Abstract
Men have tried to model spatial behavior of the natural phenomena since a long time with initiative simple models such as the weighting functions, which are supposed to represent regional dependence structure of the phenomenon concerned. Unfortunately, commonly employed weighting functions are not actual data dependent, and hence they are applicable invariably in each spatial prediction, which is not convenient since each spatial phenomenon will have its own spatial dependence function. Spatial data distribution can be uniform, randomly uniform, homogeneous, isotropic, clustering, etc. which should be tested by a convenient test as described in the text. Besides, statistically it is also possible to depict the spatial variation through trend surface fit methods by using least squares technique. Finally in this chapter, adaptive least squares techniques are suggested in the form of Kalman filter for spatial estimation.
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References
Barnes SL (1964) A technique for maximizing details in numerical weather map analysis. J Appl Meteorol 3:396–409
Benjamin JR, Cornell CA (1970) Probability statistics and decision making in civil engineering. McGraw-Hill Book, New York
Bergthorsson P, Döös BR (1955) Numerical weather map analysis. Tellus 7:329–340
Brown RG, Hwang YC (1992) Introduction to random signals and applied Kalman filtering, 2nd edn. Wiley, New York
Cressman GP (1959) An operational objective analysis system. Mon Weather Rev 87:367–374
Davis A (2002) Statistics data analysis geology. Wiley, New York, 638 pp
Dee DP (1991) Simplification of Kalman filter for meteorological data assimilation. Q J Roy Meteorol Soc 117:365–384
Donnelly KP (1978) Simulation to determine the variance and edge effect of total nearest-neighbour distances. In: Hodder I (ed) Simulation methods in archeology. Cambridge Press, London, pp 91–95
Gandin LS (1963) Objective analysis of meteorological fields. Hydromet Press, New York, 242 pp
Gilchrist B, Cressman GP (1954) An experiment in objective analysis. Tellus 6:309–318
Goodin WR, McRea GJ, Seinfeld JH (1979) A comparison of interpolation methods for sparse data: application to wind and concentration fields. J Appl Meteorol 18:761–771
Harrison PJ, Stevens CF (1975) Bayesian forecasting. University of Warwick, working paper No. 13
Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME Ser D J Basic Eng 82:35–45
Kalman RE, Bucy R (1961) New result in linear filtering and prediction theory. Trans ASME Ser D J Basic Eng 83:95–108
Koch S, Link RF (1971) Statistical analysis of geological data. Dover Publications, New York, 375 p
Koch SE, DesJardins M, Kocin PJ (1983) An iterative Barnes objective map analysis scheme for use with satellite and conventional data. J Appl Meteorol 22:1487–1503
Latif AM (1999) A Kalman filter approach to multisite precipitation modeling in meteorology. Unpublished Ph.D. thesis, Istanbul Technical University, 125 pp
Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266
Sasaki Y (1960) An objective analysis for determining initial conditions for the primitive equations. Tech Rep 60-16T
Şen Z (1989) Cumulative semivariogram models of regionalized variables. Math Geol 21:891–903
Şen Z (2004) Fuzzy logic and system models in water sciences. Turkish Water Foundation Publication, Istanbul, 315 pp
Zadeh LA (1968) Fuzzy algorithms. Inf Control 12:94–102
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Sen, Z. (2016). Classical Spatial Variation Models. In: Spatial Modeling Principles in Earth Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-41758-5_4
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DOI: https://doi.org/10.1007/978-3-319-41758-5_4
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