Generating a continuous surface used to represent a particular attribute is a key capability required in most geographic information system (GIS) applications. Perhaps the most commonly used surface type is a digital elevation model of terrain. These datasets are readily available at small scales for various parts of the world. However, just about any measurement taken at locations across a landscape, subsurface, or atmosphere can be used to generate a continuous surface. A major challenge facing most GIS modelers is to generate the most accurate surface possible from existing sample data as well as characterize the error and variability of the predicted surface. Newly generated surfaces are used in further GIS modeling and analysis as well as in 3D visualization. Understanding the quality of this data can greatly improve the utility and purpose of GIS modeling.
Geostatistical Analyst uses sample points taken at different locations in a landscape and creates (interpolates) a continuous surface. The sample points are measurements of some phenomenon, such as radiation leaking from a nuclear power plant, an oil spill, or elevation heights. Geostatistical Analyst derives a surface using the values from the measured locations to predict values for each location in the landscape.
Geostatistical Analyst provides two groups of interpolation techniques: deterministic and geostatistical. All methods rely on the similarity of nearby sample points to create the surface. Deterministic techniques use mathematical functions for interpolation. Geostatistics relies on both statistical and mathematical methods, which can be used to create surfaces and assess the uncertainty of the predictions.
In addition to providing various interpolation techniques, Geostatistical Analyst also provides many supporting tools. For example, prior to mapping, exploratory spatial data analysis (ESDA) tools can be used to assess the statistical properties of the data. Having explored the data, you can then create a variety of output map types (for example, prediction, error of prediction, probability, and quantile) using many variants of kriging and cokriging algorithms (ordinary, simple, universal, indicator, probability, disjunctive, and empirical Bayesian) and associated tools (for example, data transformation, declustering, and detrending). If the data was collected in polygons, areal interpolation will take the shape and size of the polygon into account in the creation of a continuous prediction or standard error surface.
Understanding geostatistical methods
Geostatistical methods are based on statistical models that include autocorrelation (statistical relationships among the measured points). These techniques have the capability of producing prediction surfaces, and they can also provide a measure of the accuracy of these predictions.
The main steps involved in creating a geostatistical model are:
- Examining the data (distribution, trends, directional components, outliers).
- Calculating the empirical semivariogram or covariance values.
- Fitting a model to the empirical values.
- Generating the matrices of kriging equations.
- Solving them to obtain a predicted value and the error (uncertainty) associated with it for each location in the output surface.