COVARIANCE MODELS FOR DIVERGENCE-FREE AND CURL-FREE RANDOM VECTOR FIELDS

We construct matrix-valued covariance functions (C) over right arrow (div) and (C) over right arrow (curl) in R-2 and R-3, starting from an arbitrary scalar-valued variogram. It is shown that sufficiently smooth random vector fields (RVFs) with these covariance functions have divergence-free and curl-free sample paths, respectively. Conversely, essentially all models with such sample paths can be obtained via our construction. Extensions to space-time RVFs are possible. RVFs with divergence-free and curl-free sample paths can be utilised in meteorological applications e.g. for modelling and interpolating wind fields.