Example of the diffusion operator
A simple correlation model of correlation is given by the Gaussian
Since the natural solution of the diffusion equation
with initial condition a Dirac distribution, is the Gaussian
by identification, the equivalent of the length-scale is
[WC01] have developped the idea to take advantage of this solution to build correlation model as
where
is the propagateur associated to the time integration of the diffusion equation from time
to
is the metric operator.
But what are the diffusion coefficients in real applications?
[PM08] have proposed to estimate the diffusion coefficient under a local homogeneous assumption leading the
when the time is set to
. and of course, the extension in 2D and 3D. They have applyied this for ozone assimilation.
Length-scale raw statistics vs. modelized
raw stat. (a) Lpx (b) Lpy model. with dif. (c) Lpx (d) Lpy
Anisotropy diagonis raw stat. (a-b) and modelized (c-d)
Correlation function raw stat. (a) and modelized (b)
