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\subsection{OBCS: Open boundary conditions for regional modeling} |
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|
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\label{sec:pkg:obcs} |
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\begin{rawhtml} |
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<!-- CMIREDIR:package_obcs: --> |
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\end{rawhtml} |
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|
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Authors: |
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Alistair Adcroft, Patrick Heimbach, Samar Katiwala, Martin Losch |
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|
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\subsubsection{Introduction |
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\label{sec:pkg:obcs:intro}} |
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|
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The OBCS-package is fundamental to regional ocean modelling with the |
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MITgcm, but because there are so many details to be considered in |
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regional ocean modelling that this package cannot accomodate all |
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imaginable and possible options. Therefore, for a regional simulation |
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with very particular details, it is recommended to familiarize oneself |
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not only with the compile- and runtime-options of this package, but |
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also with the code itself. In many cases it will be necessary to adapt |
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the obcs-code (in particular \code{S/R OBCS\_CALC}) to the application |
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in question; in these cases the obcs-package (together with the |
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rbcs-package, section \ref{sec:pkg:rbcs}) is a very |
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useful infrastructure for implementing special regional models. |
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|
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%---------------------------------------------------------------------- |
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|
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\subsubsection{OBCS configuration and compiling |
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\label{sec:pkg:obcs:comp}} |
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|
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As with all MITgcm packages, OBCS can be turned on or off |
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at compile time |
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% |
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\begin{itemize} |
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% |
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\item |
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using the \code{packages.conf} file by adding \code{obcs} to it, |
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% |
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\item |
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or using \code{genmake2} adding |
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\code{-enable=obcs} or \code{-disable=obcs} switches |
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% |
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\item |
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\textit{Required packages and CPP options:} \\ |
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% |
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To alternatives are available for prescribing open boundary values, |
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which differ in the way how OB's are treated in time: |
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A simple time-management (e.g. constant in time, or cyclic with |
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fixed fequency) is provided through |
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S/R \code{obcs\_external\_fields\_load}. |
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More sophisticated ``real-time'' (i.e. calendar time) management is |
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available through \code{obcs\_prescribe\_read}. |
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The latter case requires |
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packages \code{cal} and \code{exf} to be enabled. |
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% |
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\end{itemize} |
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(see also Section \ref{sec:buildingCode}). |
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|
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Parts of the OBCS code can be enabled or disabled at compile time |
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via CPP preprocessor flags. These options are set in |
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\code{OBCS\_OPTIONS.h}. Table \ref{tab:pkg:obcs:cpp} summarizes them. |
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|
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\begin{table}[!ht] |
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\centering |
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\label{tab:pkg:obcs:cpp} |
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{\footnotesize |
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\begin{tabular}{|l|l|} |
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\hline |
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\textbf{CPP option} & \textbf{Description} \\ |
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\hline \hline |
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\code{ALLOW\_OBCS\_NORTH} & |
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enable Northern OB \\ |
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\code{ALLOW\_OBCS\_SOUTH} & |
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enable Southern OB \\ |
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\code{ALLOW\_OBCS\_EAST} & |
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enable Eastern OB \\ |
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\code{ALLOW\_OBCS\_WEST} & |
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enable Western OB \\ |
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\hline |
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\code{ALLOW\_OBCS\_PRESCRIBE} & |
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enable code for prescribing OB's \\ |
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\code{ALLOW\_OBCS\_SPONGE} & |
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enable sponge layer code \\ |
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\code{ALLOW\_OBCS\_BALANCE} & |
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enable code for balancing transports through OB's \\ |
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\code{ALLOW\_ORLANSKI} & |
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enable Orlanski radiation conditions at OB's \\ |
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\code{ALLOW\_OBCS\_STEVENS} & |
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enable Stevens (1990) boundary conditions at OB's \\ |
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& (currently only implemented for eastern and western \\ |
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& boundaries and NOT for ptracers) \\ |
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\hline |
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\end{tabular} |
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} |
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\caption{~} |
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\end{table} |
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|
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|
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%---------------------------------------------------------------------- |
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|
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\subsubsection{Run-time parameters |
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\label{sec:pkg:obcs:runtime}} |
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|
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Run-time parameters are set in files |
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\code{data.pkg}, \code{data.obcs}, and \code{data.exf} |
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if ``real-time'' prescription is requested |
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(i.e. package \code{exf} enabled). |
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These parameter files are read in S/R |
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\code{packages\_readparms.F}, \code{obcs\_readparms.F}, and |
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\code{exf\_readparms.F}, respectively. |
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Run-time parameters may be broken into 3 categories: |
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(i) switching on/off the package at runtime, |
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(ii) OBCS package flags and parameters, |
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(iii) additional timing flags in \code{data.exf}, if selected. |
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|
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\paragraph{Enabling the package} |
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~ \\ |
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% |
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The OBCS package is switched on at runtime by setting |
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\code{useOBCS = .TRUE.} in \code{data.pkg}. |
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|
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\paragraph{Package flags and parameters} |
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~ \\ |
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% |
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Table \ref{tab:pkg:obcs:runtime_flags} summarizes the |
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runtime flags that are set in \code{data.obcs}, and |
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their default values. |
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|
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\begin{table}[!ht] |
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\centering |
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{\footnotesize |
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\begin{tabular}{|l|c|l|} |
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\hline |
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\textbf{Flag/parameter} & \textbf{default} & \textbf{Description} \\ |
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\hline \hline |
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\multicolumn{3}{|c|}{\textit{basic flags \& parameters} (OBCS\_PARM01) } \\ |
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\hline |
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OB\_Jnorth & 0 & |
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Nx-vector of J-indices (w.r.t. Ny) of Northern OB |
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at each I-position (w.r.t. Nx) \\ |
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OB\_Jsouth & 0 & |
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Nx-vector of J-indices (w.r.t. Ny) of Southern OB |
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at each I-position (w.r.t. Nx) \\ |
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OB\_Ieast & 0 & |
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Ny-vector of I-indices (w.r.t. Nx) of Eastern OB |
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at each J-position (w.r.t. Ny) \\ |
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OB\_Iwest & 0 & |
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Ny-vector of I-indices (w.r.t. Nx) of Western OB |
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at each J-position (w.r.t. Ny) \\ |
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useOBCSprescribe & \code{.FALSE.} & |
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~ \\ |
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useOBCSsponge & \code{.FALSE.} & |
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~ \\ |
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useOBCSbalance & \code{.FALSE.} & |
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~ \\ |
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useOrlanskiNorth/South/EastWest & \code{.FALSE.} & |
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turn on Orlanski boundary conditions for individual boundary\\ |
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useStevensNorth/South/EastWest & \code{.FALSE.} & |
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turn on Stevens boundary conditions for individual boundary\\ |
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OB\textbf{X}\textbf{y}File & ~ & |
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file name of OB field \\ |
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~ & ~ & |
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\textbf{X}: \textbf{N}(orth), \textbf{S}(outh), |
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\textbf{E}(ast), \textbf{W}(est) \\ |
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~ & ~ & |
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\textbf{y}: \textbf{t}(emperature), \textbf{s}(salinity), |
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\textbf{u}(-velocity), \textbf{v}(-velocity), \\ |
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~ & ~ & |
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\textbf{w}(-velocity), \textbf{eta}(sea surface height)\\ |
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~ & ~ & |
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\textbf{a}(sea ice area), \textbf{h}(sea ice thickness), |
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\textbf{sn}(snow thickness), \textbf{sl}(sea ice salinity)\\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Orlanski parameters} (OBCS\_PARM02) } \\ |
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\hline |
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cvelTimeScale & 2000 sec & |
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averaging period for phase speed \\ |
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CMAX & 0.45 m/s & |
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maximum allowable phase speed-CFL for AB-II \\ |
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CFIX & 0.8 m/s & |
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fixed boundary phase speed \\ |
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useFixedCEast & \code{.FALSE.} & |
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~ \\ |
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useFixedCWest & \code{.FALSE.} & |
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~ \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Sponge-layer parameters} (OBCS\_PARM03)} \\ |
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\hline |
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spongeThickness & 0 & |
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sponge layer thickness (in \# grid points) \\ |
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Urelaxobcsinner & 0 sec & |
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relaxation time scale at the |
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innermost sponge layer point of a meridional OB \\ |
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Vrelaxobcsinner & 0 sec & |
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relaxation time scale at the |
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innermost sponge layer point of a zonal OB \\ |
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Urelaxobcsbound & 0 sec & |
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relaxation time scale at the |
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outermost sponge layer point of a meridional OB \\ |
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Vrelaxobcsbound & 0 sec & |
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relaxation time scale at the |
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outermost sponge layer point of a zonal OB \\ |
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\hline |
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\multicolumn{3}{|c|}{\textit{Stevens parameters} (OBCS\_PARM04) } \\ |
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\hline |
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T/SrelaxStevens & 0~sec & relaxation time scale for |
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temperature/salinity \\ |
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useStevensPhaseVel & \code{.TRUE.} & \\ |
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useStevensAdvection & \code{.TRUE.} & \\ |
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\hline |
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\hline |
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\end{tabular} |
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} |
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\caption{pkg OBCS run-time parameters} |
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\label{tab:pkg:obcs:runtime_flags} |
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\end{table} |
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|
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|
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|
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%---------------------------------------------------------------------- |
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|
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\subsubsection{Defining open boundary positions |
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\label{sec:pkg:obcs:defining}} |
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|
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There are four open boundaries (OBs), a |
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Northern, Southern, Eastern, and Western. |
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All OB locations are specified by their absolute |
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meridional (Northern/Southern) or zonal (Eastern/Western) indices. |
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Thus, for each zonal position $i=1,\ldots,N_x$ a meridional index |
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$j$ specifies the Northern/Southern OB position, |
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and for each meridional position $j=1,\ldots,N_y$, a zonal index |
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$i$ specifies the Eastern/Western OB position. |
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For Northern/Southern OB this defines an $N_x$-dimensional |
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``row'' array $\tt OB\_Jnorth(Ny)$ / $\tt OB\_Jsouth(Ny)$, |
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and an $N_y$-dimenisonal |
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``column'' array $\tt OB\_Ieast(Nx)$ / $\tt OB\_Iwest(Nx)$. |
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Positions determined in this way allows Northern/Southern |
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OBs to be at variable $j$ (or $y$) positions, and Eastern/Western |
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OBs at variable $i$ (or $x$) positions. |
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Here, indices refer to tracer points on the C-grid. |
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A zero (0) element in $\tt OB\_I\ldots$, $\tt OB\_J\ldots$ |
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means there is no corresponding OB in that column/row. |
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For a Northern/Southern OB, the OB V point is to the South/North. |
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For an Eastern/Western OB, the OB U point is to the West/East. |
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|
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\begin{verbatim} |
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For example |
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OB_Jnorth(3)=34 means that: |
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T( 3 ,34) is a an OB point |
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U(3:4,34) is a an OB point |
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V( 4 ,34) is a an OB point |
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while |
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OB_Jsouth(3)=1 means that: |
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T( 3 ,1) is a an OB point |
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U(3:4,1) is a an OB point |
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V( 4 ,2) is a an OB point |
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\end{verbatim} |
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|
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For convenience, negative values for Jnorth/Ieast refer to |
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points relative to the Northern/Eastern edges of the model |
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eg. $\tt OB\_Jnorth(3)=-1$ means that the point $\tt (3,Ny)$ |
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is a northern OB. |
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|
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\noindent |
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\textsf{Add special comments for case \#define NONLIN\_FRSURF, |
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see obcs\_ini\_fixed.F} |
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|
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%---------------------------------------------------------------------- |
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|
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\subsubsection{Equations and key routines |
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\label{sec:pkg:obcs:equations}} |
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|
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\paragraph{OBCS\_READPARMS:} ~ \\ |
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Set OB positions through arrays |
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{\tt OB\_Jnorth(Ny), OB\_Jsouth(Ny), OB\_Ieast(Nx), OB\_Iwest(Nx)}, |
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and runtime flags (see Table \ref{tab:pkg:obcs:runtime_flags}). |
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|
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\paragraph{OBCS\_CALC:} ~ \\ |
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% |
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Top-level routine for filling values to be applied at OB for |
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$T,S,U,V,\eta$ into corresponding |
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``slice'' arrays $(x,z)$, $(y,z)$ for each OB: |
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$\tt OB[N/S/E/W][t/s/u/v]$; e.g. for salinity array at |
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Southern OB, array name is $\tt OBSt$. |
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Values filled are either |
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% |
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\begin{itemize} |
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% |
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\item |
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constant vertical $T,S$ profiles as specified in file |
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{\tt data} ({\tt tRef(Nr), sRef(Nr)}) with zero velocities $U,V$, |
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% |
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\item |
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$T,S,U,V$ values determined via Orlanski radiation conditions |
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(see below), |
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% |
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\item |
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prescribed time-constant or time-varying fields (see below). |
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% |
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\item |
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use prescribed boundary fields to compute Stevens boundary conditions. |
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\end{itemize} |
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|
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\paragraph{ORLANSKI:} ~ \\ |
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% |
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Orlanski radiation conditions \citep{orl:76}, examples can be found in |
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\code{verification/dome} and |
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\code{verification/tutorial\_plume\_on\_slope} |
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(\ref{sec:eg-gravityplume}). |
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|
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\paragraph{OBCS\_PRESCRIBE\_READ:} ~ \\ |
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% |
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When \code{useOBCSprescribe = .TRUE.} the model tries to read |
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temperature, salinity, u- and v-velocities from files specified in the |
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runtime parameters \code{OB[N/S/E/W][t/s/u/v]File}. These files are |
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the usual IEEE, big-endian files with dimensions of a section along an |
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open boundary: |
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\begin{itemize} |
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\item For North/South boundary files the dimensions are |
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$(N_x\times N_r\times\mbox{time levels})$, for East/West boundary |
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files the dimensions are $(N_y\times N_r\times\mbox{time levels})$. |
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\item If a non-linear free surface is used |
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(\ref{sec:nonlinear-freesurface}), additional files |
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\code{OB[N/S/E/W]etaFile} for the sea surface height $\eta$ with |
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dimension $(N_{x/y}\times\mbox{time levels})$ may be specified. |
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\item If non-hydrostatic dynamics are used |
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(\ref{sec:non-hydrostatic}), additional files |
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\code{OB[N/S/E/W]wFile} for the vertical velocity $w$ with |
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dimensions $(N_{x/y}\times N_r\times\mbox{time levels})$ can be |
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specified. |
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\item If \code{useSEAICE=.TRUE.} then additional files |
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\code{OB[N/S/E/W][a,h,sl,sn,uice,vice]} for sea ice area, thickness |
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(\code{HEFF}), seaice salinity, snow and ice velocities |
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$(N_{x/y}\times\mbox{time levels})$ can be specified. |
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\end{itemize} |
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As in \code{S/R external\_fields\_load} or the \code{exf}-package, the |
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code reads two time levels for each variable, e.g.\ \code{OBNu0} and |
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\code{OBNu1}, and interpolates linearly between these time levels to |
| 339 |
obtain the value \code{OBNu} at the current model time (step). When the |
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\code{exf}-package is used, the time levels are controlled for each |
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boundary separately in the same way as the \code{exf}-fields in |
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\code{data.exf}, namelist \code{EXF\_NML\_OBCS}. The runtime flags |
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follow the above naming conventions, e.g. for the western boundary the |
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corresponding flags are \code{OBCWstartdate1/2} and |
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\code{OBCWperiod}. Sea-ice boundary values are controlled separately |
| 346 |
with \code{siobWstartdate1/2} and \code{siobWperiod}. When the |
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\code{exf}-package is not used, the time levels are controlled by the |
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runtime flags \code{externForcingPeriod} and \code{externForcingCycle} |
| 349 |
in \code{data}, see \code{verification/exp4} for an example. |
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|
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\paragraph{OBCS\_CALC\_STEVENS:} ~ \\ |
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(THE IMPLEMENTATION OF THESE BOUNDARY CONDITIONS IS NOT COMPLETE. SO |
| 353 |
FAR ONLY EASTERN AND WESTERN BOUNDARIES ARE SUPPORTED.) \\ |
| 354 |
The boundary conditions following \citet{stevens:90} require the |
| 355 |
vertically averaged normal velocity (originally specified as a stream |
| 356 |
function along the open boundary) $\bar{u}_{ob}$ and the tracer fields |
| 357 |
$\chi_{ob}$ (note: passive tracers are currently not implemented and |
| 358 |
the code stops when package \code{ptracers} is used together with this |
| 359 |
option). Currently, the code vertically averages the normal velocity |
| 360 |
as specified. From these prescribed values the code computes the |
| 361 |
boundary values for the next timestep $n+1$ as follows (as an |
| 362 |
example, we use the notation for an eastern or western boundary): |
| 363 |
\begin{itemize} |
| 364 |
\item $u^{n+1}(y,z) = \bar{u}_{ob}(y) + u'(y,z)$, where $u_{n}'$ is the |
| 365 |
deviation from the vertically averaged velocity one grid point |
| 366 |
inward from the boundary. |
| 367 |
\item If $u^{n+1}$ is directed into the model domain, the boudary |
| 368 |
value for tracer $\chi$ is restored to the prescribed values: |
| 369 |
\[\chi^{n+1} = \chi^{n} + \frac{\Delta{t}}{\tau_\chi} (\chi_{ob} - |
| 370 |
\chi^{n}),\] where $\tau_\chi$ is the relaxation time |
| 371 |
scale \texttt{T/SrelaxStevens}. |
| 372 |
\item If $u^{n+1}$ is directed out of the model domain, the tracer is |
| 373 |
advected out of the domain with $u^{n+1}+c$, where $c$ is a phase |
| 374 |
velocity estimated as |
| 375 |
$\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$. |
| 376 |
For test purposes, the phase velocity contribution or the entire |
| 377 |
advection can |
| 378 |
be turned off by setting the corresponding parameters |
| 379 |
\texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to |
| 380 |
\texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details. |
| 381 |
|
| 382 |
\paragraph{OBCS\_BALANCE:} ~ \\ |
| 383 |
% |
| 384 |
This is not (yet) a separate routine in the code, but it may become |
| 385 |
one to make this code more transparent. The code is part of |
| 386 |
\code{S/R~OBCS\_CALC}. When turned on (\code{ALLOW\_OBCS\_BALANCE} |
| 387 |
defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in |
| 388 |
\code{data.obcs/OBCS\_PARM01}), the normal velocities across each of |
| 389 |
the four boundaries are modified separately, so that the net volume |
| 390 |
transport across \emph{each} boundary is zero. For example, for the |
| 391 |
western boundary at $i=i_{b}$, the modified velocity is: |
| 392 |
\[ |
| 393 |
u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k} |
| 394 |
OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}. |
| 395 |
\] |
| 396 |
This also ensures a net total inflow of zero through all boundaries to |
| 397 |
make it a useful flag to prevent infinite sea-level change within the |
| 398 |
domain, but the flag is \emph{not} useful if you want to simulate, |
| 399 |
say, a sector of the Southern Ocean with a strong ACC entering through |
| 400 |
the western and leaving through the eastern boundary, because this |
| 401 |
flag will make sure that the strong inflow is removed. It is |
| 402 |
recommended that this part of the code is adapted to the particular |
| 403 |
needs of the simulation in question. |
| 404 |
|
| 405 |
\paragraph{OBCS\_APPLY\_*:} ~ \\ |
| 406 |
~ |
| 407 |
|
| 408 |
\paragraph{OBCS\_SPONGE} Setting sponge layer characteristics \\ |
| 409 |
% |
| 410 |
~ |
| 411 |
|
| 412 |
\paragraph{OB's with nonlinear free surface} ~ \\ |
| 413 |
% |
| 414 |
~ |
| 415 |
|
| 416 |
|
| 417 |
%---------------------------------------------------------------------- |
| 418 |
|
| 419 |
\subsubsection{Flow chart |
| 420 |
\label{sec:pkg:obcs:flowchart}} |
| 421 |
|
| 422 |
|
| 423 |
{\footnotesize |
| 424 |
\begin{verbatim} |
| 425 |
|
| 426 |
C !CALLING SEQUENCE: |
| 427 |
c ... |
| 428 |
|
| 429 |
\end{verbatim} |
| 430 |
} |
| 431 |
|
| 432 |
%---------------------------------------------------------------------- |
| 433 |
|
| 434 |
\subsubsection{OBCS diagnostics |
| 435 |
\label{sec:pkg:obcs:diagnostics}} |
| 436 |
|
| 437 |
Diagnostics output is available via the diagnostics package |
| 438 |
(see Section \ref{sec:pkg:diagnostics}). |
| 439 |
Available output fields are summarized in |
| 440 |
Table \ref{tab:pkg:obcs:diagnostics}. |
| 441 |
|
| 442 |
\begin{table}[!ht] |
| 443 |
\centering |
| 444 |
\label{tab:pkg:obcs:diagnostics} |
| 445 |
{\footnotesize |
| 446 |
\begin{verbatim} |
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------------------------------------------------------ |
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<-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c) |
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------------------------------------------------------ |
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|
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\end{verbatim} |
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} |
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\caption{~} |
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\end{table} |
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|
| 456 |
%---------------------------------------------------------------------- |
| 457 |
|
| 458 |
\subsubsection{Reference experiments} |
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In the directory \code{verifcation}, the following experiments use |
| 460 |
\code{obcs}: |
| 461 |
\begin{itemize} |
| 462 |
\item \code{exp4}: box with 4 open boundaries, simulating flow over a |
| 463 |
Gaussian bump based on \citet{adcroft:97}, also tests |
| 464 |
Stevens-boundary conditions; |
| 465 |
\item \code{dome}: based on ``Denmark Strait Overflow Model |
| 466 |
Experiment'', use Orlanski-BCs; |
| 467 |
\item \code{internal\_wave}: uses a heavily modified \code{S/R~OBCS\_CALC} |
| 468 |
\item \code{seaice\_obcs}: simple example who to use the sea-ice |
| 469 |
related code, based on \code{lab\_sea}; |
| 470 |
\item \code{tutorial\_plume\_on\_slope}: uses Orlanski-BCs, see also |
| 471 |
section~\ref{sec:eg-gravityplume}. |
| 472 |
\end{itemize} |
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|
| 474 |
|
| 475 |
|
| 476 |
%---------------------------------------------------------------------- |
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|
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\subsubsection{References} |
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|
| 480 |
\subsubsection{Experiments and tutorials that use obcs} |
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\label{sec:pkg:obcs:experiments} |
| 482 |
|
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\begin{itemize} |
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\item \code{tutorial\_plume\_on\_slope} (section~\ref{sec:eg-gravityplume}) |
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\end{itemize} |
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|
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|
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%%% Local Variables: |
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%%% mode: latex |
| 490 |
%%% TeX-master: "../../manual" |
| 491 |
%%% End: |
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