--- manual/s_phys_pkgs/text/seaice.tex 2010/08/27 13:15:37 1.11 +++ manual/s_phys_pkgs/text/seaice.tex 2011/02/28 16:27:56 1.15 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.11 2010/08/27 13:15:37 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.15 2011/02/28 16:27:56 mlosch Exp $ % $Name: $ %%EH3 Copied from "MITgcm/pkg/seaice/seaice_description.tex" @@ -16,7 +16,7 @@ %---------------------------------------------------------------------- \subsubsection{Introduction -\label{sec:pkg:exf:intro}} +\label{sec:pkg:seaice:intro}} Package ``seaice'' provides a dynamic and thermodynamic interactive @@ -58,14 +58,14 @@ no additional CPP options are required. % \end{itemize} -(see Section \ref{sect:buildingCode}). +(see Section \ref{sec:buildingCode}). Parts of the SEAICE code can be enabled or disabled at compile time via CPP preprocessor flags. These options are set in either \code{SEAICE\_OPTIONS.h} or in \code{ECCO\_CPPOPTIONS.h}. Table \ref{tab:pkg:seaice:cpp} summarizes these options. -\begin{table}[h!] +\begin{table}[!ht] \centering \label{tab:pkg:seaice:cpp} {\footnotesize @@ -531,7 +531,9 @@ \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{} + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z \biggr\} - \intertext{with} +\end{align} +with +\begin{align} (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+} \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j} \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag @@ -573,7 +575,9 @@ \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{} + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C \biggr\} - \intertext{with} +\end{align} +with +\begin{align} (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+} \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j} \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} @@ -670,40 +674,47 @@ diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$. % From the various advection scheme that are available in the MITgcm, we -choose flux-limited schemes \citep[multidimensional 2nd and 3rd-order -advection scheme with flux limiter][]{roe:85, hundsdorfer94} to -preserve sharp gradients and edges that are typical of sea ice +recommend flux-limited schemes \citep[multidimensional 2nd and +3rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94} +to preserve sharp gradients and edges that are typical of sea ice distributions and to rule out unphysical over- and undershoots -(negative thickness or concentration). These scheme conserve volume +(negative thickness or concentration). These schemes conserve volume and horizontal area and are unconditionally stable, so that we can set -$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2), -\code{DIFF1} (default=0.004). +$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the +historic 2nd-order, centered difference scheme), \code{DIFF1} +(default=0.004). There is considerable doubt about the reliability of a ``zero-layer'' thermodynamic model --- \citet{semtner84} found significant errors in phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in such models --- so that today many sea ice models employ more complex thermodynamics. The MITgcm sea ice model provides the option to use -the thermodynamics model of \citet{win00}, which in turn is based -on the 3-layer model of \citet{sem76} and which treats brine -content by means of enthalpy conservation. This scheme requires -additional state variables, namely the enthalpy of the two ice layers -(instead of effective ice salinity), to be advected by ice velocities. +the thermodynamics model of \citet{win00}, which in turn is based on +the 3-layer model of \citet{sem76} and which treats brine content by +means of enthalpy conservation; the corresponding package +\code{thsice} is described in section~\ref{sec:pkg:thsice}. This +scheme requires additional state variables, namely the enthalpy of the +two ice layers (instead of effective ice salinity), to be advected by +ice velocities. % The internal sea ice temperature is inferred from ice enthalpy. To avoid unphysical (negative) values for ice thickness and concentration, a positive 2nd-order advection scheme with a SuperBee flux limiter \citep{roe:85} is used in this study to advect all -sea-ice-related quantities of the \citet{win00} thermodynamic -model. Because of the non-linearity of the advection scheme, care -must be taken in advecting these quantities: when simply using ice -velocity to advect enthalpy, the total energy (i.e., the volume -integral of enthalpy) is not conserved. Alternatively, one can advect -the energy content (i.e., product of ice-volume and enthalpy) but then -false enthalpy extrema can occur, which then leads to unrealistic ice +sea-ice-related quantities of the \citet{win00} thermodynamic model. +Because of the non-linearity of the advection scheme, care must be +taken in advecting these quantities: when simply using ice velocity to +advect enthalpy, the total energy (i.e., the volume integral of +enthalpy) is not conserved. Alternatively, one can advect the energy +content (i.e., product of ice-volume and enthalpy) but then false +enthalpy extrema can occur, which then leads to unrealistic ice temperature. In the currently implemented solution, the sea-ice mass flux is used to advect the enthalpy in order to ensure conservation of -enthalpy and to prevent false enthalpy extrema. +enthalpy and to prevent false enthalpy extrema. % +In order to use the \code{seaice}-package with the more sophisticated +thermodynamics of \code{thsice}, compile both packages and turn both +package on in \code{data.pkg}; see an example in +\code{global\_ocean.cs32x15/input.icedyn}. %---------------------------------------------------------------------- @@ -769,7 +780,7 @@ Available output fields are summarized in Table \ref{tab:pkg:seaice:diagnostics}. -\begin{table}[h!] +\begin{table}[!ht] \centering \label{tab:pkg:seaice:diagnostics} {\footnotesize @@ -834,5 +845,5 @@ %%% Local Variables: %%% mode: latex -%%% TeX-master: "../manual" +%%% TeX-master: "../../manual" %%% End: