Multivariate geostatistical approach to space‐time data analysis

A large number of hydrological phenomena may be regarded as realizations of space‐time random functions. Most available hydrological data sets exhibit time‐rich/space‐poor characteristics, as well as, some form of temporal periodicity and spatial non‐stationarity. To better understand the space‐time structure of such hydrological variables, the observed values at each measurement site are considered as separate, but correlated time series. Moreover, it is assumed that the time series are realizations of a mixture of random functions, each associated with a different temporal scale, represented by a particular basic variogram. To preserve the observed temporal periodicities, the experimental direct and cross variograms are modelled as linear combinations of a number of hole function variograms. In a further step, the principal component analysis is used to determine groupings of measurement stations at different temporal scales. The proposed procedure is then applied to monthly piezometric data in a basin south of Paris, France. The temporal scales are determined to be the 12‐month seasonal and the 12‐year climatic cycles. At each temporal scale different spatial groupings are observed which are attributed to the contrast between the nearly steady state climatic variations versus the almost transient seasonal fluctuations.