Geostatistical Methods

The Geostatistical Methods allows the user modelling spatial data. Providing accurate and reliable estimations of phenomena at locations where no measurements are available.

TerraAmazon uses a Semivariogram for mapping or estimating the interpolation between the data points. The empirical variogram is used in geostatistics as a first estimate of the (theoretical) variogram needed for spatial interpolation by kriging.

The semivariogram tries to prove that things nearby tend to be more similar than things that are farther apart. Semivariogram measure the strength of statistical correlation as a function of distance.

The process of modeling semivariograms functions fits a semivariogram curve to your empirical data. Using your knowledge of the phenomenon, the goal is to achieve the best fit. There are certain characteristics that are commonly used to describe these models.

Nugget: The height of the jump of the semivariogram at the discontinuity at the origin.

Sill: Limit of the variogram tending to infinity lag distances.

Range: The distance in which the difference of the variogram from the sill becomes negligible. In models with a fixed sill, it is the distance at which this is first reached;

Source: (TerraView 5.1.0, 2010).

TerraAmazon provides the following functions to model the empirical semivariogram:

Spherical

The spherical model is particularly good for modeling spatial correlation which decreases approximately linearly with the separation distance, and is assumed to be zero beyond a certain distance. This is probably the most commonly used variogram structure in practice.


Source: (TerraView 5.1.0, 2010).

Exponential

The exponential model has a similar shape to the spherical model but reaches the sill more quickly.


Source: (TerraView 5.1.0, 2010).

Gaussian

The Gaussian model is used when the data exhibit strong continuity at short lag distances (i.e.: when the spatial correlation between two nearby points is very high).


Source: (TerraView 5.1.0, 2010).

Spatial Correlation

Spatial autocorrelation measures dependence among nearby values in a spatial distribution.


Source: (TerraView 5.1.0, 2010).

The lag size is the size of a distance class into which pairs of locations are grouped to reduce the large number of possible combinations. A good lag distance can also help reveal spatial correlations.

The direction angle is measured clockwise from the Y-axis and defines the direction in which points should be located relative to each other. When you use a direction angle of 90°, it means that only point pairs for which the points are located in West-East or in East-West direction will be considered (i.e. +90° clockwise from the Y-axis).

The tolerance angle is a parameter with which you can limit the number of point pairs. When a tolerance of 45° is used, all point pairs in the map will contribute to calculated semivariogram values.



It is accessible through:

PROCESSING → SPATIAL ANALYSIS → GEOSTATISTICAL METHODS


Input Information:

Layer Name: Select the desired Layer.

Attribute: The attribute to be analyzed.

Parameters:

Statistics

Method: Only semivariogram method is available.

Number of lags

Lag Increment

Angular Direction

Angular Tolerance

Adjust

Model: Spherical, Exponential, Gaussian.

Nugget

Sill

Range

Output Information:

A graph will be presented with the distribution of points and a curve representing the selected template. Use the parameters to adjust the curve to the points.

Click on the Apply button and then the graph with point distribution will be calculated.

Note: This component serves only to fit a model to a distribution of points.