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-revision 1.9 by mlosch,
Thu May 14 15:35:17 2009 UTC
+revision 1.16 by mlosch,
Wed Mar  2 13:46:38 2011 UTC
 Line 16 
 Patrick Heimbach, Chris Hill and Jinlun
  %----------------------------------------------------------------------
  \subsubsection{Introduction
- \label{sec:pkg:exf:intro}}
+ \label{sec:pkg:seaice:intro}}
  Package ``seaice'' provides a dynamic and thermodynamic interactive
 Line 31 
 A description of key subroutines is give
  \ref{sec:pkg:seaice:subroutines}.
  Input fields, units and sign conventions are summarized in
  Section \ref{sec:pkg:seaice:fields_units}, and available diagnostics
- output is listed in Section \ref{sec:pkg:seaice:fields_diagnostics}.
+ output is listed in Section \ref{sec:pkg:seaice:diagnostics}.
  %----------------------------------------------------------------------
 Line 58 
 SEAICE requires the external forcing pac
  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
 Line 113 
 Table \ref{tab:pkg:seaice:cpp} summarize
  \subsubsection{Run-time parameters
  \label{sec:pkg:seaice:runtime}}
- Run-time parameters are set in files
+ Run-time parameters (see Table~\ref{tab:pkg:seaice:runtimeparms}) are set
- \code{data.pkg} (read in \code{packages\_readparms.F}),
+ in files \code{data.pkg} (read in \code{packages\_readparms.F}), and
- and \code{data.seaice} (read in \code{seaice\_readparms.F}).
+ \code{data.seaice} (read in \code{seaice\_readparms.F}).
  \paragraph{Enabling the package}
  ~ \\
 Line 127 
 A package is switched on/off at run-time
  ~ \\
  %
  Table~\ref{tab:pkg:seaice:runtimeparms} lists most run-time parameters.
- \input{part6/seaice-parms.tex}
+ \input{s_phys_pkgs/text/seaice-parms.tex}
+ \paragraph{Input fields and units\label{sec:pkg:seaice:fields_units}}
+ \begin{description}
+ \item[\code{HeffFile}:] Initial sea ice thickness averaged over grid cell
+   in meters; initializes variable \code{HEFF};
+ \item[\code{AreaFile}:] Initial fractional sea ice cover, range $[0,1]$;
+   initializes variable \code{AREA};
+ \item[\code{HsnowFile}:] Initial snow thickness on sea ice averaged
+   over grid cell in meters; initializes variable \code{HSNOW};
+ \item[\code{HsaltFile}:] Initial salinity of sea ice averaged over grid
+   cell in g/m$^2$; initializes variable \code{HSALT};
+ \item[\code{IceAgeFile}:] Initial ice age of sea ice averaged over grid
+   cell in seconds; initializes variable \code{ICEAGE};
+ \end{description}
  %----------------------------------------------------------------------
  \subsubsection{Description
-Line 202 
 relatively simpler formulation, compared
+Line 214 
 relatively simpler formulation, compared
  to use the VP model as the default dynamic component of our ice
  model. To do this we extended the line successive over relaxation
  (LSOR) method of \citet{zhang97} for use in a parallel
- configuration.
+ configuration. An EVP model and a free-drift implemtation can be
+ selected with runtime flags.
- Note, that by default the seaice-package includes the orginial
+ \paragraph{Compatibility with ice-thermodynamics package \code{thsice}\label{sec:pkg:seaice:thsice}}~\\
+ %
+ Note, that by default the \code{seaice}-package includes the orginial
  so-called zero-layer thermodynamics following \citet{hib80} with a
  snow cover as in \citet{zha98a}. The zero-layer thermodynamic model
  assumes that ice does not store heat and, therefore, tends to
  exaggerate the seasonal variability in ice thickness.  This
  exaggeration can be significantly reduced by using
- \citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic model
+ \citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic
- 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
- thermodynamic model has been reformulated by \citet{win00}.  The
+ \citet{win00}.  The reformulation improves model physics by
- reformulation improves model physics by representing the brine content
+ representing the brine content of the upper ice with a variable heat
- of the upper ice with a variable heat capacity.  It also improves
+ capacity.  It also improves model numerics and consumes less computer
- model numerics and consumes less computer time and memory.  The Winton
+ time and memory.
- sea-ice thermodynamics have been ported to the MIT GCM; they currently
- reside under pkg/thsice. The package pkg/thsice is fully compatible
+ The Winton sea-ice thermodynamics have been ported to the MIT GCM;
- with pkg/seaice and with pkg/exf. When turned on together with
+ they currently reside under \code{pkg/thsice}.  The package
- pkg/seaice, the zero-layer thermodynamics are replaced by the Winton
+ \code{thsice} is described in section~\ref{sec:pkg:thsice}; it is
- thermodynamics.
+ fully compatible with the packages \code{seaice} and \code{exf}. When
+ turned on together with \code{seaice}, the zero-layer thermodynamics
+ are replaced by the Winton thermodynamics. In order to use the
+ \code{seaice}-package with the 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}. Note, that
+ once \code{thsice} is turned on, the variables and diagnostics
+ associated to the default thermodynamics are meaningless, and the
+ diagnostics of \code{thsice} have to be used instead.
+ \paragraph{Surface forcing\label{sec:pkg:seaice:surfaceforcing}}~\\
+ %
  The sea ice model requires the following input fields: 10-m winds, 2-m
  air temperature and specific humidity, downward longwave and shortwave
  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
  global: in ice-free regions bulk formulae are used to estimate oceanic
  forcing from the atmospheric fields.
- \paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}
+ \paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}~\\
+ %
  \newcommand{\vek}[1]{\ensuremath{\vec{\mathbf{#1}}}}
  \newcommand{\vtau}{\vek{\mathbf{\tau}}}
  The momentum equation of the sea-ice model is
-Line 271 
 air and ocean drag coefficients; $\rho_{
+Line 296 
 air and ocean drag coefficients; $\rho_{
  densities; and $R_{air/ocean}$ are rotation matrices that act on the
  wind/current vectors.
+ \paragraph{Viscous-Plastic (VP) Rheology and LSOR solver \label{sec:pkg:seaice:VPdynamics}}~\\
+ %
  For an isotropic system the stress tensor $\sigma_{ij}$ ($i,j=1,2$) can
  be related to the ice strain rate and strength by a nonlinear
  viscous-plastic (VP) constitutive law \citep{hib79, zhang97}:
-Line 322 
 recommended). For stress tensor computat
+Line 349 
 recommended). For stress tensor computat
  = 2\,\Delta\zeta$ \citep{hibler95} is used so that the stress state
  always lies on the elliptic yield curve by definition.
- 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 \code{\#define SEAICE\_ALLOW\_TEM} in
- \code{SEAICE\_OPTIONS.h} and turn it on with
- \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
  \citet{zhang97}, which allows for long time steps that, in our case,
-Line 344 
 limitation because it restricts the time
+Line 358 
 limitation because it restricts the time
  same length as in the ocean model where the Coriolis term is also
  treated explicitly.
+ \paragraph{Elastic-Viscous-Plastic (EVP) Dynamics\label{sec:pkg:seaice:EVPdynamics}}~\\
+ %
  \citet{hun97}'s introduced an elastic contribution to the strain
  rate in order to regularize Eq.~\ref{eq:vpequation} in such a way that
  the resulting elastic-viscous-plastic (EVP) and VP models are
-Line 361 
 identical at steady state,
+Line 377 
 identical at steady state,
  %used and compared the present sea-ice model study.
  The EVP-model uses an explicit time stepping scheme with a short
  timestep. According to the recommendation of \citet{hun97}, the
- EVP-model is stepped forward in time 120 times within the physical
+ EVP-model should be stepped forward in time 120 times
- ocean model time step (although this parameter is under debate), to
+ ($\code{SEAICE\_deltaTevp} = \code{SEAICIE\_deltaTdyn}/120$) within
- allow for elastic waves to disappear.  Because the scheme does not
+ the physical ocean model time step (although this parameter is under
- require a matrix inversion it is fast in spite of the small internal
+ debate), to allow for elastic waves to disappear.  Because the scheme
- timestep and simple to implement on parallel computers
+ does not require a matrix inversion it is fast in spite of the small
+ internal timestep and simple to implement on parallel computers
  \citep{hun97}. For completeness, we repeat the equations for the
  components of the stress tensor $\sigma_{1} =
  \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and
-Line 386 
 abbreviations, the equations~\ref{eq:evp
+Line 403 
 abbreviations, the equations~\ref{eq:evp
    \frac{\partial\sigma_{12}}{\partial{t}} + \frac{\sigma_{12} e^{2}}{2T}
    &= \frac{P}{4T\Delta} D_S
  \end{align}
- 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
- $T$ for elastic waves \[E=\frac{\zeta}{T}.\]
+ timescale $T$ for elastic waves \[E=\frac{\zeta}{T}.\]
- $T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and
+ $T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and the external
- the external (long) timestep $\Delta{t}$. \citet{hun97} recommend
+ (long) timestep $\Delta{t}$.  $E_{0} = \frac{1}{3}$ is the default
- $E_{0} = \frac{1}{3}$ (which is the default value in the code).
+ value in the code and close to what \citet{hun97} and
+ \citet{hun01} recommend.
  To use the EVP solver, make sure that both \code{SEAICE\_CGRID} and
  \code{SEAICE\_ALLOW\_EVP} are defined in \code{SEAICE\_OPTIONS.h}
-Line 405 
 the damping time scale $T$ accordingly,
+Line 423 
 the damping time scale $T$ accordingly,
  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly
  \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
+ \paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\
+ %
+ 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 \code{\#define SEAICE\_ALLOW\_TEM} in
+ \code{SEAICE\_OPTIONS.h} and turn it on with
+ \code{SEAICEuseTEM} in \code{data.seaice}.
+ \paragraph{Ice-Ocean stress \label{sec:pkg:seaice:iceoceanstress}}~\\
+ %
  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
  applied directly to the surface layer of the ocean model. An
-Line 434 
 To turn on the stress formulation of \ci
+Line 469 
 To turn on the stress formulation of \ci
  % $P$ at vorticity points.
  \paragraph{Finite-volume discretization of the stress tensor
-   divergence\label{sec:pkg:seaice:discretization}}
+   divergence\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 519 
 widths. For the $u$-equation ($\alpha=1$
+Line 555 
 widths. For the $u$-equation ($\alpha=1$
    \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
-Line 561 
 Similarly, we have for the $v$-equation
+Line 599 
 Similarly, we have for the $v$-equation
    \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}}
-Line 591 
 free slip boundary conditions the latera
+Line 631 
 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.
- \paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}
+ \paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}~\\
+ %
  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 646 
 principle) turns snow into ice until the
+Line 686 
 principle) turns snow into ice until the
  \code{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter
  \code{SEAICEuseFlooding=.true.}.
+ \paragraph{Advection of thermodynamic variables\label{sec:pkg:seaice:advection}}~\\
+ %
  Effective ice thickness (ice volume per unit area,
  $c\cdot{h}$), concentration $c$ and effective snow thickness
  ($c\cdot{h}_{s}$) are advected by ice velocities:
-Line 658 
 where $\Gamma_X$ are the thermodynamic s
+Line 700 
 where $\Gamma_X$ are the thermodynamic s
  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
+ recommend flux-limited schemes \citep[multidimensional 2nd and
- advection scheme with flux limiter][]{roe:85, hundsdorfer94} to
+rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94}
- preserve sharp gradients and edges that are typical of sea ice
+ 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),
+ $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the
- \code{DIFF1} (default=0.004).
+ historic 2nd-order, centered difference scheme), \code{DIFF1} =
+ $D_{X}/\Delta{x}$
- There is considerable doubt about the reliability of a ``zero-layer''
+ (default=0.004).
- thermodynamic model --- \citet{semtner84} found significant errors in
- phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in
+ The MITgcm sea ice model provides the option to use
- such models --- so that today many sea ice models employ more complex
+ the thermodynamics model of \citet{win00}, which in turn is based on
- thermodynamics. The MITgcm sea ice model provides the option to use
+ the 3-layer model of \citet{sem76} and which treats brine content by
- the thermodynamics model of \citet{win00}, which in turn is based
+ means of enthalpy conservation; the corresponding package
- on the 3-layer model of \citet{sem76} and which treats brine
+ \code{thsice} is described in section~\ref{sec:pkg:thsice}. This
- content by means of enthalpy conservation. This scheme requires
+ scheme requires additional state variables, namely the enthalpy of the
- additional state variables, namely the enthalpy of the two ice layers
+ two ice layers (instead of effective ice salinity), to be advected by
- (instead of effective ice salinity), to be advected by ice velocities.
+ ice velocities.
  %
  The internal sea ice temperature is inferred from ice enthalpy.  To
  avoid unphysical (negative) values for ice thickness and
  concentration, a positive 2nd-order advection scheme with a SuperBee
- flux limiter \citep{roe:85} is used in this study to advect all
+ flux limiter \citep{roe:85} should be used to advect all
- sea-ice-related quantities of the \citet{win00} thermodynamic
+ sea-ice-related quantities of the \citet{win00} thermodynamic model
- model.  Because of the non-linearity of the advection scheme, care
+ (runtime flag \code{thSIceAdvScheme=77} and
- must be taken in advecting these quantities: when simply using ice
+ \code{thSIce\_diffK}=$D_{X}$=0 in \code{data.ice}, defaults are 0).  Because of the
- velocity to advect enthalpy, the total energy (i.e., the volume
+ non-linearity of the advection scheme, care must be taken in advecting
- integral of enthalpy) is not conserved. Alternatively, one can advect
+ these quantities: when simply using ice velocity to advect enthalpy,
- 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
- false enthalpy extrema can occur, which then leads to unrealistic ice
+ conserved. Alternatively, one can advect the energy content (i.e.,
- temperature.  In the currently implemented solution, the sea-ice mass
+ product of ice-volume and enthalpy) but then false enthalpy extrema
- flux is used to advect the enthalpy in order to ensure conservation of
+ can occur, which then leads to unrealistic ice temperature.  In the
- enthalpy and to prevent false enthalpy extrema.
+ 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. %
  %----------------------------------------------------------------------
-Line 757 
 Diagnostics output is available via the
+Line 801 
 Diagnostics output is available via the
  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
-Line 816 
 Table \ref{tab:pkg:seaice:diagnostics}.
+Line 860 
 Table \ref{tab:pkg:seaice:diagnostics}.
  \label{sec:pkg:seaice:experiments}
  \begin{itemize}
- \item{Labrador Sea experiment in lab\_sea verification directory. }
+ \item{Labrador Sea experiment in \code{lab\_sea} verification directory. }
+ \item \code{seaice\_obcs}, based on \code{lab\_sea}
+ \item \code{offline\_exf\_seaice/input.seaicetd}, based on \code{lab\_sea}
+ \item \code{global\_ocean.cs32x15/input.icedyn} and
+   \code{global\_ocean.cs32x15/input.seaice}, global
+   cubed-sphere-experiment with combinations of \code{seaice} and
+   \code{thsice}
  \end{itemize}
  %%% Local Variables:
  %%% mode: latex
- %%% TeX-master: "../manual"
+ %%% TeX-master: "../../manual"
  %%% End:

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