Extending Multivariate Space-Time Geostatistics for Environmental Data Analysis

Abstract Environmental studies require multivariate data such as chemical concentrations with space-time coordinates. There are two general conditions related to such data: the existence of correlations among the coregionalized variables and the differences in numbers of data which occur because of insufficient data caused by measurement error or bad weather conditions. This study proposes geostatistical techniques for space-time multivariate modeling that take into consideration these correlations and data absences. These techniques consist of suitable modeling of semivariograms and cross-semivariograms for quantifying correlation structures among multivariables and of extending standardized ordinary cokriging. The tensor product cubic smoothing surface method is used for space-time semivariogram modeling. These methods are applied to the chemical component data of the Ariake Sea, a typical closed sea in southwest Japan. In order to clarify environmental changes in the Ariake Sea, the concentration data of four nutritive salts (NO2–N, NO3–N, NH4–N, and PO4–P) at 38 stations over 25 years are used as environmental indicators. For each of the kinds of data, there are spaces and times for which there is no data available. The effectiveness of the modeling of space-time semivariograms and the high estimation capability of the extended cokriging are demonstrated by cross-validation. Compared with ordinary kriging for a single variable, multivariate space-time standardized ordinary cokriging can provide a more detailed concentration map of nutritive salts and while elucidating their temporal changes over sparsely spaced data areas. In the space-time models by ordinary kriging, on the other hand, smooth trends are obvious.

[1]  P. Goovaerts.  Spatial orthogonality of the principal components computed from coregionalized variables , 1993 .

[2]  S. De Iaco,et al.  Space-time variograms and a functional form for total air pollution measurements , 2002, Comput. Stat. Data Anal..

[3]  J. Aitchison,et al.  Logratio Analysis and Compositional Distance , 2000 .

[4]  D. E. Myers,et al.  Nonseparable Space-Time Covariance Models: Some Parametric Families , 2002 .

[5]  D. E. Myers,et al.  The Linear Coregionalization Model and the Product–Sum Space–Time Variogram , 2003 .

[6]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[7]  V. Pawlowsky-Glahn,et al.  BLU Estimators and Compositional Data , 2002 .

[8]  Shahrokh Rouhani,et al.  Multivariate geostatistical approach to space‐time data analysis , 1990 .

[9]  V. Pawlowsky-Glahn,et al.  Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation , 2003 .

[10]  D. Myers,et al.  Estimating and modeling space–time correlation structures , 2001 .

[11]  D. Myers,et al.  Space–time analysis using a general product–sum model , 2001 .

[12]  K. Koike,et al.  Spatio-Temporal Distribution Modeling of Ion Component Concentrations in Groundwater Using Geostatistics , 2002 .

[13]  Katsuaki Koike,et al.  Application of Spatio-Temporal Geostatistics to Detection of Secular Changes of Environments in a Closed Sea , 2005 .

[14]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .

[15]  P. Goovaerts,et al.  Study of Spatial and Temporal Variations of Hydrogeochemical Variables Using Factorial Kriging Analysis , 1993 .

[16]  E. Andrews.  Bed material transport in the Virgin River, Utah , 2000 .