Spatio-Temporal Distribution Modeling of Ion Component Concentrations in Groundwater Using Geostatistics

Koike Katsuaki, Narikiyo Kouji, Matsuda Setsuro

doi:10.5023/jappstat.31.41

Environmental data acquired by periodic or continuous measurements at many points are expressed in the spatio-temporal region. Therefore, it is necessary to combine a spatial analysis and a time-series analysis for characterizing data distribution. This study adopts geostatistics to construct a distribution model, which can consider spatio-temporal correlation structures peculiar to the regionalized data and has ability to predict the near future values. The concentration data of seven ion components, Na+, Mg2+, K+, Ca2+, C1-, SO2-4, and HCO-3 contented in the groundwater in the Kumamoto city area, southwest Japan, were chosen for a case study of hydrologic environmental related problem. These data were sampled two times per year between 1994 and 2000 at the 31 groundwater observation wells. Omnidirectional semivariograms of univariate and cross-semivariograms of two variates were made and approximated by polynomials. They clarified two features of correlation structures of the components, which are monotonous increase type and periodic change type of semivariances between data pair with increase of distance and time interval. Through the cross-validation from the two viewpoints, (1) temporal extrapolation capability of ordinary kriging and ordinary co-kriging and (2) validness for considering both the spatial and temporal directions, it was demonstrated that the kriging methods can estimate properly the ion component concentrations and produce less smoothing effect. The concentrations in four June times in 1994, 1996, 1998, and 2000 were estimated and characteristics of fluctuation patterns of each component were detected. A cluster analysis of the hexadiagrams using the seven ion component concentrations estimated in each observation year clarified the zones having similar water quality. The lithologies and groundwater flows in the shallow depths are regarded as influence factors on water quality. In addition, the temporal changes of water qualities were found to be interpretable by a combination of the precipitation and groundwater flows. Water management is specially required for the portions where the qualities are changeable.

Spatio-Temporal Distribution Modeling of Ion Component Concentrations in Groundwater Using Geostatistics

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