Spatial Modeling
In general, spatial variability is concerned with different values for any property, which is measured at a set of irregularly distributed geographic locations in an area. The aim is to construct a regional model on the basis of measurement locations with
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Spatial Modeling
Abstract In general, spatial variability is concerned with different values for any property, which is measured at a set of irregularly distributed geographic locations in an area. The aim is to construct a regional model on the basis of measurement locations with records and then to use this model for regional estimations at any desired point within the area. Earth sciences phenomenon varies both in time and space; and its sampling is based on measurement stations’ configuration. In many practical applications, measured data are seldom available at the point of interest, and consequently the only way to transfer the solar irradiation data from the measurement sites to the estimation point is through regional interpolation techniques using powerful models. The spatial variability is measured in the most common way through the recorded solar irradiation time series at individual points. The square differences between each pairs of spatial variable location values help to construct the spatial autocorrelation function as representative of regional dependence function. Spatial variability is the main feature of regionalized variables, which are very common in the physical sciences. In practical applications, the spatial variation rates of the phenomenon concerned are of great significance in fields such as in solar engineering, agriculture, remote sensing, and other earth and planetary sciences. A set of measurement stations during a fixed time interval (hour, day, month, etc.) provides records of the regionalized variable at irregular sites, and there are few methodologies to deal with this type of scattered data. There are various difficulties in making spatial estimations originating not only from the regionalized random behavior but also from the irregular site configuration. Optimum interpolation modeling technique is presented for spatio-temporal prediction of regionalized variable (ReV) with application to precipitation data from Turkey. Kriging method is explained with simple basic concepts and graphics, and then various Kriging application methodologies are explained for the spatial data modeling. The distinctions between simple, ordinary, universal, and block Kriging alternatives are presented in detail. Finally, triple diagram mapping methodology for spatial modeling is presented with applications at five different climate locations.
© Springer International Publishing Switzerland 2016 Z. Sen, Spatial Modeling Principles in Earth Sciences, DOI 10.1007/978-3-319-41758-5_6
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6 Spatial Modeling
Keywords Spatial estimation • Optimum interpolation • Spatial correlation function • Cross-validation • Geostatistics • Kriging • Intrinsic property • Simple Kriging • Ordinary Kriging • Universal Kriging • Block Kriging • Triple diagram • Regional rainfall pattern
6.1
General
Modeling is a procedure that helps researchers, planners, politicians, and many experts alike to make future predictions in time or spatial estimations in a region. It is an interactive procedure where the natural
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