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revision 1.11 by mlosch, Sat Mar 8 20:40:47 2008 UTC revision 1.20 by mlosch, Sat Jul 5 10:39:16 2008 UTC
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1  \section{Forward sensitivity experiments}  \section{Forward Sensitivity Experiments in an Arctic Domain with Open
2    Boundaries}
3  \label{sec:forward}  \label{sec:forward}
4    
5  This section presents results from global and regional coupled ocean and sea  This section presents results from regional coupled ocean and sea
6  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
7  model.  The first set of results is from a global, eddy-permitting, ocean and  model.
8  sea ice configuration.  The second set of results is from a regional Arctic  The objective is to
9  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
10  and various other capabilities of the MITgcm sea ice model.    EVP solvers. Additional experiments are carried out to illustrate
11  %  the differences between different ice advection schemes, ocean-ice
12  \ml{[do we really want to do this?:] The third set of  stress formulations and the two main options for sea ice
13  results is from a yet smaller regional domain, which is used to illustrate  thermodynamics in the MITgcm.
 treatment of sea ice open boundary condition in the MITgcm.}  
   
 \subsection{Global Ocean and Sea Ice Simulation}  
 \label{sec:global}  
14    
15  The global ocean and sea ice results presented below were carried out as part  \subsection{Model configuration and experiments}
16    \label{sec:arcticmodel}
17    The Arctic model domain is illustrated in \reffig{arctic_topog}.
18    \begin{figure*}
19    %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
20    %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
21    %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
22    %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
23    \includegraphics*[width=\linewidth]{\fpath/topography}
24    \caption{Left: Bathymetry and domain boundaries of Arctic
25      Domain.
26      %; the dashed line marks the boundaries of the inset on the right hand side.
27      The letters in the inset label sections in the
28      Canadian Archipelago, where ice transport is evaluated:
29      A: Nares Strait; %
30      B: \ml{Meighen Island}; %
31      C: Prince Gustaf Adolf Sea; %
32      D: \ml{Brock Island}; %
33      E: M'Clure Strait; %
34      F: Amundsen Gulf; %
35      G: Lancaster Sound; %
36      H: Barrow Strait \ml{W.}; %
37      I: Barrow Strait \ml{E.}; %
38      J: Barrow Strait \ml{N.}; %
39      K: Fram Strait. %
40      The sections A through F comprise the total inflow into the Canadian
41      Archipelago. \ml{[May still need to check the geography.]}
42      \label{fig:arctic_topog}}
43    \end{figure*}
44    It has 420 by 384 grid boxes and is carved out, and obtains open
45    boundary conditions from, a global cubed-sphere configuration
46    similar to that described in \citet{menemenlis05}.
47    
48    \ml{[Some of this could be part of the introduction?]}%
49    The global ocean and sea ice results presented in \citet{menemenlis05}
50    were carried out as part
51  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
52  project.  ECCO2 aims to produce increasingly accurate syntheses of all  project.  ECCO2 aims to produce increasingly accurate syntheses of all
53  available global-scale ocean and sea-ice data at resolutions that start to  available global-scale ocean and sea-ice data at resolutions that start to
54  resolve ocean eddies and other narrow current systems, which transport heat,  resolve ocean eddies and other narrow current systems, which transport heat,
55  carbon, and other properties within the ocean \citep{menemenlis05}.  The  carbon, and other properties within the ocean \citep{menemenlis05}.  The
56  particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)  particular ECCO2 simulation from which we obtain the boundary
57    conditions is a baseline 28-year (1979-2006)
58  integration, labeled cube76, which has not yet been constrained by oceanic and  integration, labeled cube76, which has not yet been constrained by oceanic and
59  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
60  relatively even grid spacing throughout the domain and which avoids polar  relatively even grid spacing throughout the domain and which avoids polar
61  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
62  510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are  510 by 510 grid cells for a mean horizontal grid spacing of 18\,km. There are
63  50 vertical levels ranging in thickness from 10 m near the surface to  50 vertical levels ranging in thickness from 10 m near the surface to
64  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
65  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  
66  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
67  bathymetry. The model is integrated in a volume-conserving configuration using  bathymetry. Bathymetry is from the S2004 (W.~Smith, unpublished) blend of the
68    \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one
69    arc-minute bathymetric grid. % (see Fig.~\ref{fig:CubeBathymetry}).
70    The model is integrated in a volume-conserving configuration using
71  a finite volume discretization with C-grid staggering of the prognostic  a finite volume discretization with C-grid staggering of the prognostic
72  variables. In the ocean, the non-linear equation of state of \citet{jac95} is  variables. In the ocean, the non-linear equation of state of \citet{jac95} is
73  used.  used.
74    %
75  The ocean model is coupled to the sea-ice model discussed in  The global ocean model is coupled to a sea ice model in a
76  \refsec{model} using the following specific options.  The  configuration similar to the case C-LSR-ns (see \reftab{experiments}),
77  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is  with open water, dry ice, wet ice, dry snow, and wet snow albedos of,
78  used to compute sea ice thickness and concentration.  Snow cover and  respectively, 0.15, 0.88, 0.79, 0.97, and 0.83.
 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.  
79    
80  This particular ECCO2 simulation is initialized from temperature and salinity  This particular ECCO2 simulation is initialized from temperature and salinity
81  fields derived from the Polar science center Hydrographic Climatology (PHC)  fields derived from the Polar science center Hydrographic Climatology (PHC)
# Line 65  radiations, and precipitation are conver Line 91  radiations, and precipitation are conver
91  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
92  radiation decays exponentially as per \citet{pau77}.  Low frequency  radiation decays exponentially as per \citet{pau77}.  Low frequency
93  precipitation has been adjusted using the pentad (5-day) data from the Global  precipitation has been adjusted using the pentad (5-day) data from the Global
94  Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river  Precipitation Climatology Project \citep[GPCP,][]{huf01}.  The time-mean river
95  run-off from \citet{lar01} is applied globally, except in the Arctic Ocean  run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
96  where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)  where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
97  and prepared by P. Winsor (personnal communication, 2007) is specificied.  and prepared by P. Winsor (personnal communication, 2007) is specificied.
# Line 84  advection scheme \citep{dar04} is employ Line 110  advection scheme \citep{dar04} is employ
110  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
111  the divergent flow as per \citet{kem08}.  the divergent flow as per \citet{kem08}.
112    
113  \ml{[Dimitris, here you need to either provide figures, so that I can  The model configuration of cube76 carries over to the Arctic domain
114    write text, or you can provide both figures and text. I guess, one  configuration except for numerical details related to the non-linear
115    figure, showing the northern and southern hemisphere in summer and  free surface that are not supported by the open boundary code, and the
116    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
117    the next section.]}  are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
118    
119    The model is integrated from Jan~01, 1992 to Mar~31, 2000.
120  \subsection{Arctic Domain with Open Boundaries}  \reftab{experiments} gives an overview over the experiments discussed
121  \label{sec:arctic}  in \refsec{arcticresults}.
122    \begin{table}
123  A series of forward sensitivity experiments have been carried out on    \caption{Overview over model simulations in \refsec{arcticresults}.
124  an Arctic Ocean domain with open boundaries.  The objective is to      \label{tab:experiments}}
125  compare the old B-grid LSR dynamic solver with the new C-grid LSR and    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
126  EVP solvers.  Additional experiments are is carried out to illustrate      experiment name & description \\ \hline
127  the differences between different ice advection schemes, ocean-ice      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
 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}  
 \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}  
 \caption{Bathymetry and domain boudaries of Arctic  
   Domain. The letters label sections in the Canadian Archipelago,  
   where ice transport is evaluated.  
   \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,  
 0.76, 0.94, and 0.8.  
   
 The model is integrated from January, 1992 to March \ml{[???]}, 2000,  
 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  
128    Arakawa B-grid, implying no-slip lateral boundary conditions    Arakawa B-grid, implying no-slip lateral boundary conditions
129    ($\vek{u}=0$ exactly);    ($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order
130  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral    central difference scheme plus explicit diffusion for stability \\
131    boundary conditions (implemented via ghost-points);      C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
132  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary    boundary conditions (implemented via ghost-points) \\
133    conditions;      C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
134  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with    conditions \\
135    no-slip lateral boundary conditions; and      C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
136  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
137    boundary conditions.    150\text{\,s}$ \\
138  \end{description}      C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
139      no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
140      10\text{\,s}$ \\
141        C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
142      to \citet{hibler87}\\
143        C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
144      rheology \citep{hibler97} \\
145        C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
146      \citet{winton00} \\
147        C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
148      direct-space-time advection scheme for thermodynamic variables
149      \citep{hundsdorfer94}
150      \end{tabular}
151    \end{table}
152    %\begin{description}
153    %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
154    %  Arakawa B-grid, implying no-slip lateral boundary conditions
155    %  ($\vek{u}=0$ exactly);
156    %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
157    %  boundary conditions (implemented via ghost-points);
158    %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
159    %  conditions;
160    %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
161    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
162    %  150\text{\,s}$;
163    %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
164    %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
165    %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
166    %  direct-space-time advection scheme \citep{hundsdorfer94};
167    %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
168    %  rheology \citep{hibler97};
169    %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
170    %  to \citet{hibler87};
171    %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
172    %  \citet{winton00};
173    %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
174    %%  scale noise \citep{hunke01};
175    %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
176    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
177    %  10\text{\,s}$.
178    %\end{description}
179  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
180  that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be  that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
181  interpreted as pure model error. Lateral boundary conditions on a  interpreted as pure model error. Lateral boundary conditions on a
182  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
183  unclear, so that comparing the no-slip solutions to the free-slip  unclear, so that comparing the no-slip solutions to the free-slip
184  solutions gives another measure of uncertainty in sea ice modeling.  solutions gives another measure of uncertainty in sea ice modeling.
185    The remaining experiments explore further sensitivities of the system
186  A principle difficulty in comparing the solutions obtained with  to different physics (change in rheology, advection and diffusion
187  different variants of the dynamics solver lies in the non-linear  properties, stress coupling, and thermodynamics) and different time
188  feedback of the ice dynamics and thermodynamics. Already after a few  steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
189  months the solutions have diverged so far from each other that  for the EVP solution. We use two interpretations of this choice where
190  comparing velocities only makes sense within the first 3~months of the  the EVP model is subcycled 120 times within a (short) model timestep
191    of 1200\,s resulting in a very long and expensive integration
192    ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 144 times within the
193    forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
194    
195    \subsection{Results}
196    \label{sec:arcticresults}
197    
198    Comparing the solutions obtained with different realizations of the
199    model dynamics is difficult because of the non-linear feedback of the
200    ice dynamics and thermodynamics. Already after a few months the
201    solutions have diverged so far from each other that comparing
202    velocities only makes sense within the first 3~months of the
203  integration while the ice distribution is still close to the initial  integration while the ice distribution is still close to the initial
204  conditions. At the end of the integration, the differences between the  conditions. At the end of the integration, the differences between the
205  model solutions can be interpreted as cumulated model uncertainties.  model solutions can be interpreted as cumulated model uncertainties.
206    
207    \subsubsection{Ice velocities in JFM 1992}
208    
209  \reffig{iceveloc} shows ice velocities averaged over Janunary,  \reffig{iceveloc} shows ice velocities averaged over Janunary,
210  February, and March (JFM) of 1992 for the C-LSR-ns solution; also  February, and March (JFM) of 1992 for the C-LSR-ns solution; also
211  shown are the differences between B-grid and C-grid, LSR and EVP, and  shown are the differences between this reference solution and various
212  no-slip and free-slip solution. The velocity field of the C-LSR-ns  sensitivity experiments. The velocity field of the C-LSR-ns
213  solution (\reffig{iceveloc}a) roughly resembles the drift velocities  solution (\reffig{iceveloc}a) roughly resembles the drift velocities
214  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
215  models in an cyclonic circulation regime (CCR) \citep[their  models in a cyclonic circulation regime (CCR) \citep[their
216  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
217  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
218    %
219    \newcommand{\subplotwidth}{0.47\textwidth}
220    %\newcommand{\subplotwidth}{0.3\textwidth}
221    \begin{figure}[tp]
222      \centering
223      \subfigure[{\footnotesize C-LSR-ns}]
224      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-ns}}
225      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
226      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_B-LSR-ns-C-LSR-ns}}
227      \\
228      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
229      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-fs-C-LSR-ns}}
230      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
231      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-EVP-ns150-C-LSR-ns}}
232    %  \\
233    %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
234    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
235    %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
236    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
237    %  \\
238    %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
239    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
240    %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
241    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
242      \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
243        over the first 3 months of integration [cm/s]; (b)-(h) difference
244        between solutions with B-grid, free lateral slip, EVP-solver,
245        truncated ellipse method (TEM), different ice-ocean stress
246        formulation (HB87), different thermodynamics (WTD), different
247        advection for thermodynamic variables (DST3FL) and the C-LSR-ns
248        reference solution [cm/s]; color indicates speed (or differences
249        of speed), vectors indicate direction only.}
250      \label{fig:iceveloc}
251    \end{figure}
252    \addtocounter{figure}{-1}
253    \setcounter{subfigure}{4}
254    \begin{figure}[tp]
255      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
256      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
257      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
258      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
259      \\
260      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
261      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
262      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
263      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
264      \caption{continued}
265    \end{figure}
266    
267  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
268  is most pronounced along the coastlines, where the discretization  is most pronounced along the coastlines, where the discretization
269  differs most between B and C-grids: On a B-grid the tangential  differs most between B and C-grids: On a B-grid the tangential
270  velocity lies on the boundary (and thus zero per the no-slip boundary  velocity lies on the boundary (and is thus zero through the no-slip
271  conditions), whereas on the C-grid the its half a cell width away from  boundary conditions), whereas on the C-grid it is half a cell width
272  the boundary, thus allowing more flow. The B-LSR-ns solution has less  away from the boundary, thus allowing more flow. The B-LSR-ns solution
273  ice drift through the Fram Strait and especially the along Greenland's  has less ice drift through the Fram Strait and along
274  east coast; also, the flow through Baffin Bay and Davis Strait into  Greenland's east coast; also, the flow through Baffin Bay and Davis
275  the Labrador Sea is reduced with respect the C-LSR-ns solution.  Strait into the Labrador Sea is reduced with respect the C-LSR-ns
276  \ml{[Do we expect this? Say something about that]}  solution.  \ml{[Do we expect this? Say something about that]}
277  %  %
278  Compared to the differences between B and C-grid solutions,the  Compared to the differences between B and C-grid solutions, the
279  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
280  (\reffig{iceveloc}c).  As expected the differences are largest along  (\reffig{iceveloc}c).  As expected the differences are largest along
281  coastlines: because of the free-slip boundary conditions, flow is  coastlines: because of the free-slip boundary conditions, flow is
282  faster in the C-LSR-fs solution, for example, along the east coast  faster in the C-LSR-fs solution, for example, along the east coast
283  of Greenland, the north coast of Alaska, and the east Coast of Baffin  of Greenland, the north coast of Alaska, and the east Coast of Baffin
284  Island.  Island.
 \begin{figure}[htbp]  
   \centering  
   \subfigure[{\footnotesize C-LSR-ns}]  
   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}  
   \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]  
   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\  
   \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]  
   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}  
   \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]  
   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}  
   \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged  
     over the first 3 months of integration [cm/s]; (b)-(d) difference  
     between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions  
     [cm/s]; color indicates speed (or differences of speed), vectors  
     indicate direction only.}  
   \label{fig:iceveloc}  
 \end{figure}  
285    
286  The C-EVP-ns solution is very different from the C-LSR-ns solution  The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
287  (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
288  for increased drift by over 2\,cm/s in the Beaufort Gyre and the  EVP-approximation of the VP-dynamics allows for increased drift by up
289  transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska  to 8\,cm/s in the Beaufort Gyre and the transarctic drift.  In
290    in the C-EVP-ns solution. [Really?]} In general, drift velocities are  general, drift velocities are strongly biased towards higher values in
291  biased towards higher values in the EVP solutions as can be seen from  the EVP solutions.
292  a histogram of the differences in \reffig{drifthist}.  
293  \begin{figure}[htbp]  Compared to the other parameters, the ice rheology TEM
294    \centering  (\reffig{iceveloc}e) has a very small effect on the solution. In
295    \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}  general the ice drift tends to be increased, because there is no
296    \caption{Histogram of drift velocity differences for C-LSR-ns and  tensile stress and ice can be ``pulled appart'' at no cost.
297      C-EVP-ns solution [cm/s].}  Consequently, the largest effect on drift velocity can be observed
298    \label{fig:drifthist}  near the ice edge in the Labrador Sea. In contrast, the drift is
299  \end{figure}  stronger almost everywhere in the computational domain in the run with
300    the ice-ocean stress formulation of \citet{hibler87}
301    (\reffig{iceveloc}f). The increase is mostly aligned with the general
302    direction of the flow, implying that the different stress formulation
303    reduces the deceleration of drift by the ocean.
304    
305    The 3-layer thermodynamics following \citet{winton00} requires
306    additional information on initial conditions for enthalphy. These
307    different initial conditions make a comparison of the first months
308    difficult to interpret. The drift in the Beaufort Gyre is slightly
309    reduced relative to the reference run C-LSR-ns, but the drift through
310    the Fram Strait is increased. The drift velocities near the ice edge
311    are very different, because the ice extend is already larger in
312    \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
313    drift velocities, because the ice motion is more contrained by a
314    larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
315    geographical position is nearly in free drift.
316    
317    A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
318    \reffig{iceveloc}h) has some effect along the ice edge, where
319    the gradients of thickness and concentration are largest. Everywhere
320    else the effect is very small and can mostly be attributed to smaller
321    numerical diffusion (and to the absense of explicit diffusion that is
322    requird for numerical stability in a simple second order central
323    differences scheme).
324    
325    \subsubsection{Ice volume during JFM 2000}
326    
327  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
328  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
329  of year 2000. By this time of the integration, the differences in the  of year 2000. By this time of the integration, the differences in the
330  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
331  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--h, and
332  area distributions (not shown).  \ml{Compared to other solutions, for  concentrations (not shown).
333    example, AOMIP the ice thickness distribution blablabal}  \begin{figure}[tp]
 \begin{figure}[htbp]  
334    \centering    \centering
335    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
336    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
337    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
338    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
339      \\
340    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
341    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
342    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
343    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
344    \caption{(a) Effective thickness (volume per unit area) of the    \caption{(a) Effective thickness (volume per unit area) of the
345      C-LSR-ns solution, averaged over the months Janurary through March      C-LSR-ns solution, averaged over the months Janurary through March
346      2000 [m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,      2000 [m]; (b)-(h) difference between solutions with B-grid, free
347      and C-LSR-ns solutions [cm/s].}      lateral slip, EVP-solver, truncated ellipse method (TEM),
348        different ice-ocean stress formulation (HB87), different
349        thermodynamics (WTD), different advection for thermodynamic
350        variables (DST3FL) and the C-LSR-ns reference solution [m].}
351    \label{fig:icethick}    \label{fig:icethick}
352  \end{figure}  \end{figure}
353  %  \addtocounter{figure}{-1}
354    \setcounter{subfigure}{4}
355    \begin{figure}[tp]
356      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
357      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
358      \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
359      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
360      \\
361      \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
362      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
363      \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
364      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
365      \caption{continued}
366    \end{figure}
367  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
368  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
369  narrow passages in the Canadian Archipelago, lead to a larger build-up  narrow passages in the Canadian Archipelago, lead to a larger build-up
# Line 248  the ice volume in not larger everywhere: Line 373  the ice volume in not larger everywhere:
373  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
374  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
375  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
376  differences with more ice on the \ml{luv [what is this in English?,  differences with more ice on the upstream side of island groups and
377    upstream]} and less ice in the the lee of island groups, such as  less ice in their lee, such as Franz-Josef-Land and
378  Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along  Severnaya Semlya\ml{/or Nordland?},
379  coasts less easily in the B-LSR-ns solution.  because ice tends to flow along coasts less easily in the B-LSR-ns
380    solution.
381  Imposing a free-slip boundary condition in C-LSR-fs leads to a much  
382  smaller differences to C-LSR-ns than the transition from the B-grid to  Imposing a free-slip boundary condition in C-LSR-fs leads to much
383  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it  smaller differences to C-LSR-ns in the central Arctic than the
384  still reduces the effective ice thickness by up to 2\,m where the ice  transition from the B-grid to the C-grid (\reffig{icethick}c), except
385  is thick and the straits are narrow. Dipoles of ice thickness  in the Canadian Archipelago. There it reduces the effective ice
386  differences can also be observed around islands, because the free-slip  thickness by 2\,m and more where the ice is thick and the straits are
387  solution allows more flow around islands than the no-slip solution.  narrow.  Dipoles of ice thickness differences can also be observed
388  Everywhere else the ice volume is affected only slightly by the  around islands, because the free-slip solution allows more flow around
389  different boundary condition.  islands than the no-slip solution. Everywhere else the ice volume is
390    affected only slightly by the different boundary condition.
391  %  %
392  The C-EVP-ns solution has generally stronger drift velocities than the  The C-EVP-ns solution has much thicker ice in the central Arctic Ocean
393  C-LSR-ns solution. Consequently, more ice can be moved from the eastern  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).
394  part of the Arctic, where ice volumes are smaller, to the western  Within the Canadian Archipelago, more drift leads to faster ice export
395  Arctic where ice piles up along the coast (\reffig{icethick}d). Within  and reduced effective ice thickness. With a shorter time step of
396  the Canadian Archipelago, more drift leads to faster ice export and  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to
397  reduced effective ice thickness.  the LSOR solution (not shown). Only in the narrow straits in the
398    Archipelago the ice thickness is not affected by the shorter time step
399    and the ice is still thinner by 2\,m and more, as in the EVP solution
400    with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
401    
402    In year 2000, there is more ice everywhere in the domain in
403    C-LSR-ns~WTD (\reffig{icethick}g, note the color scale).
404    This difference, which is even more pronounced in summer (not shown),
405    can be attributed to direct effects of the different thermodynamics in
406    this run. The remaining runs have the largest differences in effective
407    ice thickness long the north coasts of Greenland and Ellesmere Island.
408    Although the effects of TEM and \citet{hibler87}'s ice-ocean stress
409    formulation are so different on the initial ice velocities, both runs
410    have similarly reduced ice thicknesses in this area. The 3rd-order
411    advection scheme has an opposite effect of similar magnitude, pointing
412    towards more implicit lateral stress with this numerical scheme.
413    
414    The observed difference of order 2\,m and less are smaller than the
415    differences that were observed between different hindcast models and climate
416    models in \citet{gerdes07}. There the range of sea ice volume of
417    different sea ice-ocean models (which shared very similar forcing
418    fields) was on the order of $10,000\text{km$^{3}$}$; this range was
419    even larger for coupled climate models. Here, the range (and the
420    averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
421    the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
422    leads to generally thicker ice (\reffig{icethick} and
423    \reftab{icevolume}).
424    \begin{table}[t]
425      \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
426        model run & ice volume
427        & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
428            km$^{3}$\,y$^{-1}$}$]}\\
429        & [$\text{km$^{3}$}$]
430        & \multicolumn{2}{c}{FS}
431        & \multicolumn{2}{c}{NI}
432        & \multicolumn{2}{c}{LS} \\ \hline
433        B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
434        C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
435        C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
436        C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
437        C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
438        C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
439        C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
440        C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
441        C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
442      \end{tabular}
443      \caption{Arctic ice volume averaged over Jan--Mar 2000, in
444        $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
445        period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
446        total northern inflow into the Canadian Archipelago (NI), and the
447        export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.
448      \label{tab:icevolume}}
449    \end{table}
450    
451    \subsubsection{Ice transports}
452    
453  The difference in ice volume and ice drift velocities between the  The difference in ice volume and ice drift velocities between the
454  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
455  the Arctic. Although the main export of ice goes through the Fram  the Arctic. Although by far the most exported ice drifts through the
456  Strait, a considerable amoung of ice is exported through the Canadian  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
457  Archipelago \citep{???}. \reffig{archipelago} shows a time series of  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
458  \ml{[maybe smooth to longer time scales:] daily averaged} ice  exported through the Canadian Archipelago \citep[and references
459  transport through various straits in the Canadian Archipelago and the  therein]{serreze06}. Note, that ice transport estimates are associated
460  Fram Strait for the different model solutions.  Generally, the  with large uncertainties; also note that tuning an Arctic sea
461  C-EVP-ns solution has highest maximum (export out of the Artic) and  ice-ocean model to reproduce observations is not our goal, but we use
462  minimum (import into the Artic) fluxes as the drift velocities are  the published numbers as an orientation.
463  largest in this solution \ldots  
464    \reffig{archipelago} shows an excerpt of a time series of daily
465    averaged ice transports, smoothed with a monthly running mean, through
466    various straits in the Canadian Archipelago and the Fram Strait for
467    the different model solutions; \reftab{icevolume} summarizes the
468    time series.
469  \begin{figure}  \begin{figure}
470  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
471    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
472    %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
473    \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
474  \caption{Transport through Canadian Archipelago for different solver  \caption{Transport through Canadian Archipelago for different solver
475    flavors. The letters refer to the labels of the sections in    flavors. The letters refer to the labels of the sections in
476    \reffig{arctic_topog}.    \reffig{arctic_topog}; positive values are flux out of the Arctic;
477      legend abbreviations are explained in \reftab{experiments}. The mean
478      range of the different model solution is taken over the period Jan
479      1992 to Dec 1999.
480  \label{fig:archipelago}}  \label{fig:archipelago}}
481  \end{figure}  \end{figure}
482    The export through Fram Strait agrees with the observations in all
483    model solutions (annual averages range from $2110$ to
484    $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
485    $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
486    time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
487    while the export through the Candian Archipelago is smaller than
488    generally thought. For example, the ice transport through Lancaster
489    Sound is lower (annual averages are $43$ to
490    $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
491    inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
492    a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
493    upstream in Barrow Strait in the 1970ies from satellite images.
494    Generally, the EVP solutions have the highest maximum (export out of
495    the Artic) and lowest minimum (import into the Artic) fluxes as the
496    drift velocities are largest in these solutions.  In the extreme of
497    the Nares Strait, which is only a few grid points wide in our
498    configuration, both B- and C-grid LSOR solvers lead to practically no
499    ice transport, while the C-EVP solutions allow up to
500    $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
501    report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
502    the import into the Candian Archipelago is larger in all EVP solutions
503    %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
504    than in the LSOR solutions.
505    %get the order of magnitude right (range: $132$ to
506    %$165\text{\,km$^3$\,y$^{-1}$}$);
507    The B-LSR-ns solution is even smaller by another factor of two than the
508    C-LSR solutions (an exception is the WTD solution, where larger ice thickness
509    tends to block the transport).
510    %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
511    
512    %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
513    %  schemes, Winton TD, discussion about differences in terms of model
514    %  error? that's tricky as it means refering to Tremblay, thus our ice
515    %  models are all erroneous!]}
516    
517  \ml{[Transport to narrow straits, area?, more runs, TEM, advection  \subsubsection{Discussion}
   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!]}  
518    
519  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
520  different solutions. In contrast, the differences between free-slip  different solutions. In constrast to that, the differences between
521  and no-slip solutions \emph{with the same solver} are considerably  free-slip and no-slip solutions \emph{with the same solver} are
522  smaller (the difference for the EVP solver is not shown, but similar  considerably smaller (the difference for the EVP solver is not shown,
523  to that for the LSOR solver). Albeit smaller, the differences between  but similar to that for the LSOR solver). Albeit smaller, the
524  free and no-slip solutions in ice drift can lead to large differences  differences between free and no-slip solutions in ice drift can lead
525  in ice volume over the integration time. At first, this observation  to equally large differences in ice volume, especially in the Canadian
526    Archipelago over the integration time. At first, this observation
527  seems counterintuitive, as we expect that the solution  seems counterintuitive, as we expect that the solution
528  \emph{technique} should not affect the \emph{solution} to a higher  \emph{technique} should not affect the \emph{solution} to a higher
529  degree than actually modifying the equations. A more detailed study on  degree than actually modifying the equations. A more detailed study on
# Line 313  communication]{hunke01}: if the converge Line 536  communication]{hunke01}: if the converge
536  equations is not complete for all linearized solvers, then one can  equations is not complete for all linearized solvers, then one can
537  imagine that each solver stops at a different point in velocity-space  imagine that each solver stops at a different point in velocity-space
538  thus leading to different solutions for the ice drift velocities. If  thus leading to different solutions for the ice drift velocities. If
539  this were true, this tantalizing circumstance had a dramatic impact on  this were true, this tantalizing circumstance would have a dramatic
540  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
541  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
542  compuational cost (Bruno Tremblay, personal communication).  high compuational cost (Bruno Tremblay, personal communication).
543    
544    Further, we observe that the EVP solutions tends to produce
545    effectively ``weaker'' ice that yields more easily to stress. This was
546  \begin{itemize}  also observed by \citet{hunke99} in a fast response to changing winds,
547  \item Configuration  their Figures\,10--12, where the EVP model adjusts quickly to a
548  \item OBCS from cube  cyclonic wind pattern, while the LSOR solution lags in time. This
549  \item forcing  property of the EVP solutions allows larger ice transports through
550  \item 1/2 and full resolution  narrow straits, where the implicit solver LSOR forms rigid ice. The
551  \item with a few JFM figs from C-grid LSR no slip  underlying reasons for this striking difference need further
552    ice transport through Canadian Archipelago  exploration.
553    thickness distribution  
554    ice velocity and transport  % THIS is now almost all in the text:
555  \end{itemize}  %\begin{itemize}
556    %\item Configuration
557  \begin{itemize}  %\item OBCS from cube
558  \item Arctic configuration  %\item forcing
559  \item ice transport through straits and near boundaries  %\item 1/2 and full resolution
560  \item focus on narrow straits in the Canadian Archipelago  %\item with a few JFM figs from C-grid LSR no slip
561  \end{itemize}  %  ice transport through Canadian Archipelago
562    %  thickness distribution
563  \begin{itemize}  %  ice velocity and transport
564  \item B-grid LSR no-slip: B-LSR-ns  %\end{itemize}
565  \item C-grid LSR no-slip: C-LSR-ns  
566  \item C-grid LSR slip:    C-LSR-fs  %\begin{itemize}
567  \item C-grid EVP no-slip: C-EVP-ns  %\item Arctic configuration
568  \item C-grid EVP slip:    C-EVP-fs  %\item ice transport through straits and near boundaries
569  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,  %\item focus on narrow straits in the Canadian Archipelago
570    new flag): C-LSR-ns+TEM  %\end{itemize}
571  \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?  
572  \item C-grid LSR no-slip + Winton:  %\begin{itemize}
573  \item  speed-performance-accuracy (small)  %\item B-grid LSR no-slip: B-LSR-ns
574    ice transport through Canadian Archipelago differences  %\item C-grid LSR no-slip: C-LSR-ns
575    thickness distribution differences  %\item C-grid LSR slip:    C-LSR-fs
576    ice velocity and transport differences  %\item C-grid EVP no-slip: C-EVP-ns
577  \end{itemize}  %\item C-grid EVP slip:    C-EVP-fs
578    %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
579  We anticipate small differences between the different models due to:  %  new flag): C-LSR-ns+TEM
580  \begin{itemize}  %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
581  \item advection schemes: along the ice-edge and regions with large  %\item C-grid LSR no-slip + Winton:
582    gradients  %\item  speed-performance-accuracy (small)
583  \item C-grid: less transport through narrow straits for no slip  %  ice transport through Canadian Archipelago differences
584    conditons, more for free slip  %  thickness distribution differences
585  \item VP vs.\ EVP: speed performance, accuracy?  %  ice velocity and transport differences
586  \item ocean stress: different water mass properties beneath the ice  %\end{itemize}
587  \end{itemize}  
588    %We anticipate small differences between the different models due to:
589  %\begin{figure}  %\begin{itemize}
590  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}  %\item advection schemes: along the ice-edge and regions with large
591  %\caption{Surface sea ice velocity for different solver flavors.  %  gradients
592  %\label{fig:iceveloc}}  %\item C-grid: less transport through narrow straits for no slip
593  %\end{figure}  %  conditons, more for free slip
594    %\item VP vs.\ EVP: speed performance, accuracy?
595  %\begin{figure}  %\item ocean stress: different water mass properties beneath the ice
596  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}  %\end{itemize}
 %\caption{Sea ice thickness for different solver flavors.  
 %\label{fig:icethick}}  
 %\end{figure}  
597    
598  %%% Local Variables:  %%% Local Variables:
599  %%% mode: latex  %%% mode: latex
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