium on computer-assisted cartography, Falls Church, VA: American Society for Photogrammetry and Remote Sensing, 155-163.
33.
Csillag, F., Kertesz, M. and Kummert, A.1996: Sampling and mapping of heterogeneous surfaces: multi-resolution tiling adjusted to spatial variability. International Journal of Geographical Information Systems10, 851-875.
34.
Curran, P. J.1988: The semi-variogram in remote sensing: an introduction. Remote Sensing of Environment37, 493-507.
35.
Curran, P. J. and Dungan, J..L.1989: Estimation of signal-to-noise: a new procedure applied to AVIRIS data. IEEE Transactions on Geoscience and Remote Sensing27, 620-628.
36.
Dancy, K. J., Webster, R. and Abel, N. O. J.1986: Estimating and mapping grass cover and biomass from low-level photographic sampling. International Journal of Remote Sensing7, 1679-1704.
Davidson, D. A. and Watson, A. I.1995: Spatial variability in soil moisture as predicted from Airborne Thematic Mapper (ATM) data. Earth Surface Processes and Landforms20, 219-230.
39.
Davis, F. W., Quattrochi, D. A., Ridd, M. K., Lam, N. S. M., Walsh, S. J., Michaelsen, J. C., Franklin, J., Stow, D. A., Johannsen, C. J. and Johnson, C. A.1991: Environmental analysis using integrated GIS and remotely sensed data: some research needs and priorities. Photogrammetric Engineering and Remote Sensing57, 689-697.
40.
de Jong, S. M.1995: Mapping spatial variability in landscapes: an example using fractal dimensions. In Wilkinson, G. G., Kanellopoulos, I. and Mégier, J., editors, Fractals in geoscience and remote sensing. Image Understanding Research Series Vol. 1, Luxembourg, Joint Research Centre, European Commission, 176-210.
41.
de Jong, S. M. and Burrough, P. A.1995: A fractal approach to the classification of Mediterranean vegetation types in remotely sensed images. Photogrammetric Engineering and Remote Sensing61, 1041-1053.
42.
de Roos, A. M. and Sabelis, M. W.1995: Why does space matter? In a spatial world it is hard to see the forest before the trees. Oikos74, 347-348.
43.
Deutsch, C. V. and Journel, A. G.1992: GSLIB geo-statistical software library. Oxford: Oxford University Press.
44.
Dungan, J. L.1995: Geostatistical approaches for spatial estimation of vegetation quantities using ground and image data. In RSS95: remote sensing in action, Nottingham: Remote Sensing Society, 947-954.
45.
Dungan, J. L. submitted: Spatial prediction of vegetation quantities using ground and image data. International Journal of Remote Sensing.
46.
Dungan, J. L. and Coughlan, J. C. 1996: Redefining the spatial support of environmental data in the Regional HydroEcological Simulation System. In Proceedings, third international conference/workshop on integrating geographic information systems and environmental modelling, Santa Barbara, CA: National Centre for Geographic Information and Analysis (http://www.ncgia.ucsb.edu/conf/SANTA7FE7CD-ROM/main.html).
47.
Dungan, J. L., Peterson, D. L. and Curran, P. J.1994: Alternative approaches for mapping vegetation quantities using ground and image data. In Michener, W., Brunt, J. and Stafford, S., editors, Environmental information management and analysis: ecosystem to global scales, London: Taylor & Francis, 237-261.
48.
Gamon, J. A., Field, C. B., Roberts, D. A., Ustin, S. L. and Valentini, R.1993: Functional patterns in an annual grassland during an AVIRIS overflight. Remote Sensing of Environment44, 239-253.
49.
Glass, C. E., Carr, J. R., Yang, H. M. and Myers, D. E.1988: Application of spatial statistics to analysing multiple remote sensing data sets. In Petterson, C. B., editor, Geotechnical applications of remote sensing and remote data transmission, Philadelphia, PA: American Society for Testing and Materials, 138-150.
50.
Gohin, F. and Langlois, G.1993: Using geo-statistics to merge in situ measurements and remotely-sensed observations of sea surface temperature. International Journal of Remote Sensing14, 9-19.
51.
Haining, R. P., Griffith, D. A. and Bennett, R. J.1989: Maximum likelihood estimation with missing spatial data and with an application to remotely sensed data. Statistical Theory and Methods18, 1875-1894.
52.
Harvey, D.1969: Explanation in geography. London: Edward Arnold.
53.
Hay, G. J., Niemann, K. O. and McLean, G. F.1996: An object-specific image-texture analysis of H-resolution forest imagery. Remote Sensing of Environment55, 108-122.
54.
Hedger, R. D., Atkinson, P. M., Malthus, T. J. and George, D. G.1996: Planning optimal sampling strategies for estimating the regional mean water quality in lakes. In RSS96: remote sensing science and industry, Nottingham: Remote Sensing Society, 221-228.
55.
Heisenberg, W.1932: Nobel prize in physics award address: W. Heisenberg. New York: Nobel Foundation/Elsevier.
56.
Herzfeld, U. C. and Brodscholl, A. L.1994: On the geologic structure of the Explora Escarpment (Weddell Sea, Antarctica) revealed by satellite and shipboard data evaluation. Marine Geophysical Research16, 325-345.
57.
Houghton, J. T., Meira Filho, L. G., Callander, B. A., Harris, N., Kattenberg, A. and Maskell, K., editors, 1996: Climate change 1995: the science of climate change. Cambridge: Cambridge University Press.
58.
Hyppänen, H.1996: Spatial autocorrelation and optimal spatial resolution of optical remote sensing data in boreal forest environment. International Journal of Remote Sensing17, 3441-3452.
59.
IGBP1992: Global change: reducing the uncertainties. Stockholm: International Geosphere Biosphere Programme, Royal Swedish Academy of Sciences.
60.
Isaaks, E. H. and Srivastava, R. M.1989: Applied geostatistics. Oxford: Oxford University Press.
61.
Journel, A. G.1986: Geostatistics: models and tools for the earth sciences. Mathematical Geology18, 119-140.
62.
Journel, A. G.1989: Fundamentals of geostatistics in five lessons. Short course in geology. Volume 8. Washington, DC: American Geophysical Union.
63.
Journel, A. G.1996: Modelling uncertainty and spatial dependence: stochastic imaging. International Journal of Geographical Information Systems10, 517-522.
64.
Journel, A. G. and Alabert, F.1989: Non-Gaussian data expansion in the earth sciences. Terra Nova1, 123-134.
65.
Journel, A. J. and Huijbregts, C. J.1978: Mining geostatistics. London: Academic Press.
66.
Jupp, D. L. B., Strahler, A. H. and Woodcock, C. E.1988: Autocorrelation and regularization in digital images. I. Basic theory. IEEE Transactions on Geoscience and Remote Sensing26, 463-473.
67.
Jupp, D. L. B., Strahler, A. H. and Woodcock, C. E.1989: Autocorrelation and regularization in digital images. II. Simple image models. IEEE Transactions on Geoscience and Remote Sensing27, 247-258.
68.
Lacaze, B., Raubal, S. and Winkel, T.1994: Identifying spatial patterns of Mediterranean landscapes from geostatistical analysis of remotely-sensed data. International Journal of Remote Sensing15, 2437-2450.
69.
Lam, N. S.-N.1983: Spatial interpolation methods: a review. American Cartographer10, 129-149.
70.
Lam, N. S.-N. and Quattrochi, D. A.1992: On the issues of scale, resolution and fractal analysis in the mapping sciences. The Professional Geographer44, 88-98.
71.
Lark, R. M.1996: Geostatistical description of texture on an aerial photograph for discriminating classes of land cover. International Journal of Remote Sensing17, 2115-2133.
72.
Lathrop, R. G. and Pierce, L. L.1991: Ground-based canopy transmittance and satellite remotely sensed measurements for estimation of coniferous forest canopy structure. Remote Sensing of Environment36, 179-188.
73.
Legg, C. A. 1990: Digital satellite imagery from the Soviet Union: an important new tool for environmental monitoring. In Proceedings, 16th annual conference of the Remote Sensing Society, Nottingham: Remote Sensing Society, 65-74.
74.
MacDonald, J.A. 1991: Automatic classification of satellite images in the textural domain using semivariograms. Unpublished MSc thesis, University of Nevada, Reno.
75.
Mandelbrot, B. B.1983: The fractal geometry of nature. San Francisco, CA: Freeman.
76.
Marceau, D. J., Gratton, D. J., Fournier, R. A. and Fortin, J.-P.1994a: Remote sensing and the measurement of geographical entities in a forested environment. 2. The optimal spatial resolution. Remote Sensing of Environment49, 105-117.
77.
Marceau, D. J., Howarth, P. J. and Gratton, D. J.1994b: Remote sensing and the measurement of geographical entities in a forested environment. 1. The scale and spatial aggregation problem. Remote Sensing of Environment49, 93-104.
78.
Matheron, G. 1965: Les variables régionalisées et leur estimation. Paris: Masson.
79.
Matheron, G. 1971: The theory of regionalized variables and its applications. Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau 5. Fontainebleau: CMMF.
80.
McBratney, A.B. and Webster, R.1983a: How many observations are needed for regional estimation of soil properties?Soil Science135, 177-183.
81.
McBratney, A.B. and Webster, R.1983b: Optimal interpolation and isarithmic mapping of soil properties. V. Co-regionalization and multiple sampling strategy. Journal of Soil Science34, 137-162.
82.
McGwire, K., Friedl, M. and Estes, J. E.1993: Spatial structure, sampling design and scale in remotely sensed imagery of a Californian savanna woodland. International Journal of Remote Sensing14, 2137-2164.
83.
Meentemeyer, V.1989: Geographical perspectives of space, time and scale. Landscape Ecology3, 163-173.
84.
Mercer, W. B. and Hall, A. D.1911: Experimental error of field trials. Journal of Agricultural Science4, 107-132.
85.
Miranda, F. P. and Carr, J. R.1994: Application of the semivariogram textural classifier (STC) for vegetation discrimination using SIR-B data on the Guiana Shield, northwestern Brazil. Remote Sensing Reviews10, 155-168.
86.
Miranda, F. P., Fonesca, L. E. N. and Carr, J. R. submitted: Semivariogram textural classification of JERS-1 (Fuyo-I) SAR data obtained over a flooded area of the Amazonian rainforest. International Journal of Remote Sensing.
87.
Miranda, F. P., Fonseca, L. E. N., Carr, J. R. and Taranik, J. V.1996: Analysis of JERS-I (Fuyo-I) SAR data for vegetation discrimination in northwestern Brazil using the semivariogram textural classifier (STC). International Journal of Remote Sensing17, 3523-3529.
88.
Miranda, F. P., MacDonald, J. A. and Carr, J. R.1992: Application of the semivariogram textural classifier (STC) for vegetation discrimination using SIR-B data of Borneo. International Journal of Remote Sensing13, 2349-2354.
89.
Moody, A. and Woodcock, C. E.1994: Scale-dependent errors in the estimation of land-cover proportions. Implications for a global land-cover dataset. Photogrammetric Engineering and Remote Sensing60, 585-594.
90.
NASA1988: Earth system science: a closer view. Report of the Earth System Sciences Committee, NASA Advisory Council. Washington, DC: NASA.
91.
N’Kanza, S. and Naizot, T.1993: A method for the structural analysis of degraded images. Photo-Interpretation1, 5-16.
92.
Olea, R. A., editor, 1990: Geostatistical glossary and multilingual dictionary. Oxford: Oxford University Press.
93.
Oliver, M. A. and Webster, R.1991: How geo-statistics can help you. Soil Use and Management7, 206-217.
94.
Oliver, M. A., Webster, R. and Gerrard, J.1989a: Geostatistics in physical geography. Part I. Theory. Transactions, Institute of British Geographers14, 259-269.
95.
Oliver, M. A., Webster, R. and Gerrard, J.1989b: Geostatistics in physical geography. Part II. Applications. Transactions, Institute of British Geographers14, 270-280.
96.
Quattrochi, D. A. and Pelletier, R. E.1990: Remote sensing for analysis of landscapes: an introduction. In Turner, M. G. and Gardiner, R. H., editors, Quantitative methods in landscape ecology, New York: Springer-Verlag, 51-76.
97.
Raffy, M.1993: Remotely sensed quantification of covered areas and spatial resolution. International Journal of Remote Sensing14, 135-159.
98.
Raffy, M.1994a: Change of scale theory: a capital challenge for space observation of the earth. International Journal of Remote Sensing15, 2353-2357.
99.
Raffy, M.1994b: The role of spatial resolution in quantification problems: spatialization method. International Journal of Remote Sensing15, 2381-2392.
100.
Ramstein, G. and Raffy, M.1989: Analysis of the structure of radiometric remotely sensed images. International Journal of Remote Sensing10, 1049-1073.
101.
Ripley, B. D.1981: Spatial statistics. London: Wiley.
102.
Rossi, R. E., Dungan, J. L. and Beck, L. R.1994: Kriging in the shadows: geostatistical interpolation for remote sensing. Remote Sensing of Environment49, 32-40.
103.
Rossi, R. E., Mulla, D. J., Journel, A. G. and Franz, E. H.1992: Geostatistical tools for modelling and interpreting ecological spatial dependence. Ecological Monographs63, 277-314.
104.
Rubin, T. 1990: Analysis of radar texture with variograms and other simplified descriptors. In Proceedings, Image Processing ’89, Church Falls, VA: American Society for Photogrammetry and Remote Sensing, 185-195.
105.
Sanderson, E. W., Zhang, M., Ustin, S. L. and Rejmankova, E. in press: Geostatistical scaling of canopy water content in a California salt marsh: bridging the gap between ecology and remote sensing. Landscape Ecology.
106.
Servain, J., Gohin, F. and Muzellec, A.1993: Wind fields at the sea surface determined from combined ship and satellite altimeter data. Journal of Atmospheric and Ocean Technology10, 880-886.
107.
Smith, G. M. and Curran, P. J.1996: The signal-to-noise ratio (SNR) required for the estimation of foliar biochemical concentrations. International Journal of Remote Sensing17, 1031-1058.
108.
Smith, G. M. and Curran, P. J. in press: Methods for estimating image signal-to-noise ratio (SNR). In Atkinson, P. M. and Tate, N. J., editors, Advances in spatial analysis for remote sensing and GIS, Chichester: Wiley.
109.
Smith, H. F.1938: An empirical law describing heterogeneity in the yields of agricultural crops. Journal of Agricultural Science28, 1-23.
110.
Smith, R. C. G., Prathapar, S. A., Barrs, H. D. and Slavich, P.1989: Use of a thermal scanner image of a water stressed crop to study soil spatial variability. Remote Sensing of Environment29, 111-120.
111.
St-Onge, B. A. and Cavayas, F.1995: Estimating forest stand structure from high resolution imagery using the directional variogram. International Journal of Remote Sensing16, 1999-2021.
112.
Tsang, T. and Barnsley, M.1996: A comparative analysis of various methods for quantifying landscape heterogeneity. In RSS96: remote sensing science and industry, Nottingham: Remote Sensing Society, 513-520.
113.
van der Meer, F.1994a: Sequential indictor conditional simulation and indicator kriging applied to discrimination of dolomitization in GER 63-channel imaging spectrometer data. Nonrenewable Resources3, 146-164.
114.
van der Meer, F.1994b: Calibration of Airborne Visible/Infrared Imaging Spectrometer Data (AVIRIS) to reflectance and mineral mapping in hydro-thermal alteration zones: an example from the ‘Cuprite Mining District’. Geocarto International3, 23-37.
115.
van der Meer, F.1994c: Mapping the degree of serpentinization within ultramatic rock bodies using imaging spectrometer data. International Journal of Remote Sensing15, 3851-3857.
116.
van der Meer, F.1994d: Extraction of mineral absorption features from high-spectral resolution data using non-parametric geostatistical techniques. International Journal of Remote Sensing15, 2193-2214.
117.
van der Meer, F.1996a: Performance characteristics of the indicator classifier on simulated image data. International Journal of Remote Sensing17, 621-627.
118.
van der Meer, F.1996b: Classification of remotely-sensed imagery using an indicator kriging approach: application to the problem of calcite-dolomite mineral mapping. International Journal of Remote Sensing17, 1233-1249.
119.
van der Meer, F.1997: What does multisensor image fusion add in terms of information content for visual interpretation?International Journal of Remote Sensing18, 445-452.
120.
Vogt, J.1992: Characterising the spatio-temporal variability of surface parameters from NOAA AVHRR data. Joint Research Centre Report EUR 14637 EN. Ispra: Commission of the European Communities.
121.
Wald, L.1989: Some examples of the use of structure functions in the analysis of satellite images of the ocean. Photogrammetric Engineering and Remote Sensing55, 1487-1490.
122.
Webster, R.1985: Quantitative spatial analysis of soil in the field. Advances in Soil Science3, 1-70.
123.
Webster, R., Curran, P. J. and Munden, J. W.1989: Spatial correlation in reflected radiation of land cover and its implication for sampling and mapping by ground-based radiometry. Remote Sensing of Environment29, 67-78.
124.
Webster, R. and Oliver, M.1990: Statistical methods in land and resource survey. Oxford: Oxford University Press.
125.
Weiler, R. A. and Stow, D. A.1991: Spatial analysis of land cover patterns and corresponding remotely sensed image brightness. International Journal of Remote Sensing12, 2237-2257.
126.
Wickham, J. D. and Riitters, K. H.1995: Sensitivity of landscape metrics to pixel size. International Journal of Remote Sensing16, 3585-3594.
127.
Woodcock, C. E. and Strahler, A. H.1987: The factor of scale in remote sensing. Remote Sensing of Environment21, 311-322.
128.
Woodcock, C. E., Strahler, A. H. and Jupp, D. L. B.1988a: The use of variograms in remote sensing. I. Scene models and simulated images. Remote Sensing of Environment25, 323-348.
129.
Woodcock, C. E., Strahler, A. H. and Jupp, D. L. B.1988b: The use of variograms in remote sensing. II. Real digital images. Remote Sensing of Environment25, 349-379.
130.
Yates, F.1948: Systematic sampling. Philosophical Transactions of the Royal Society, Series A241, 345-377.
131.
Yoder, J. A., McClain, C. R., Blanton, J. O. and Oey, L.-Y.1987: Spatial scales in CZCS-chlorophyll imagery of the southeastern US continental shelf. Limnology and Oceanography32, 929-941.
