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lecture13 - Stochastic Modeling CWR 6536 Stochastic...

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Stochastic Modeling CWR 6536 Stochastic Subsurface Hydrology
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Source of uncertainty in model predictions include Input parameters boundary conditions initial conditions model error measurement error
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Stochastic Models Characterize pdfs/moments of input parameters, BCs, and Ics. Quantify model error and measurement error if possible Use model to derive pdfs and moments of output random fields
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Operator T(x) can be: algebraic relationship, e.g. rational formula difference equation, e.g. reservoir mass balance differential equation, e.g. groundwater flow/transport integral equation, e.g. unit hydrograph equation In each case, y= state of output x= parameters or input A,B,C, operators which may depend on time and location
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Output pdfs and moments may be derived in several ways: Exact analytical solutions Monte Carlo techniques approximate analytical solutions Approximate numerical solutions We will consider a very simple model to briefly illustrate each technique
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