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Spatial Statistics Glossary

Autocorrelation, autocovariance; autocorelatie, autocovarianta

- statistical concepts expressing the degree to which the value of an attribute at spatially adjacent points varies with the distance or time separating the observations.

Co-kriging

- estimation of a regionalized variable using observations of that variable supplemented by observations of one or more additional variables from within the same geographical area, thereby reducing the estimation variance if the original variable has been undersampled.

Delaunay triangulation; triangulatie Delauney

- the graph obtained by joining pairs of points whose polyhedra are Thiessen (Voronoi/Dirichlet) divisions of the plane.

Disjunctive kriging

- a non-linear distribution-dependent estimator for regionalized variables that do not have simple (Gaussian) distributions. It is the most demanding kriging method in terms of computer resources, mathematical understanding, and stationarity conditions.

Experimental variogram; variograma expewrimentala

- an estimate of a (semi-) vario gram based on sampling.

Fractal

- an object having a fractional dimension; one which has variation that is self-similar at all scales, in which the final level of detail is never reached and never can be reached by increasing the scale at which observations are made.

Hole effect; efect de gaura

- a condition in which the variogram does not increase monotonically beyond the range. The cause may be real or due to pseudo periodicities in the sample data.

Indicator kriging

- a kriging interpolation method which is non-linear and in which the original data are transformed from a continuous to a binary scale.

Inexact interpolator; interpolator incorect

- interpolation methods that provide estimates at data locations that are not necessarily the same as the original measurements.

Interpolation; interpolare

- the estimation of values of an attribute at unsampled points from measurements made at surrounding sites.

Intrinsic hypothesis; ipoteza intrinseca

- a form of spatial stationarity less restrictive than second order stationarity, in which the stationarity requirements are confined to the first differences and not the underlying regionalized variable. The intrinsic hypothesis is useful for modeling regionalized variables in which the form of the variogram is a function of domain size.

Kriging (named after D. G. Krige)

- a suite of interpolation techniques that use regionalized variable theory to incorporate information about the stochastic aspects of spatial variation when estimating interpolation weights.

Kriging variance; varianta kriging

- a measure of the uncertainty of estimation for values predicted by kriging.

Lag;

- a user-specified distance class within which semivariance is computed for a set of data points.

Landscape metrics; metrica terenului

- a suite of scale-dependent spatial statistics that describe landscapes in terms of patchiness, mosaics, and fragmentation. Some of these metrics are invariant under changes in map scale.

Linear interpolator; interpolator liniar

- describes a method whereby the weights assigned to different data points are computed using a linear function of distance between sets of data points and the point to be predicted.

Non-transitive variogram; variograma netranzitiva

- a variogram in which the sill is not reached within the domain of interest.

Nugget

- in kriging and variogram modeling, that part of the variance of a regionalized variable that has no spatial component (variation due to measurement errors and short-range spatial variation at distances within the smallest inter-sample spacing).

Ordinary kriging

- a method for interpolating data values from sample data using regionalized variable theory in which the prediction weights are derived from a fitted variogram model.

Range

- the distance at which the maximum semivariance is attained by a transitive semi-variogram.

Regionalized variable; variabila regionalizata

- a single-values function defined over a metric space (a set of coordinates) that represent the variation of natural phenomena that are too irregular at the scale of interest to be modeled analytically.

Semi-variogram; semivariograma

- 1. Given two locations x and (x + h), a measure of one-half of the mean square differences (the semivariance) produced by assigning the value z(x + h) to the value z(x), where h (known as the lag) is the inter-sample distance.
- 2. A graph of semivariance versus lag h.

Sill

- the maximum level of semivariance reached by a transitive semi-variogram.

Simple kriging

- an interpolation technique in which the prediction is based on a generalized linear regression under the assumption of second order stationarity and a known mean.

Spline

- a polynomial curve or surface used to represent spatial variation smoothly.

Stationarity; stationaritate

- a statistical name for expressing degrees of invariance in the properties of random functions; it refers to the statistical model, and not to the data. Most commonly used to indicate invariance in the mean and variance, but also in the variance of first differences.

Stratified kriging

- interpolation by any kriging method within a set of strata or divisions of the land into different classes.

Tessellation

- the process of dividing an area into smaller, contiguous tiles with no gaps in between them.

Thiessen polygons

- a tesselation of the plane such that any given location is assigned to a tile according to the minimum distance between it and a single, previously sampled point.

Transitive variogram

- a semivariogram having a range and a sill.

Universal kriging

- simple kriging of the residuals of a regionalized variable after systematic variation has been modeled by a drift or trend surface.

Voxels; voxeli

- three-dimensional, cubic units of space.

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