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

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-revision 1.22 by mlosch,
Wed Jan 21 18:18:22 2015 UTC
+revision 1.23 by mlosch,
Thu Jan 22 09:10:27 2015 UTC
 Line 63 
 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
  \code{SEAICE\_OPTIONS.h}.
- Table \ref{tab:pkg:seaice:cpp} summarizes the most important ones.
+ Table \ref{tab:pkg:seaice:cpp} summarizes the most important ones. For
+ more options see the default \code{pkg/seaice/SEAICE\_OPTIONS.h}.
  \begin{table}[!ht]
  \centering
-Line 527 
 non-linear iterations $\code{SEAICEnewto
+Line 528 
 non-linear iterations $\code{SEAICEnewto
  number of Krylov iterations $\code{SEAICEkrylovIterMax} = 50$, because
  the Krylov subspace has a fixed dimension of 50.
+ Setting \code{SEAICEuseStrImpCpl = .TRUE.,} turns on ``strength
+ implicit coupling'' \citep{hutchings04} in the LSR-solver and in the
+ LSR-preconditioner for the JFNK-solver. In this mode, the different
+ contributions of the stress divergence terms are re-ordered in order
+ to increase the diagonal dominance of the system
+ matrix. Unfortunately, the convergence rate of the LSR solver is
+ increased only slightly, while the JFNK-convergence appears to be
+ unaffected.
  \paragraph{Elastic-Viscous-Plastic (EVP) Dynamics\label{sec:pkg:seaice:EVPdynamics}}~\\
  %
  \citet{hun97}'s introduced an elastic contribution to the strain
-Line 605 
 time-discretization of the momentum equa
+Line 615 
 time-discretization of the momentum equa
    + \beta^{*}\frac{u^{p+1}-u^{p}}{\Delta{t}_{\mathrm{EVP}}}
  \end{equation}
  where $n$ is the previous time step index, and $p$ is the previous
- sub-cycling index. The term allows the definition of a residual
+ sub-cycling index. The extra ``intertial'' term
+ $m\,(u^{p+1}-u^{n})/\Delta{t})$ allows the definition of a residual
  $|u^{p+1}-u^{p}|$ that, as $u^{p+1} \rightarrow u^{n+1}$, converges to
- $0$ and a re-interpretation of EVP as a pure iterative solver where
+ $0$. In this way EVP can be re-interpreted as a pure iterative solver
- the sub-cycling has lost all time-relation \citep{bouillon13,
+ where the sub-cycling has no association with time-relation (through
-   kimmritz15}. Using the terminology of \citet{kimmritz15}, the
+ $\Delta{t}_{\mathrm{EVP}}$) \citep{bouillon13, kimmritz15}. Using the
- evolution equations of stress $\sigma_{ij}$ and momentum $\vec{u}$ can
+ terminology of \citet{kimmritz15}, the evolution equations of stress
- be written as:
+ $\sigma_{ij}$ and momentum $\vec{u}$ can be written as:
  \begin{align}
    \label{eq:evpstarsigma}
    \sigma_{ij}^{p+1}&=\sigma_{ij}^p+\frac{1}{\alpha}
-Line 620 
 be written as:
+Line 631 
 be written as:
    \label{eq:evpstarmom}
    \vec{u}^{p+1}&=\vec{u}^p+\frac{1}{\beta}
    \Big(\frac{\Delta t}{m}\nabla \cdot{\bf \sigma}^{p+1}+
-   \frac{\Delta t}{m}\vec{R}^{p+1/2}+\vec{u}_n-\vec{u}^p\Big).
+   \frac{\Delta t}{m}\vec{R}^{p}+\vec{u}_n-\vec{u}^p\Big).
  \end{align}
  $\vec{R}$ contains all terms in the momentum equations except for the
- rheology terms and the time derivative, $\alpha$ and $\beta$ are free
+ rheology terms and the time derivative; $\alpha$ and $\beta$ are free
  parameters (\code{SEAICE\_evpAlpha}, \code{SEAICE\_evpBeta}) that
  replace the time stepping parameters \code{SEAICE\_deltaTevp}
  ($\Delta{T}_{\mathrm{EVP}}$), \code{SEAICE\_elasticParm} ($E_{0}$), or
  \code{SEAICE\_evpTauRelax} ($T$). $\alpha$ and $\beta$ determine the
  speed of convergence and the stability. Usually, it makes sense to use
- $\alpha = \beta$, and \code{SEAICEnEVPstarSteps} $>> \alpha = \beta$
+ $\alpha = \beta$, and \code{SEAICEnEVPstarSteps} $\gg
- \citep{kimmritz15}.
+ (\alpha,\,\beta)$ \citep{kimmritz15}. Currently, there is no
+ termination criterion and the number of EVP* iterations is fixed to
+ \code{SEAICEnEVPstarSteps}.
  In order to use EVP* in the MITgcm, set \code{SEAICEuseEVPstar =
-   .TRUE.,} in \code{data.seaice}. \code{SEAICEuseEVPrev =.TRUE.,} uses
+   .TRUE.,} in \code{data.seaice}. If \code{SEAICEuseEVPrev =.TRUE.,}
  the actual form of equations (\ref{eq:evpstarsigma}) and
- (\ref{eq:evpstarmom}) with fewer implicit terms and the factor of
+ (\ref{eq:evpstarmom}) is used with fewer implicit terms and the factor
- $e^{2}$ dropped in the stress equations (\ref{eq:evpstresstensor2})
+ of $e^{2}$ dropped in the stress equations (\ref{eq:evpstresstensor2})
- and (\ref{eq:evpstresstensor12}).  This turns out to improve
+ and (\ref{eq:evpstresstensor12}). Although this modifies the original
- convergence \citep{bouillon13}.
+ EVP-equations, it turns out to improve convergence \citep{bouillon13}.
  Note, that for historical reasons, \code{SEAICE\_deltaTevp} needs to
- be set to some value in order to use also EVP*. Also note, that
+ be set to some (any!) value in order to use also EVP*; this behavoir
+ many change in the future. Also note, that
  probably because of the C-grid staggering of velocities and stresses,
  EVP* does not converge as successfully as in \citet{kimmritz15}.
  \paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\
  %
  In the so-called truncated ellipse method the shear viscosity $\eta$
-Line 857 
 $\sigma_{21}^{Z}=0$, or equivalently $\e
+Line 870 
 $\sigma_{21}^{Z}=0$, or equivalently $\e
  \paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}~\\
  %
+ \noindent\textbf{NOTE: THIS SECTION IS TERRIBLY OUT OF DATE}\\
  In its original formulation the sea ice model \citep{menemenlis05}
  uses simple thermodynamics following the appendix of
  \citet{sem76}. This formulation does not allow storage of heat,
-Line 872 
 way to that of \citet{parkinson79} and \
+Line 886 
 way to that of \citet{parkinson79} and \
  The conductive heat flux depends strongly on the ice thickness $h$.
  However, the ice thickness in the model represents a mean over a
  potentially very heterogeneous thickness distribution.  In order to
- parameterize a sub-grid scale distribution for heat flux
+ parameterize a sub-grid scale distribution for heat flux computations,
- computations, the mean ice thickness $h$ is split into seven thickness
+ the mean ice thickness $h$ is split into $N$ thickness categories
- categories $H_{n}$ that are equally distributed between $2h$ and a
+ $H_{n}$ that are equally distributed between $2h$ and a minimum
- minimum imposed ice thickness of $5\text{\,cm}$ by $H_n=
+ imposed ice thickness of $5\text{\,cm}$ by $H_n= \frac{2n-1}{7}\,h$
- \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each
+ for $n\in[1,N]$. The heat fluxes computed for each thickness category
- thickness category is area-averaged to give the total heat flux
+ is area-averaged to give the total heat flux \citep{hibler84}. To use
- \citep{hibler84}. To use this thickness category parameterization set
+ this thickness category parameterization set \code{SEAICE\_multDim} to
- \code{\#define SEAICE\_MULTICATEGORY}; note that this requires
+ the number of desired categories (7 is a good guess, for anything
- different restart files and switching this flag on in the middle of an
+ larger than 7 modify \code{SEAICE\_SIZE.h}) in
- integration is not possible.
+ \code{data.seaice}; note that this requires different restart files
+ and switching this flag on in the middle of an integration is not
+ advised. In order to include the same distribution for snow, set
+ \code{SEAICE\_useMultDimSnow = .TRUE.}; only then, the
+ parameterization of always having a fraction of thin ice is efficient
+ and generally thicker ice is produced \citep{castro-morales14}.
  The atmospheric heat flux is balanced by an oceanic heat flux from
  below.  The oceanic flux is proportional to

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