lecture7and8 - Properties of Covariance and Variogram...

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

View Full Document Right Arrow Icon
Properties of Covariance and Variogram Functions CWR 6536 Stochastic Subsurface Hydrology
Background image of page 1

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

View Full DocumentRight Arrow Icon
The Covariance Function The covariance function must be positive definite which requires that: positive definiteness guarantees that all linear combinations of the random variable will have non-negative variances. This implies:
Background image of page 2
The Variogram Function The negative semivariogram function must be conditionally positive definite which requires that: conditional positive definiteness guarantees that all linear combinations of the random variable will have non-negative variances. This implies:
Background image of page 3

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

View Full DocumentRight Arrow Icon
Positive-definiteness is related to the number of dimensions in space over which the function is defined. Positive definiteness in higher order dimensional space guarantees positive definiteness in lower order dimensional space, but not vice-versa Must fit functions to sample covariances/ variograms which are positive definite in the appropriate dimensional space
Background image of page 4
Behavior of Covariance/Variogram functions near the origin Parabolic behavior Linear behavior
Background image of page 5

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

View Full DocumentRight Arrow Icon
Behavior of Covariance/Variogram functions near the origin The nugget effect Pure nugget effect
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.

This note was uploaded on 03/27/2012 for the course CWR 6536 taught by Professor Graham during the Spring '11 term at University of Florida.

Page1 / 15

lecture7and8 - Properties of Covariance and Variogram...

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