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% $Header: /u/gcmpack/manual/s_phys_pkgs/text/shelfice.tex,v 1.3 2009/05/15 08:10:23 mlosch Exp $ |
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% $Name: $ |
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|
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\subsection{SHELFICE Package} |
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\label{sec:pkg:shelfice} |
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\begin{rawhtml} |
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<!-- CMIREDIR:package_shelfice: --> |
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\end{rawhtml} |
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|
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Authors: Martin Losch, Jean-Michel Campin |
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|
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%---------------------------------------------------------------------- |
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\subsubsection{Introduction |
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\label{sec:pkg:shelfice:intro}} |
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|
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|
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Package ``shelfice'' provides a thermodynamic model for basal melting |
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underneath floating ice shelves. |
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|
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CPP options enable or disable different aspects of the package |
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(Section \ref{sec:pkg:shelfice:config}). |
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Run-Time options, flags, filenames and field-related dates/times are |
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set in \code{data.shelfice} |
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(Section \ref{sec:pkg:shelfice:runtime}). |
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A description of key subroutines is given in Section |
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\ref{sec:pkg:shelfice:subroutines}. |
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Input fields, units and sign conventions are summarized in |
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Section \ref{sec:pkg:shelfice:fields_units}, and available diagnostics |
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output is listed in Section \ref{sec:pkg:shelfice:diagnostics}. |
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|
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%---------------------------------------------------------------------- |
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|
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\subsubsection{SHELFICE configuration, compiling \& running} |
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|
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\paragraph{Compile-time options |
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\label{sec:pkg:shelfice:config}} |
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~ |
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|
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As with all MITgcm packages, SHELFICE can be turned on or off 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{shelfice} 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=shelfice} or \code{-disable=shelfice} switches |
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% |
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\item |
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\textit{required packages and CPP options}: \\ |
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SHELFICE does not require any additional packages, but it will only |
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work with conventional vertical $z$-coordinates (pressure coordinates |
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are not implemented, yet). If you use it together with vertical mixing |
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schemes, be aware, that non-local parameterizations have been turned |
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off, e.g.\ for KPP (\ref{sec:pkg:kpp}). |
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% |
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\end{itemize} |
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(see Section \ref{sec:buildingCode}). |
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|
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Parts of the SHELFICE code can be enabled or disabled at compile time |
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via CPP preprocessor flags. These options are set |
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\code{SHELFICE\_OPTIONS.h}. |
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Table \ref{tab:pkg:shelfice:cpp} summarizes these options. |
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|
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\begin{table}[!ht] |
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\centering |
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\label{tab:pkg:shelfice: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\_SHELFICE\_DEBUG} & |
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Include code for enhanged diagnosis \\ |
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\code{ALLOW\_ISOMIP\_TD} & |
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Include code for simplifed ISOMIP thermodynamics \\ |
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\hline |
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\end{tabular} |
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} |
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\caption{Available CPP-flags to be set in \code{SHELFICE\_OPTIONS.h}} |
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\end{table} |
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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:shelfice:runtime}} |
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|
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Run-time parameters are set in files |
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\code{data.pkg} (read in \code{packages\_readparms.F}), |
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and \code{data.shelfice} (read in \code{shelfice\_readparms.F}). |
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|
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\paragraph{Enabling the package} |
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~ \\ |
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% |
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A package is switched on/off at run-time by setting |
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(e.g. for SHELFICE) \code{useSHELFICE = .TRUE.} in \code{data.pkg}. |
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|
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\paragraph{General flags and parameters} |
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~ \\ |
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% |
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Table~\ref{tab:pkg:shelfice:runtimeparms} lists all run-time parameters. |
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\begin{table}[!ht] |
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\caption{Run-time parameters and default values |
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\label{tab:pkg:shelfice:runtimeparms}} |
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{\footnotesize |
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% \hspace*{-1.5in} |
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\begin{tabular}{|lp{4cm}p{4cm}c|} |
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\hline |
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& & & \\ |
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\textbf{Name} & \textbf{Default value} |
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& \textbf{Description} & \textbf{Reference} \\ |
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& & & \\ |
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\hline \hline |
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useISOMIPTD & F |
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& use simplified ISOMIP thermodynamics instead of default |
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& %---ref--- |
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\\ |
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SHELFICEconserve & F |
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& use conservative form of temperature boundary conditions |
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& %---ref--- |
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\\ |
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SHELFICEboundaryLayer & F |
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& use simple boundary layer mixing parameterization |
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& %---ref--- |
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\\ |
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SHELFICEloadAnomalyFile & UNSET |
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& inital geopotential anomaly |
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& %---ref--- |
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\\ |
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SHELFICEtopoFile & UNSET |
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& under-ice topography of ice shelves |
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& %---ref--- |
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\\ |
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SHELFICElatentHeat & 334.0E+03 |
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& latent heat of fusion ($L$) |
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& %---ref--- |
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\\ |
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SHELFICEHeatCapacity\_Cp & 2000.0E+00 |
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& latent heat of fusion ($c_{p,I}$) |
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& %---ref--- |
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\\ |
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rhoShelfIce & 917.0E+00 |
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& (constant) mean density of ice shelf ($\rho_{I}$) |
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& %---ref--- |
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\\ |
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SHELFICEheatTransCoeff & 1.0E-04 |
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& transfer coefficient (exchange velocity) for temperature |
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($\gamma_T$) |
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& %---ref--- |
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\\ |
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SHELFICEsaltTransCoeff & 5.05E-03 $\times$~SHELFICEheatTransCoeff |
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& transfer coefficient (exchange velocity) for salinity |
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($\gamma_S$) |
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& %---ref--- |
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\\ |
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SHELFICEkappa & 1.54E-06 |
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& temperature diffusion coefficient of the ice shelf ($kappa$) |
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& %---ref--- |
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\\ |
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SHELFICEthetaSurface & -20.0E+00 |
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& (constant) surface temperature above the ice shelf ($T_{S}$) |
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& %---ref--- |
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\\ |
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no\_slip\_shelfice & no\_slip\_bottom (data) |
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& flag for slip along bottom of ice shelf |
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& %---ref--- |
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\\ |
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SHELFICEDragLinear & bottomDragLinear (data) |
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& linear drag coefficient at bottom ice shelf |
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& %---ref--- |
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\\ |
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SHELFICEDragQuadratic & bottomDragQuadratic (data) |
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& quadratic drag coefficient at bottom ice shelf |
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& %---ref--- |
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\\ |
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SHELFICEwriteState & F |
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& write ice shelf state to file |
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& %---ref--- |
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\\ |
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SHELFICE\_dumpFreq & dumpFreq (data) |
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& dump frequency |
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& %---ref--- |
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\\ |
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SHELFICE\_taveFreq & taveFreq (data) |
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& time-averaging frequency |
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& %---ref--- |
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\\ |
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SHELFICE\_tave\_mnc & timeave\_mnc (data.mnc) |
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& write snap-shot using MNC |
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& %---ref--- |
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\\ |
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SHELFICE\_dump\_mnc & snapshot\_mnc (data.mnc) |
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& write TimeAverage using MNC |
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& %---ref--- |
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\\ |
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\hline |
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\end{tabular} |
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} |
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\end{table} |
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|
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\paragraph{Input fields and units\label{sec:pkg:shelfice:fields_units}} |
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|
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\begin{description} |
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\item[\code{SHEFLICEtopoFile}:] under-ice topography of ice shelves in |
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meters; upwards is positive, that as for the bathymetry files, |
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negative values are required for topography below the sea-level; |
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\item[\code{SHEFLICEloadAnomalyFile}:] pressure load anomaly at the bottom of |
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the ice shelves in pressure units (Pa); this field is absolutely |
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required to avoid large excursions of the free surface during |
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initial adjustment processes; obtained by integrating an approximate |
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density from the surface at $z=0$ down to the bottom of the last |
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fully dry cell within the ice shelf, see |
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Eq.~(\ref{eq:surfacepressure}); however, the file |
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\code{SHEFLICEloadAnomalyFile} must not be $p_{top}$, but |
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$p_{top}-g\sum_{k'=1}^{n-1}\rho_{0}\Delta{z}_{k'}$, with |
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$\rho_{0}=$~\code{rhoConst}, so that in the absenses of a $\rho^{*}$ |
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that is different from $\rho_{0}$, the anomaly is zero. |
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\end{description} |
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|
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%---------------------------------------------------------------------- |
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\subsubsection{Description |
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\label{sec:pkg:shelfice:descr}} |
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|
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In the light of isomorphic equations for pressure and height |
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coordinates, the ice shelf topography on top of the water column has a |
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similar role as (and in the language of \citet{marshall:04} is |
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isomorphic to) the orography and the pressure boundary conditions at |
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the bottom of the fluid for atmospheric and oceanic models in pressure |
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coordinates. |
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% |
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|
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The total pressure $p_{tot}$ in the ocean can be divided into the |
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pressure at the top of the water column $p_{top}$, the hydrostatic |
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pressure and the non-hydrostatic pressure contribution $p_{NH}$: |
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\begin{equation} |
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\label{eq:pressureocean} |
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p_{tot} = p_{top} + \int_z^{\eta-h} g\,\rho\,dz + p_{NH}, |
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\end{equation} |
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with the gravitational acceleration $g$, the density $\rho$, the |
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vertical coordinate $z$ (positive upwards), and the dynamic |
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sea-surface height $\eta$. For the open ocean, $p_{top}=p_{a}$ |
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(atmospheric pressure) and $h=0$. Underneath an ice-shelf that is |
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assumed to be floating in isostatic equilibrium, $p_{top}$ at the top |
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of the water column is the atmospheric pressure $p_{a}$ plus the |
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weight of the ice-shelf. It is this weight of the ice-shelf that has |
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to be provided as a boundary condition at the top of the water column |
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(in run-time parameter \code{SHELFICEloadAnomalyFile}). |
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The weight is conveniently computed by integrating a density profile |
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$\rho^*$, that is constant in time and corresponds to the sea-water |
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replaced by ice, from $z=0$ to a ``reference'' ice-shelf draft at |
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$z=-h$ \citep{beckmann99}, so that |
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\begin{equation} |
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\label{eq:ptop} |
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p_{top} = p_{a} + \int_{-h}^{0}g\,\rho^{*}\,dz. |
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\end{equation} |
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Underneath the ice shelf, the ``sea-surface height'' $\eta$ is the |
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deviation from the ``reference'' ice-shelf draft $h$. During a model |
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integration, $\eta$ adjusts so that the isostatic equilibrium is |
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maintained for sufficiently slow and large scale motion. |
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|
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In the MITgcm, the total pressure anomaly $p'_{tot}$ which is used for |
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pressure gradient computations is defined by substracting a purely |
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depth dependent contribution $-g\rho_{0}z$ with a constant reference |
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density $\rho_{0}$ from $p_{tot}$. Eq.~(\ref{eq:pressureocean}) becomes |
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\begin{alignat}{2} |
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\label{eq:pressure} |
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p_{tot} =& \,p_{top} - g\,\rho_0\,(z+h) &+ g\,\rho_0\,\eta + \int_z^{\eta-h} |
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g\,(\rho-\rho_0)\,dz + p_{NH}, \\ |
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\intertext{and after rearranging} |
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p'_{tot} =& \,p'_{top} |
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&+ g\,\rho_0\,\eta + \int_z^{\eta-h}g\,(\rho-\rho_0)\,dz + p_{NH}, |
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\end{alignat} |
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with $p'_{tot} = p_{tot} + g\,\rho_0\,z$ and $p'_{top} = p_{top} - |
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g\,\rho_0\,h$. The non-hydrostatic pressure contribution $p_{NH}$ is |
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neglected in the following. |
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|
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In practice, the ice shelf contribution to $p_{top}$ is computed by |
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integrating Eq.~(\ref{eq:ptop}) from $z=0$ to the bottom of the last |
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fully dry cell within the ice shelf: |
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\begin{equation} |
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\label{eq:surfacepressure} |
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p_{top} = g\,\sum_{k'=1}^{n-1}\rho_{k'}^{*}\Delta{z_{k'}} + p_{a} |
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\end{equation} |
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where $n$ is the vertical index of the first (at least partially) |
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``wet'' cell and $\Delta{z_{k'}}$ is the thickness of the $k'$-th |
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layer (counting downwards). The pressure anomaly for evaluating the pressure |
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gradient is computed in the center of the ``wet'' cell $k$ as |
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\begin{equation} |
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\label{eq:discretizedpressure} |
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p'_{k} = p'_{top} + g\rho_{n}\eta + |
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g\,\sum_{k'=n}^{k}\left((\rho_{k'}-\rho_{0})\Delta{z_{k'}} |
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\frac{1+H(k'-k)}{2}\right) |
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\end{equation} |
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where $H(k'-k)=1$ for $k'<k$ and $0$ otherwise. |
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|
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Setting \code{SHELFICEboundaryLayer=.true.} introduces a simple |
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boundary layer that reduces the potential noise problem at the cost of |
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increased vertical mixing. For this purpose the water temperature at |
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the $k$-th layer abutting ice shelf topography for use in the heat |
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flux parameterizations is computed as a mean temperature |
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$\overline{\theta}_{k}$ over a boundary layer of the same thickness as |
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the layer thickness $\Delta{z}_{k}$: |
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\begin{equation} |
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\label{eq:thetabl} |
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\overline{\theta}_{k} = \theta_{k} h_{k} + \theta_{k+1} (1-h_{k}) |
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\end{equation} |
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where $h_{k}\in(0,1]$ is the fractional layer thickness of the $k$-th |
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layer. The original contributions due to ice shelf-ocean interaction |
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$g_{\theta}$ to the total tendency terms $G_{\theta}$ in the |
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time-stepping equation |
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%$\theta^{n+1} = \theta^{n} + \Delta{t}\, g_{\theta}^{n}$ |
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$\theta^{n+1} = f(\theta^{n},\Delta{t},G_{\theta}^{n})$ |
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% |
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are |
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\begin{equation} |
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\label{eq:orgtendency} |
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g_{\theta,k} = \frac{Q}{\rho_{0} c_{p} h_{k} \Delta{z}_{k}} |
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\text{ and } g_{\theta,k+1} = 0 |
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\end{equation} |
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for layers $k$ and $k+1$ ($c_{p}$ is the heat capacity). Averaging |
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these terms over a layer thickness $\Delta{z_{k}}$ (e.g., extending |
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from the ice shelf base down to the dashed line in cell C) and |
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applying the averaged tendency to cell A (in layer $k$) and to the |
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appropriate fraction of cells C (in layer $k+1$) yields |
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\begin{align} |
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\label{eq:tendencyk} |
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g_{\theta,k}^* &= \frac{Q}{\rho_{0} c_{p} \Delta{z}_{k}} \\ |
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\label{eq:tendencykp1} |
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g_{\theta,k+1}^* |
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&= \frac{Q}{\rho_{0} c_{p} \Delta{z}_{k}} |
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\frac{ \Delta{z}_{k} ( 1- h_{k} )}{\Delta{z}_{k+1}}. |
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\end{align} |
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Eq.~(\ref{eq:tendencykp1}) describes averaging over the part of the |
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grid cell $k+1$ that is part of the boundary layer with tendency |
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$g_{\theta,k}^*$ and the part with no tendency. Salinity is treated in |
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the same way. The momentum equations are not modified. |
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|
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\paragraph{Three-Equations-Thermodynamics} |
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\label{sec:pkg:shelfice:thermodynamics} |
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|
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Freezing and melting form a boundary layer between ice shelf and |
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ocean. % |
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Phase transitions at the boundary between saline water and ice imply |
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the following fluxes across the boundary: the freshwater mass flux |
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$q$ ($<0$ for melting); the heat flux that consists of the diffusive |
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flux through the ice, the latent heat flux due to melting and freezing |
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and the heat that is carried by the mass flux; and the salinity that |
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is carried by the mass flux, if the ice has a non-zero salinity $S_I$. |
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Further, the position of the interface between ice and ocean changes |
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because of $q$, so that, say, in the case of melting the volume of sea |
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water increases. As a consequence salinity and temperature are |
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modified. |
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|
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The turbulent exchange terms for tracers at the ice-ocean interface |
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are generally expressed as diffusive fluxes. Following |
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\citet{jenkins01}, the boundary conditions for a tracer take |
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into account that this boundary is not a material surface. |
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%The position of this surface changes when ice is melted or water freezes. % |
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The implied upward freshwater flux $q$ (in mass units, negative for |
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melting) is included in the boundary conditions for the temperature |
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and salinity equation as an advective flux: |
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\begin{equation} |
364 |
\label{eq:jenkinsbc} |
365 |
{\rho}K\frac{\partial{X}}{\partial{z}}\biggl|_{b} |
366 |
= (\rho\gamma_{X}-q) ( X_{b} - X ) |
367 |
\end{equation} |
368 |
where tracer $X$ stands for either temperature $T$ or salinity $S$. |
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$X_b$ is the tracer at the interface (taken to be at freezing), $X$ is |
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the tracer at the first interior grid point, $\rho$ is the density of |
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seawater, and $\gamma_X$ is the turbulent exchange coefficient (in |
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units of an exchange velocity). The left hand side of |
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Eq.~(\ref{eq:jenkinsbc}) is shorthand for the (downward) flux of tracer $X$ |
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across the boundary. $T_b$, $S_b$ and the freshwater flux $q$ are |
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obtained from solving a system of three equations that is derived from |
376 |
the heat and freshwater balance at the ice ocean interface. |
377 |
|
378 |
In this so-called three-equation-model \citep[e.g.,][]{hellmer89, |
379 |
jenkins01} the heat balance at the ice-ocean interface is expressed |
380 |
as |
381 |
|
382 |
\begin{equation} |
383 |
\label{eq:hellmerheatbalance} |
384 |
c_{p} \rho \gamma_T (T - T_{b}) |
385 |
+\rho_{I} c_{p,I} \kappa \frac{(T_{S} - T_{b})}{h} |
386 |
= -Lq |
387 |
\end{equation} |
388 |
where % |
389 |
$\rho$ is the density of sea-water, % |
390 |
$c_{p} = 3974\text{\,J\,kg$^{-1}$\,K$^{-1}$}$ is the specific heat |
391 |
capacity of water and % |
392 |
$\gamma_T$ the turbulent exchange coefficient of temperature. % |
393 |
The value of $\gamma_T$ is discussed in \citet{holland99}. $L = |
394 |
334000\text{\,J\,kg$^{-1}$}$ is the latent heat of fusion. $\rho_{I} = |
395 |
920\text{\,kg\,m$^{-3}$}$, $c_{p,I} = |
396 |
2000\text{\,J\,kg$^{-1}$\,K$^{-1}$}$, and $T_{S}$ are the density, |
397 |
heat capacity and the surface temperature of the ice shelf; |
398 |
$\kappa=1.54\times10^{-6}\text{\,m$^2$\,s$^{-1}$}$ is the heat |
399 |
diffusivity through the ice-shelf and $h$ is the ice-shelf draft. The |
400 |
second term on the right hand side describes the heat flux through the |
401 |
ice shelf. A constant surface temperature $T_S=-20^{\circ}$ is |
402 |
imposed. $T$ is the temperature of the model cell adjacent to the |
403 |
ice-water interface. The temperature at the interface $T_{b}$ is |
404 |
assumed to be the in-situ freezing point temperature of sea-water |
405 |
$T_{f}$ which is computed from a linear equation of state |
406 |
|
407 |
\begin{equation} |
408 |
\label{eq:helmerfreeze} |
409 |
T_{f} = (0.0901 - 0.0575\ S_{b})^{\circ} |
410 |
- 7.61 \times 10^{-4}\frac{^{\circ}}{\text{dBar}}\ p_{b} |
411 |
\end{equation} |
412 |
with the salinity $S_{b}$ and the pressure $p_{b}$ (in dBar) in the |
413 |
cell at the ice-water interface. From the salt budget, the salt flux |
414 |
across the shelf ice-ocean interface is equal to the salt flux due to |
415 |
melting and freezing: |
416 |
\begin{equation} |
417 |
\label{eq:hellmersaltbalance} |
418 |
\rho \gamma_{S} (S - S_{b}) = - q\,(S_{b}-S_{I}), |
419 |
\end{equation} |
420 |
where $\gamma_S = 5.05\times10^{-3}\gamma_T$ is the turbulent salinity |
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exchange coefficient, and $S$ and $S_{b}$ are defined in analogy to |
422 |
temperature as the salinity of the model cell adjacent to the |
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ice-water interface and at the interface, respectively. Note, that the |
424 |
salinity of the ice shelf is generally neglected ($S_{I}=0$). |
425 |
Equations~(\ref{eq:hellmerheatbalance}) to (\ref{eq:hellmersaltbalance}) can |
426 |
be solved for $S_{b}$, $T_{b}$, and the freshwater flux $q$ due to |
427 |
melting. These values are substituted into expression~(\ref{eq:jenkinsbc}) |
428 |
to obtain the boundary conditions for the temperature and salinity |
429 |
equations of the ocean model. |
430 |
% Then upward heat and (virtual) salt fluxes out of the ocean |
431 |
%are computed following \citet[their equations 6, 7, 25, 28, and 29, note |
432 |
%that $q = -\text{their melt rate $m$}\times\text{density of |
433 |
% freshwater}$, and that salinity within the ice is assumed to be |
434 |
%zero]{jenkins01} |
435 |
%\begin{align} |
436 |
% \label{eq:hellmerthetaflux} |
437 |
% K\frac{\partial{T}}{\partial{z}}\biggl|_{b} =& |
438 |
% (\rho\gamma_{T}-q) ( T_{b} - T ) \\\notag |
439 |
% =& - q \left[ \frac{L}{c_{p}} + (T - T_{b}) \right] |
440 |
% - \frac{\rho_{I} c_{p,I} \kappa}{c_{p}} \frac{(T_{S} - T_{b})}{h} \\ |
441 |
% \label{eq:hellmersaltflux} |
442 |
% K\frac{\partial{S}}{\partial{z}}\bigg|_{b} =& |
443 |
% (\rho\gamma_{S}-q)(S_{b} - S) \\\notag |
444 |
% =& q\,S \\ |
445 |
% \label{eq:hellmerheatflux} |
446 |
%% Q =& qc_{p} (T - T_{b}) - qL - \rho_{I} c_{p,I} \kappa |
447 |
%% \frac{(T_{S} - T_{b})}{h} \\ |
448 |
% Q =& - c_{p} (\rho\gamma_{T}-q) ( T_{b} - T ) \\\notag |
449 |
% =& - q \left[ L + c_{p} (T - T_{b}) \right] |
450 |
% - \rho_{I} c_{p,I} \kappa \frac{(T_{S} - T_{b})}{h} \\ |
451 |
% \label{eq:hellmerfwflux} |
452 |
% Q_{S} =& (\rho\gamma_{S}-q)(S_{b} - S) \\\notag |
453 |
% =& q\,S |
454 |
%\end{align} |
455 |
|
456 |
This formulation tends to yield smaller melt rates than the simpler |
457 |
formulation of the ISOMIP protocol because the freshwater flux due to |
458 |
melting decreases the salinity which raises the freezing point |
459 |
temperature and thus leads to less melting at the interface. For a |
460 |
simpler thermodynamics model where $S_b$ is not computed explicitly, |
461 |
for example as in the ISOMIP protocol, equation~(\ref{eq:jenkinsbc}) cannot |
462 |
be applied directly. In this case equation~(\ref{eq:hellmersaltbalance}) |
463 |
can be used with Eq.~(\ref{eq:jenkinsbc}) to obtain: |
464 |
\begin{equation} |
465 |
\rho{K}\frac{\partial{S}}{\partial{z}}\biggl|_{b} = q\,(S-S_I). |
466 |
\end{equation} |
467 |
This formulation can be used for all cases for which |
468 |
equation~(\ref{eq:hellmersaltbalance}) is valid. Further, in this |
469 |
formulation it is obvious that melting ($q<0$) leads to a reduction of |
470 |
salinity. |
471 |
|
472 |
The default value of \code{SHELFICEconserve=.false.} removes the |
473 |
contribution $q ( X_{b}-X )$ from Eq.~(\ref{eq:jenkinsbc}), making the |
474 |
boundary conditions for temperature non-conservative. |
475 |
|
476 |
\paragraph{ISOMIP-Thermodynamics} |
477 |
\label{sec:pkg:shelfice:isomip} |
478 |
|
479 |
A simpler formulation follows the ISOMIP protocol |
480 |
(\url{http://efdl.cims.nyu.edu/project_oisi/isomip/overview.html}). The |
481 |
freezing and melting in the boundary layer between ice shelf and ocean |
482 |
is parameterized following \citet{grosfeld97}. In this formulation |
483 |
Eq.~(\ref{eq:hellmerheatbalance}) reduces to |
484 |
\begin{equation} |
485 |
\label{eq:isomipheatbalance} |
486 |
c_{p} \rho \gamma_T (T - T_{b}) = -Lq |
487 |
\end{equation} |
488 |
and the fresh water flux $q$ is computed from |
489 |
\begin{equation} |
490 |
\label{eq:isomipfwflx} |
491 |
q = - \frac{c_{p} \rho \gamma_T (T - T_{b})}{L}. |
492 |
\end{equation} |
493 |
In order to use this formulation, set run-time parameter |
494 |
\code{useISOMIPTD=.true.} in data.shelfice. |
495 |
|
496 |
\paragraph{Remark} The shelfice package and experiments demonstrating |
497 |
its strenghts and weaknesses are also described in |
498 |
\citet{losch08}. However, note that unfortunately the description of |
499 |
the thermodynamics in the appendix of \citet{losch08} is wrong. |
500 |
|
501 |
|
502 |
%---------------------------------------------------------------------- |
503 |
|
504 |
\subsubsection{Key subroutines |
505 |
\label{sec:pkg:shelfice:subroutines}} |
506 |
|
507 |
Top-level routine: \code{shelfice\_model.F} |
508 |
|
509 |
{\footnotesize |
510 |
\begin{verbatim} |
511 |
C !CALLING SEQUENCE: |
512 |
C ... |
513 |
C |-FORWARD_STEP :: Step forward a time-step ( AT LAST !!! ) |
514 |
C ... |
515 |
C | |-DO_OCEANIC_PHY :: Control oceanic physics and parameterization |
516 |
C ... |
517 |
C | | |-SHELFICE_THERMODYNAMICS :: main routine for thermodynamics |
518 |
C with diagnostics |
519 |
C ... |
520 |
C | |-THERMODYNAMICS :: theta, salt + tracer equations driver. |
521 |
C ... |
522 |
C | | |-EXTERNAL_FORCING_T :: Problem specific forcing for temperature. |
523 |
C | | |-SHELFICE_FORCING_T :: apply heat fluxes from ice shelf model |
524 |
C ... |
525 |
C | | |-EXTERNAL_FORCING_S :: Problem specific forcing for temperature. |
526 |
C | | |-SHELFICE_FORCING_S :: apply fresh water fluxes from ice shelf model |
527 |
C ... |
528 |
C | |-DYNAMICS :: Momentum equations driver. |
529 |
C ... |
530 |
C | | |-MOM_FLUXFORM :: Flux form mom eqn. package ( see |
531 |
C ... |
532 |
C | | | |-SHELFICE_U_DRAG :: apply drag along ice shelf to u-equation |
533 |
C with diagnostics |
534 |
C ... |
535 |
C | | |-MOM_VECINV :: Vector invariant form mom eqn. package ( see |
536 |
C ... |
537 |
C | | | |-SHELFICE_V_DRAG :: apply drag along ice shelf to v-equation |
538 |
C with diagnostics |
539 |
C ... |
540 |
C o |
541 |
\end{verbatim} |
542 |
} |
543 |
|
544 |
|
545 |
%---------------------------------------------------------------------- |
546 |
|
547 |
\subsubsection{SHELFICE diagnostics |
548 |
\label{sec:pkg:shelfice:diagnostics}} |
549 |
|
550 |
Diagnostics output is available via the diagnostics package |
551 |
(see Section \ref{sec:pkg:diagnostics}). |
552 |
Available output fields are summarized in |
553 |
Table \ref{tab:pkg:shelfice:diagnostics}. |
554 |
|
555 |
\begin{table}[!ht] |
556 |
\centering |
557 |
\label{tab:pkg:shelfice:diagnostics} |
558 |
{\footnotesize |
559 |
\begin{verbatim} |
560 |
---------+----+----+----------------+----------------- |
561 |
<-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c) |
562 |
---------+----+----+----------------+----------------- |
563 |
SHIfwFlx| 1 |SM |kg/m^2/s |Ice shelf fresh water flux (positive upward) |
564 |
SHIhtFlx| 1 |SM |W/m^2 |Ice shelf heat flux (positive upward) |
565 |
SHIUDrag| 30 |UU |m/s^2 |U momentum tendency from ice shelf drag |
566 |
SHIVDrag| 30 |VV |m/s^2 |V momentum tendency from ice shelf drag |
567 |
SHIForcT| 1 |SM |W/m^2 |Ice shelf forcing for theta, >0 increases theta |
568 |
SHIForcS| 1 |SM |g/m^2/s |Ice shelf forcing for salt, >0 increases salt |
569 |
\end{verbatim} |
570 |
} |
571 |
\caption{Available diagnostics of the shelfice-package} |
572 |
\end{table} |
573 |
|
574 |
|
575 |
%\subsubsection{Package Reference} |
576 |
|
577 |
\subsubsection{Experiments and tutorials that use shelfice} |
578 |
\label{sec:pkg:shelfice:experiments} |
579 |
|
580 |
\begin{itemize} |
581 |
\item{ISOMIP, Experiment 1 |
582 |
(\url{http://efdl.cims.nyu.edu/project_oisi/isomip/overview.html}) |
583 |
in isomip verification directory.} |
584 |
\end{itemize} |
585 |
|
586 |
|
587 |
%%% Local Variables: |
588 |
%%% mode: latex |
589 |
%%% TeX-master: "../manual" |
590 |
%%% End: |