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

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-revision 1.15 by mlosch,
Mon Feb 28 16:27:56 2011 UTC
+revision 1.16 by mlosch,
Wed Mar  2 13:46:38 2011 UTC
 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 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 244 
 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 283 
 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 334 
 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 356 
 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 373 
 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 398 
 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 417 
 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 446 
 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 607 
 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 662 
 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 681 
 distributions and to rule out unphysical
+Line 707 
 distributions and to rule out unphysical
  (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, is the
- historic 2nd-order, centered difference scheme), \code{DIFF1}
+ historic 2nd-order, centered difference scheme), \code{DIFF1} =
+ $D_{X}/\Delta{x}$
  (default=0.004).
- There is considerable doubt about the reliability of a ``zero-layer''
+ The MITgcm sea ice model provides the option to use
- thermodynamic model --- \citet{semtner84} found significant errors in
- phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in
- such models --- so that today many sea ice models employ more complex
- thermodynamics. The MITgcm sea ice model provides the option to use
  the thermodynamics model of \citet{win00}, which in turn is based on
  the 3-layer model of \citet{sem76} and which treats brine content by
  means of enthalpy conservation; the corresponding package
-Line 700 
 ice velocities.
+Line 723 
 ice velocities.
  The internal sea ice temperature is inferred from ice enthalpy.  To
  avoid unphysical (negative) values for ice thickness and
  concentration, a positive 2nd-order advection scheme with a SuperBee
- flux limiter \citep{roe:85} is used in this study to advect all
+ flux limiter \citep{roe:85} should be used to advect all
- sea-ice-related quantities of the \citet{win00} thermodynamic model.
+ sea-ice-related quantities of the \citet{win00} thermodynamic model
- Because of the non-linearity of the advection scheme, care must be
+ (runtime flag \code{thSIceAdvScheme=77} and
- taken in advecting these quantities: when simply using ice velocity to
+ \code{thSIce\_diffK}=$D_{X}$=0 in \code{data.ice}, defaults are 0).  Because of the
- advect enthalpy, the total energy (i.e., the volume integral of
+ non-linearity of the advection scheme, care must be taken in advecting
- enthalpy) is not conserved. Alternatively, one can advect the energy
+ these quantities: when simply using ice velocity to advect enthalpy,
- content (i.e., product of ice-volume and enthalpy) but then false
+ the total energy (i.e., the volume integral of enthalpy) is not
- 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
- In order to use the \code{seaice}-package with the more sophisticated
+ advect the enthalpy in order to ensure conservation of enthalpy and to
- thermodynamics of \code{thsice}, compile both packages and turn both
+ prevent false enthalpy extrema. %
- package on in \code{data.pkg}; see an example in
- \code{global\_ocean.cs32x15/input.icedyn}.
  %----------------------------------------------------------------------
-Line 839 
 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}

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