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revision 1.16 by dimitri, Wed Jun 4 00:39:25 2008 UTC revision 1.22 by dimitri, Thu Aug 14 16:12:41 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  \subsection{Global Ocean and Sea Ice Simulation}  stress formulations and the two main options for sea ice
13  \label{sec:global}  thermodynamics in the MITgcm.
   
 The global ocean and sea ice results presented below 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)  
 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  
 relatively even grid spacing throughout the domain and which avoids polar  
 singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises  
 510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are  
 50 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  
 \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}  
14    
15  The ocean model is coupled to the sea-ice model discussed in  \subsection{Model configuration and experiments}
16  \refsec{model} using the following specific options.  The  \label{sec:arcticmodel}
17  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is  The Arctic model domain is illustrated in \reffig{arctic_topog}.
18  used to compute sea ice thickness and concentration.  Snow cover and  \begin{figure*}
19  sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
20  snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
21  and 0.83. Ice mechanics follow the viscous plastic rheology of  %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
22  \citet{hibler79} and the ice momentum equation is solved numerically  %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
23  using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics  \includegraphics*[width=\linewidth]{\fpath/topography}
24  model discussed hereinabove.  The ice is coupled to the ocean using  \caption{Left: Bathymetry and domain boundaries of Arctic
25  the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},    Domain.
26  that is, sea ice does not float above the ocean model but rather    %; the dashed line marks the boundaries of the inset on the right hand side.
27  deforms the ocean's model surface level.    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 boundary
45    conditions from, a global cubed-sphere \citep{adcroft04:_cubed_sphere}
46    configuration similar to that described in \citet{menemenlis05}. The
47    particular simulation from which we obtain boundary conditions is a baseline
48    integration, labeled {\em ``cube76''}. Each face of the cube comprises 510 by
49    510 grid cells for a mean horizontal grid spacing of 18\,km. There are 50
50    vertical levels ranging in thickness from 10 m near the surface to
51    approximately 450 m at a maximum model depth of 6150 m. The model employs the
52    partial-cell formulation of \citet{adcroft97:_shaved_cells}, which permits
53    accurate representation of the bathymetry. Bathymetry is from the S2004
54    (W.~Smith, unpublished) blend of the \citet{smi97} and the General Bathymetric
55    Charts of the Oceans (GEBCO) one arc-minute bathymetric grid.  The model is
56    integrated in a volume-conserving configuration using a finite volume
57    discretization with C-grid staggering of the prognostic variables. In the
58    ocean, the non-linear equation of state of \citet{jac95} is used.  The global
59    ocean model is coupled to a sea ice model in a configuration similar to the
60    case C-LSR-ns (see \reftab{experiments}).
61    
62  This particular ECCO2 simulation is initialized from temperature and salinity  The {\em cube76} simulation is initialized from temperature and salinity
63  fields derived from the Polar science center Hydrographic Climatology (PHC)  fields derived from the Polar science center Hydrographic Climatology (PHC)
64  3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to  3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to
65  July 2002 are derived from the European Centre for Medium-Range Weather  July 2002 are derived from the European Centre for Medium-Range Weather
66  Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}.  Surface  Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}.  Six-hourly
 boundary conditions after September 2002 are derived from the ECMWF  
 operational analysis.  There is a one month transition period, August 2002,  
 during which the ERA-40 contribution decreases linearly from 1 to 0 and the  
 ECMWF analysis contribution increases linearly from 0 to 1.  Six-hourly  
67  surface winds, temperature, humidity, downward short- and long-wave  surface winds, temperature, humidity, downward short- and long-wave
68  radiations, and precipitation are converted to heat, freshwater, and wind  radiations, and precipitation are converted to heat, freshwater, and wind
69  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
70  radiation decays exponentially as per \citet{pau77}.  Low frequency  radiation decays exponentially as per \citet{pau77}.  Low frequency
71  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
72  Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river  Precipitation Climatology Project \citep[GPCP,][]{huf01}.  The time-mean river
73  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
74  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)
75  and prepared by P. Winsor (personnal communication, 2007) is specificied.  and prepared by P. Winsor (personnal communication, 2007) is specificied.
76  Additionally, there is a relaxation to the monthly-mean climatological sea  Additionally, there is a relaxation to the monthly-mean climatological sea
77  surface salinity values from PHC 3.0, a relaxation time scale of 101 days.  surface salinity values from PHC 3.0, with a relaxation time scale of 101 days.
78    
79  Vertical mixing follows \citet{lar94} but with meridionally and vertically  Vertical mixing follows \citet{lar94} but with meridionally and vertically
80  varying background vertical diffusivity; at the surface, vertical diffusivity  varying background vertical diffusivity; at the surface, vertical diffusivity
# Line 91  advection scheme \citep{dar04} is employ Line 88  advection scheme \citep{dar04} is employ
88  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
89  the divergent flow as per \citet{kem08}.  the divergent flow as per \citet{kem08}.
90    
91  \ml{[Dimitris, here you need to either provide figures, so that I can  The model configuration of {\em cube76} carries over to the Arctic domain
92    write text, or you can provide both figures and text. I guess, one  configuration except for numerical details related to the non-linear
93    figure, showing the northern and southern hemisphere in summer and  free surface that are not supported by the open boundary code, and the
94    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
95    the next section.]}  are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.  The Arctic Ocean
96    model is integrated from Jan~01, 1992 to Mar~31, 2000.
97    \reftab{experiments} gives an overview over the experiments discussed
98  \subsection{Arctic Domain with Open Boundaries}  in \refsec{arcticresults}.
99  \label{sec:arctic}  \begin{table}
100      \caption{Overview over model simulations in \refsec{arcticresults}.
101  A series of forward sensitivity experiments have been carried out on      \label{tab:experiments}}
 an Arctic Ocean domain with open boundaries.  The objective is to  
 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]  
102    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
103      experiment name & description \\ \hline      experiment name & description \\ \hline
104      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
105    Arakawa B-grid, implying no-slip lateral boundary conditions    Arakawa B-grid, implying no-slip lateral boundary conditions
106    ($\vek{u}=0$ exactly) \\    ($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order
107      central difference scheme plus explicit diffusion for stability \\
108      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
109    boundary conditions (implemented via ghost-points) \\    boundary conditions (implemented via ghost-points) \\
110      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
# Line 177  discussed in this section. Line 125  discussed in this section.
125    direct-space-time advection scheme for thermodynamic variables    direct-space-time advection scheme for thermodynamic variables
126    \citep{hundsdorfer94}    \citep{hundsdorfer94}
127    \end{tabular}    \end{tabular}
   \caption{Overview over model simulations in \refsec{arctic}.  
     \label{tab:experiments}}  
128  \end{table}  \end{table}
129  %\begin{description}  %\begin{description}
130  %\item[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
# Line 220  steps for the EVP solutions: \citet{hunk Line 166  steps for the EVP solutions: \citet{hunk
166  for the EVP solution. We use two interpretations of this choice where  for the EVP solution. We use two interpretations of this choice where
167  the EVP model is subcycled 120 times within a (short) model timestep  the EVP model is subcycled 120 times within a (short) model timestep
168  of 1200\,s resulting in a very long and expensive integration  of 1200\,s resulting in a very long and expensive integration
169  ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the  ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 144 times within the
170  forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).  forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
171    
172  A principle difficulty in comparing the solutions obtained with  \subsection{Results}
173  different realizations of the model dynamics lies in the non-linear  \label{sec:arcticresults}
174  feedback of the ice dynamics and thermodynamics. Already after a few  
175  months the solutions have diverged so far from each other that  Comparing the solutions obtained with different realizations of the
176  comparing velocities only makes sense within the first 3~months of the  model dynamics is difficult because of the non-linear feedback of the
177    ice dynamics and thermodynamics. Already after a few months the
178    solutions have diverged so far from each other that comparing
179    velocities only makes sense within the first 3~months of the
180  integration while the ice distribution is still close to the initial  integration while the ice distribution is still close to the initial
181  conditions. At the end of the integration, the differences between the  conditions. At the end of the integration, the differences between the
182  model solutions can be interpreted as cumulated model uncertainties.  model solutions can be interpreted as cumulated model uncertainties.
183    
184    \subsubsection{Ice velocities in JFM 1992}
185    
186  \reffig{iceveloc} shows ice velocities averaged over Janunary,  \reffig{iceveloc} shows ice velocities averaged over January,
187  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
188  shown are the differences between B-grid and C-grid, LSR and EVP, and  shown are the differences between this reference solution and various
189  no-slip and free-slip solution. The velocity field of the C-LSR-ns  sensitivity experiments. The velocity field of the C-LSR-ns
190  solution (\reffig{iceveloc}a) roughly resembles the drift velocities  solution (\reffig{iceveloc}a) roughly resembles the drift velocities
191  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
192  models in a cyclonic circulation regime (CCR) \citep[their  models in a cyclonic circulation regime (CCR) \citep[their
193  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
194  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
   
 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]}  
195  %  %
196  Compared to the differences between B and C-grid solutions,the  \newcommand{\subplotwidth}{0.47\textwidth}
197  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution  %\newcommand{\subplotwidth}{0.3\textwidth}
198  (\reffig{iceveloc}c).  As expected the differences are largest along  \begin{figure}[tp]
 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]  
199    \centering    \centering
200    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
201    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-ns}}
202    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
203    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_B-LSR-ns-C-LSR-ns}}
204    \\    \\
205    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
206    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-fs-C-LSR-ns}}
207    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
208    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-EVP-ns150-C-LSR-ns}}
209    \\  %  \\
210    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
211    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
212    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
213    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
214    \\  %  \\
215    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
216    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
217    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
218    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
219    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
220      over the first 3 months of integration [cm/s]; (b)-(h) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
221      between solutions with B-grid, free lateral slip, EVP-solver,      between solutions with B-grid, free lateral slip, EVP-solver,
# Line 293  Island. Line 226  Island.
226      of speed), vectors indicate direction only.}      of speed), vectors indicate direction only.}
227    \label{fig:iceveloc}    \label{fig:iceveloc}
228  \end{figure}  \end{figure}
229    \addtocounter{figure}{-1}
230    \setcounter{subfigure}{4}
231    \begin{figure}[tp]
232      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
233      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
234      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
235      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
236      \\
237      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
238      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
239      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
240      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
241      \caption{continued}
242    \end{figure}
243    
244    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
245    is most pronounced along the coastlines, where the discretization
246    differs most between B and C-grids: On a B-grid the tangential
247    velocity lies on the boundary (and is thus zero through the no-slip
248    boundary conditions), whereas on the C-grid it is half a cell width
249    away from the boundary, thus allowing more flow. The B-LSR-ns solution
250    has less ice drift through the Fram Strait and along
251    Greenland's east coast; also, the flow through Baffin Bay and Davis
252    Strait into the Labrador Sea is reduced with respect to the C-LSR-ns
253    solution.  \ml{[Do we expect this? Say something about that]}
254    %
255    Compared to the differences between B and C-grid solutions, the
256    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
257    (\reffig{iceveloc}c).  As expected the differences are largest along
258    coastlines: because of the free-slip boundary conditions, flow is
259    faster in the C-LSR-fs solution, for example, along the east coast
260    of Greenland, the north coast of Alaska, and the east Coast of Baffin
261    Island.
262    
263  The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is  The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
264  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
265  EVP-approximation of the VP-dynamics allows for increased drift by  EVP-approximation of the VP-dynamics allows for increased drift by up
266  over 2\,cm/s in the Beaufort Gyre and the transarctic drift.  to 8\,cm/s in the Beaufort Gyre and the transarctic drift.  In
267  %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns  general, drift velocities are strongly biased towards higher values in
268  %solution. [Really?, No]}  the EVP solutions.
269  In general, drift velocities are biased towards higher values in the  
270  EVP solutions.  Compared to the other parameters, the ice rheology TEM
271  % as can be seen from a histogram of the differences in  (\reffig{iceveloc}e) has a very small effect on the solution. In
272  %\reffig{drifthist}.  general the ice drift tends to be increased, because there is no
273  %\begin{figure}[htbp]  tensile stress and ice can be ``pulled appart'' at no cost.
274  %  \centering  Consequently, the largest effect on drift velocity can be observed
275  %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}  near the ice edge in the Labrador Sea. In contrast, the drift is
276  %  \caption{Histogram of drift velocity differences for C-LSR-ns and  stronger almost everywhere in the computational domain in the run with
277  %    C-EVP-ns solution [cm/s].}  the ice-ocean stress formulation of \citet{hibler87}
278  %  \label{fig:drifthist}  (\reffig{iceveloc}f). The increase is mostly aligned with the general
279  %\end{figure}  direction of the flow, implying that the different stress formulation
280    reduces the deceleration of drift by the ocean.
281    
282    The 3-layer thermodynamics following \citet{winton00} requires
283    additional information on initial conditions for enthalphy. These
284    different initial conditions make a comparison of the first months
285    difficult to interpret. The drift in the Beaufort Gyre is slightly
286    reduced relative to the reference run C-LSR-ns, but the drift through
287    the Fram Strait is increased. The drift velocities near the ice edge
288    are very different, because the ice extent is already larger in
289    \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
290    drift velocities, because the ice motion is more contrained by a
291    larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
292    geographical position is nearly in free drift.
293    
294    A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
295    \reffig{iceveloc}h) has some effect along the ice edge, where
296    the gradients of thickness and concentration are largest. Everywhere
297    else the effect is very small and can mostly be attributed to smaller
298    numerical diffusion (and to the absense of explicit diffusion that is
299    required for numerical stability in a simple second order central
300    differences scheme).
301    
302    \subsubsection{Ice volume during JFM 2000}
303    
304  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
305  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
306  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
307  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
308  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--h, and
309  concentrations (not shown).  concentrations (not shown).
310  \begin{figure}[htbp]  \begin{figure}[tp]
311    \centering    \centering
312    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
313    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
# Line 329  concentrations (not shown). Line 318  concentrations (not shown).
318    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
319    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
320    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
321    \\    \caption{(a) Effective thickness (volume per unit area) of the
322        C-LSR-ns solution, averaged over the months Janurary through March
323        2000 [m]; (b)-(h) difference between solutions with B-grid, free
324        lateral slip, EVP-solver, truncated ellipse method (TEM),
325        different ice-ocean stress formulation (HB87), different
326        thermodynamics (WTD), different advection for thermodynamic
327        variables (DST3FL) and the C-LSR-ns reference solution [m].}
328      \label{fig:icethick}
329    \end{figure}
330    \addtocounter{figure}{-1}
331    \setcounter{subfigure}{4}
332    \begin{figure}[tp]
333    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
334    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
335    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
# Line 339  concentrations (not shown). Line 339  concentrations (not shown).
339    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
340    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
341    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
342    \caption{(a) Effective thickness (volume per unit area) of the    \caption{continued}
     C-LSR-ns solution, averaged over the months Janurary through March  
     2000 [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}  
343  \end{figure}  \end{figure}
 %  
344  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
345  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
346  narrow passages in the Canadian Archipelago, lead to a larger build-up  narrow passages in the Canadian Arctic Archipelago, lead to a larger build-up
347  of ice north of Greenland and the Archipelago by 2\,m effective  of ice north of Greenland and the Archipelago by 2\,m effective
348  thickness and more in the B-grid solution (\reffig{icethick}b). But  thickness and more in the B-grid solution (\reffig{icethick}b). But
349  the ice volume in not larger everywhere: further west, there are  the ice volume in not larger everywhere: further west, there are
# Line 364  Severnaya Semlya\ml{/or Nordland?}, Line 356  Severnaya Semlya\ml{/or Nordland?},
356  because ice tends to flow along coasts less easily in the B-LSR-ns  because ice tends to flow along coasts less easily in the B-LSR-ns
357  solution.  solution.
358    
359  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
360  smaller differences to C-LSR-ns in the central Arctic than the  smaller differences to C-LSR-ns in the central Arctic than the
361  transition from the B-grid to the C-grid (\reffig{icethick}c), except  transition from the B-grid to the C-grid (\reffig{icethick}c), except
362  in the Canadian Archipelago. There it reduces the effective ice  in the Canadian Arctic Archipelago. There it reduces the effective ice
363  thickness by 2\,m and more where the ice is thick and the straits are  thickness by 2\,m and more where the ice is thick and the straits are
364  narrow.  Dipoles of ice thickness differences can also be observed  narrow.  Dipoles of ice thickness differences can also be observed
365  around islands, because the free-slip solution allows more flow around  around islands, because the free-slip solution allows more flow around
366  islands than the no-slip solution.  Everywhere else the ice volume is  islands than the no-slip solution. Everywhere else the ice volume is
367  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
368  %  %
369  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
370  C-LSR-ns solution. Consequently, more ice can be moved from the  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).
371  eastern part of the Arctic, where ice volumes are smaller, to the  Within the Canadian Arctic Archipelago, more drift leads to faster ice export
372  western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,  and reduced effective ice thickness. With a shorter time step of
373  more drift leads to faster ice export and reduced effective ice  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to
374  thickness. With a shorter time step of  the LSOR solution (not shown). Only in the narrow straits in the
375  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to  Archipelago the ice thickness is not affected by the shorter time step
376  converge to the LSOR solution (not shown). Only in the narrow straits  and the ice is still thinner by 2\,m and more, as in the EVP solution
377  in the Archipelago the ice thickness is not affected by the shorter  with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
378  time step and the ice is still thinner by 2\,m and more, as in the EVP  
379  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.  In year 2000, there is more ice everywhere in the domain in
380    C-LSR-ns~WTD (\reffig{icethick}g, note the color scale).
381    This difference, which is even more pronounced in summer (not shown),
382    can be attributed to direct effects of the different thermodynamics in
383    this run. The remaining runs have the largest differences in effective
384    ice thickness along the north coasts of Greenland and Ellesmere Island.
385    Although the effects of TEM and \citet{hibler87}'s ice-ocean stress
386    formulation are so different on the initial ice velocities, both runs
387    have similarly reduced ice thicknesses in this area. The 3rd-order
388    advection scheme has an opposite effect of similar magnitude, pointing
389    towards more implicit lateral stress with this numerical scheme.
390    
391  The observed difference of order 2\,m and less are smaller than the  The observed difference of order 2\,m and less are smaller than the
392  differences that were observed between different hindcast and climate  differences that were observed between different hindcast models and climate
393  models in \citet{gerdes07}. There the range of sea ice volume of  models in \citet{gerdes07}. There the range of sea ice volume of
394  different sea ice-ocean models (which shared very similar forcing  different sea ice-ocean models (which shared very similar forcing
395  fields) was on the order of $10,000\text{km$^{3}$}$; this range was  fields) was on the order of $10,000\text{km$^{3}$}$; this range was
396  even larger for coupled climate models. Here, the range (and the  even larger for coupled climate models. Here, the range (and the
397  averaging period) is smaller than $4,000\text{km$^{3}$}$ except for  averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
398  the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics  the run \mbox{C-LSR-ns~WTD} where the more complete thermodynamics
399  leads to generally thicker ice (\reffig{icethick} and  lead to generally thicker ice (\reffig{icethick} and
400  \reftab{icevolume}).  \reftab{icevolume}).
401  \begin{table}[htbp]  \begin{table}[t]
402    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
403      model run & ice volume      model run & ice volume
404      & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,      & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
# Line 418  leads to generally thicker ice (\reffig{ Line 420  leads to generally thicker ice (\reffig{
420    \caption{Arctic ice volume averaged over Jan--Mar 2000, in    \caption{Arctic ice volume averaged over Jan--Mar 2000, in
421      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
422      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
423      total northern inflow into the Canadian Archipelago (NI), and the      total northern inflow into the Canadian Arctic Archipelago (NI), and the
424      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.
425    \label{tab:icevolume}    \label{tab:icevolume}}
426  \end{table}  \end{table}
427    
428    \subsubsection{Ice transports}
429    
430  The difference in ice volume and ice drift velocities between the  The difference in ice volume and ice drift velocities between the
431  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
432  the Arctic. Although by far the most exported ice drifts through the  the Arctic. Although by far the most exported ice drifts through the
433  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
434  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) of ice is
435  exported through the Canadian Archipelago \citep[and references  exported through the Canadian Arctic Archipelago \citep[and references
436  therein]{serreze06}. Note, that ice transport estimates are associated  therein]{serreze06}. Note, that ice transport estimates are associated
437  with large uncertainties; also note that tuning an Arctic sea  with large uncertainties and that the results presented herein have not
438  ice-ocean model to reproduce observations is not our goal, but we use  yet been constrained by observations; we use
439  the published numbers as an orientation.  the published numbers as an orientation.
440    
441  \reffig{archipelago} shows a time series of daily averaged, smoothed  \reffig{archipelago} shows an excerpt of a time series of daily
442  with monthly running means, ice transports through various straits in  averaged ice transports, smoothed with a monthly running mean, through
443  the Canadian Archipelago and the Fram Strait for the different model  various straits in the Canadian Arctic Archipelago and the Fram Strait for
444  solutions and \reftab{icevolume} summarizes the time series. The  the different model solutions; \reftab{icevolume} summarizes the
445  export through Fram Strait agrees with the observations in all model  time series.
446  solutions (annual averages range from $2110$ to  \begin{figure}
447    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
448    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
449    %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
450    \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
451    \caption{Transport through Canadian Arctic Archipelago for different solver
452      flavors. The letters refer to the labels of the sections in
453      \reffig{arctic_topog}; positive values are flux out of the Arctic;
454      legend abbreviations are explained in \reftab{experiments}. The mean
455      range of the different model solution is taken over the period Jan
456      1992 to Dec 1999.
457    \label{fig:archipelago}}
458    \end{figure}
459    The export through Fram Strait agrees with the observations in all
460    model solutions (annual averages range from $2110$ to
461  $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with  $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
462  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
463  time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),  time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
464  while the export through the Candian Archipelago is smaller than  while the export through the Candian Arctic Archipelago is smaller than
465  generally thought. For example, the ice transport through Lancaster  generally thought. For example, the ice transport through Lancaster
466  Sound is lower (annual averages are $43$ to  Sound is lower (annual averages are $43$ to
467  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
468  inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but  inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
469  a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further  a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
470  upstream in Barrow Strait in the 1970ies from satellite images.  upstream in Barrow Strait in the 1970's from satellite images.
471  Generally, the EVP solutions have the highest maximum (export out of  Generally, the EVP solutions have the highest maximum (export out of
472  the Artic) and lowest minimum (import into the Artic) fluxes as the  the Artic) and lowest minimum (import into the Artic) fluxes as the
473  drift velocities are largest in these solutions.  In the extreme of  drift velocities are largest in these solutions.  In the extreme of
474  the Nares Strait, which is only a few grid points wide in our  the Nares Strait, which is only a few grid points wide in our
475  configuration, both B- and C-grid LSOR solvers lead to practically no  configuration, both B- and C-grid LSOR solvers lead to practically no
476  ice transport, while the C-EVP solutions allow up to  ice transport, while the C-EVP solutions allow up to
477  $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
478  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,
479  the Candian Archipelago is larger in all EVP solutions  the import into the Candian Arctic Archipelago is larger in all EVP solutions
480  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
481  than in the LSOR solutions.  than in the LSOR solutions.
482  %get the order of magnitude right (range: $132$ to  %get the order of magnitude right (range: $132$ to
# Line 467  The B-LSR-ns solution is even smaller by Line 485  The B-LSR-ns solution is even smaller by
485  C-LSR solutions (an exception is the WTD solution, where larger ice thickness  C-LSR solutions (an exception is the WTD solution, where larger ice thickness
486  tends to block the transport).  tends to block the transport).
487  %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.  %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}  
488    
489  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
490  %  schemes, Winton TD, discussion about differences in terms of model  %  schemes, Winton TD, discussion about differences in terms of model
491  %  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
492  %  models are all erroneous!]}  %  models are all erroneous!]}
493    
494    \subsubsection{Discussion}
495    
496  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
497  different solutions. In constrast to that, the differences between  different solutions. In constrast to that, the differences between
498  free-slip and no-slip solutions \emph{with the same solver} are  free-slip and no-slip solutions \emph{with the same solver} are
# Line 490  considerably smaller (the difference for Line 500  considerably smaller (the difference for
500  but similar to that for the LSOR solver). Albeit smaller, the  but similar to that for the LSOR solver). Albeit smaller, the
501  differences between free and no-slip solutions in ice drift can lead  differences between free and no-slip solutions in ice drift can lead
502  to equally large differences in ice volume, especially in the Canadian  to equally large differences in ice volume, especially in the Canadian
503  Archipelago over the integration time. At first, this observation  Arctic Archipelago over the integration time. At first, this observation
504  seems counterintuitive, as we expect that the solution  seems counterintuitive, as we expect that the solution
505  \emph{technique} should not affect the \emph{solution} to a higher  \emph{technique} should not affect the \emph{solution} to a higher
506  degree than actually modifying the equations. A more detailed study on  degree than actually modifying the equations. A more detailed study on
# Line 506  thus leading to different solutions for Line 516  thus leading to different solutions for
516  this were true, this tantalizing circumstance would have a dramatic  this were true, this tantalizing circumstance would have a dramatic
517  impact on sea-ice modeling in general, and we would need to improve  impact on sea-ice modeling in general, and we would need to improve
518  the solution techniques for dynamic sea ice models, most likely at a very  the solution techniques for dynamic sea ice models, most likely at a very
519  high compuational cost (Bruno Tremblay, personal communication). Further,  high compuational cost (Bruno Tremblay, personal communication).
520  we observe that the EVP solutions tends to produce effectively  
521  ``weaker'' ice that yields more easily to stress. The fast response to  Further, we observe that the EVP solutions tends to produce
522  changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,  effectively ``weaker'' ice that yields more easily to stress. This was
523  where the EVP model adjusts quickly to a cyclonic wind pattern, while  also observed by \citet{hunke99} in a fast response to changing winds,
524  the LSOR solution does not. This property of the EVP solutions allows  their Figures\,10--12, where the EVP model adjusts quickly to a
525  larger ice transports through narrow straits, where the implicit  cyclonic wind pattern, while the LSOR solution lags in time. This
526  solver LSOR forms rigid ice. The underlying reasons for this striking  property of the EVP solutions allows larger ice transports through
527  difference need further exploration.  narrow straits, where the implicit solver LSOR forms rigid ice. The
528    underlying reasons for this striking difference need further
529    exploration.
530    
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