Sampling design for spatially distributed hydrogeologic and environmental processes

Abstract A methodology for the design of sampling networks over space is proposed. The methodology is based on spatial random field representations of nonhomogeneous natural processes, and on optimal spatial estimation techniques. One of the most important results of random field theory for physical sciences is its rationalization of correlations in spatial variability of natural processes. This correlation is extremely important both for interpreting spatially distributed observations and for predictive performance. The extent of site sampling and the types of data to be collected will depend on the relationship of subsurface variability to predictive uncertainty. While hypothesis formulation and initial identification of spatial variability characteristics are based on scientific understanding (such as knowledge of the physics of the underlying phenomena, geological interpretations, intuition and experience), the support offered by field data is statistically modelled. This model is not limited by the geometric nature of sampling and covers a wide range in subsurface uncertainties. A factorization scheme of the sampling error variance is derived, which possesses certain atttactive properties allowing significant savings in computations. By means of this scheme, a practical sampling design procedure providing suitable indices of the sampling error variance is established. These indices can be used by way of multiobjective decision criteria to obtain the best sampling strategy. Neither the actual implementation of the in-situ sampling nor the solution of the large spatial estimation systems of equations are necessary. The required values of the accuracy parameters involved in the network design are derived using reference charts (readily available for various combinations of data configurations and spatial variability parameters) and certain simple yet accurate analytical formulas. Insight is gained by applying the proposed sampling procedure to realistic examples related to sampling problems in two dimensions.

[1]  J. Delhomme.  Kriging in the hydrosciences , 1978 .

[2]  A. Bárdossy,et al.  Multicriterion Network Design Using Geostatistics , 1985 .

[3]  George Christakos,et al.  Recursive parameter estimation with applications in earth sciences , 1985 .

[4]  Allan L. Gutjahr,et al.  Stochastic models of subsurface flow: infinite versus finite domains and stationarity , 1981 .

[5]  John H. Cushman,et al.  On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory , 1984 .

[6]  Ignacio Rodriguez-Iturbe,et al.  Rainfall network design for runoff prediction , 1976 .

[7]  R. O. Gilbert.  Statistical Methods for Environmental Pollution Monitoring , 1987 .

[8]  Ching-Lai Hwang,et al.  Methods for Multiple Objective Decision Making , 1979 .

[9]  Ricardo A. Olea,et al.  Sampling design optimization for spatial functions , 1984 .

[10]  H. Loáiciga.  An optimization approach for groundwater quality monitoring network design , 1989 .

[11]  Alex B. McBratney,et al.  The design of optimal sampling schemes for local estimation and mapping of of regionalized variables—I: Theory and method , 1981 .

[12]  S. Rouhani.  Variance Reduction Analysis , 1985 .

[13]  F. Yates,et al.  Sampling Methods for Censuses and Surveys , 1950 .

[14]  Massimo Guarascio,et al.  Advanced Geostatistics in the Mining Industry , 1977 .

[15]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[16]  G. Matheron.  The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[17]  Network design using optimal estimation procedures , 1979 .

[18]  Kiyosi Itô,et al.  Stationary random distributions , 1954 .

[19]  George Christakos,et al.  On certain classes of spatiotemporal random fields with applications to space-time data processing , 1991, IEEE Trans. Syst. Man Cybern..