Multivariate geostatistical approach to space-time data analysis (original) (raw)

Abstract

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. 1. INTRODUCTION A great number of variables in hydrology can be viewed as spatiotempora! processes. Monthly precipitation readings or ß '.daily piezometric measurements may be considered as space-time functions presenting continuous complex fluctuations. Geostatistics offers a variety of methods to model such processes as realizations of random functions. These procedures, however, have been primarily applied to spatial .data. Most published works in geostatistical hydrology also st•ow a tendency to de-emphasize the role of the time ß mension in order to comply with spatial models. Temporal integration of variables or steady-state assumptions are corn.mon approaches to accomplish this spatial conversion. For instance, one may consider annual rainfall depths in •ce as a regionalized variable. Steady-state piezometric satface is another example of a complex spatial function. Applying such space-oriented approaches to spatiotemporal processes, however, may lead to the loss of valuable information in the time dimension.

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References (20)

  1. Bilonick, R. A., Monthly hydrogen ion deposition maps for the northeastern U.S. from July 1982 to September !984, Consolida- tion Coal Co., Pittsburgh, 1987.
  2. Chatfield, C., The Analysis of Time Series, 3rd ed., 286 pp., Chapman and Hall, London, 1984.
  3. Courant, R., and D. Hilbert, Methoden der Mathematischen Physik, 3rd ed., vol. 1,469 p., Springer-Verlag, New York, 1968.
  4. Goulard, M., Inference in a coregionalization model, in Geostatis- tics, vol. 1, edited by M. Armstrong, pp. 397-408, Kluwer Academic, Dordrecht, 1989.
  5. Journel, A. G., and C. J. Huijbregts, Mining Geostatistics, 600 pp., Academic, San Diego, Calif., 1978.
  6. Matheron, G., The Theory of Regionalized Variables and its Appli- cations, Les Cahiers du Centre de Morphologie Math•matique de Fontainebleau, No. 5, 211 pp., 1971.
  7. Myers, D. E., Matrix formulation of co-kriging, Math. Geol., 14, 249-257, 1982.
  8. Rodriguez-Iturbe, I., and J. M. Mejia, The design of rainfall net- works in time and space, Water Resour. Res., 10(4), 7!3-728, 1974.
  9. Rouhani, S., and T. J. Hall, Space-time kriging of groundwater data, in Geostatistics, vol. 2, pp. 639-650, edited by M. Armstrong, Kluwer Academic, Dordrecht, 1989.
  10. Seguret, S. A., Filtering periodic noise by using trigonometric kriging, in Geostatistics, vol. 1, edited by M. Armstrong, pp. 481-491, Kluwer Academic, Dordrecht, 1989.
  11. Service G•ologique Ile-de-France, Etude quantitative sur module math•matique des ressource en eau souterraine des bassins de la Juine et de l'Essonne, rep. 84 AGI 257 IDF, Brie-Comte-Robert, France, July 1984.
  12. Solow, A. R., and S. M. Gorelick, Estimating monthly streamflow values by cokriging, Math. Geol., 18(8), 785-810, 1986.
  13. Switzer, P., Non-stationary spatial correlations estimated from monitoring data, in Geostatistics, vol. 1, edited by M. Armstrong, pp. 127-138, Kluwer Academic, Dordrecht, 1989.
  14. Wackernagel, H., Geostatistical techniques for interpreting multi- variate spatial information, in Quantitative Analysis for Mineral and Energy Resources, edited by C. F. Chung, pp. 393-409, D. Reidel, Hingham, Mass., 1988.
  15. Wackernagel, H., Description of a computer program for analyzing multivariate spatially distributed data, Cornput. Geosci., I5(4), 539-598, 1989.
  16. Wackernagel, H., R. Webster, and M. A. Oliver, A geostatistical method for segmenting multivariate sequences of soil data, in Classification and Related Methods of Data Analysis, edited by H. H. Bock, pp. 641-650, Elsevier, New York, 1988.
  17. Volle, M., Analyse des Donndes, 3rd ed., 324 pp., Economica, Pads, 1985.
  18. Yaglom, A.M., Correlation Theory of Stationary and Related Random Functions, vol. 1, p. 366, Springer-Verlag, New York, 1986.
  19. S. Rouhani, School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA 30332.
  20. H. Wackernagel, Centre de G•ostatistique, Ecole Nationale Su- p•rieure des Mines de Paris, 35 Rue Saint HonorS, 77305 Fon- tainebleau, France. (Received July 17, 1989;