@BeginModule
@NewPage
@Name      = Seasstat
@Title     = Seasonal statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = ifile ofile
@Operators = seasmin seasmax seassum seasmean seasavg seasvar seasstd

@BeginDescription
This module computes statistical values over time steps of the same season.
Depending on the actual operator the minimum, maximum, sum, average, variance
or standard deviation of time steps of the same season is written to @file{ofile}.
The date information of a time step in @file{ofile} is the date of the last 
contributing time step in @file{ifile}. Be careful about the first and the last 
output time step, they may be incorrect values if the seasons have incomplete 
time steps.
@EndDescription
@EndModule


@BeginOperator_seasmin
@Title     = Seasonal minimum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = min{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf min}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasmax
@Title     = Seasonal maximum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = max{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf max}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seassum
@Title     = Seasonal sum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = sum{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf sum}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasmean
@Title     = Seasonal mean

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = mean{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf mean}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasavg
@Title     = Seasonal average

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = avg{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf avg}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasvar
@Title     = Seasonal variance

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = var{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf var}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasstd
@Title     = Seasonal standard deviation

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of time steps of the same season it is

o(t,x) = std{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of time steps of 
the same season it is: \\
@BeginMath
o(t,x) = \mbox{\bf std}\{i(t',x), t_1 < t' \le t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginExample
To compute the seasonal mean of a time series use:
@BeginVerbatim
   cdo seasmean ifile ofile
@EndVerbatim
@EndExample
