Calibration and Reliability in Groundwater
Modelling: Credibility of Modelling
(Proceedings of ModelCARE 2007 Conference, held in
Denmark, September 2007). IAHS Publ. 320, 2008, 3-8.
On the
geostatistical characterization of hierarchical media
SHLOMO P. NEUMAN1, MONICA RIVA2 & ALBERTO GUADAGNINI2
1 Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721, USA
2 DIIAR, Politecnico di Milano, Piazza L. Da
Vinci 32, 20133 Milano, Italy
Abstract The
subsurface exhibits hierarchical structures with multiscale hydraulic and
transport properties. The structure and properties are often well characterized
by stationary variograms. We propose that the latter is an artefact of sampling
over finite windows, which disappears when one uses truncated power variograms
(TPVs). We cite evidence that parameters of traditional stationary variograms
vary with support and window scales; demonstrate the ability of TPVs to capture
these scale variations; show that stationary variograms are often difficult to
distinguish from TPVs; note that TPVs are unique in their ability to represent
multiscale random fields having either Gaussian or heavy-tailed symmetric Levy
stable probability distributions; detail the way in which TPVs allow
conditioning on multiscale measurements via co-kriging; and illustrate these
capabilities on multiscale hydraulic data from TŸbingen, Germany.
Key words hierarchy; multiscale; fractal; variogram; exponential; power; cutoff; co-kriging; Gaussian; Levy stable