{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture18

# lecture18 - Approximate Analytical Solutions to the...

This preview shows pages 1–6. Sign up to view the full content.

Approximate Analytical Solutions to the Groundwater Flow Problem CWR 6536 Stochastic Subsurface Hydrology

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

View Full Document
3-D Steady Saturated Groundwater Flow K(x,y,z) random hydraulic conductivity field φ (x,y,z) random hydraulic head field want approximate analytical solutions to the 1st and 2nd ensemble moments of the head field + + = z K z y K y x K x φ φ φ 0
System of Approximate Moment Eqns to order ε 2 • Use φ 0 (x), as best estimate of φ (x) • Use σ φ 2 =P φφ (x,x) as measure of uncertainty Use P φφ (x,x’) and P f φ (x,x’) for cokriging to optimally estimate f or φ based on field observations ) ( ) ' , ( ) ' , ( ) ( ) ' , ( 0 ) ' ( ) ' , ( ) ' , ( ) ' ( ) ' , ( 0 ) ( ) ( ) ( 0 0 2 0 ' ' ' ' 2 ' 0 0 2 1 1 1 1 1 1 1 x x x P x x P x F x x P x x x P x x P x F x x P x x F x f x ff x f x x f x φ φ φ φ φ φ φ φ φ φ φ + + = + + = + =

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

View Full Document
Possible Solution Techniques Fourier Transform Methods (Gelhar et al.) Greens Function Methods (Dagan et al.) Numerical Techniques (McLaughlin and Wood, James and Graham)
Fourier Transform Methods Require A solution that applies over an infinite domain Coefficients in equations that are constant, or can be approximated as constants or simple functions Stationarity of the input and output covariance

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}