Geostatistics for the Environmental Sciences

GS+ Quickly perform geostatistical analysis

Geostatistics provides a way to better understand the autocorrelation inherent in spatial data – and to define and use this variation to make better estimates of values for places not sampled and thereby create optimal, unbiased maps.

GS+ provides easy access to these computationally intense analyses. Whether you are analyzing oil deposits, plankton distributions, sun spot patterns, infectious disease outbreaks, or soil resources, GS+ allows you ready access to the power of geostatistics.

Create variograms on the fly

GS+ gives you complete control over variogram parameters such as
the active lag distance and the size of individual lag classes. Default values provide reasonable starting places from which you can optimize an analysis to suit a particular data set.

Model your variograms automatically – GS+ can automatically create a model for kriging that honors your data to the maximum extent possible using iterative techniques to optimize good model fits. A model window lets you override the values that GS+ chooses and slider controls allow you to immediately see the results of changes. GS+ provides models sufficient for almost all kriging applications.
Variograms are sometimes erratic due to data anomalies – outliers that become
apparent when they are the only values not autocorrelated with other values at a particular scale. GS+ provides h-Scattergram and Variance Cloud analyses to allow you to visualize and identify outliers fast, and a new masking command allows you to surgically remove (either temporarily or permanently) the offending data record.
Directional (anisotropic) variograms are produced at the same time as isotropic variograms so you can readily evaluate whether autocorrelation is dependent on compass direction. This occurs, for example, when there is a slope effect or some other environmental feature that causes autocorrelation in one direction to be different from autocorrelation in another.
It’s easy to recognize anisotropy in GS+ by creating variogram maps – graphs of semivariance in different compass directions. If present, you can then easily define an angle of maximum variation to use for the anisotropic variogram models.

Calculate 11 different types of autocorrelation measures

Variograms are only one type of autocorrelation provided by GS+. Also included are correlograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms. All are evaluated in both isotropic and anisotropic directions.

Import data from a wide variety of sources

The GS+ worksheet can be directly edited and you can import data into the worksheet from a variety of sources – text files formatted in different ways, Excel spreadsheets, Access and other database files, or cut and paste from any other Windows program. There are also several ways to indicate missing values, and any value in the spreadsheet can be removed from a particular analysis by setting a temporary missing value attribute. The worksheet accepts over a billion records.

Summarize your data prior to geostatistical analysis

GS+ also provides basic parametric statistics to enable you to characterize your data prior to geostatistical analysis. When a data set is prepared for analysis, GS+ reports stats such as the mean, range, standard deviation, and kurtosis and skewness, and also creates frequency and probability distributions so you can evaluate departures from normality. Quantile scattergrams provide a visual map of your sample locations and identify the locations of data with particular values.

Interpolation methods to meet every need

Three different types of interpolation are provided by GS+. Ordinary kriging (both block and punctual) provide optimal estimates for a property across the spatial domain. Conditional simulation also provides optimal estimates but honors original data at their locations so can be used to map sharp boundaries in a domain. Inverse distance weighting is probably the best non-geostatistical interpolation technique, based on simple nearest neighbor calculations.

GS+ also provides cokriging, which can be useful when your primary data are supported by secondary data collected at many additional locations. Cokriging is available for both block and punctual kriging and co-located cokriging is available for conditional simulation.

Polygon masks allow you to include or exclude complex shapes in the domain being mapped. Interpolate across an island or avoid interpolating across a parking lot – you can also nest polygons and overlap them.

Create interpolation output files that are usable by many other programs

GS+ creates interpolation output files (from kriging, cokriging, simulation, or inverse distance techniques) that can be read into many other types of mapping programs. GS+ will use these files to create it’s own maps or you can read the data into any GIS or mapping program that supports ArcInfo® or Surfer® input formats.

Cross-validation allows you to test your interpolation system against sampled data

In cross-validation analysis each measured point in a spatial domain is individually removed from the domain and its value estimated via kriging or inverse distance weighting as though it were never there. In this way a graph of estimated vs. actual values for each sample location in the domain can be constructed and used to test the interpolation system.

Customize all details of your GS+ graphs and maps and publish to anywhere

A rich set of graph editing options allow you to change axes, fonts, perspective, titles, symbols and many other graph attributes. Maps and graphs can be printed or sent to the Windows clipboard or to a file that can be read by web browsers, word processors, or any other Windows program that accepts wmf, jpeg, png, or bmp formats.