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-revision 1.16 by dimitri,
Wed Jun  4 00:39:25 2008 UTC
+revision 1.19 by mlosch,
Fri Jul  4 11:51:09 2008 UTC
 Line 1
- \section{Forward sensitivity experiments}
+ \section{Forward Sensitivity Experiments in an Arctic Domain with Open
+ Boundaries}
  \label{sec:forward}
- This section presents results from global and regional coupled ocean and sea
+ This section presents results from regional coupled ocean and sea
- ice simulations that exercise various capabilities of the MITgcm sea ice
+ ice simulations of the Arctic Ocean that exercise various capabilities of the MITgcm sea ice
- model.  The first set of results is from a global, eddy-permitting, ocean and
+ model.
- sea ice configuration.  The second set of results is from a regional Arctic
+ The objective is to
- configuration, which is used to compare the B-grid and C-grid dynamic solvers
+ compare the old B-grid LSOR dynamic solver with the new C-grid LSOR and
- and various other capabilities of the MITgcm sea ice model.
+ EVP solvers. Additional experiments are carried out to illustrate
+ the differences between different ice advection schemes, ocean-ice
- \subsection{Global Ocean and Sea Ice Simulation}
+ stress formulations and the two main options for sea ice
- \label{sec:global}
+ thermodynamics in the MITgcm.
- The global ocean and sea ice results presented below were carried out as part
+ \subsection{Model configuration and experiments}
+ \label{sec:arcticmodel}
+ The Arctic model domain is illustrated in \reffig{arctic_topog}.
+ \begin{figure*}
+ %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
+ %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
+ %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
+ %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
+ \includegraphics*[width=\linewidth]{\fpath/topography}
+ \caption{Left: Bathymetry and domain boundaries 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*}
+ It has 420 by 384 grid boxes and is carved out, and obtains open
+ boundary conditions from, a global cubed-sphere configuration
+ similar to that described in \citet{menemenlis05}.
+ \ml{[Some of this could be part of the introduction?]}%
+ The global ocean and sea ice results presented in \citet{menemenlis05}
+ were carried out as part
  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
  project.  ECCO2 aims to produce increasingly accurate syntheses of all
  available global-scale ocean and sea-ice data at resolutions that start to
  resolve ocean eddies and other narrow current systems, which transport heat,
  carbon, and other properties within the ocean \citep{menemenlis05}.  The
- particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)
+ particular ECCO2 simulation from which we obtain the boundary
+ conditions is a baseline 28-year (1979-2006)
  integration, labeled cube76, which has not yet been constrained by oceanic and
- by sea ice data.  A cube-sphere grid projection is employed, which permits
+ by sea ice data. A cube-sphere grid projection is employed, which permits
  relatively even grid spacing throughout the domain and which avoids polar
  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
+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. The model employs the
  partial-cell formulation of
  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
- bathymetry. Bathymetry is from the S2004 (Smith, unpublished) blend of the
+ bathymetry. Bathymetry is from the S2004 (W.~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}).
+ 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]
+ The global ocean model is coupled to a sea ice model in a
-   \centering
+ configuration similar to the case C-LSR-ns (see \reftab{experiments}),
-   \includegraphics[width=\textwidth]{\fpath/CubeBathymetry}
+ with open water, dry ice, wet ice, dry snow, and wet snow albedos of,
-   \caption{Bathymetry of the global cubed sphere model configuration.  The
+ respectively, 0.15, 0.88, 0.79, 0.97, and 0.83.
-     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 compute sea ice thickness and concentration.  Snow cover and
- sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry
- snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,
- and 0.83. Ice mechanics follow the viscous plastic rheology of
- \citet{hibler79} and the ice momentum equation is solved numerically
- using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
- model discussed hereinabove.  The ice is coupled to the ocean using
- the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
- 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 72 
 radiations, and precipitation are conver
+Line 91 
 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 \citep[GPCP][]{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 91 
 advection scheme \citep{dar04} is employ
+Line 110 
 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
+ The model configuration of cube76 carries over to the Arctic domain
-   write text, or you can provide both figures and text. I guess, one
+ configuration except for numerical details related to the non-linear
-   figure, showing the northern and southern hemisphere in summer and
+ free surface that are not supported by the open boundary code, and the
-   winter is fine (four panels), as we are showing so many figures in
+ albedos of open water, dry ice, wet ice, dry snow, and wet snow, which
-   the next section.]}
+ are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
+ The model is integrated from Jan~01, 1992 to Mar~31, 2000.
- \subsection{Arctic Domain with Open Boundaries}
+ \reftab{experiments} gives an overview over the experiments discussed
- \label{sec:arctic}
+ in \refsec{arcticresults}.
+ \begin{table}
- A series of forward sensitivity experiments have been carried out on
+   \caption{Overview over model simulations in \refsec{arcticresults}.
- an Arctic Ocean domain with open boundaries.  The objective is to
+     \label{tab:experiments}}
- compare the old B-grid LSR dynamic solver with the new C-grid LSR and
- EVP solvers.  Additional experiments are carried out to illustrate
- the differences between different ice advection schemes, ocean-ice
- stress formulations and the two main options for sea ice
- thermodynamics in the MITgcm.
- The Arctic domain of integration is illustrated in
- \reffig{arctic_topog}.  It is carved out from, and obtains open
- boundary conditions from, the global cubed-sphere configuration
- described above.  The horizontal domain size is 420 by 384 grid boxes.
- \begin{figure*}
- %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
- %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
- \includegraphics*[width=0.44\linewidth]{\fpath/topography}
- \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
- \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.}. %
-   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 model is integrated from Jan~01, 1992 to Mar~31, 2000,
- with three different dynamical solvers, two different boundary
- conditions, different stress coupling, rheology, and advection
- schemes. \reftab{experiments} gives an overview over the experiments
- discussed in this section.
- \begin{table}[htbp]
    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
      experiment name & description \\ \hline
      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) \\
+   ($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order
+   central difference scheme plus explicit diffusion for stability \\
      C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
    boundary conditions (implemented via ghost-points) \\
      C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
-Line 177 
 discussed in this section.
+Line 148 
 discussed in this section.
    direct-space-time advection scheme for thermodynamic variables
    \citep{hundsdorfer94}
    \end{tabular}
-   \caption{Overview over model simulations in \refsec{arctic}.
-     \label{tab:experiments}}
  \end{table}
  %\begin{description}
  %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
-Line 220 
 steps for the EVP solutions: \citet{hunk
+Line 189 
 steps for the EVP solutions: \citet{hunk
  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
+ ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 144 times within the
  forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
- A principle difficulty in comparing the solutions obtained with
+ \subsection{Results}
- different realizations of the model dynamics lies in the non-linear
+ \label{sec:arcticresults}
- feedback of the ice dynamics and thermodynamics. Already after a few
- months the solutions have diverged so far from each other that
+ Comparing the solutions obtained with different realizations of the
- comparing velocities only makes sense within the first 3~months of the
+ model dynamics is difficult because of 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
  integration while the ice distribution is still close to the initial
  conditions. At the end of the integration, the differences between the
  model solutions can be interpreted as cumulated model uncertainties.
+ \subsubsection{Ice velocities in JFM 1992}
  \reffig{iceveloc} shows ice velocities averaged over Janunary,
  February, and March (JFM) of 1992 for the C-LSR-ns solution; also
- shown are the differences between B-grid and C-grid, LSR and EVP, and
+ shown are the differences between this reference solution and various
- no-slip and free-slip solution. The velocity field of the C-LSR-ns
+ sensitivity experiments. 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 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 along the coastlines, where the discretization
+ %\newcommand{\subplotwidth}{0.3\textwidth}
- differs most between B and C-grids: On a B-grid the tangential
+ \begin{figure}[tp]
- 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.
- %\newcommand{\subplotwidth}{0.44\textwidth}
- \newcommand{\subplotwidth}{0.3\textwidth}
- \begin{figure}[htbp]
    \centering
    \subfigure[{\footnotesize C-LSR-ns}]
    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
-Line 273 
 Island.
+Line 229 
 Island.
    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
-   \\
+ %  \\
-   \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
+ %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
-   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
-   \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
+ %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
-   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
-   \\
+ %  \\
-   \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
+ %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
-   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
+ %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
-   \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
+ %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
-   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-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)-(h) difference
      between solutions with B-grid, free lateral slip, EVP-solver,
-Line 293 
 Island.
+Line 249 
 Island.
      of speed), vectors indicate direction only.}
    \label{fig:iceveloc}
  \end{figure}
+ \addtocounter{figure}{-1}
+ \setcounter{subfigure}{4}
+ \begin{figure}[t]
+   \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{continued}
+ \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 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
-Line 312 
 EVP solutions.
+Line 300 
 EVP solutions.
  %  \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, the drift is
+ stronger almost everywhere in the computational domain in the run with
+ the ice-ocean stress formulation of \citet{hibler87}
+ (\reffig{iceveloc}f). 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
+ geographical position is nearly in free drift.
+ 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 explicit diffusion for
+ numerical stability).
+ \subsubsection{Ice volume during JFM 2000}
  \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
+ thickness distributions, which are shown in \reffig{icethick}b--h, and
  concentrations (not shown).
- \begin{figure}[htbp]
+ \begin{figure}[tp]
    \centering
    \subfigure[{\footnotesize C-LSR-ns}]
    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
-Line 329 
 concentrations (not shown).
+Line 350 
 concentrations (not shown).
    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
    {\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)-(h) difference between solutions with B-grid, free
+     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}]
-Line 339 
 concentrations (not shown).
+Line 371 
 concentrations (not shown).
    {\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{(a) Effective thickness (volume per unit area) of the
+   \caption{continued}
-     C-LSR-ns solution, averaged over the months Janurary through March
-[m]; (b)-(d) difference between solutions with B-grid, free
-     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}
- %
  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 364 
 Severnaya Semlya\ml{/or Nordland?},
+Line 388 
 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
+ Imposing a free-slip boundary condition in C-LSR-fs leads to much
  smaller differences to C-LSR-ns in the central Arctic than the
  transition from the B-grid to the C-grid (\reffig{icethick}c), except
  in the Canadian Archipelago. There it reduces the effective ice
  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
+ 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 than the
-Line 386 
 in the Archipelago the ice thickness is
+Line 410 
 in the Archipelago the ice thickness is
  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 is more ice everywhere in the domain in
+ 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, pointing 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 and climate
+ 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
-Line 423 
 leads to generally thicker ice (\reffig{
+Line 459 
 leads to generally thicker ice (\reffig{
    \label{tab:icevolume}
  \end{table}
+ \subsubsection{Ice transports}
  The difference in ice volume and ice drift velocities between the
  different experiments has consequences for the ice transport out of
  the Arctic. Although by far the most exported ice drifts through the
-Line 434 
 with large uncertainties; also note that
+Line 472 
 with large uncertainties; also note that
  ice-ocean model to reproduce observations is not our goal, but we use
  the published numbers as an orientation.
- \reffig{archipelago} shows a time series of daily averaged, smoothed
+ \reffig{archipelago} shows an excerpt of a time series of daily
- with monthly running means, ice transports through various straits in
+ averaged ice transports, smoothed with a monthly running mean, through
- the Canadian Archipelago and the Fram Strait for the different model
+ various straits in the Canadian Archipelago and the Fram Strait for
- solutions and \reftab{icevolume} summarizes the time series. The
+ the different model solutions; \reftab{icevolume} summarizes the
- export through Fram Strait agrees with the observations in all model
+ time series.
- solutions (annual averages range from $2110$ to
+ \begin{figure}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
+ %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
+ \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
+ \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}. The mean
+   range of the different model solution is taken over the period Jan
+to Dec 1999.
+ \label{fig:archipelago}}
+ \end{figure}
+ 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}$}$),
-Line 456 
 drift velocities are largest in these so
+Line 508 
 drift velocities are largest in these so
  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 $300$
+ $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
- to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
+ report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
- the Candian Archipelago is larger in all EVP solutions
+ 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
-Line 467 
 The B-LSR-ns solution is even smaller by
+Line 519 
 The B-LSR-ns solution is even smaller by
  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/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
  %  schemes, Winton TD, discussion about differences in terms of model
  %  error? that's tricky as it means refering to Tremblay, thus our ice
  %  models are all erroneous!]}
+ \subsubsection{Discussion}
  In summary, we find that different dynamical solvers can yield very
  different solutions. In constrast to that, the differences between
  free-slip and no-slip solutions \emph{with the same solver} are
-Line 506 
 thus leading to different solutions for
+Line 550 
 thus leading to different solutions for
  this were true, this tantalizing circumstance would have a dramatic
  impact on sea-ice modeling in general, and we would need to improve
  the solution techniques for dynamic sea ice models, most likely at a very
- high compuational cost (Bruno Tremblay, personal communication). Further,
+ high compuational cost (Bruno Tremblay, personal communication).
- we observe that the EVP solutions tends to produce effectively
- ``weaker'' ice that yields more easily to stress. The fast response to
+ Further, we observe that the EVP solutions tends to produce
- changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
+ effectively ``weaker'' ice that yields more easily to stress. This was
- where the EVP model adjusts quickly to a cyclonic wind pattern, while
+ also observed by \citet{hunke99} in a fast response to changing winds,
- the LSOR solution does not. This property of the EVP solutions allows
+ their Figures\,10--12, where the EVP model adjusts quickly to a
- larger ice transports through narrow straits, where the implicit
+ cyclonic wind pattern, while the LSOR solution lags in time. This
- solver LSOR forms rigid ice. The underlying reasons for this striking
+ property of the EVP solutions allows larger ice transports through
- difference need further exploration.
+ narrow straits, where the implicit solver LSOR forms rigid ice. The
+ underlying reasons for this striking difference need further
+ exploration.
  % THIS is now almost all in the text:
  %\begin{itemize}

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