@BeginModule
@NewPage
@Name      = Yhourstat
@Title     = Multi-year hourly statistical values
@Section   = Statistical values
@Class     = Statistic
@Arguments = ifile ofile
@Operators = yhourmin yhourmax yhoursum yhourmean yhouravg yhourstd yhourstd1 yhourvar yhourvar1

@BeginDescription
This module computes statistical values of each hour and day of year.
Depending on the chosen operator the minimum, maximum, sum, average, variance
or standard deviation of each hour and day of year in @file{ifile} is written to @file{ofile}.
The date information in an output field is the date of the last contributing input field.
@EndModule


@BeginOperator_yhourmin
@Title     = Multi-year hourly minimum

@BeginDescription
@IfMan
o(0001,x) = min{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = min{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf min}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf min}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourmax
@Title     = Multi-year hourly maximum

@BeginDescription
@IfMan
o(0001,x) = max{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = max{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf max}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf max}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhoursum
@Title     = Multi-year hourly sum

@BeginDescription
@IfMan
o(0001,x) = sum{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = sum{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf sum}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf sum}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourmean
@Title     = Multi-year hourly mean

@BeginDescription
@IfMan
o(0001,x) = mean{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = mean{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf mean}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf mean}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhouravg
@Title     = Multi-year hourly average

@BeginDescription
@IfMan
o(0001,x) = avg{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = avg{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf avg}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf avg}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourvar
@Title     = Multi-year hourly variance

@BeginDescription
Divisor is n. 

@IfMan
o(0001,x) = var{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = var{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf var}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf var}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourvar1
@Title     = Multi-year hourly variance (n-1)

@BeginDescription
Divisor is (n-1). 

@IfMan
o(0001,x) = var1{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = var1{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf var1}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf var1}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourstd
@Title     = Multi-year hourly standard deviation

@BeginDescription
Divisor is n. 

@IfMan
o(0001,x) = std{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = std{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf std}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf std}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@BeginOperator_yhourstd1
@Title     = Multi-year hourly standard deviation (n-1)

@BeginDescription
Divisor is (n-1). 

@IfMan
o(0001,x) = std1{i(t,x), day(i(t)) = 0001}
                 ...
o(8784,x) = std1{i(t,x), day(i(t)) = 8784}
@EndifMan
@IfDoc
@BeginMath
\begin{array}{c}
o(\mbox{0001},x) = \mbox{\bf std1}\{i(t,x), \mbox{day}(i(t)) = \mbox{0001}\} \\
\vdots \\
o(\mbox{8784},x) = \mbox{\bf std1}\{i(t,x), \mbox{day}(i(t)) = \mbox{8784}\} \\
\end{array}
@EndMath
@EndifDoc
@EndDescription
@EndOperator


@C @BeginExample
@C To compute the hourly mean for all days over all input years use:
@C @BeginVerbatim
@C    cdo yhourmean ifile ofile
@C @EndVerbatim
@C @EndExample
