Semivariance

Semivariance is a statistical measure used in geostatistics to describe the spatial variability of a dataset. It is a modification of the semivariogram, which is a fundamental tool for spatial data analysis. While the semivariogram considers the squared difference between all pairs of data points, semivariance focuses only on pairs where one point is below the mean and the other is above the mean. This directional focus makes it sensitive to skewness and asymmetry in the spatial distribution of data.

The semivariance is calculated by averaging the squared differences between data points that fall below the mean and data points that fall above the mean for a given distance lag. This contrasts with the standard semivariogram, which averages all pairs regardless of their relationship to the mean. The resulting semivariance function can reveal whether spatial correlation is stronger or weaker in areas with high or low values, providing insights into heterogeneous spatial processes.

Applications of semivariance can be found in various fields, including environmental science, mining, and agriculture, where understanding the spatial distribution of skewed phenomena is crucial. For example, it can help in analyzing the spread of pollutants or the distribution of mineral grades, where extreme values might be clustered in specific areas. By highlighting directional trends relative to the mean, semivariance offers a complementary perspective to traditional semivariogram analysis, aiding in more nuanced spatial modeling and prediction.