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revision 1.8 by mlosch, Wed May 13 12:54:45 2009 UTC revision 1.18 by heimbach, Sat Aug 13 15:50:05 2011 UTC
# Line 16  Patrick Heimbach, Chris Hill and Jinlun Line 16  Patrick Heimbach, Chris Hill and Jinlun
16    
17  %----------------------------------------------------------------------  %----------------------------------------------------------------------
18  \subsubsection{Introduction  \subsubsection{Introduction
19  \label{sec:pkg:exf:intro}}  \label{sec:pkg:seaice:intro}}
20    
21    
22  Package ``seaice'' provides a dynamic and thermodynamic interactive  Package ``seaice'' provides a dynamic and thermodynamic interactive
# Line 25  sea-ice model. Line 25  sea-ice model.
25  CPP options enable or disable different aspects of the package  CPP options enable or disable different aspects of the package
26  (Section \ref{sec:pkg:seaice:config}).  (Section \ref{sec:pkg:seaice:config}).
27  Run-Time options, flags, filenames and field-related dates/times are  Run-Time options, flags, filenames and field-related dates/times are
28  set in \texttt{data.seaice}  set in \code{data.seaice}
29  (Section \ref{sec:pkg:seaice:runtime}).  (Section \ref{sec:pkg:seaice:runtime}).
30  A description of key subroutines is given in Section  A description of key subroutines is given in Section
31  \ref{sec:pkg:seaice:subroutines}.  \ref{sec:pkg:seaice:subroutines}.
32  Input fields, units and sign conventions are summarized in  Input fields, units and sign conventions are summarized in
33  Section \ref{sec:pkg:seaice:fields_units}, and available diagnostics  Section \ref{sec:pkg:seaice:fields_units}, and available diagnostics
34  output is listed in Section \ref{sec:pkg:seaice:fields_diagnostics}.  output is listed in Section \ref{sec:pkg:seaice:diagnostics}.
35    
36  %----------------------------------------------------------------------  %----------------------------------------------------------------------
37    
# Line 46  As with all MITgcm packages, SEAICE can Line 46  As with all MITgcm packages, SEAICE can
46  \begin{itemize}  \begin{itemize}
47  %  %
48  \item  \item
49  using the \texttt{packages.conf} file by adding \texttt{seaice} to it,  using the \code{packages.conf} file by adding \code{seaice} to it,
50  %  %
51  \item  \item
52  or using \texttt{genmake2} adding  or using \code{genmake2} adding
53  \texttt{-enable=seaice} or \texttt{-disable=seaice} switches  \code{-enable=seaice} or \code{-disable=seaice} switches
54  %  %
55  \item  \item
56  \textit{required packages and CPP options}: \\  \textit{required packages and CPP options}: \\
57  SEAICE requires the external forcing package \texttt{exf} to be enabled;  SEAICE requires the external forcing package \code{exf} to be enabled;
58  no additional CPP options are required.  no additional CPP options are required.
59  %  %
60  \end{itemize}  \end{itemize}
61  (see Section \ref{sect:buildingCode}).  (see Section \ref{sec:buildingCode}).
62    
63  Parts of the SEAICE code can be enabled or disabled at compile time  Parts of the SEAICE code can be enabled or disabled at compile time
64  via CPP preprocessor flags. These options are set in either  via CPP preprocessor flags. These options are set in either
65  \texttt{SEAICE\_OPTIONS.h} or in \texttt{ECCO\_CPPOPTIONS.h}.  \code{SEAICE\_OPTIONS.h} or in \code{ECCO\_CPPOPTIONS.h}.
66  Table \ref{tab:pkg:seaice:cpp} summarizes these options.  Table \ref{tab:pkg:seaice:cpp} summarizes these options.
67    
68  \begin{table}[h!]  \begin{table}[!ht]
69  \centering  \centering
70    \label{tab:pkg:seaice:cpp}    \label{tab:pkg:seaice:cpp}
71    {\footnotesize    {\footnotesize
# Line 73  Table \ref{tab:pkg:seaice:cpp} summarize Line 73  Table \ref{tab:pkg:seaice:cpp} summarize
73        \hline        \hline
74        \textbf{CPP option}  &  \textbf{Description}  \\        \textbf{CPP option}  &  \textbf{Description}  \\
75        \hline \hline        \hline \hline
76          \texttt{SEAICE\_DEBUG} &          \code{SEAICE\_DEBUG} &
77            Enhance STDOUT for debugging \\            Enhance STDOUT for debugging \\
78          \texttt{SEAICE\_ALLOW\_DYNAMICS} &          \code{SEAICE\_ALLOW\_DYNAMICS} &
79            sea-ice dynamics code \\            sea-ice dynamics code \\
80          \texttt{SEAICE\_CGRID} &          \code{SEAICE\_CGRID} &
81            LSR solver on C-grid (rather than original B-grid) \\            LSR solver on C-grid (rather than original B-grid) \\
82          \texttt{SEAICE\_ALLOW\_EVP} &          \code{SEAICE\_ALLOW\_EVP} &
83            use EVP rather than LSR rheology solver \\            use EVP rather than LSR rheology solver \\
84          \texttt{SEAICE\_EXTERNAL\_FLUXES} &          \code{SEAICE\_EXTERNAL\_FLUXES} &
85            use EXF-computed fluxes as starting point \\            use EXF-computed fluxes as starting point \\
86          \texttt{SEAICE\_MULTICATEGORY} &          \code{SEAICE\_MULTICATEGORY} &
87            enable 8-category thermodynamics (by default undefined)\\            enable 8-category thermodynamics (by default undefined)\\
88          \texttt{SEAICE\_VARIABLE\_FREEZING\_POINT} &          \code{SEAICE\_VARIABLE\_FREEZING\_POINT} &
89            enable linear dependence of the freezing point on salinity            enable linear dependence of the freezing point on salinity
90            (by default undefined)\\            (by default undefined)\\
91          \texttt{ALLOW\_SEAICE\_FLOODING} &          \code{ALLOW\_SEAICE\_FLOODING} &
92            enable snow to ice conversion for submerged sea-ice \\            enable snow to ice conversion for submerged sea-ice \\
93          \texttt{SEAICE\_SALINITY} &          \code{SEAICE\_SALINITY} &
94            enable "salty" sea-ice (by default undefined) \\            enable "salty" sea-ice (by default undefined) \\
95          \texttt{SEAICE\_AGE} &          \code{SEAICE\_AGE} &
96            enable "age tracer" sea-ice (by default undefined) \\            enable "age tracer" sea-ice (by default undefined) \\
97          \texttt{SEAICE\_CAP\_HEFF} &          \code{SEAICE\_CAP\_HEFF} &
98            enable capping of sea-ice thickness to MAX\_HEFF \\ \hline            enable capping of sea-ice thickness to MAX\_HEFF \\ \hline
99          \texttt{SEAICE\_BICE\_STRESS} &          \code{SEAICE\_BICE\_STRESS} &
100            B-grid only for backward compatiblity: turn on ice-stress on            B-grid only for backward compatiblity: turn on ice-stress on
101            ocean\\            ocean\\
102          \texttt{EXPLICIT\_SSH\_SLOPE} &          \code{EXPLICIT\_SSH\_SLOPE} &
103            B-grid only for backward compatiblity: use ETAN for tilt            B-grid only for backward compatiblity: use ETAN for tilt
104            computations rather than geostrophic velocities \\            computations rather than geostrophic velocities \\
105        \hline        \hline
# Line 113  Table \ref{tab:pkg:seaice:cpp} summarize Line 113  Table \ref{tab:pkg:seaice:cpp} summarize
113  \subsubsection{Run-time parameters  \subsubsection{Run-time parameters
114  \label{sec:pkg:seaice:runtime}}  \label{sec:pkg:seaice:runtime}}
115    
116  Run-time parameters are set in files  Run-time parameters (see Table~\ref{tab:pkg:seaice:runtimeparms}) are set
117  \texttt{data.pkg} (read in \texttt{packages\_readparms.F}),  in files \code{data.pkg} (read in \code{packages\_readparms.F}), and
118  and \texttt{data.seaice} (read in \texttt{seaice\_readparms.F}).  \code{data.seaice} (read in \code{seaice\_readparms.F}).
119    
120  \paragraph{Enabling the package}  \paragraph{Enabling the package}
121  ~ \\  ~ \\
122  %  %
123  A package is switched on/off at run-time by setting  A package is switched on/off at run-time by setting
124  (e.g. for SEAICE) \texttt{useSEAICE = .TRUE.} in \texttt{data.pkg}.  (e.g. for SEAICE) \code{useSEAICE = .TRUE.} in \code{data.pkg}.
125    
126  \paragraph{General flags and parameters}  \paragraph{General flags and parameters}
127  ~ \\  ~ \\
128  %  %
129  Table~\ref{tab:pkg:seaice:runtimeparms} lists most run-time parameters.  Table~\ref{tab:pkg:seaice:runtimeparms} lists most run-time parameters.
130  \input{part6/seaice-parms.tex}  \input{s_phys_pkgs/text/seaice-parms.tex}
   
131    
132    \paragraph{Input fields and units\label{sec:pkg:seaice:fields_units}}
133    \begin{description}
134    \item[\code{HeffFile}:] Initial sea ice thickness averaged over grid cell
135      in meters; initializes variable \code{HEFF};
136    \item[\code{AreaFile}:] Initial fractional sea ice cover, range $[0,1]$;
137      initializes variable \code{AREA};
138    \item[\code{HsnowFile}:] Initial snow thickness on sea ice averaged
139      over grid cell in meters; initializes variable \code{HSNOW};
140    \item[\code{HsaltFile}:] Initial salinity of sea ice averaged over grid
141      cell in g/m$^2$; initializes variable \code{HSALT};
142    \item[\code{IceAgeFile}:] Initial ice age of sea ice averaged over grid
143      cell in seconds; initializes variable \code{ICEAGE};
144    \end{description}
145    
146  %----------------------------------------------------------------------  %----------------------------------------------------------------------
147  \subsubsection{Description  \subsubsection{Description
# Line 202  relatively simpler formulation, compared Line 214  relatively simpler formulation, compared
214  to use the VP model as the default dynamic component of our ice  to use the VP model as the default dynamic component of our ice
215  model. To do this we extended the line successive over relaxation  model. To do this we extended the line successive over relaxation
216  (LSOR) method of \citet{zhang97} for use in a parallel  (LSOR) method of \citet{zhang97} for use in a parallel
217  configuration.  configuration. An EVP model and a free-drift implemtation can be
218    selected with runtime flags.
219    
220  Note, that by default the seaice-package includes the orginial  \paragraph{Compatibility with ice-thermodynamics package \code{thsice}\label{sec:pkg:seaice:thsice}}~\\
221    %
222    Note, that by default the \code{seaice}-package includes the orginial
223  so-called zero-layer thermodynamics following \citet{hib80} with a  so-called zero-layer thermodynamics following \citet{hib80} with a
224  snow cover as in \citet{zha98a}. The zero-layer thermodynamic model  snow cover as in \citet{zha98a}. The zero-layer thermodynamic model
225  assumes that ice does not store heat and, therefore, tends to  assumes that ice does not store heat and, therefore, tends to
226  exaggerate the seasonal variability in ice thickness.  This  exaggerate the seasonal variability in ice thickness.  This
227  exaggeration can be significantly reduced by using  exaggeration can be significantly reduced by using
228  \citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic model  \citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic
229  that permits heat storage in ice.  Recently, the three-layer  model that permits heat storage in ice. Recently, the three-layer thermodynamic model has been reformulated by
230  thermodynamic model has been reformulated by \citet{win00}.  The  \citet{win00}.  The reformulation improves model physics by
231  reformulation improves model physics by representing the brine content  representing the brine content of the upper ice with a variable heat
232  of the upper ice with a variable heat capacity.  It also improves  capacity.  It also improves model numerics and consumes less computer
233  model numerics and consumes less computer time and memory.  The Winton  time and memory.
234  sea-ice thermodynamics have been ported to the MIT GCM; they currently  
235  reside under pkg/thsice. The package pkg/thsice is fully compatible  The Winton sea-ice thermodynamics have been ported to the MIT GCM;
236  with pkg/seaice and with pkg/exf. When turned on together with  they currently reside under \code{pkg/thsice}.  The package
237  pkg/seaice, the zero-layer thermodynamics are replaced by the Winton  \code{thsice} is described in section~\ref{sec:pkg:thsice}; it is
238  thermodynamics.  fully compatible with the packages \code{seaice} and \code{exf}. When
239    turned on together with \code{seaice}, the zero-layer thermodynamics
240    are replaced by the Winton thermodynamics. In order to use the
241    \code{seaice}-package with the thermodynamics of \code{thsice},
242    compile both packages and turn both package on in \code{data.pkg}; see
243    an example in \code{global\_ocean.cs32x15/input.icedyn}. Note, that
244    once \code{thsice} is turned on, the variables and diagnostics
245    associated to the default thermodynamics are meaningless, and the
246    diagnostics of \code{thsice} have to be used instead.
247    
248    \paragraph{Surface forcing\label{sec:pkg:seaice:surfaceforcing}}~\\
249    %
250  The sea ice model requires the following input fields: 10-m winds, 2-m  The sea ice model requires the following input fields: 10-m winds, 2-m
251  air temperature and specific humidity, downward longwave and shortwave  air temperature and specific humidity, downward longwave and shortwave
252  radiations, precipitation, evaporation, and river and glacier runoff.  radiations, precipitation, evaporation, and river and glacier runoff.
# Line 232  surface heat flux, and net shortwave flu Line 257  surface heat flux, and net shortwave flu
257  global: in ice-free regions bulk formulae are used to estimate oceanic  global: in ice-free regions bulk formulae are used to estimate oceanic
258  forcing from the atmospheric fields.  forcing from the atmospheric fields.
259    
260  \subsubsection{Dynamics}  \paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}~\\
261  \label{sec:pkg:seaice:dynamics}  %
   
262  \newcommand{\vek}[1]{\ensuremath{\vec{\mathbf{#1}}}}  \newcommand{\vek}[1]{\ensuremath{\vec{\mathbf{#1}}}}
263  \newcommand{\vtau}{\vek{\mathbf{\tau}}}  \newcommand{\vtau}{\vek{\mathbf{\tau}}}
264  The momentum equation of the sea-ice model is  The momentum equation of the sea-ice model is
# Line 264  terms are given by Line 288  terms are given by
288    \vtau_{air}   = & \rho_{air}  C_{air}   |\vek{U}_{air}  -\vek{u}|    \vtau_{air}   = & \rho_{air}  C_{air}   |\vek{U}_{air}  -\vek{u}|
289                     R_{air}  (\vek{U}_{air}  -\vek{u}), \\                     R_{air}  (\vek{U}_{air}  -\vek{u}), \\
290    \vtau_{ocean} = & \rho_{ocean}C_{ocean} |\vek{U}_{ocean}-\vek{u}|    \vtau_{ocean} = & \rho_{ocean}C_{ocean} |\vek{U}_{ocean}-\vek{u}|
291                     R_{ocean}(\vek{U}_{ocean}-\vek{u}), \\                     R_{ocean}(\vek{U}_{ocean}-\vek{u}),
292  \end{align*}  \end{align*}
293  where $\vek{U}_{air/ocean}$ are the surface winds of the atmosphere  where $\vek{U}_{air/ocean}$ are the surface winds of the atmosphere
294  and surface currents of the ocean, respectively; $C_{air/ocean}$ are  and surface currents of the ocean, respectively; $C_{air/ocean}$ are
# Line 272  air and ocean drag coefficients; $\rho_{ Line 296  air and ocean drag coefficients; $\rho_{
296  densities; and $R_{air/ocean}$ are rotation matrices that act on the  densities; and $R_{air/ocean}$ are rotation matrices that act on the
297  wind/current vectors.  wind/current vectors.
298    
299    \paragraph{Viscous-Plastic (VP) Rheology and LSOR solver \label{sec:pkg:seaice:VPdynamics}}~\\
300    %
301  For an isotropic system the stress tensor $\sigma_{ij}$ ($i,j=1,2$) can  For an isotropic system the stress tensor $\sigma_{ij}$ ($i,j=1,2$) can
302  be related to the ice strain rate and strength by a nonlinear  be related to the ice strain rate and strength by a nonlinear
303  viscous-plastic (VP) constitutive law \citep{hib79, zhang97}:  viscous-plastic (VP) constitutive law \citep{hib79, zhang97}:
# Line 294  both thickness $h$ and compactness (conc Line 320  both thickness $h$ and compactness (conc
320    P_{\max} = P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},    P_{\max} = P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},
321  \label{eq:icestrength}  \label{eq:icestrength}
322  \end{equation}  \end{equation}
323  with the constants $P^{*}$ (run-time parameter \texttt{SEAICE\_strength}) and  with the constants $P^{*}$ (run-time parameter \code{SEAICE\_strength}) and
324  $C^{*}=20$. The nonlinear bulk and shear  $C^{*}=20$. The nonlinear bulk and shear
325  viscosities $\eta$ and $\zeta$ are functions of ice strain rate  viscosities $\eta$ and $\zeta$ are functions of ice strain rate
326  invariants and ice strength such that the principal components of the  invariants and ice strength such that the principal components of the
# Line 313  minor axis $e$ equal to $2$; they are gi Line 339  minor axis $e$ equal to $2$; they are gi
339  \end{align*}  \end{align*}
340  The bulk viscosities are bounded above by imposing both a minimum  The bulk viscosities are bounded above by imposing both a minimum
341  $\Delta_{\min}$ (for numerical reasons, run-time parameter  $\Delta_{\min}$ (for numerical reasons, run-time parameter
342  \texttt{SEAICE\_EPS} with a default value of  \code{SEAICE\_EPS} with a default value of
343  $10^{-10}\text{\,s}^{-1}$) and a maximum $\zeta_{\max} =  $10^{-10}\text{\,s}^{-1}$) and a maximum $\zeta_{\max} =
344  P_{\max}/\Delta^*$, where  P_{\max}/\Delta^*$, where
345  $\Delta^*=(5\times10^{12}/2\times10^4)\text{\,s}^{-1}$. (There is also  $\Delta^*=(5\times10^{12}/2\times10^4)\text{\,s}^{-1}$. (There is also
346  the option of bounding $\zeta$ from below by setting run-time  the option of bounding $\zeta$ from below by setting run-time
347  parameter \texttt{SEAICE\_zetaMin} $>0$, but this is generally not  parameter \code{SEAICE\_zetaMin} $>0$, but this is generally not
348  recommended). For stress tensor computation the replacement pressure $P  recommended). For stress tensor computation the replacement pressure $P
349  = 2\,\Delta\zeta$ \citep{hibler95} is used so that the stress state  = 2\,\Delta\zeta$ \citep{hibler95} is used so that the stress state
350  always lies on the elliptic yield curve by definition.  always lies on the elliptic yield curve by definition.
351    
 In the so-called truncated ellipse method the shear viscosity $\eta$  
 is capped to suppress any tensile stress \citep{hibler97, geiger98}:  
 \begin{equation}  
   \label{eq:etatem}  
   \eta = \min\left(\frac{\zeta}{e^2},  
   \frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}  
   {\sqrt{(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})^2  
       +4\dot{\epsilon}_{12}^2}}\right).  
 \end{equation}  
 To enable this method, set \texttt{\#define SEAICE\_ALLOW\_TEM} in  
 \texttt{SEAICE\_OPTIONS.h} and turn it on with  
 \texttt{SEAICEuseTEM=.TRUE.} in \texttt{data.seaice}.  
   
352  In the current implementation, the VP-model is integrated with the  In the current implementation, the VP-model is integrated with the
353  semi-implicit line successive over relaxation (LSOR)-solver of  semi-implicit line successive over relaxation (LSOR)-solver of
354  \citet{zhang97}, which allows for long time steps that, in our case,  \citet{zhang97}, which allows for long time steps that, in our case,
# Line 345  limitation because it restricts the time Line 358  limitation because it restricts the time
358  same length as in the ocean model where the Coriolis term is also  same length as in the ocean model where the Coriolis term is also
359  treated explicitly.  treated explicitly.
360    
361    \paragraph{Elastic-Viscous-Plastic (EVP) Dynamics\label{sec:pkg:seaice:EVPdynamics}}~\\
362    %
363  \citet{hun97}'s introduced an elastic contribution to the strain  \citet{hun97}'s introduced an elastic contribution to the strain
364  rate in order to regularize Eq.~\ref{eq:vpequation} in such a way that  rate in order to regularize Eq.~\ref{eq:vpequation} in such a way that
365  the resulting elastic-viscous-plastic (EVP) and VP models are  the resulting elastic-viscous-plastic (EVP) and VP models are
# Line 362  identical at steady state, Line 377  identical at steady state,
377  %used and compared the present sea-ice model study.  %used and compared the present sea-ice model study.
378  The EVP-model uses an explicit time stepping scheme with a short  The EVP-model uses an explicit time stepping scheme with a short
379  timestep. According to the recommendation of \citet{hun97}, the  timestep. According to the recommendation of \citet{hun97}, the
380  EVP-model is stepped forward in time 120 times within the physical  EVP-model should be stepped forward in time 120 times
381  ocean model time step (although this parameter is under debate), to  ($\code{SEAICE\_deltaTevp} = \code{SEAICIE\_deltaTdyn}/120$) within
382  allow for elastic waves to disappear.  Because the scheme does not  the physical ocean model time step (although this parameter is under
383  require a matrix inversion it is fast in spite of the small internal  debate), to allow for elastic waves to disappear.  Because the scheme
384  timestep and simple to implement on parallel computers  does not require a matrix inversion it is fast in spite of the small
385    internal timestep and simple to implement on parallel computers
386  \citep{hun97}. For completeness, we repeat the equations for the  \citep{hun97}. For completeness, we repeat the equations for the
387  components of the stress tensor $\sigma_{1} =  components of the stress tensor $\sigma_{1} =
388  \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and  \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and
# Line 387  abbreviations, the equations~\ref{eq:evp Line 403  abbreviations, the equations~\ref{eq:evp
403    \frac{\partial\sigma_{12}}{\partial{t}} + \frac{\sigma_{12} e^{2}}{2T}    \frac{\partial\sigma_{12}}{\partial{t}} + \frac{\sigma_{12} e^{2}}{2T}
404    &= \frac{P}{4T\Delta} D_S    &= \frac{P}{4T\Delta} D_S
405  \end{align}  \end{align}
406  Here, the elastic parameter $E$ is redefined in terms of a damping timescale  Here, the elastic parameter $E$ is redefined in terms of a damping
407  $T$ for elastic waves \[E=\frac{\zeta}{T}.\]  timescale $T$ for elastic waves \[E=\frac{\zeta}{T}.\]
408  $T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and  $T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and the external
409  the external (long) timestep $\Delta{t}$. \citet{hun97} recommend  (long) timestep $\Delta{t}$.  $E_{0} = \frac{1}{3}$ is the default
410  $E_{0} = \frac{1}{3}$ (which is the default value in the code).  value in the code and close to what \citet{hun97} and
411    \citet{hun01} recommend.
412    
413  To use the EVP solver, make sure that both \texttt{SEAICE\_CGRID} and  To use the EVP solver, make sure that both \code{SEAICE\_CGRID} and
414  \texttt{SEAICE\_ALLOW\_EVP} are defined in \texttt{SEAICE\_OPTIONS.h}  \code{SEAICE\_ALLOW\_EVP} are defined in \code{SEAICE\_OPTIONS.h}
415  (default). The solver is turned on by setting the sub-cycling time  (default). The solver is turned on by setting the sub-cycling time
416  step \texttt{SEAICE\_deltaTevp} to a value larger than zero. The  step \code{SEAICE\_deltaTevp} to a value larger than zero. The
417  choice of this time step is under debate. \citet{hun97} recommend  choice of this time step is under debate. \citet{hun97} recommend
418  order(120) time steps for the EVP solver within one model time step  order(120) time steps for the EVP solver within one model time step
419  $\Delta{t}$ (\texttt{deltaTmom}). One can also choose order(120) time  $\Delta{t}$ (\code{deltaTmom}). One can also choose order(120) time
420  steps within the forcing time scale, but then we recommend adjusting  steps within the forcing time scale, but then we recommend adjusting
421  the damping time scale $T$ accordingly, by setting either  the damping time scale $T$ accordingly, by setting either
422  \texttt{SEAICE\_elasticParm} ($E_{0}$), so that  \code{SEAICE\_elasticParm} ($E_{0}$), so that
423  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly
424  \texttt{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.  \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
425    
426    \paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\
427    %
428    In the so-called truncated ellipse method the shear viscosity $\eta$
429    is capped to suppress any tensile stress \citep{hibler97, geiger98}:
430    \begin{equation}
431      \label{eq:etatem}
432      \eta = \min\left(\frac{\zeta}{e^2},
433      \frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}
434      {\sqrt{(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})^2
435          +4\dot{\epsilon}_{12}^2}}\right).
436    \end{equation}
437    To enable this method, set \code{\#define SEAICE\_ALLOW\_TEM} in
438    \code{SEAICE\_OPTIONS.h} and turn it on with
439    \code{SEAICEuseTEM} in \code{data.seaice}.
440    
441    \paragraph{Ice-Ocean stress \label{sec:pkg:seaice:iceoceanstress}}~\\
442    %
443  Moving sea ice exerts a stress on the ocean which is the opposite of  Moving sea ice exerts a stress on the ocean which is the opposite of
444  the stress $\vtau_{ocean}$ in Eq.~\ref{eq:momseaice}. This stess is  the stress $\vtau_{ocean}$ in Eq.~\ref{eq:momseaice}. This stess is
445  applied directly to the surface layer of the ocean model. An  applied directly to the surface layer of the ocean model. An
# Line 422  advect tracers, is really an average ove Line 456  advect tracers, is really an average ove
456  velocity and the ice velocity leading to an inconsistency as the ice  velocity and the ice velocity leading to an inconsistency as the ice
457  temperature and salinity are different from the oceanic variables.  temperature and salinity are different from the oceanic variables.
458  To turn on the stress formulation of \citet{hibler87}, set  To turn on the stress formulation of \citet{hibler87}, set
459  \texttt{useHB87StressCoupling=.TRUE.} in \texttt{data.seaice}.  \code{useHB87StressCoupling=.TRUE.} in \code{data.seaice}.
460    
461    
462  % Our discretization differs from \citet{zhang97, zhang03} in the  % Our discretization differs from \citet{zhang97, zhang03} in the
# Line 434  To turn on the stress formulation of \ci Line 468  To turn on the stress formulation of \ci
468  % differences and averaging is only involved in computing $\Delta$ and  % differences and averaging is only involved in computing $\Delta$ and
469  % $P$ at vorticity points.  % $P$ at vorticity points.
470    
471  \subsubsection{Finite-volume discretization of the stress tensor  \paragraph{Finite-volume discretization of the stress tensor
472    divergence}    divergence\label{sec:pkg:seaice:discretization}}~\\
473  \label{sec:pkg:seaice:discretization}  %
474  On an Arakawa C~grid, ice thickness and concentration and thus ice  On an Arakawa C~grid, ice thickness and concentration and thus ice
475  strength $P$ and bulk and shear viscosities $\zeta$ and $\eta$ are  strength $P$ and bulk and shear viscosities $\zeta$ and $\eta$ are
476  naturally defined a C-points in the center of the grid  naturally defined a C-points in the center of the grid
# Line 515  widths. For the $u$-equation ($\alpha=1$ Line 549  widths. For the $u$-equation ($\alpha=1$
549    + \Delta{x}_1\sigma_{21}\biggl|_{x_{2}}^{x_{2}+\Delta{x}_{2}}    + \Delta{x}_1\sigma_{21}\biggl|_{x_{2}}^{x_{2}+\Delta{x}_{2}}
550    \biggr\} \\ \notag    \biggr\} \\ \notag
551    =& \frac{1}{A_{i,j}^w} \biggl\{    =& \frac{1}{A_{i,j}^w} \biggl\{
552    (\Delta{x}_2\sigma_{11})_{i,j}^C - (\Delta{x}_2\sigma_{11})_{i-1,j}^C \\\notag    (\Delta{x}_2\sigma_{11})_{i,j}^C -
553      (\Delta{x}_2\sigma_{11})_{i-1,j}^C
554      \\\notag
555    \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{}    \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{}
556    + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z    + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z
557    \biggr\}    \biggr\}
558    \intertext{with}  \end{align}
559    with
560    \begin{align}
561    (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+}    (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+}
562    \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j}    \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j}
563    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag
# Line 530  widths. For the $u$-equation ($\alpha=1$ Line 568  widths. For the $u$-equation ($\alpha=1$
568    \phantom{=}& + \Delta{y}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}    \phantom{=}& + \Delta{y}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}
569    k_{1,i,j}^{C}\frac{u_{i+1,j}+u_{i,j}}{2} \\ \notag    k_{1,i,j}^{C}\frac{u_{i+1,j}+u_{i,j}}{2} \\ \notag
570    \phantom{=}& - \Delta{y}_{i,j}^{F} \frac{P}{2} \\    \phantom{=}& - \Delta{y}_{i,j}^{F} \frac{P}{2} \\
   %  
571    (\Delta{x}_1\sigma_{21})_{i,j}^Z =& \phantom{+}    (\Delta{x}_1\sigma_{21})_{i,j}^Z =& \phantom{+}
572    \Delta{x}_{i,j}^{V}\overline{\eta}^{Z}_{i,j}    \Delta{x}_{i,j}^{V}\overline{\eta}^{Z}_{i,j}
573    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} \\ \notag    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} \\ \notag
# Line 562  Similarly, we have for the $v$-equation Line 599  Similarly, we have for the $v$-equation
599    \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{}    \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{}
600    + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C    + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C
601    \biggr\}    \biggr\}
602    \intertext{with}  \end{align}
603    with
604    \begin{align}
605    (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+}    (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+}
606    \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}    \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
607    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} \\\notag    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}}
608    &+ \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}    \\\notag &
609    \frac{v_{i,j}-v_{i-1,j}}{\Delta{x}_{i,j}^{V}} \\ \notag    + \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
610    &- \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}    \frac{v_{i,j}-v_{i-1,j}}{\Delta{x}_{i,j}^{V}} \\\notag
   k_{2,i,j}^{Z}\frac{u_{i,j}+u_{i,j-1}}{2} \\ \notag  
611    &- \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}    &- \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
612      k_{2,i,j}^{Z}\frac{u_{i,j}+u_{i,j-1}}{2}
613      \\\notag &
614      - \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
615    k_{1,i,j}^{Z}\frac{v_{i,j}+v_{i-1,j}}{2} \\ \notag    k_{1,i,j}^{Z}\frac{v_{i,j}+v_{i-1,j}}{2} \\ \notag
   %  
616    (\Delta{x}_2\sigma_{22})_{i,j}^C =& \phantom{+}    (\Delta{x}_2\sigma_{22})_{i,j}^C =& \phantom{+}
617    \Delta{x}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}    \Delta{x}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}
618    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag
# Line 591  free slip boundary conditions the latera Line 631  free slip boundary conditions the latera
631  analogy to $(\epsilon_{12})^Z=0$ on boundaries, we set  analogy to $(\epsilon_{12})^Z=0$ on boundaries, we set
632  $\sigma_{21}^{Z}=0$, or equivalently $\eta_{i,j}^{Z}=0$, on boundaries.  $\sigma_{21}^{Z}=0$, or equivalently $\eta_{i,j}^{Z}=0$, on boundaries.
633    
634  \subsubsection{Thermodynamics}  \paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}~\\
635  \label{sec:pkg:seaice:thermodynamics}  %
   
636  In its original formulation the sea ice model \citep{menemenlis05}  In its original formulation the sea ice model \citep{menemenlis05}
637  uses simple thermodynamics following the appendix of  uses simple thermodynamics following the appendix of
638  \citet{sem76}. This formulation does not allow storage of heat,  \citet{sem76}. This formulation does not allow storage of heat,
# Line 616  minimum imposed ice thickness of $5\text Line 655  minimum imposed ice thickness of $5\text
655  \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each  \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each
656  thickness category is area-averaged to give the total heat flux  thickness category is area-averaged to give the total heat flux
657  \citep{hibler84}. To use this thickness category parameterization set  \citep{hibler84}. To use this thickness category parameterization set
658  \texttt{\#define SEAICE\_MULTICATEGORY}; note that this requires  \code{\#define SEAICE\_MULTICATEGORY}; note that this requires
659  different restart files and switching this flag on in the middle of an  different restart files and switching this flag on in the middle of an
660  integration is not possible.  integration is not possible.
661    
# Line 626  $\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ w Line 665  $\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ w
665  the density and heat capacity of sea water and $T_{fr}$ is the local  the density and heat capacity of sea water and $T_{fr}$ is the local
666  freezing point temperature that is a function of salinity. This flux  freezing point temperature that is a function of salinity. This flux
667  is not assumed to instantaneously melt or create ice, but a time scale  is not assumed to instantaneously melt or create ice, but a time scale
668  of three days (run-time parameter \texttt{SEAICE\_gamma\_t}) is used  of three days (run-time parameter \code{SEAICE\_gamma\_t}) is used
669  to relax $T_{w}$ to the freezing point.  to relax $T_{w}$ to the freezing point.
670  %  %
671  The parameterization of lateral and vertical growth of sea ice follows  The parameterization of lateral and vertical growth of sea ice follows
672  that of \citet{hib79, hib80}; the so-called lead closing parameter  that of \citet{hib79, hib80}; the so-called lead closing parameter
673  $h_{0}$ (run-time parameter \texttt{HO}) has a default value of  $h_{0}$ (run-time parameter \code{HO}) has a default value of
674  0.5~meters.  0.5~meters.
675    
676  On top of the ice there is a layer of snow that modifies the heat flux  On top of the ice there is a layer of snow that modifies the heat flux
# Line 644  the snow is flooded, a simple mass conse Line 683  the snow is flooded, a simple mass conse
683  snowice formation (a flood-freeze algorithm following Archimedes'  snowice formation (a flood-freeze algorithm following Archimedes'
684  principle) turns snow into ice until the ice surface is back at $z=0$  principle) turns snow into ice until the ice surface is back at $z=0$
685  \citep{leppaeranta83}. The flood-freeze algorithm is enabled with the CPP-flag  \citep{leppaeranta83}. The flood-freeze algorithm is enabled with the CPP-flag
686  \texttt{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter  \code{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter
687  \texttt{SEAICEuseFlooding=.true.}.  \code{SEAICEuseFlooding=.true.}.
688    
689    \paragraph{Advection of thermodynamic variables\label{sec:pkg:seaice:advection}}~\\
690    %
691  Effective ice thickness (ice volume per unit area,  Effective ice thickness (ice volume per unit area,
692  $c\cdot{h}$), concentration $c$ and effective snow thickness  $c\cdot{h}$), concentration $c$ and effective snow thickness
693  ($c\cdot{h}_{s}$) are advected by ice velocities:  ($c\cdot{h}_{s}$) are advected by ice velocities:
# Line 659  where $\Gamma_X$ are the thermodynamic s Line 700  where $\Gamma_X$ are the thermodynamic s
700  diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$.  diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$.
701  %  %
702  From the various advection scheme that are available in the MITgcm, we  From the various advection scheme that are available in the MITgcm, we
703  choose flux-limited schemes \citep[multidimensional 2nd and 3rd-order  recommend flux-limited schemes \citep[multidimensional 2nd and
704  advection scheme with flux limiter][]{roe:85, hundsdorfer94} to  3rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94}
705  preserve sharp gradients and edges that are typical of sea ice  to preserve sharp gradients and edges that are typical of sea ice
706  distributions and to rule out unphysical over- and undershoots  distributions and to rule out unphysical over- and undershoots
707  (negative thickness or concentration). These scheme conserve volume  (negative thickness or concentration). These schemes conserve volume
708  and horizontal area and are unconditionally stable, so that we can set  and horizontal area and are unconditionally stable, so that we can set
709  $D_{X}=0$. Run-timeflags: \texttt{SEAICEadvScheme} (default=2),  $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the
710  \texttt{DIFF1} (default=0.004).  historic 2nd-order, centered difference scheme), \code{DIFF1} =
711    $D_{X}/\Delta{x}$
712  There is considerable doubt about the reliability of a ``zero-layer''  (default=0.004).
713  thermodynamic model --- \citet{semtner84} found significant errors in  
714  phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in  The MITgcm sea ice model provides the option to use
715  such models --- so that today many sea ice models employ more complex  the thermodynamics model of \citet{win00}, which in turn is based on
716  thermodynamics. The MITgcm sea ice model provides the option to use  the 3-layer model of \citet{sem76} and which treats brine content by
717  the thermodynamics model of \citet{win00}, which in turn is based  means of enthalpy conservation; the corresponding package
718  on the 3-layer model of \citet{sem76} and which treats brine  \code{thsice} is described in section~\ref{sec:pkg:thsice}. This
719  content by means of enthalpy conservation. This scheme requires  scheme requires additional state variables, namely the enthalpy of the
720  additional state variables, namely the enthalpy of the two ice layers  two ice layers (instead of effective ice salinity), to be advected by
721  (instead of effective ice salinity), to be advected by ice velocities.  ice velocities.
722  %  %
723  The internal sea ice temperature is inferred from ice enthalpy.  To  The internal sea ice temperature is inferred from ice enthalpy.  To
724  avoid unphysical (negative) values for ice thickness and  avoid unphysical (negative) values for ice thickness and
725  concentration, a positive 2nd-order advection scheme with a SuperBee  concentration, a positive 2nd-order advection scheme with a SuperBee
726  flux limiter \citep{roe:85} is used in this study to advect all  flux limiter \citep{roe:85} should be used to advect all
727  sea-ice-related quantities of the \citet{win00} thermodynamic  sea-ice-related quantities of the \citet{win00} thermodynamic model
728  model.  Because of the non-linearity of the advection scheme, care  (runtime flag \code{thSIceAdvScheme=77} and
729  must be taken in advecting these quantities: when simply using ice  \code{thSIce\_diffK}=$D_{X}$=0 in \code{data.ice}, defaults are 0).  Because of the
730  velocity to advect enthalpy, the total energy (i.e., the volume  non-linearity of the advection scheme, care must be taken in advecting
731  integral of enthalpy) is not conserved. Alternatively, one can advect  these quantities: when simply using ice velocity to advect enthalpy,
732  the energy content (i.e., product of ice-volume and enthalpy) but then  the total energy (i.e., the volume integral of enthalpy) is not
733  false enthalpy extrema can occur, which then leads to unrealistic ice  conserved. Alternatively, one can advect the energy content (i.e.,
734  temperature.  In the currently implemented solution, the sea-ice mass  product of ice-volume and enthalpy) but then false enthalpy extrema
735  flux is used to advect the enthalpy in order to ensure conservation of  can occur, which then leads to unrealistic ice temperature.  In the
736  enthalpy and to prevent false enthalpy extrema.  currently implemented solution, the sea-ice mass flux is used to
737    advect the enthalpy in order to ensure conservation of enthalpy and to
738    prevent false enthalpy extrema. %
739    
740  %----------------------------------------------------------------------  %----------------------------------------------------------------------
741    
742  \subsubsection{Key subroutines  \subsubsection{Key subroutines
743  \label{sec:pkg:seaice:subroutines}}  \label{sec:pkg:seaice:subroutines}}
744    
745  Top-level routine: \texttt{seaice\_model.F}  Top-level routine: \code{seaice\_model.F}
746    
747  {\footnotesize  {\footnotesize
748  \begin{verbatim}  \begin{verbatim}
# Line 758  Diagnostics output is available via the Line 801  Diagnostics output is available via the
801  Available output fields are summarized in  Available output fields are summarized in
802  Table \ref{tab:pkg:seaice:diagnostics}.  Table \ref{tab:pkg:seaice:diagnostics}.
803    
804  \begin{table}[h!]  \input{s_phys_pkgs/text/seaice_diags.tex}
 \centering  
 \label{tab:pkg:seaice:diagnostics}  
 {\footnotesize  
 \begin{verbatim}  
 ---------+----+----+----------------+-----------------  
  <-Name->|Levs|grid|<--  Units   -->|<- Tile (max=80c)  
 ---------+----+----+----------------+-----------------  
  SIarea  |  1 |SM  |m^2/m^2         |SEAICE fractional ice-covered area [0 to 1]  
  SIheff  |  1 |SM  |m               |SEAICE effective ice thickness  
  SIuice  |  1 |UU  |m/s             |SEAICE zonal ice velocity, >0 from West to East  
  SIvice  |  1 |VV  |m/s             |SEAICE merid. ice velocity, >0 from South to North  
  SIhsnow |  1 |SM  |m               |SEAICE snow thickness  
  SIhsalt |  1 |SM  |g/m^2           |SEAICE effective salinity  
  SIatmFW |  1 |SM  |kg/m^2/s        |Net freshwater flux from the atmosphere (+=down)  
  SIuwind |  1 |SM  |m/s             |SEAICE zonal 10-m wind speed, >0 increases uVel  
  SIvwind |  1 |SM  |m/s             |SEAICE meridional 10-m wind speed, >0 increases uVel  
  SIfu    |  1 |UU  |N/m^2           |SEAICE zonal surface wind stress, >0 increases uVel  
  SIfv    |  1 |VV  |N/m^2           |SEAICE merid. surface wind stress, >0 increases vVel  
  SIempmr |  1 |SM  |kg/m^2/s        |SEAICE upward freshwater flux, > 0 increases salt  
  SIqnet  |  1 |SM  |W/m^2           |SEAICE upward heatflux, turb+rad, >0 decreases theta  
  SIqsw   |  1 |SM  |W/m^2           |SEAICE upward shortwave radiat., >0 decreases theta  
  SIpress |  1 |SM  |m^2/s^2         |SEAICE strength (with upper and lower limit)  
  SIzeta  |  1 |SM  |m^2/s           |SEAICE nonlinear bulk viscosity  
  SIeta   |  1 |SM  |m^2/s           |SEAICE nonlinear shear viscosity  
  SIsigI  |  1 |SM  |no units        |SEAICE normalized principle stress, component one  
  SIsigII |  1 |SM  |no units        |SEAICE normalized principle stress, component two  
  SIthdgrh|  1 |SM  |m/s             |SEAICE thermodynamic growth rate of effective ice thickness  
  SIsnwice|  1 |SM  |m/s             |SEAICE ice formation rate due to flooding  
  SIuheff |  1 |UU  |m^2/s           |Zonal Transport of effective ice thickness  
  SIvheff |  1 |VV  |m^2/s           |Meridional Transport of effective ice thickness  
  ADVxHEFF|  1 |UU  |m.m^2/s         |Zonal      Advective Flux of eff ice thickn  
  ADVyHEFF|  1 |VV  |m.m^2/s         |Meridional Advective Flux of eff ice thickn  
  DFxEHEFF|  1 |UU  |m.m^2/s         |Zonal      Diffusive Flux of eff ice thickn  
  DFyEHEFF|  1 |VV  |m.m^2/s         |Meridional Diffusive Flux of eff ice thickn  
  ADVxAREA|  1 |UU  |m^2/m^2.m^2/s   |Zonal      Advective Flux of fract area  
  ADVyAREA|  1 |VV  |m^2/m^2.m^2/s   |Meridional Advective Flux of fract area  
  DFxEAREA|  1 |UU  |m^2/m^2.m^2/s   |Zonal      Diffusive Flux of fract area  
  DFyEAREA|  1 |VV  |m^2/m^2.m^2/s   |Meridional Diffusive Flux of fract area  
  ADVxSNOW|  1 |UU  |m.m^2/s         |Zonal      Advective Flux of eff snow thickn  
  ADVySNOW|  1 |VV  |m.m^2/s         |Meridional Advective Flux of eff snow thickn  
  DFxESNOW|  1 |UU  |m.m^2/s         |Zonal      Diffusive Flux of eff snow thickn  
  DFyESNOW|  1 |VV  |m.m^2/s         |Meridional Diffusive Flux of eff snow thickn  
  ADVxSSLT|  1 |UU  |psu.m^2/s       |Zonal      Advective Flux of seaice salinity  
  ADVySSLT|  1 |VV  |psu.m^2/s       |Meridional Advective Flux of seaice salinity  
  DFxESSLT|  1 |UU  |psu.m^2/s       |Zonal      Diffusive Flux of seaice salinity  
  DFyESSLT|  1 |VV  |psu.m^2/s       |Meridional Diffusive Flux of seaice salinity  
 \end{verbatim}  
 }  
 \caption{Available diagnostics of the seaice-package}  
 \end{table}  
   
805    
806  %\subsubsection{Package Reference}  %\subsubsection{Package Reference}
807    
# Line 817  Table \ref{tab:pkg:seaice:diagnostics}. Line 809  Table \ref{tab:pkg:seaice:diagnostics}.
809  \label{sec:pkg:seaice:experiments}  \label{sec:pkg:seaice:experiments}
810    
811  \begin{itemize}  \begin{itemize}
812  \item{Labrador Sea experiment in lab\_sea verification directory. }  \item{Labrador Sea experiment in \code{lab\_sea} verification directory. }
813    \item \code{seaice\_obcs}, based on \code{lab\_sea}
814    \item \code{offline\_exf\_seaice/input.seaicetd}, based on \code{lab\_sea}
815    \item \code{global\_ocean.cs32x15/input.icedyn} and
816      \code{global\_ocean.cs32x15/input.seaice}, global
817      cubed-sphere-experiment with combinations of \code{seaice} and
818      \code{thsice}
819  \end{itemize}  \end{itemize}
820    
821    
822  %%% Local Variables:  %%% Local Variables:
823  %%% mode: latex  %%% mode: latex
824  %%% TeX-master: "../manual"  %%% TeX-master: "../../manual"
825  %%% End:  %%% End:
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