Stochastic hydrogeology is the study of hydrogeology using physical and probabilistic concepts. It is an applied science because it is oriented toward applications. Its goal is to develop tools for analyzing measurements and observations taken over a sample region in space, and extract information which can then be used for evaluating and modeling the properties of physical processes taking place in this domain, and make risk-qualified predictions of their outcome. By invoking probabilistic concepts to deal with problems of physics, stochastic hydrogeology joins a well-established tradition followed in mining (Matheron, 1965; David, 1977; Journel and Huijbregts, 1978), turbulence (Kolmogorov, 1941; Batchelor, 1949), acoustics (Tatarski, 1961), atmospheric science (Lumley and Panofsky, 1964), composite materials and electrical engineering (Beran, 1968; Batchelor, 1974), and of course statistical mechanics. Stochastic hydrogeology broadens the scope of the deterministic approach to hydrogeology by considering the last as an end member to a wide spectrum of states of knowledge, stretching from deterministic knowledge at one end all the way to maximum uncertainty at the other, with a continuum of states, representing varying degrees of uncertainty in the hydrogeological processes, in between. It provides a formalism for addressing this continuum of states systematically. The departure from the confines of determinism is an important and intuitively appealing paradigm shift, representing the maturing of hydrogeology from an exploratory into an applied discipline. Deterministic knowledge of a site’s hydrogeology is a state we rarely, if ever, find ourselves in, although from a fundamental point of view there is no inherent element of chance in the hydrogeological processes. For example, we know that mass conservation is a deterministic concept, and we are also confident that Darcy’s law works under conditions which are fairly well understood. However, the application of these principles involves a fair amount of conjecture and speculation, and hence when dealing with real-life applications, determinism exists only in the fact that uncertainty and ambiguity are unavoidable, and might as well be studied and understood. The other end of the spectrum is where uncertainty is the largest. Generally speaking, two types of uncertainty exist: intrinsic variability and epistemic uncertainty.
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