Another Look at Non-Euclidean Variography

Tobler’s first law of geography states: “Everything is related to everything else, but near things are more related than distant things”. This property, which holds for most environmental variables, is used in spatial statistics: a weighted moving average is often applied to estimate data, and the weights can be a simple function of distance or derived from a model of the spatial covariance. However, many situations in which observations are close in space but distant in a physical sense, require some means to infringe on Tobler’s law. This is typically the case with measurements made in streams, as the water distance can be very different from the Euclidean distance. Exploring the use of non-Euclidean spaces may thus be interesting although many fundamental theoretical and practical problems exist. If modelling of the variogram is often at stake when applied to non-Euclidean spaces, we argue, however, that exploratory non-Euclidean variography may provide valuable information. It is the purpose of this paper to discuss non-Euclidean variography by means of a case study in which information provided by a digital elevation model (DEM) is used to explore monthly rainfall observations made at 36 meteorological stations in the Algarve region, Portugal. KEYWORDS: Exploratory variography, non-Euclidean, cost-weighted distances, magnifying factorJRC.H.4-Transport and air qualit