Veldscheefheid

Veldscheefheid is a concept used in spatial statistics to describe the skewness of a scalar field defined over a spatial domain. The term combines veld (field) and scheefheid (skewness) in Dutch.

Definition and formulation: For a scalar field F(x) defined over a region D with measure |D|, the global veldscheefheid S can be defined as the third standardized moment of the field values: S = E[(F(x) - μ)^3]/σ^3, where μ is the mean of F over D and σ its standard deviation, computed with area (or volume) weighting. Local variants use a moving window W to produce S_W(x) = E_W[(F - μ_W)^3]/σ_W^3, enabling a map of skewness across space.

Computation and interpretation: In practice, μ and σ are estimated from samples F_i over grid cells or pixels i in D, using the usual sample moments. A high positive S indicates a distribution with a long tail toward high field values; negative S indicates a tail toward low values. The measure is sensitive to outliers and to the choice of weighting and domain size. Proper application requires handling missing data and boundary effects, and may involve normalization when comparing fields of different units or scales.

Applications: Veldscheefheid can be used to characterize heterogeneity in geophysical fields (such as precipitation or soil moisture), climate fields, remote-sensing imagery, sensor networks, or simulated fields. It complements mean and variance by capturing asymmetry in the spatial distribution of field values and can guide interpretation of spatial processes.

See also: Skewness; Spatial statistics; Local indicators of spatial association.