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-revision 1.10 by mlosch,
Tue Mar  4 20:33:07 2008 UTC
+revision 1.17 by mlosch,
Wed Jun  4 13:32:05 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.
- results is from a yet smaller regional domain, which is used to illustrate
- treatment of sea ice open boundary condition sin the MITgcm.
  \subsection{Global Ocean and Sea Ice Simulation}
  \label{sec:global}
-Line 26 
 relatively even grid spacing throughout
+Line 24 
 relatively even grid spacing throughout
  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are
 vertical levels ranging in thickness from 10 m near the surface to
- approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the
+ approximately 450 m at a maximum model depth of 6150 m. The model employs the
- National Geophysical Data Center (NGDC) 2-minute gridded global relief data
+ partial-cell formulation of
- (ETOPO2) and the model employs the partial-cell formulation of
  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
- bathymetry. The model is integrated in a volume-conserving configuration using
+ bathymetry. Bathymetry is from the S2004 (Smith, unpublished) blend of the
+ \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one
+ arc-minute bathymetric grid (see Fig.~\ref{fig:CubeBathymetry}).
+ The model is integrated in a volume-conserving configuration using
  a finite volume discretization with C-grid staggering of the prognostic
  variables. In the ocean, the non-linear equation of state of \citet{jac95} is
  used.
+ \begin{figure}[h]
+   \centering
+   \includegraphics[width=\textwidth]{\fpath/CubeBathymetry}
+   \caption{Bathymetry of the global cubed sphere model configuration.  The
+     solid lines indicate domain boundaries for the regional Arctic
+     configuration discussed in Section~\ref{sec:arctic}.}
+   \label{fig:CubeBathymetry}
+ \end{figure}
  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 72 
 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 91 
 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 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,viewport=139 210 496 606,clip]{\fpath/topography}
-   Domain.\label{fig:arctic1}}
+ %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
- \end{figure}
+ %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
+ %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
+ \includegraphics*[width=\linewidth]{\fpath/topography}
+ \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: M'Clure Strait; %
+   F: Amundsen Gulf; %
+   G: Lancaster Sound; %
+   H: Barrow Strait \ml{W.}; %
+   I: Barrow Strait \ml{E.}; %
+   J: Barrow Strait \ml{N.}; %
+   K: Fram Strait. %
+   The sections A through F comprise the total inflow into the Canadian
+   Archipelago. \ml{[May still need to check the geography.]}
+   \label{fig:arctic_topog}}
+ \end{figure*}
+ The main dynamic difference from cube sphere is that the Arctic domain
+ configuration 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, 0.76, 0.94, and 0.8.
- The main dynamic difference from cube sphere is that it does not use
+ The model is integrated from Jan~01, 1992 to Mar~31, 2000,
- rescaled vertical coordinates (z$^\ast$) and the surface boundary
+ with three different dynamical solvers, two different boundary
- conditions for freshwater input are different, because those features
+ conditions, different stress coupling, rheology, and advection
- are not supported by the open boundary code.
+ schemes. \reftab{experiments} gives an overview over the experiments
+ discussed in this section.
- Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
+ \begin{table}[t]
-.76, 0.94, and 0.8.
+   \caption{Overview over model simulations in \refsec{arctic}.
+     \label{tab:experiments}}
- The model is integrated from January, 1992 to March \ml{[???]}, 2000,
+   \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
- with five different dynamical solvers:
+     experiment name & description \\ \hline
- \begin{description}
+     B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
- \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa
+   Arakawa B-grid, implying no-slip lateral boundary conditions
-   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
+     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
+     C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
-   conditions;
+   conditions \\
- \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
+     C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
-   no-slip lateral boundary conditions; and
+   no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
- \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
+\text{\,s}$ \\
-   boundary conditions.
+     C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
- \end{description}
+   no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+\text{\,s}$ \\
+     C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
+   to \citet{hibler87}\\
+     C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
+   rheology \citep{hibler97} \\
+     C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
+   \citet{winton00} \\
+     C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
+   direct-space-time advection scheme for thermodynamic variables
+   \citep{hundsdorfer94}
+   \end{tabular}
+ \end{table}
+ %\begin{description}
+ %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
+ %  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 (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
+ %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+ %  150\text{\,s}$;
+ %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
+ %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
+ %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
+ %  direct-space-time advection scheme \citep{hundsdorfer94};
+ %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
+ %  rheology \citep{hibler97};
+ %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
+ %  to \citet{hibler87};
+ %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
+ %  \citet{winton00};
+ %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
+ %%  scale noise \citep{hunke01};
+ %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
+ %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+ %  10\text{\,s}$.
+ %\end{description}
  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
  that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
  interpreted as pure model error. Lateral boundary conditions on a
- coarse grid (compared to the roughness of the true coast line) are
+ coarse grid (coarse compared to the roughness of the true coast line) are
  unclear, so that comparing the no-slip solutions to the free-slip
  solutions gives another measure of uncertainty in sea ice modeling.
+ The remaining experiments explore further sensitivities of the system
+ to different physics (change in rheology, advection and diffusion
+ properties, stress coupling, and thermodynamics) and different time
+ steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
+ for the EVP solution. We use two interpretations of this choice where
+ the EVP model is subcycled 120 times within a (short) model timestep
+ of 1200\,s resulting in a very long and expensive integration
+ ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
+ forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
  A principle difficulty in comparing the solutions obtained with
- different variants of the dynamics solver lies in the non-linear
+ different realizations of the model dynamics lies in the non-linear
  feedback of the ice dynamics and thermodynamics. Already after a few
  months the solutions have diverged so far from each other that
  comparing velocities only makes sense within the first 3~months of the
-Line 145 
 shown are the differences between B-grid
+Line 240 
 shown are the differences between B-grid
  no-slip and free-slip solution. The velocity field of the C-LSR-ns
  solution (\reffig{iceveloc}a) roughly resembles the drift velocities
  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
- models in an cyclonic circulation regime (CCR) \citep[their
+ models in a cyclonic circulation regime (CCR) \citep[their
  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
  shifted eastwards towards Alaska.
- The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
+ \newcommand{\subplotwidth}{0.44\textwidth}
- is most pronounced
+ %\newcommand{\subplotwidth}{0.3\textwidth}
- along the coastlines, where the discretization differs most between B
+ \begin{figure}[tp]
- and C-grids: On a B-grid the tangential velocity is on the boundary
- (and thus zero per the no-slip boundary conditions), whereas on the
- C-grid the its half a cell width away from the boundary, thus allowing
- more flow. The B-LSR-ns solution has less ice drift through the Fram
- Strait and especially the along Greenland's east coast; also, the flow
- through Baffin Bay and Davis Strait into the Labrador Sea is reduced
- with respect the C-LSR-ns solution. \ml{[Do we expect this? Say
-   something about that]}
- %
- 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
- faster in the C-LSR-fs solution, for example, along the east coast
- of Greenland, the north coast of Alaska, and the east Coast of Baffin
- Island.
- \begin{figure}[htbp]
    \centering
    \subfigure[{\footnotesize C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}
+   \\
    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
+ %  \\
+ %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
+ %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
+ %  \\
+ %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
+ %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
-     over the first 3 months of integration [cm/s]; (b)-(d) difference
+     over the first 3 months of integration [cm/s]; (b)-(h) difference
-     between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions
+     between solutions with B-grid, free lateral slip, EVP-solver,
-     [cm/s]; color indicates speed (or differences of speed), vectors
+     truncated ellipse method (TEM), different ice-ocean stress
-     indicate direction only.}
+     formulation (HB87), different thermodynamics (WTD), different
+     advection for thermodynamic variables (DST3FL) and the C-LSR-ns
+     reference solution [cm/s]; color indicates speed (or differences
+     of speed), vectors indicate direction only.}
    \label{fig:iceveloc}
  \end{figure}
+ \addtocounter{figure}{-1}
- The C-EVP-ns solution is very different from the C-LSR-ns solution
+ \setcounter{subfigure}{4}
- (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows
+ \begin{figure}[t]
- for increased drift by over 2\,cm/s in the Beaufort Gyre and the
+   \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
- transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
-   in the C-EVP-ns solution. [Really?]} In general, drift velocities are
+   \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
- biased towards higher values in the EVP solutions as can be seen from
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
- a histogram of the differences in \reffig{drifthist}.
+   \\
- \begin{figure}[htbp]
+   \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
-   \centering
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
-   \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}
+   \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
-   \caption{Histogram of drift velocity differences for C-LSR-ns and
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
-     C-EVP-ns solution [cm/s].}
+   \caption{continued}
-   \label{fig:drifthist}
  \end{figure}
+ The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
+ is most pronounced along the coastlines, where the discretization
+ differs most between B and C-grids: On a B-grid the tangential
+ velocity lies on the boundary (and is thus zero through the no-slip
+ boundary conditions), whereas on the C-grid it is half a cell width
+ away from the boundary, thus allowing more flow. The B-LSR-ns solution
+ has less ice drift through the Fram Strait and especially the along
+ Greenland's east coast; also, the flow through Baffin Bay and Davis
+ Strait into the Labrador Sea is reduced with respect the C-LSR-ns
+ solution.  \ml{[Do we expect this? Say something about that]}
+ %
+ 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
+ faster in the C-LSR-fs solution, for example, along the east coast
+ of Greenland, the north coast of Alaska, and the east Coast of Baffin
+ Island.
+ The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
+ very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
+ EVP-approximation of the VP-dynamics allows for increased drift by
+ over 2\,cm/s in the Beaufort Gyre and the transarctic drift.
+ %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns
+ %solution. [Really?, No]}
+ In general, drift velocities are biased towards higher values in the
+ EVP solutions.
+ % as can be seen from a histogram of the differences in
+ %\reffig{drifthist}.
+ %\begin{figure}[htbp]
+ %  \centering
+ %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
+ %  \caption{Histogram of drift velocity differences for C-LSR-ns and
+ %    C-EVP-ns solution [cm/s].}
+ %  \label{fig:drifthist}
+ %\end{figure}
+ Compared to the other parameters, the ice rheology TEM
+ (\reffig{iceveloc}(e)) has a very small effect on the solution. In
+ general the ice drift tends to be increased, because there is no
+ tensile stress and ice can be ``pulled appart'' at no cost.
+ Consequently, the largest effect on drift velocity can be observed
+ near the ice edge in the Labrador Sea. In contrast, in the run with
+ the ice-ocean stress formulation of \citet{hibler87},
+ \reffig{iceveloc}(f) the drift is stronger almost everywhere in the
+ computational domain. The increase is mostly aligned with the general
+ direction of the flow, implying that the different stress formulation
+ reduces the deceleration of drift by the ocean.
+ The 3-layer thermodynamics following \citet{winton00} requires
+ additional information on initial conditions for enthalphy. These
+ different initial conditions make a comparison of the first months
+ difficult to interpret. The drift in the Beaufort Gyre is slightly
+ reduced relative to the reference run C-LSR-ns, but the drift through
+ the Fram Strait is increased. The drift velocities near the ice edge
+ are very different, because the ice extend is already larger in
+ \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
+ drift velocities, because the ice motion is more contrained by a
+ larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
+ place is drifting nearly freely.
+ A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
+ \reffig{iceveloc}(h)) has its largest effect along the ice edge, where
+ the gradients of thickness and concentration are largest. Everywhere
+ else the effect is very small and can mostly be attributed to smaller
+ numerical diffusion (and to the absense of explicitly diffusion for
+ numerical stability).
  \reffig{icethick}a shows the effective thickness (volume per unit
  area) of the C-LSR-ns solution, averaged over January, February, March
  of year 2000. By this time of the integration, the differences in the
  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
+ concentrations (not shown).
-   example, AOMIP the ice thickness distribution blablabal} \ml{[What
+ \begin{figure}[tp]
-   can I say about effective thickness?]}
- \begin{figure}[htbp]
    \centering
    \subfigure[{\footnotesize C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
+   \\
    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
-   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
    \caption{(a) Effective thickness (volume per unit area) of the
      C-LSR-ns solution, averaged over the months Janurary through March
-[m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,
+[m]; (b)-(h) difference between solutions with B-grid, free
-     and C-LSR-ns solutions [cm/s].}
+     lateral slip, EVP-solver, truncated ellipse method (TEM),
+     different ice-ocean stress formulation (HB87), different
+     thermodynamics (WTD), different advection for thermodynamic
+     variables (DST3FL) and the C-LSR-ns reference solution [m].}
    \label{fig:icethick}
  \end{figure}
+ \addtocounter{figure}{-1}
+ \setcounter{subfigure}{4}
+ \begin{figure}[t]
+   \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
+   \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
+   \\
+   \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
+   \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
+   \caption{continued}
+ \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 409 
 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 upstream side of island groups and
- island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which
+ less ice in their lee, such as Franz-Josef-Land and
- \ml{\ldots [I find hard to interpret].}
+ Severnaya Semlya\ml{/or Nordland?},
+ 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
+ smaller differences to C-LSR-ns in the central Arctic than the
- the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
+ transition from the B-grid to the C-grid (\reffig{icethick}c), except
- still reduces the effective ice thickness by up to 2\,m where the ice
+ in the Canadian Archipelago. There it reduces the effective ice
- is thick and the straits are narrow. Everywhere else the ice volume is
+ thickness by 2\,m and more where the ice is thick and the straits are
+ narrow.  Dipoles of ice thickness 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
- part of the Arctic, where ice volumes are smaller, to the western
+ eastern part of the Arctic, where ice volumes are smaller, to the
- Arctic where ice piles up along the coast (\reffig{icethick}d). Within
+ western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,
- the Canadian Archipelago, more drift leads to faster ice export and
+ more drift leads to faster ice export and reduced effective ice
- reduced effective ice thickness.
+ thickness. With a shorter time step of
+ $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to
+ converge to the LSOR solution (not shown). Only in the narrow straits
+ in the Archipelago the ice thickness is not affected by the shorter
+ time step and the ice is still thinner by 2\,m and more, as in the EVP
+ solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
+ In year 2000, there more ice everywhere in the domain in
+ \mbox{C-LSR-ns WTD}, \reffig{icethick}(g). This difference, which is
+ even more pronounced in summer (not shown), can be attributed to
+ direct effects of the different thermodynamics in this run. The
+ remaining runs have the largest differences in effective ice thickness
+ long the north coasts of Greenland and Ellesmere Island. Although the
+ effects of TEM and \citet{hibler87}'s ice-ocean stress formulation are
+ so different on the initial ice velocities, both runs have similarly
+ reduced ice thicknesses in this area. The 3rd-order advection scheme
+ has an opposite effect of similar magnitude, point towards more
+ implicit lateral stress with this numerical scheme.
+ The observed difference of order 2\,m and less are smaller than the
+ differences that were observed between different hindcast models and climate
+ models in \citet{gerdes07}. There the range of sea ice volume of
+ different sea ice-ocean models (which shared very similar forcing
+ fields) was on the order of $10,000\text{km$^{3}$}$; this range was
+ even larger for coupled climate models. Here, the range (and the
+ averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
+ the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
+ leads to generally thicker ice (\reffig{icethick} and
+ \reftab{icevolume}).
+ \begin{table}[htbp]
+   \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
+     model run & ice volume
+     & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
+         km$^{3}$\,y$^{-1}$}$]}\\
+     & [$\text{km$^{3}$}$]
+     & \multicolumn{2}{c}{FS}
+     & \multicolumn{2}{c}{NI}
+     & \multicolumn{2}{c}{LS} \\ \hline
+     B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
+     C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
+     C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
+     C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
+     C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
+     C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
+     C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
+     C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
+     C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
+   \end{tabular}
+   \caption{Arctic ice volume averaged over Jan--Mar 2000, in
+     $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
+     period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
+     total northern inflow into the Canadian Archipelago (NI), and the
+     export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}
+   \label{tab:icevolume}
+ \end{table}
  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 by far the most exported ice drifts through the
- Strait, a considerable amoung of ice is exported through the Canadian
+ Fram 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}. Note, that ice transport estimates are associated
- Generally, the C-EVP-ns solution has highest maxiumum (export out of
+ with large uncertainties; also note that tuning an Arctic sea
- the Artic) and minimum (import into the Artic) fluxes as the drift
+ ice-ocean model to reproduce observations is not our goal, but we use
- velocities area largest in this solution \ldots
+ the published numbers as an orientation.
+ \reffig{archipelago} shows a time series of daily averaged, smoothed
+ with monthly running means, ice transports through various straits in
+ the Canadian Archipelago and the Fram Strait for the different model
+ solutions and \reftab{icevolume} summarizes the time series. The
+ export through Fram Strait agrees with the observations in all model
+ solutions (annual averages range from $2110$ to
+ $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
+ $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
+ time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
+ while the export through the Candian Archipelago is smaller than
+ generally thought. For example, the ice transport through Lancaster
+ Sound is lower (annual averages are $43$ to
+ $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
+ inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
+ a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
+ upstream in Barrow Strait in the 1970ies from satellite images.
+ Generally, the EVP solutions have the highest maximum (export out of
+ the Artic) and lowest minimum (import into the Artic) fluxes as the
+ drift velocities are largest in these solutions.  In the extreme of
+ the Nares Strait, which is only a few grid points wide in our
+ configuration, both B- and C-grid LSOR solvers lead to practically no
+ ice transport, while the C-EVP solutions allow up to
+ $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$
+ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
+ the Candian Archipelago is larger in all EVP solutions
+ %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
+ than in the LSOR solutions.
+ %get the order of magnitude right (range: $132$ to
+ %$165\text{\,km$^3$\,y$^{-1}$}$);
+ The B-LSR-ns solution is even smaller by another factor of two than the
+ C-LSR solutions (an exception is the WTD solution, where larger ice thickness
+ tends to block the transport).
+ %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
  \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}}}
+ \centerline{{\includegraphics[width=\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;
+   legend abbreviations are explained in \reftab{experiments}.
  \label{fig:archipelago}}
  \end{figure}
- \ml{[Transport to narrow straits, area?, more runs, TEM, advection
+ %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
-   schemes, Winton TD, discussion about differences in terms of model
+ %  schemes, Winton TD, discussion about differences in terms of model
-   error? that's tricky as it means refering to Tremblay, thus our ice
+ %  error? that's tricky as it means refering to Tremblay, thus our ice
-   models are all erroneous!]}
+ %  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 constrast to that, the differences between
  free-slip and no-slip solutions \emph{with the same solver} are
  considerably smaller (the difference for the EVP solver is not shown,
- but comparable to that for the LSOR solver)---albeit smaller, the
+ but similar to that for the LSOR solver). Albeit smaller, the
  differences between free and no-slip solutions in ice drift can lead
- to large differences in ice volume over integration time. At first,
+ to equally large differences in ice volume, especially in the Canadian
- this observation appears counterintuitive, as we expect that the
+ Archipelago over the integration time. At first, this observation
- solution \emph{technique} should not affect the \emph{solution} to a
+ seems counterintuitive, as we expect that the solution
- lower degree than actually modifying the equations. A more detailed
+ \emph{technique} should not affect the \emph{solution} to a higher
- study on these differences is beyond the scope of this paper, but at
+ degree than actually modifying the equations. A more detailed study on
- this point we may speculate, that the large difference between B-grid,
+ these differences is beyond the scope of this paper, but at this point
- C-grid, LSOR, and EVP solutions stem from incomplete convergence of
+ we may speculate, that the large difference between B-grid, C-grid,
- the solvers due to linearization \citep[and Bruno Tremblay, personal
+ LSOR, and EVP solutions stem from incomplete convergence of the
+ 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
  thus leading to different solutions for the ice drift velocities. If
- this were true, this tantalizing circumstance had a dramatic impact on
+ this were true, this tantalizing circumstance would have a dramatic
- sea-ice modeling in general, and we would need to improve the solution
+ impact on sea-ice modeling in general, and we would need to improve
- technique of dynamic sea ice model, most likely at a very high
+ the solution techniques for dynamic sea ice models, most likely at a very
- compuational cost (Bruno Tremblay, personal communication).
+ high compuational cost (Bruno Tremblay, personal communication). Further,
+ we observe that the EVP solutions tends to produce effectively
+ ``weaker'' ice that yields more easily to stress. The fast response to
+ changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
- \begin{itemize}
+ where the EVP model adjusts quickly to a cyclonic wind pattern, while
- \item Configuration
+ the LSOR solution does not. This property of the EVP solutions allows
- \item OBCS from cube
+ larger ice transports through narrow straits, where the implicit
- \item forcing
+ solver LSOR forms rigid ice. The underlying reasons for this striking
- \item 1/2 and full resolution
+ difference need further exploration.
- \item with a few JFM figs from C-grid LSR no slip
-   ice transport through Canadian Archipelago
+ % THIS is now almost all in the text:
-   thickness distribution
+ %\begin{itemize}
-   ice velocity and transport
+ %\item Configuration
- \end{itemize}
+ %\item OBCS from cube
+ %\item forcing
- \begin{itemize}
+ %\item 1/2 and full resolution
- \item Arctic configuration
+ %\item with a few JFM figs from C-grid LSR no slip
- \item ice transport through straits and near boundaries
+ %  ice transport through Canadian Archipelago
- \item focus on narrow straits in the Canadian Archipelago
+ %  thickness distribution
- \end{itemize}
+ %  ice velocity and transport
+ %\end{itemize}
- \begin{itemize}
- \item B-grid LSR no-slip: B-LSR-ns
+ %\begin{itemize}
- \item C-grid LSR no-slip: C-LSR-ns
+ %\item Arctic configuration
- \item C-grid LSR slip:    C-LSR-fs
+ %\item ice transport through straits and near boundaries
- \item C-grid EVP no-slip: C-EVP-ns
+ %\item focus on narrow straits in the Canadian Archipelago
- \item C-grid EVP slip:    C-EVP-fs
+ %\end{itemize}
- \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
-   new flag): C-LSR-ns+TEM
+ %\begin{itemize}
- \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
+ %\item B-grid LSR no-slip: B-LSR-ns
- \item C-grid LSR no-slip + Winton:
+ %\item C-grid LSR no-slip: C-LSR-ns
- \item  speed-performance-accuracy (small)
+ %\item C-grid LSR slip:    C-LSR-fs
-   ice transport through Canadian Archipelago differences
+ %\item C-grid EVP no-slip: C-EVP-ns
-   thickness distribution differences
+ %\item C-grid EVP slip:    C-EVP-fs
-   ice velocity and transport differences
+ %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
- \end{itemize}
+ %  new flag): C-LSR-ns+TEM
+ %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
- We anticipate small differences between the different models due to:
+ %\item C-grid LSR no-slip + Winton:
- \begin{itemize}
+ %\item  speed-performance-accuracy (small)
- \item advection schemes: along the ice-edge and regions with large
+ %  ice transport through Canadian Archipelago differences
-   gradients
+ %  thickness distribution differences
- \item C-grid: less transport through narrow straits for no slip
+ %  ice velocity and transport differences
-   conditons, more for free slip
+ %\end{itemize}
- \item VP vs.\ EVP: speed performance, accuracy?
- \item ocean stress: different water mass properties beneath the ice
+ %We anticipate small differences between the different models due to:
- \end{itemize}
+ %\begin{itemize}
+ %\item advection schemes: along the ice-edge and regions with large
- %\begin{figure}
+ %  gradients
- %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
+ %\item C-grid: less transport through narrow straits for no slip
- %\caption{Surface sea ice velocity for different solver flavors.
+ %  conditons, more for free slip
- %\label{fig:iceveloc}}
+ %\item VP vs.\ EVP: speed performance, accuracy?
- %\end{figure}
+ %\item ocean stress: different water mass properties beneath the ice
+ %\end{itemize}
- %\begin{figure}
- %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
- %\caption{Sea ice thickness for different solver flavors.
- %\label{fig:icethick}}
- %\end{figure}
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