@BeginModule
@NewPage
@Name      = Ydrunstat
@Title     = Multi-year daily running statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = ifile ofile
@Operators = ydrunmin ydrunmax ydrunsum ydrunmean ydrunavg ydrunvar ydrunstd

@BeginDescription
This module writes running statistical values for each day of year
in @file{ifile} to @file{ofile}. Depending on the actual operator, the minimum,
maximum, sum, average, variance or standard deviation of all time steps in
running windows of wich the medium time step corresponds to a certain day of
year is computed. The date information in an output field is the date of the
medium time step in the last contributing running window.
Note that the operator have to be applied to a continuous time series of daily
measurements in order to yield physically meaningful results. Also note that
the output time series begins (nts-1)/2 time steps after the first time step
of the input time series and ends (nts-1)/2 time steps before the last one.
For input data which are complete but not continuous, such as time series of
daily measurements for the same month or season within different years, the
operator yields physically meaningful results only if the input time series
does include the (nts-1)/2 days before and after each period of interest.
@EndModule


@BeginOperator_ydrunmin
@Title     = Multi-year daily running minimum
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = min{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = min{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf min}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf min}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunmax
@Title     = Multi-year daily running maximum
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = max{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = max{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf max}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf max}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunsum
@Title     = Multi-year daily running sum
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = sum{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = sum{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf sum}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf sum}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunmean
@Title     = Multi-year daily running mean
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = mean{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = mean{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf mean}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf mean}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunavg
@Title     = Multi-year daily running average
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = avg{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = avg{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf avg}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf avg}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunvar
@Title     = Multi-year daily running variance
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = var{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = var{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[(i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf var}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf var}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_ydrunstd
@Title     = Multi-year daily running standard deviation
@Parameter = nts

@BeginDescription
@IfMan
o(001,x) = std{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[i(t+(nts-1)/2)] = 001}
                 ...
o(366,x) = std{i(t,x), i(t+1,x), ..., i(t+nts-1,x); day[i(t+(nts-1)/2)] = 366}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{001},x) = \mbox{\bf std}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{001}\} \\
\vdots \\
o(\mbox{366},x) = \mbox{\bf std}\{i(t,x), i(t+1,x), ..., i(t+nts-1,x); \mbox{day}[(i(t+(nts-1)/2)] = \mbox{366}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginParameter
@Item = nts
INTEGER  Number of time steps
@EndParameter


@BeginExample
Assume the input data provide a continuous time series of daily measurements. To compute
the running multi-year daily mean over all input time steps for a running window of five
days use:
@BeginVerbatim
   cdo ydrunmean,5 ifile ofile
@EndVerbatim
Note that except for the standard deviation the results of the operators in this module
are equivalent to a composition of corresponding operators from the @mod{YDAYSTAT} and
@mod{RUNSTAT} modules. For instance, the above command yields the same result as:
@BeginVerbatim
   cdo ydaymean -runmean,5 ifile ofile
@EndVerbatim
@EndExample
