Skip to content. | Skip to navigation

Laboratoire d’Etudes en Géophysique et Océanographie Spatiales

Personal tools

Log in

This is SunRain Plone Theme

Navigation

You are here: Home / Research teams / Research / ECOLA / Softwares and products / Tidal data assimilation: SpEnOI / documentations / decorrelation

decorrelation

by Laurent Roblou — last modified Apr 23, 2012 01:55 PM

Observations influence in the model error subspace can be decreased using decorrelation functions. The data assimilation code provide users with a large range of isotropic functions for this purpose.

The following lines describes the shape functions collection.

linear function: $\mbox{$ w(r) = 1 - r $}$

step function: $R-STEP$

spherical function: $w(r) = 1 - \frac{3}{2}r + \frac{1}{2} r^{3}$

sinusoidal function: $w(r) = \frac{1 + \cos(r)}{2}$

exponential function class

$w(r) = e^{-r}$

$w(r) = e^{-r} \thickspace \mbox{for} \thickspace r \leq 1, \thickspace \mbox{0 otherwise}$

$w(r) = (1 + r + \frac{1}{6} r^{2} - \frac{1}{6}r ^{3} ) e^{-r}$

Gaussian functions class:

$w(r) = e^{\frac{-r ^ {2}}{2 \sigma ^ {2} }}, \thickspace \sigma = \frac{1}{\sqrt{2 \ln(2)}}$

$w(r) = e^{\frac{-r ^ {2}}{2 \sigma ^ {2} }}, \thickspace \sigma = \frac{1}{\sqrt{2 \ln(2)}} \thickspace \mbox{for} \thickspace r \leq 2 \sigma, \thickspace \mbox{0 otherwise}$

$w(r) = (1 - \frac{1}{6} r) e^{\frac{-r ^ {2}}{2 \sigma ^ {2} }} , \thickspace \sigma = \frac{1}{\sqrt{2 \ln(2)}} \thickspace \mbox{for r \leq 1}, \thickspace \mbox{0 otherwise}$

Document Actions