What is an experimental variogram?

A variogram is a description of the spatial continuity of the data. The experimental variogram is a discrete function calculated using a measure of variability between pairs of points at various distances. The exact measure used depends on the variogram type selected (Deutsch & Journel 44-47).

How do you interpret a variogram?

A variogram value at a given h is the average squared difference between the values of the paired locations. If two locations, u and u + h, are close to each other in terms of the distance measurement, two values are similar, so the difference in their values, Z- Z, will be small.

What is variogram and semivariogram?

From Wikipedia, the free encyclopedia. In spatial statistics the theoretical variogram is a function describing the degree of spatial dependence of a spatial random field or stochastic process . The semivariogram. is half the variogram.

What is the purpose of a variogram?

A variogram is an effective tool for describing the behavior of non-stationary, spatial random processes. It is used primarily in spatial statistics, geostatistics, and statistical design; In geostatistics, it is an “essential step” for analyzing spatial variability (Gómez-Hernández et al., 1999).

What is the difference between experimental and theoretical variogram?

The experimental variogram was then calculated on the residuals. A “theoretical” variogram was obtained as a model, chosen among exponential, circular, spherical and penta-spherical usual functions adjusted to the “experimental” variogram to determine the nugget, sill and range (Fig. 2).

What is variogram map?

The Variogram surface operation uses a point map or a raster map as input and calculates a surface of semi-variogram values where each cell (pixel) in the surface represents a directional distance class. The output of the Variogram surface operation is a plot, depicted as a raster map, with the origin in the center.

What is the range in a variogram?

The range is the distance after which the variogram levels off. The physical meaning of the range is that pairs of points that are this distance or greater apart are not spatially correlated. The sill is the total variance contribution, or the maximum variability between pairs of points.

What is kriging in geostatistics?

In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations.

What is a Semivariogram model?

The semivariogram depicts the spatial autocorrelation of the measured sample points. Once each pair of locations is plotted, a model is fit through them. There are certain characteristics that are commonly used to describe these models.

What is geostatistical data?

Geostatistics is a class of statistics used to analyze and predict the values associated with spatial or spatiotemporal phenomena. It incorporates the spatial (and in some cases temporal) coordinates of the data within the analyses.

What is sill variogram?

The sill is the total variance where the empirical variogram appears to level off, and is the sum of the nugget plus the sills of each nested structure. Variogram points above the sill indicate negative spatial correlation, while points below the sill indicate positive correlation .