lecture12 - CWR 6536 Stochastic Subsurface Hydrology...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
CWR 6536 Stochastic Subsurface Hydrology Optimal Estimation of Hydrologic Parameters
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Block Kriging Kriging systems discussed to date use point measurements to estimate point values of the random field at unmeasured locations…. called point, or punctual, kriging Block kriging uses point measurements to estimate average values of the random field over a prescribed area. Useful if trying to estimate parameters for discretized models
Background image of page 2
Block Kriging Block Kriging equations are similar to point kriging equations, e.g. for simple kriging: Where is the covariance between a particular sample location and all the points within A0 = ) , ( ~ ) , ( ~ ) , ( ~ ) , ( ~ ) ( ) ( ) ( ) ( 0 3 0 2 0 1 0 0 0 3 0 2 0 1 3 2 1 3 3 3 2 3 1 3 2 3 2 2 2 1 2 1 3 1 2 1 1 1 N N N N N N N N N N x A P x A P x A P x A P A A A A ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P ) ,x (x P YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY YY λ = 0 ) , ( 1 ) , ( ~ 0 0 A i YY i x d x x P A x A P YY
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Block Kriging Once λ i are determined construct estimate from And estimation variance from Where ) , ( ~ ) ( ) ( ) ( ˆ 0 1 0 0 2 0 2 Y i N i i x A P A A A YY Y - = = λ σ ) ( ) ( ) ( ) ( ˆ 0 1 0 0 i N i x Y A A m A Y + = y d x d y x P A A A P A A YY A YY Y = = 0 0 ) , ( 1 ) , ( ~ ~ ) ( 2 0 0 0 0 2
Background image of page 4
Block Kriging Integrals can either be determined analytically from analytical point covariance functions or estimated by a discrete sum: If estimating average covariances numerically a balance must be struck between too few discretizing points which may not accurately estimate the average and too many discretizing points which can be computationally expensive It is important to use the same number of discretization points for the calculation of the point-block covariances and the block-block covariance = N j i j YY i x x P N x A P YY 1 0 ) , ( 1 ) , ( ~ = = = N k k j YY N j x x P N A A P A YY Y 1 1 2 0 0 0 2 ) , ( 1 ) , ( ~ ~ ) ( σ
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Block Kriging Each block kriging weight can be shown to be the average of the point kriging weights throughout the area A Thus the block kriging system yields an estimate
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

lecture12 - CWR 6536 Stochastic Subsurface Hydrology...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online