lecture11 - CWR 6536 Stochastic Subsurface Hydrology...

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Unformatted text preview: CWR 6536 Stochastic Subsurface Hydrology Optimal Estimation of Hydrologic Parameters using Kriging Types of Kriging Simple kriging is optimal estimation of a random field, e.g. T(x), with a known mean, m(x), and a known covariance PTT(x,x). Ordinary kriging is optimal estimation of a random field, e.g. T(x), with an unknown constant or linearly trending mean, but a known semivariogram TT(x,x). Universal kriging is optimal estimation of a random field, e.g. T(x), with an unknown polynomial trending mean, but a known semivariogram TT(x,x). Universal Kriging Assume random field has the form: Define kriging estimate as: To ensure unbiasedness: Therefore must choose i so that: ) ( ) ( 1 i N i i x T x T = = [ ] [ ] 2 1 1 1 ) ( ) ( ) ( ) ( cx by ax m x m x T E x T E x T E N i i i i N i i i N i i + + + = = = = = = = = = = = = = = = N i i i N i i i N i i i N i i x x y y x x 1 2 2 1 1 1 1 ... ) ( where (x) ) ( ) ( 2 + + + + = + = cx by ax m x m x m x T Universal Kriging Proceed as before minimizing the estimation variance subject to these 4 constraints, i.e. Use the method of Lagrange multipliers which adjoins the constraints to the objective function....
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lecture11 - CWR 6536 Stochastic Subsurface Hydrology...

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