/[MITgcm]/manual/s_phys_pkgs/text/seaice.tex

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-revision 1.8 by mlosch,
Wed May 13 12:54:45 2009 UTC
+revision 1.9 by mlosch,
Thu May 14 15:35:17 2009 UTC
 Line 25 
 sea-ice model.
  CPP options enable or disable different aspects of the package
  (Section \ref{sec:pkg:seaice:config}).
  Run-Time options, flags, filenames and field-related dates/times are
- set in \texttt{data.seaice}
+ set in \code{data.seaice}
  (Section \ref{sec:pkg:seaice:runtime}).
  A description of key subroutines is given in Section
  \ref{sec:pkg:seaice:subroutines}.
 Line 46 
 As with all MITgcm packages, SEAICE can
  \begin{itemize}
  %
  \item
- using the \texttt{packages.conf} file by adding \texttt{seaice} to it,
+ using the \code{packages.conf} file by adding \code{seaice} to it,
  %
  \item
- or using \texttt{genmake2} adding
+ or using \code{genmake2} adding
- \texttt{-enable=seaice} or \texttt{-disable=seaice} switches
+ \code{-enable=seaice} or \code{-disable=seaice} switches
  %
  \item
  \textit{required packages and CPP options}: \\
- SEAICE requires the external forcing package \texttt{exf} to be enabled;
+ SEAICE requires the external forcing package \code{exf} to be enabled;
  no additional CPP options are required.
  %
  \end{itemize}
 Line 62 
 no additional CPP options are required.
  Parts of the SEAICE code can be enabled or disabled at compile time
  via CPP preprocessor flags. These options are set in either
- \texttt{SEAICE\_OPTIONS.h} or in \texttt{ECCO\_CPPOPTIONS.h}.
+ \code{SEAICE\_OPTIONS.h} or in \code{ECCO\_CPPOPTIONS.h}.
  Table \ref{tab:pkg:seaice:cpp} summarizes these options.
  \begin{table}[h!]
 Line 73 
 Table \ref{tab:pkg:seaice:cpp} summarize
        \hline
        \textbf{CPP option}  &  \textbf{Description}  \\
        \hline \hline
-         \texttt{SEAICE\_DEBUG} &
+         \code{SEAICE\_DEBUG} &
            Enhance STDOUT for debugging \\
-         \texttt{SEAICE\_ALLOW\_DYNAMICS} &
+         \code{SEAICE\_ALLOW\_DYNAMICS} &
            sea-ice dynamics code \\
-         \texttt{SEAICE\_CGRID} &
+         \code{SEAICE\_CGRID} &
            LSR solver on C-grid (rather than original B-grid) \\
-         \texttt{SEAICE\_ALLOW\_EVP} &
+         \code{SEAICE\_ALLOW\_EVP} &
            use EVP rather than LSR rheology solver \\
-         \texttt{SEAICE\_EXTERNAL\_FLUXES} &
+         \code{SEAICE\_EXTERNAL\_FLUXES} &
            use EXF-computed fluxes as starting point \\
-         \texttt{SEAICE\_MULTICATEGORY} &
+         \code{SEAICE\_MULTICATEGORY} &
            enable 8-category thermodynamics (by default undefined)\\
-         \texttt{SEAICE\_VARIABLE\_FREEZING\_POINT} &
+         \code{SEAICE\_VARIABLE\_FREEZING\_POINT} &
            enable linear dependence of the freezing point on salinity
            (by default undefined)\\
-         \texttt{ALLOW\_SEAICE\_FLOODING} &
+         \code{ALLOW\_SEAICE\_FLOODING} &
            enable snow to ice conversion for submerged sea-ice \\
-         \texttt{SEAICE\_SALINITY} &
+         \code{SEAICE\_SALINITY} &
            enable "salty" sea-ice (by default undefined) \\
-         \texttt{SEAICE\_AGE} &
+         \code{SEAICE\_AGE} &
            enable "age tracer" sea-ice (by default undefined) \\
-         \texttt{SEAICE\_CAP\_HEFF} &
+         \code{SEAICE\_CAP\_HEFF} &
            enable capping of sea-ice thickness to MAX\_HEFF \\ \hline
-         \texttt{SEAICE\_BICE\_STRESS} &
+         \code{SEAICE\_BICE\_STRESS} &
            B-grid only for backward compatiblity: turn on ice-stress on
            ocean\\
-         \texttt{EXPLICIT\_SSH\_SLOPE} &
+         \code{EXPLICIT\_SSH\_SLOPE} &
            B-grid only for backward compatiblity: use ETAN for tilt
            computations rather than geostrophic velocities \\
        \hline
 Line 114 
 Table \ref{tab:pkg:seaice:cpp} summarize
  \label{sec:pkg:seaice:runtime}}
  Run-time parameters are set in files
- \texttt{data.pkg} (read in \texttt{packages\_readparms.F}),
+ \code{data.pkg} (read in \code{packages\_readparms.F}),
- and \texttt{data.seaice} (read in \texttt{seaice\_readparms.F}).
+ and \code{data.seaice} (read in \code{seaice\_readparms.F}).
  \paragraph{Enabling the package}
  ~ \\
  %
  A package is switched on/off at run-time by setting
- (e.g. for SEAICE) \texttt{useSEAICE = .TRUE.} in \texttt{data.pkg}.
+ (e.g. for SEAICE) \code{useSEAICE = .TRUE.} in \code{data.pkg}.
  \paragraph{General flags and parameters}
  ~ \\
 Line 232 
 surface heat flux, and net shortwave flu
  global: in ice-free regions bulk formulae are used to estimate oceanic
  forcing from the atmospheric fields.
- \subsubsection{Dynamics}
+ \paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}
- \label{sec:pkg:seaice:dynamics}
  \newcommand{\vek}[1]{\ensuremath{\vec{\mathbf{#1}}}}
  \newcommand{\vtau}{\vek{\mathbf{\tau}}}
-Line 264 
 terms are given by
+Line 263 
 terms are given by
    \vtau_{air}   = & \rho_{air}  C_{air}   |\vek{U}_{air}  -\vek{u}|
                     R_{air}  (\vek{U}_{air}  -\vek{u}), \\
    \vtau_{ocean} = & \rho_{ocean}C_{ocean} |\vek{U}_{ocean}-\vek{u}|
-                    R_{ocean}(\vek{U}_{ocean}-\vek{u}), \\
+                    R_{ocean}(\vek{U}_{ocean}-\vek{u}),
  \end{align*}
  where $\vek{U}_{air/ocean}$ are the surface winds of the atmosphere
  and surface currents of the ocean, respectively; $C_{air/ocean}$ are
-Line 294 
 both thickness $h$ and compactness (conc
+Line 293 
 both thickness $h$ and compactness (conc
    P_{\max} = P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},
  \label{eq:icestrength}
  \end{equation}
- with the constants $P^{*}$ (run-time parameter \texttt{SEAICE\_strength}) and
+ with the constants $P^{*}$ (run-time parameter \code{SEAICE\_strength}) and
  $C^{*}=20$. The nonlinear bulk and shear
  viscosities $\eta$ and $\zeta$ are functions of ice strain rate
  invariants and ice strength such that the principal components of the
-Line 313 
 minor axis $e$ equal to $2$; they are gi
+Line 312 
 minor axis $e$ equal to $2$; they are gi
  \end{align*}
  The bulk viscosities are bounded above by imposing both a minimum
  $\Delta_{\min}$ (for numerical reasons, run-time parameter
- \texttt{SEAICE\_EPS} with a default value of
+ \code{SEAICE\_EPS} with a default value of
  $10^{-10}\text{\,s}^{-1}$) and a maximum $\zeta_{\max} =
  P_{\max}/\Delta^*$, where
  $\Delta^*=(5\times10^{12}/2\times10^4)\text{\,s}^{-1}$. (There is also
  the option of bounding $\zeta$ from below by setting run-time
- parameter \texttt{SEAICE\_zetaMin} $>0$, but this is generally not
+ parameter \code{SEAICE\_zetaMin} $>0$, but this is generally not
  recommended). For stress tensor computation the replacement pressure $P
  = 2\,\Delta\zeta$ \citep{hibler95} is used so that the stress state
  always lies on the elliptic yield curve by definition.
-Line 332 
 is capped to suppress any tensile stress
+Line 331 
 is capped to suppress any tensile stress
    {\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
+ To enable this method, set \code{\#define SEAICE\_ALLOW\_TEM} in
- \texttt{SEAICE\_OPTIONS.h} and turn it on with
+ \code{SEAICE\_OPTIONS.h} and turn it on with
- \texttt{SEAICEuseTEM=.TRUE.} in \texttt{data.seaice}.
+ \code{SEAICEuseTEM=.TRUE.} in \code{data.seaice}.
  In the current implementation, the VP-model is integrated with the
  semi-implicit line successive over relaxation (LSOR)-solver of
-Line 393 
 $T=E_{0}\Delta{t}$ with the tunable para
+Line 392 
 $T=E_{0}\Delta{t}$ with the tunable para
  the external (long) timestep $\Delta{t}$. \citet{hun97} recommend
  $E_{0} = \frac{1}{3}$ (which is the default value in the code).
- 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
- \texttt{SEAICE\_ALLOW\_EVP} are defined in \texttt{SEAICE\_OPTIONS.h}
+ \code{SEAICE\_ALLOW\_EVP} are defined in \code{SEAICE\_OPTIONS.h}
  (default). The solver is turned on by setting the sub-cycling time
- step \texttt{SEAICE\_deltaTevp} to a value larger than zero. The
+ step \code{SEAICE\_deltaTevp} to a value larger than zero. The
  choice of this time step is under debate. \citet{hun97} recommend
  order(120) time steps for the EVP solver within one model time step
- $\Delta{t}$ (\texttt{deltaTmom}). One can also choose order(120) time
+ $\Delta{t}$ (\code{deltaTmom}). One can also choose order(120) time
  steps within the forcing time scale, but then we recommend adjusting
  the damping time scale $T$ accordingly, by setting either
- \texttt{SEAICE\_elasticParm} ($E_{0}$), so that
+ \code{SEAICE\_elasticParm} ($E_{0}$), so that
  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly
- \texttt{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
+ \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
  Moving sea ice exerts a stress on the ocean which is the opposite of
  the stress $\vtau_{ocean}$ in Eq.~\ref{eq:momseaice}. This stess is
-Line 422 
 advect tracers, is really an average ove
+Line 421 
 advect tracers, is really an average ove
  velocity and the ice velocity leading to an inconsistency as the ice
  temperature and salinity are different from the oceanic variables.
  To turn on the stress formulation of \citet{hibler87}, set
- \texttt{useHB87StressCoupling=.TRUE.} in \texttt{data.seaice}.
+ \code{useHB87StressCoupling=.TRUE.} in \code{data.seaice}.
  % Our discretization differs from \citet{zhang97, zhang03} in the
-Line 434 
 To turn on the stress formulation of \ci
+Line 433 
 To turn on the stress formulation of \ci
  % differences and averaging is only involved in computing $\Delta$ and
  % $P$ at vorticity points.
- \subsubsection{Finite-volume discretization of the stress tensor
+ \paragraph{Finite-volume discretization of the stress tensor
-   divergence}
+   divergence\label{sec:pkg:seaice:discretization}}
- \label{sec:pkg:seaice:discretization}
  On an Arakawa C~grid, ice thickness and concentration and thus ice
  strength $P$ and bulk and shear viscosities $\zeta$ and $\eta$ are
  naturally defined a C-points in the center of the grid
-Line 515 
 widths. For the $u$-equation ($\alpha=1$
+Line 513 
 widths. For the $u$-equation ($\alpha=1$
    + \Delta{x}_1\sigma_{21}\biggl|_{x_{2}}^{x_{2}+\Delta{x}_{2}}
    \biggr\} \\ \notag
    =& \frac{1}{A_{i,j}^w} \biggl\{
-   (\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 -
+   (\Delta{x}_2\sigma_{11})_{i-1,j}^C
+   \\\notag
    \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\}
 Line 530 
 widths. For the $u$-equation ($\alpha=1$
    \phantom{=}& + \Delta{y}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}
    k_{1,i,j}^{C}\frac{u_{i+1,j}+u_{i,j}}{2} \\ \notag
    \phantom{=}& - \Delta{y}_{i,j}^{F} \frac{P}{2} \\
-   %
    (\Delta{x}_1\sigma_{21})_{i,j}^Z =& \phantom{+}
    \Delta{x}_{i,j}^{V}\overline{\eta}^{Z}_{i,j}
    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} \\ \notag
-Line 565 
 Similarly, we have for the $v$-equation
+Line 564 
 Similarly, we have for the $v$-equation
    \intertext{with}
    (\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}} \\\notag
+   \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}}
-   &+ \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
+   \\\notag &
-   \frac{v_{i,j}-v_{i-1,j}}{\Delta{x}_{i,j}^{V}} \\ \notag
+   + \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
-   &- \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
    &- \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
+   k_{2,i,j}^{Z}\frac{u_{i,j}+u_{i,j-1}}{2}
+   \\\notag &
+   - \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
    k_{1,i,j}^{Z}\frac{v_{i,j}+v_{i-1,j}}{2} \\ \notag
-   %
    (\Delta{x}_2\sigma_{22})_{i,j}^C =& \phantom{+}
    \Delta{x}_{i,j}^{F}(\zeta - \eta)^{C}_{i,j}
    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag
 Line 591 
 free slip boundary conditions the latera
  analogy to $(\epsilon_{12})^Z=0$ on boundaries, we set
  $\sigma_{21}^{Z}=0$, or equivalently $\eta_{i,j}^{Z}=0$, on boundaries.
- \subsubsection{Thermodynamics}
+ \paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}
- \label{sec:pkg:seaice:thermodynamics}
  In its original formulation the sea ice model \citep{menemenlis05}
  uses simple thermodynamics following the appendix of
-Line 616 
 minimum imposed ice thickness of $5\text
+Line 615 
 minimum imposed ice thickness of $5\text
  \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each
  thickness category is area-averaged to give the total heat flux
  \citep{hibler84}. To use this thickness category parameterization set
- \texttt{\#define SEAICE\_MULTICATEGORY}; note that this requires
+ \code{\#define SEAICE\_MULTICATEGORY}; note that this requires
  different restart files and switching this flag on in the middle of an
  integration is not possible.
-Line 626 
 $\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ w
+Line 625 
 $\rho\,c_{p}\left(T_{w}-T_{fr}\right)$ w
  the density and heat capacity of sea water and $T_{fr}$ is the local
  freezing point temperature that is a function of salinity. This flux
  is not assumed to instantaneously melt or create ice, but a time scale
- of three days (run-time parameter \texttt{SEAICE\_gamma\_t}) is used
+ of three days (run-time parameter \code{SEAICE\_gamma\_t}) is used
  to relax $T_{w}$ to the freezing point.
  %
  The parameterization of lateral and vertical growth of sea ice follows
  that of \citet{hib79, hib80}; the so-called lead closing parameter
- $h_{0}$ (run-time parameter \texttt{HO}) has a default value of
+ $h_{0}$ (run-time parameter \code{HO}) has a default value of
 .5~meters.
  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 643 
 the snow is flooded, a simple mass conse
  snowice formation (a flood-freeze algorithm following Archimedes'
  principle) turns snow into ice until the ice surface is back at $z=0$
  \citep{leppaeranta83}. The flood-freeze algorithm is enabled with the CPP-flag
- \texttt{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter
+ \code{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter
- \texttt{SEAICEuseFlooding=.true.}.
+ \code{SEAICEuseFlooding=.true.}.
  Effective ice thickness (ice volume per unit area,
  $c\cdot{h}$), concentration $c$ and effective snow thickness
-Line 665 
 preserve sharp gradients and edges that
+Line 664 
 preserve sharp gradients and edges that
  distributions and to rule out unphysical over- and undershoots
  (negative thickness or concentration). These scheme conserve volume
  and horizontal area and are unconditionally stable, so that we can set
- $D_{X}=0$. Run-timeflags: \texttt{SEAICEadvScheme} (default=2),
+ $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2),
- \texttt{DIFF1} (default=0.004).
+ \code{DIFF1} (default=0.004).
  There is considerable doubt about the reliability of a ``zero-layer''
  thermodynamic model --- \citet{semtner84} found significant errors in
-Line 699 
 enthalpy and to prevent false enthalpy e
+Line 698 
 enthalpy and to prevent false enthalpy e
  \subsubsection{Key subroutines
  \label{sec:pkg:seaice:subroutines}}
- Top-level routine: \texttt{seaice\_model.F}
+ Top-level routine: \code{seaice\_model.F}
  {\footnotesize
  \begin{verbatim}

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