Sampling and Kriging Spatial Means: Efficiency and Conditions

Sampling and estimation of geographical attributes that vary across space (e.g., area temperature, urban pollution level, provincial cultivated land, regional population mortality and state agricultural production) are common yet important constituents of many real-world applications. Spatial attribute estimation and the associated accuracy depend on the available sampling design and statistical inference modelling. In the present work, our concern is areal attribute estimation, in which the spatial sampling and Kriging means are compared in terms of mean values, variances of mean values, comparative efficiencies and underlying conditions. Both the theoretical analysis and the empirical study show that the mean Kriging technique outperforms other commonly-used techniques. Estimation techniques that account for spatial correlation (dependence) are more efficient than those that do not, whereas the comparative efficiencies of the various methods change with surface features. The mean Kriging technique can be applied to other spatially distributed attributes, as well.

[1]  R. Haining,et al.  Heterogeneity of attribute sampling error in spatial data sets , 2010 .

[2]  Zhe Jiang,et al.  Spatial Statistics , 2013 .

[3]  D. Mcgrath,et al.  Use of trans-Gaussian kriging for national soil geochemical mapping in Ireland , 2008, Geochemistry: Exploration, Environment, Analysis.

[4]  Xiaoping Yang,et al.  Late Quaternary environmental changes and organic carbon density in the Hunshandake Sandy Land, eastern Inner Mongolia, China , 2008 .

[5]  Wenzhong Shi,et al.  A hybrid interpolation method for the refinement of a regular grid digital elevation model , 2006, Int. J. Geogr. Inf. Sci..

[6]  K. Modis,et al.  A BME solution of the stochastic three-dimensional Laplace equation representing a geothermal field subject to site-specific information , 2006 .

[7]  Ali Esmaili,et al.  Probability and Random Processes , 2005, Technometrics.

[8]  Eulogio Pardo-Igúzquiza,et al.  Empirical Maximum Likelihood Kriging: The General Case , 2005 .

[9]  H. Bayraktar,et al.  A Kriging-based approach for locating a sampling site—in the assessment of air quality , 2005 .

[10]  Sean A. McKenna,et al.  Geostatistical interpolation of object counts collected from multiple strip transects: Ordinary kriging versus finite domain kriging , 2005 .

[11]  Alexander Kolovos,et al.  Total ozone mapping by integrating databases from remote sensing instruments and empirical models , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Wu Bing-fang,et al.  China Crop Watch System with Remote Sensing , 2004 .

[13]  Partha Dasgupta,et al.  Evaluating Projects and Assessing Sustainable Development in Imperfect Economies , 2003 .

[14]  Robert Haining,et al.  Spatial Data Analysis: Theory and Practice , 2003 .

[15]  Cass T. Miller,et al.  Computational Bayesian maximum entropy solution of a stochastic advection‐reaction equation in the light of site‐specific information , 2002 .

[16]  Pavel Krejcir.  Development of the Kriging Method with Application , 2002 .

[17]  Istvan Szunyogh,et al.  A Local Ensemble Kalman Filter for Atmospheric Data Assimilation , 2002 .

[18]  A-Xing Zhu,et al.  Soil Mapping Using GIS, Expert Knowledge, and Fuzzy Logic , 2001 .

[19]  George Christakos,et al.  Modern Spatiotemporal Geostatistics , 2000 .

[20]  Xia Li,et al.  Modelling sustainable urban development by the integration of constrained cellular automata and GIS , 2000, Int. J. Geogr. Inf. Sci..

[21]  Ricardo A. Olea,et al.  Geostatistics for Engineers and Earth Scientists , 1999, Technometrics.

[22]  A. Winsor.  Sampling techniques. , 2000, Nursing times.

[23]  G. Christakos,et al.  BME STUDIES OF STOCHASTIC DIFFERENTIAL EQUATIONS REPRESENTING PHYSICAL LAWS -PART I , 1999 .

[24]  George Christakos,et al.  Spatiotemporal information systems in soil and environmental sciences , 1998 .

[25]  Luc Fillion,et al.  Variational Assimilation of Precipitation Data Using Moist Convective Parameterization Schemes: A 1D-Var Study , 1997 .

[26]  D. J. Brus,et al.  Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion) , 1997 .

[27]  P. Courtier,et al.  Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology , 1993 .

[28]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[29]  R. Daley.  Atmospheric Data Analysis , 1991 .

[30]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[31]  P. Courtier,et al.  Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations , 1990 .

[32]  G. Christakos.  A Bayesian/maximum-entropy view to the spatial estimation problem , 1990 .

[33]  J. Derber.  A Variational Continuous Assimilation Technique , 1989 .

[34]  S. Dingman,et al.  Application of kriging to estimating mean annual precipitation in a region of orographic influence , 1988 .

[35]  R. Haining,et al.  Estimating spatial means with an application to remotely sensed data , 1988 .

[36]  George Christakos.  Modern statistical analysis and optimal estimation of geotechnical data , 1985 .

[37]  George Christakos,et al.  Recursive parameter estimation with applications in earth sciences , 1985 .

[38]  I. Rodríguez‐Iturbe,et al.  The design of rainfall networks in time and space , 1974 .

[39]  W. Tobler.  A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[40]  L. Gandin.  Objective Analysis of Meteorological Fields , 1963 .

[41]  G. P. Cressman.  AN OPERATIONAL OBJECTIVE ANALYSIS SYSTEM , 1959 .