/[MITgcm]/MITgcm_contrib/articles/ceaice/ceaice_forward.tex

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-revision 1.10 by mlosch,
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+revision 1.13 by mlosch,
Fri Mar 14 23:05:34 2008 UTC
 Line 6 
 ice simulations that exercise various ca
  model.  The first set of results is from a global, eddy-permitting, ocean and
  sea ice configuration.  The second set of results is from a regional Arctic
  configuration, which is used to compare the B-grid and C-grid dynamic solvers
- and various other capabilities of the MITgcm sea ice model.  The third set of
+ and various other capabilities of the MITgcm sea ice model.
+ %
+ \ml{[do we really want to do this?:] The third set of
  results is from a yet smaller regional domain, which is used to illustrate
- treatment of sea ice open boundary condition sin the MITgcm.
+ treatment of sea ice open boundary condition in the MITgcm.}
  \subsection{Global Ocean and Sea Ice Simulation}
  \label{sec:global}
-Line 37 
 used.
+Line 39 
 used.
  The ocean model is coupled to the sea-ice model discussed in
  \refsec{model} using the following specific options.  The
- zero-heat-capacity thermodynamics formulation of \citet{hibler80} is used to
+ zero-heat-capacity thermodynamics formulation of \citet{hibler80} is
- compute sea ice thickness and concentration.  Snow cover and sea ice salinity
+ used to compute sea ice thickness and concentration.  Snow cover and
- are prognostic.  Open water, dry ice, wet ice, dry snow, and wet snow albedo
+ sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry
- are, respectively, 0.15, 0.88, 0.79, 0.97, and 0.83. Ice mechanics follow the
+ snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,
- viscous plastic rheology of \citet{hibler79} and the ice momentum equation is
+ and 0.83. Ice mechanics follow the viscous plastic rheology of
- solved numerically using the C-grid implementation of the \citet{zhang97} LSR
+ \citet{hibler79} and the ice momentum equation is solved numerically
- dynamics model discussed hereinabove.  The ice is coupled to the ocean using
+ using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
- the rescaled vertical coordinate system, z$^\ast$, of
+ model discussed hereinabove.  The ice is coupled to the ocean using
- \citet{cam08}, that is, sea ice does not float above the ocean model but
+ the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
- rather deforms the ocean's model surface level.
+ that is, sea ice does not float above the ocean model but rather
+ deforms the ocean's model surface level.
  This particular ECCO2 simulation is initialized from temperature and salinity
  fields derived from the Polar science center Hydrographic Climatology (PHC)
-Line 62 
 radiations, and precipitation are conver
+Line 65 
 radiations, and precipitation are conver
  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
  radiation decays exponentially as per \citet{pau77}.  Low frequency
  precipitation has been adjusted using the pentad (5-day) data from the Global
- Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river
+ Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river
  run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
  where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
  and prepared by P. Winsor (personnal communication, 2007) is specificied.
-Line 81 
 advection scheme \citep{dar04} is employ
+Line 84 
 advection scheme \citep{dar04} is employ
  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
  the divergent flow as per \citet{kem08}.
+ \ml{[Dimitris, here you need to either provide figures, so that I can
+   write text, or you can provide both figures and text. I guess, one
+   figure, showing the northern and southern hemisphere in summer and
+   winter is fine (four panels), as we are showing so many figures in
+   the next section.]}
  \subsection{Arctic Domain with Open Boundaries}
  \label{sec:arctic}
- A series of forward sensitivity experiments have been carried out on an
+ A series of forward sensitivity experiments have been carried out on
- Arctic Ocean domain with open boundaries.  The objective is to compare the old
+ an Arctic Ocean domain with open boundaries.  The objective is to
- B-grid LSR dynamic solver with the new C-grid LSR and EVP solvers.  One
+ compare the old B-grid LSR dynamic solver with the new C-grid LSR and
- additional experiment is carried out to illustrate the differences between the
+ EVP solvers.  Additional experiments are is carried out to illustrate
- two main options for sea ice thermodynamics in the MITgcm.
+ the differences between different ice advection schemes, ocean-ice
+ stress formulations and the two main options for sea ice
- The Arctic domain of integration is illustrated in \reffig{arctic1}.  It
+ thermodynamics in the MITgcm.
- is carved out from, and obtains open boundary conditions from, the global
- cubed-sphere configuration described above.  The horizontal domain size is
+ The Arctic domain of integration is illustrated in
-by 384 grid boxes.
+ \reffig{arctic_topog}.  It is carved out from, and obtains open
+ boundary conditions from, the global cubed-sphere configuration
- \begin{figure}
+ described above.  The horizontal domain size is 420 by 384 grid boxes.
- \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}
+ \begin{figure*}
- \caption{Bathymetry and domain boudaries of Arctic
+ \includegraphics*[width=0.44\linewidth]{\fpath/topography}
-   Domain.\label{fig:arctic1}}
+ \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
- \end{figure}
+ \caption{Left: Bathymetry and domain boudaries of Arctic
+   Domain; the dashed line marks the boundaries of the inset on the
+   right hand side. The letters in the inset label sections in the
+   Canadian Archipelago, where ice transport is evaluated:
+   A: Nares Strait; %
+   B: \ml{Meighen Island}; %
+   C: Prince Gustaf Adolf Sea; %
+   D: \ml{Brock Island}; %
+   E: McClure Strait; %
+   F: Amundsen Gulf; %
+   G: Lancaster Sound; %
+   H: Barrow Strait \ml{W.}; %
+   I: Barrow Strait \ml{E.}; %
+   J: Barrow Strait \ml{N.}. %
+   \label{fig:arctic_topog}}
+ \end{figure*}
  The main dynamic difference from cube sphere is that it does not use
  rescaled vertical coordinates (z$^\ast$) and the surface boundary
  conditions for freshwater input are different, because those features
  are not supported by the open boundary code.
- Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
+ Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
-.76, 0.94, and 0.8.
+ respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
  The model is integrated from January, 1992 to March \ml{[???]}, 2000,
- with five different dynamical solvers:
+ with three different dynamical solvers and two different boundary
+ conditions:
  \begin{description}
- \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa
+ \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
-   B-grid, implying no-slip lateral boundary conditions;
+   Arakawa B-grid, implying no-slip lateral boundary conditions
+   ($\vek{u}=0$ exactly);
  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
-   boundary conditions;
+   boundary conditions (implemented via ghost-points);
  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
    conditions;
  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
-Line 150 
 Figure\,6]{martin07} with a Beaufort Gyr
+Line 177 
 Figure\,6]{martin07} with a Beaufort Gyr
  shifted eastwards towards Alaska.
  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
- is most pronounced
+ is most pronounced along the coastlines, where the discretization
- along the coastlines, where the discretization differs most between B
+ differs most between B and C-grids: On a B-grid the tangential
- and C-grids: On a B-grid the tangential velocity is on the boundary
+ velocity lies on the boundary (and thus zero per the no-slip boundary
- (and thus zero per the no-slip boundary conditions), whereas on the
+ conditions), whereas on the C-grid the its half a cell width away from
- C-grid the its half a cell width away from the boundary, thus allowing
+ the boundary, thus allowing more flow. The B-LSR-ns solution has less
- more flow. The B-LSR-ns solution has less ice drift through the Fram
+ ice drift through the Fram Strait and especially the along Greenland's
- Strait and especially the along Greenland's east coast; also, the flow
+ east coast; also, the flow through Baffin Bay and Davis Strait into
- through Baffin Bay and Davis Strait into the Labrador Sea is reduced
+ the Labrador Sea is reduced with respect the C-LSR-ns solution.
- with respect the C-LSR-ns solution. \ml{[Do we expect this? Say
+ \ml{[Do we expect this? Say something about that]}
-   something about that]}
  %
- Compared to the differences between B and C-grid solutions the
+ Compared to the differences between B and C-grid solutions,the
  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
  (\reffig{iceveloc}c).  As expected the differences are largest along
  coastlines: because of the free-slip boundary conditions, flow is
-Line 207 
 of year 2000. By this time of the integr
+Line 233 
 of year 2000. By this time of the integr
  ice drift velocities have led to the evolution of very different ice
  thickness distributions, which are shown in \reffig{icethick}b--d, and
  area distributions (not shown).  \ml{Compared to other solutions, for
-   example, AOMIP the ice thickness distribution blablabal} \ml{[What
+   example, AOMIP the ice thickness distribution blablabal}
-   can I say about effective thickness?]}
  \begin{figure}[htbp]
    \centering
    \subfigure[{\footnotesize C-LSR-ns}]
-Line 225 
 area distributions (not shown).  \ml{Com
+Line 250 
 area distributions (not shown).  \ml{Com
      and C-LSR-ns solutions [cm/s].}
    \label{fig:icethick}
  \end{figure}
+ %
  The generally weaker ice drift velocities in the B-LSR-ns solution,
  when compared to the C-LSR-ns solution, in particular through the
  narrow passages in the Canadian Archipelago, lead to a larger build-up
-Line 235 
 the ice volume in not larger everywhere:
+Line 260 
 the ice volume in not larger everywhere:
  patches of smaller ice volume in the B-grid solution, most likely
  because the Beaufort Gyre is weaker and hence not as effective in
  transporting ice westwards. There are also dipoles of ice volume
- differences on the \ml{luv [what is this in English?]} and the lee of
+ differences with more ice on the \ml{luv [what is this in English?,
- island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which
+   upstream]} and less ice in the the lee of island groups, such as
- \ml{\ldots [I find hard to interpret].}
+ Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along
+ coasts less easily in the B-LSR-ns solution.
  Imposing a free-slip boundary condition in C-LSR-fs leads to a much
  smaller differences to C-LSR-ns than the transition from the B-grid to
  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
  still reduces the effective ice thickness by up to 2\,m where the ice
- is thick and the straits are narrow. Everywhere else the ice volume is
+ is thick and the straits are narrow. Dipoles of ice thickness
- affected only slightly by the different boundary condition.
+ differences can also be observed around islands, because the free-slip
+ solution allows more flow around islands than the no-slip solution.
+ Everywhere else the ice volume is affected only slightly by the
+ different boundary condition.
  %
- The C-EVP-ns solution has generally stronger drift velocities then the
+ The C-EVP-ns solution has generally stronger drift velocities than the
- C-LSR-ns solution. Consequently, more ice can be moved the eastern
+ C-LSR-ns solution. Consequently, more ice can be moved from the eastern
  part of the Arctic, where ice volumes are smaller, to the western
  Arctic where ice piles up along the coast (\reffig{icethick}d). Within
  the Canadian Archipelago, more drift leads to faster ice export and
-Line 255 
 reduced effective ice thickness.
+Line 284 
 reduced effective ice thickness.
  The difference in ice volume and ice drift velocities between the
  different experiments has consequences for the ice transport out of
- the Arctic. Although the main export of ice goes through the Fram
+ the Arctic. Although the most exported ice drifts through the Fram
- Strait, a considerable amoung of ice is exported through the Canadian
+ Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
- Archipelago \citep{???}. \reffig{archipelago} shows a time series of
+ considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
- daily averages ice transport through various straits in the Canadian
+ exported through the Canadian Archipelago \citep[and references
- Archipelago and the Fram Strait for the different model solutions.
+ therein]{serreze06}.  \reffig{archipelago} shows a time series of
- Generally, the C-EVP-ns solution has highest maxiumum (export out of
+ \ml{[maybe smooth to different time scales:] daily averaged, smoothed
- the Artic) and minimum (import into the Artic) fluxes as the drift
+   with monthly running means,} ice transports through various straits
- velocities area largest in this solution \ldots
+ in the Canadian Archipelago and the Fram Strait for the different
+ model solutions. The export through Fram Strait is too high in all
+ model (annual averages ranges from $3324$ to
+ $3931\text{\,km$^3$\,y$^{-1}$}$) solutions, while the export through
+ Lancaster Sound is lower (annual averages are $41$ to
+ $201\text{\,km$^3$\,y$^{-1}$}$) than compared to observations.
+ Generally, the C-EVP solutions have highest maximum (export out of the
+ Artic) and minimum (import into the Artic) fluxes as the drift
+ velocities are largest in this solution. In the extreme, both B- and
+ C-grid LSOR solvers have practically no ice transport through the
+ Nares Strait, which is only a few grid points wide, while the C-EVP
+ solutions allow up to 500\,km$^3$\,y$^{-1}$ in summer.
  \begin{figure}
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
- \caption{Transport through Canadian Archipelago for different solver flavors.
+ \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
+ \caption{Transport through Canadian Archipelago for different solver
+   flavors. The letters refer to the labels of the sections in
+   \reffig{arctic_topog}; positive values are flux out of the Arctic.
  \label{fig:archipelago}}
  \end{figure}
-Line 275 
 velocities area largest in this solution
+Line 318 
 velocities area largest in this solution
    models are all erroneous!]}
  In summary, we find that different dynamical solvers can yield very
- different solutions. Compared to that the differences between
+ different solutions. In contrast, the differences between free-slip
- free-slip and no-slip solutions \emph{with the same solver} are
+ and no-slip solutions \emph{with the same solver} are considerably
- considerably smaller (the difference for the EVP solver is not shown,
+ smaller (the difference for the EVP solver is not shown, but similar
- but comparable to that for the LSOR solver)---albeit smaller, the
+ to that for the LSOR solver). Albeit smaller, the differences between
- differences between free and no-slip solutions in ice drift can lead
+ free and no-slip solutions in ice drift can lead to large differences
- to large differences in ice volume over integration time. At first,
+ in ice volume over the integration time. At first, this observation
- this observation appears counterintuitive, as we expect that the
+ seems counterintuitive, as we expect that the solution
- solution \emph{technique} should not affect the \emph{solution} to a
+ \emph{technique} should not affect the \emph{solution} to a higher
- lower degree than actually modifying the equations. A more detailed
+ degree than actually modifying the equations. A more detailed study on
- study on these differences is beyond the scope of this paper, but at
+ these differences is beyond the scope of this paper, but at this point
- this point we may speculate, that the large difference between B-grid,
+ we may speculate, that the large difference between B-grid, C-grid,
- C-grid, LSOR, and EVP solutions stem from incomplete convergence of
+ LSOR, and EVP solutions stem from incomplete convergence of the
- the solvers due to linearization \citep[and Bruno Tremblay, personal
+ solvers due to linearization and due to different methods of
+ linearization \citep[and Bruno Tremblay, personal
  communication]{hunke01}: if the convergence of the non-linear momentum
  equations is not complete for all linearized solvers, then one can
  imagine that each solver stops at a different point in velocity-space

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