Geostatistics in Groundwater Modelling

Abstract

Geostatistics is a collection of statistical techniques for the analysis of spatial data. Geostatistics has been described by several authors (Matheron 1971; David 1977, 1986; Isaak and Srivastava 1989; Kitanidis 1997). In recent years, these tools have developed from research topics into basic techniques in the design and, such as mining, geology and hydrology, among others. The aim of this chapter is to present application of geostatistical tools in groundwater modelling and mapping. A typical spatial data set, such as groundwater levels, monthly precipitations, or transmissivities, is composed of scattered readings in space, denoted by z(x), where x represents the measurement location. Having such information, geostatistics provides many techniques to solve a variety of hydrogeological resources problems, such as: (i) Estimation of z at an unmeasured location: interpolation and mapping of z; (ii) Estimation of one variable based on measurements of other variables: co-estimation of piezometric head and transmissivity; (iii) Estimation of the gradient of z at an arbitrary site: estimation of groundwater flow velocity based on observed heads; (iv) Estimation of the integral of Z over a defined block: estimation of contamination volume based on point measurements; and (v) Design of sampling and monitoring networks, such as groundwater quality monitoring. Many of the groundwater related variables are spatial functions presenting complex variations that cannot be effectively described by simple deterministic functions, such as polynomials. Such phenomena are subject of geostatistics that are named as regionalized variables. Annual point precipitation is an example of a regionalized variable. Transmissivity also displays spatial variations due to complex processes governing the transport, deposition and compression of materials in sedimentary deposits. Another example of a regionalized variable is the concentration of a chemical compound in groundwater that varies in both space and time.