@BeginModule
@NewPage
@Name      = Yearstat
@Title     = Yearly statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = ifile ofile
@Operators = yearmin yearmax yearsum yearmean yearavg yearstd yearstd1 yearvar yearvar1

@BeginDescription
This module computes statistical values over timesteps of the same year.
Depending on the chosen operator the minimum, maximum, sum, average, variance
or standard deviation of timesteps of the same year is written to @file{ofile}.
The time stamp in @file{ofile} is from the middle contributing timestep of @file{ifile}.
@EndDescription
@EndModule


@BeginOperator_yearmin
@Title     = Yearly minimum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

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


@BeginOperator_yearmax
@Title     = Yearly maximum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

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


@BeginOperator_yearsum
@Title     = Yearly sum

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

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


@BeginOperator_yearmean
@Title     = Yearly mean

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

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


@BeginOperator_yearavg
@Title     = Yearly average

@BeginDescription
@IfMan
For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

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


@BeginOperator_yearvar
@Title     = Yearly variance

@BeginDescription
@IfMan
Divisor is n. For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

o(t,x) = var{i(t',x), t_1 < t' <= t_n}
@EndifMan
@IfDoc
Divisor is n. For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same year it is: \\
@BeginMath
o(t,x) = \mbox{\bf var}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yearvar1
@Title     = Yearly variance

@BeginDescription
@IfMan
Divisor is (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

o(t,x) = var1{i(t',x), t_1 < t' <= t_n}
@EndifMan
@IfDoc
Divisor is (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same year it is: \\
@BeginMath
o(t,x) = \mbox{\bf var1}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yearstd
@Title     = Yearly standard deviation

@BeginDescription
@IfMan
Divisor is n. For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

o(t,x) = std{i(t',x), t_1 < t' <= t_n}
@EndifMan
@IfDoc
Divisor is n. For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same year it is: \\
@BeginMath
o(t,x) = \mbox{\bf std}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yearstd1
@Title     = Yearly standard deviation

@BeginDescription
@IfMan
Divisor is (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same year it is

o(t,x) = std1{i(t',x), t_1 < t' <= t_n}
@EndifMan
@IfDoc
Divisor is (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same year it is: \\
@BeginMath
o(t,x) = \mbox{\bf std1}\{i(t',x), t_1 < t' \leq t_n\}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginNote
The operators yearmean and yearavg compute only arithmetical means!
@EndNote


@BeginExample
To compute the yearly mean of a time series use:
@BeginVerbatim
   cdo yearmean ifile ofile
@EndVerbatim
To compute the yearly mean from the correct weighted monthly mean use:
@BeginVerbatim
   cdo yearmonmean ifile ofile
@EndVerbatim
@EndExample
