@BeginModule
@Name      = Timcovar
@Title     = Covariance over time
@Section   = Correlation and co.
@Class     = Correlation and co.
@Arguments = ifile1 ifile2 ofile
@Operators = timcovar
@EndModule


@BeginOperator_timcovar
@Title     = Covariance over time

@BeginDescription
This operator calculates the covariance of two fields at each gridpoint
over all timesteps. With
@IfMan

S(x) = {t, i_1(t,x) != missval and i_2(t,x) != missval}
@EndifMan
@IfDoc
@BeginDisplayMath
S(x) = \{t, i_1(t,x) \neq missval \wedge i_2(t,x) \neq missval\}
@EndDisplayMath
@EndifDoc
it is
@IfMan

o(1,x) = Covar{(i_1(t,x), i_2(t,x)), t_1 < t <= t_n}
@EndifMan
@IfDoc
@BeginDisplayMath
o(1,x) = n^{-1} \sum\limits_{t \in S(x)} \left(i_1(t,x) - \overline{i_1(t,x)} \right)^2 \left(i_2(t,x) - \overline{i_2(t,x)} \right)^2
@EndDisplayMath
@EndifDoc
For every gridpoint @math{x} only those timesteps @math{t} belong to the sample,
which have @math{i_1(t,x) \neq missval} and @math{i_2(t,x) \neq missval}.
@EndDescription
@EndOperator
