Geostatistics
The term refers to specific geostatistics stochastic methods for characterization and estimation of spatially correlated georeferenced data, for example surface temperatures at various points of a lake. The aim is to use the point by way of measured data as a basis for spatial interpolation, ie of a finite number of measurements to derive an infinite number of estimates that are as close as possible to the real present values.
The estimated value of a physical quantity (such as the surface temperature) of a Schätzort is stronger due to the spatial correlation of the measured values as a function of such adjacent remote measuring places. For the estimation of these adjacent measured values are therefore to be considered stronger. We distinguish two methods, the non-statistical and statistical interpolation, the latter based on a geostatistical model.
In order to ascertain up to what maximum distance (range) and to what extent depend readings from neighboring or more distant readings, so-called experimental semi- variograms are modeled: For all distances ( as the x- values), the two measurement locations of the data set to each other have, the differences of the respective measurement values are plotted ( as the y- values): the growing dissimilarity with increasing distance is reflected in the increase in the y- values with increasing x values up to a certain limit resist. This dependency is a model function, for example a quadratic function expressed.
The function that has been obtained from the analysis of the measured values is the basis for the subsequent interpolation of a distribution of estimated values in the space in a process referred to as the kriging. The measurement values are obtained depending on the proximity to the searched estimate value depending on the modeled semivariogram different weighting factors with which they enter into the calculation of the estimated value ( counter-example: arithmetic mean as an estimator: obtain all readings without distinction the same weight ).
Is a prerequisite for the interpolation, that in the study area, the measured value distribution is homogeneous ( criterion of stationarity / homogeneity ). Example of inhomogeneity: the aluminum content of rocks of the study area, in which there are offset by a malfunction of two completely different rock units adjacent to and contiguous with no transition zone.
For example, the surface temperature of a lake, the result would be a distribution of the kriging estimate values in the plane of, for example, as isothermal map or surface relief ( " flying carpet " ) can be visualized with the elevational axis as the temperature axis.