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@BeginModule
@NewPage
@Name      = Seasstat
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@Title     = Seasonal statistical values
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@Section   = Statistical values
@Class     = Statistic
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@Arguments = infile outfile
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@Operators = seasmin seasmax seasrange seassum seasmean seasavg seasstd seasstd1 seasvar seasvar1
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@BeginDescription
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This module computes statistical values over timesteps of the same season.
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Depending on the chosen operator the minimum, maximum, range, sum, average, variance
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or standard deviation of timesteps of the same season is written to @file{outfile}.
The time of @file{outfile} is determined by the time in the middle of all contributing timesteps of @file{infile}.
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Be careful about the first and the last output timestep, they may be incorrect values 
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if the seasons have incomplete timesteps.
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@EndDescription
@EndModule


@BeginOperator_seasmin
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@Title     = Seasonal minimum
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@BeginDescription
@IfMan
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For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = min{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{min}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_seasmax
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@Title     = Seasonal maximum
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@BeginDescription
@IfMan
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For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = max{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{max}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


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@BeginOperator_seasrange
@Title     = Seasonal range

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

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


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


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


@BeginOperator_seasavg
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@Title     = Seasonal average
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@BeginDescription
@IfMan
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For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = avg{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{avg}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


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@BeginOperator_seasvar
@Title     = Seasonal variance

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


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@BeginOperator_seasvar1
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@Title     = Seasonal variance (n-1)
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@BeginDescription
@IfMan
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Normalize by (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = var1{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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Normalize by (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{var1}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


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@BeginOperator_seasstd
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@Title     = Seasonal standard deviation
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@BeginDescription
@IfMan
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Normalize by n. For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = std{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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Normalize by n. For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{std}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


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@BeginOperator_seasstd1
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@Title     = Seasonal standard deviation (n-1)
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@BeginDescription
@IfMan
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Normalize by (n-1). For every adjacent sequence t_1, ...,t_n of timesteps of the same season it is:
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o(t,x) = std1{i(t',x), t1 < t' <= tn}
@EndifMan
@IfDoc
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Normalize by (n-1). For every adjacent sequence \begin{math}t_1, ...,t_n\end{math} of timesteps of the same season it is: \\
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@BeginMath
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o(t,x) = \mbox{\textbf{std1}}\{i(t',x), t_1 < t' \le t_n\}
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@EndMath
@EndifDoc
@EndDescription
@EndOperator


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