lecture3and4 - Review of Random Process Theory CWR 6536...

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Review of Random Process Theory CWR 6536 Stochastic Subsurface Hydrology
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Random Process A random process may be thought of as a collection or ensemble of random variables which change through time, any realization of which might be observed on any trial of an experiment Example: Daily rainfall. Random process is the ensemble of daily rainfall profiles for each year. Each year is one realization or trial of the experiment. Daily rainfall is the r.v.
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Random Field A random field may be thought of as a collection or ensemble of random variables which vary over space, any realization of which may be observed on any trial of an experiment Example: Saturated hydraulic conductivity. Random field is the ensemble of aquifers with the same geologic origin. Each aquifer is one realization or trial of the experiment,hydraulic conductivity is the r.v.
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Random Processes vs Random Fields Random processes arise mostly in the analysis of spatially lumped systems (e.g. reservoir analysis) Random fields arise mostly in the analysis of spatially distributed systems (e.g. groundwater flow)
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Consider a 1-D random field At a fixed depth, Ksat is a random variable which takes on different values for different realizations ( i.e. location in the field)
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sat is characterized by univariate cdf univariate pdf moments > However must also consider another possibility. Does knowledge of K
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lecture3and4 - Review of Random Process Theory CWR 6536...

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