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revision 1.13 by mlosch, Fri Mar 14 23:05:34 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  \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.
14  treatment of sea ice open boundary condition in the MITgcm.}  
15    \subsection{Model configuration and experiments}
16  \subsection{Global Ocean and Sea Ice Simulation}  \label{sec:arcticmodel}
17  \label{sec:global}  The Arctic model domain is illustrated in \reffig{arctic_topog}.
18    \begin{figure*}
19  The global ocean and sea ice results presented below were carried out as part  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
20  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
21  project.  ECCO2 aims to produce increasingly accurate syntheses of all  %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
22  available global-scale ocean and sea-ice data at resolutions that start to  %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
23  resolve ocean eddies and other narrow current systems, which transport heat,  \includegraphics*[width=\linewidth]{\fpath/topography}
24  carbon, and other properties within the ocean \citep{menemenlis05}.  The  \caption{Left: Bathymetry and domain boundaries of Arctic
25  particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)    Domain.
26  integration, labeled cube76, which has not yet been constrained by oceanic and    %; the dashed line marks the boundaries of the inset on the right hand side.
27  by sea ice data.  A cube-sphere grid projection is employed, which permits    The letters in the inset label sections in the
28  relatively even grid spacing throughout the domain and which avoids polar    Canadian Archipelago, where ice transport is evaluated:
29  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises    A: Nares Strait; %
30  510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are    B: \ml{Meighen Island}; %
31  50 vertical levels ranging in thickness from 10 m near the surface to    C: Prince Gustaf Adolf Sea; %
32  approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the    D: \ml{Brock Island}; %
33  National Geophysical Data Center (NGDC) 2-minute gridded global relief data    E: M'Clure Strait; %
34  (ETOPO2) and the model employs the partial-cell formulation of    F: Amundsen Gulf; %
35  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the    G: Lancaster Sound; %
36  bathymetry. The model is integrated in a volume-conserving configuration using    H: Barrow Strait \ml{W.}; %
37  a finite volume discretization with C-grid staggering of the prognostic    I: Barrow Strait \ml{E.}; %
38  variables. In the ocean, the non-linear equation of state of \citet{jac95} is    J: Barrow Strait \ml{N.}; %
39  used.    K: Fram Strait. %
40      The sections A through F comprise the total inflow into the Canadian
41  The ocean model is coupled to the sea-ice model discussed in    Archipelago. \ml{[May still need to check the geography.]}
42  \refsec{model} using the following specific options.  The    \label{fig:arctic_topog}}
43  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is  \end{figure*}
44  used to compute sea ice thickness and concentration.  Snow cover and  It has 420 by 384 grid boxes and is carved out, and obtains open boundary
45  sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry  conditions from, a global cubed-sphere \citep{adcroft04:_cubed_sphere}
46  snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,  configuration similar to that described in \citet{menemenlis05}. The
47  and 0.83. Ice mechanics follow the viscous plastic rheology of  particular simulation from which we obtain boundary conditions is a baseline
48  \citet{hibler79} and the ice momentum equation is solved numerically  integration, labeled {\em ``cube76''}. Each face of the cube comprises 510 by
49  using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics  510 grid cells for a mean horizontal grid spacing of 18\,km. There are 50
50  model discussed hereinabove.  The ice is coupled to the ocean using  vertical levels ranging in thickness from 10 m near the surface to
51  the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},  approximately 450 m at a maximum model depth of 6150 m. The model employs the
52  that is, sea ice does not float above the ocean model but rather  partial-cell formulation of \citet{adcroft97:_shaved_cells}, which permits
53  deforms the ocean's model surface level.  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 84  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}}
102  an Arctic Ocean domain with open boundaries.  The objective is to    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
103  compare the old B-grid LSR dynamic solver with the new C-grid LSR and      experiment name & description \\ \hline
104  EVP solvers.  Additional experiments are is carried out to illustrate      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
 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]{\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: McClure Strait; %  
   F: Amundsen Gulf; %  
   G: Lancaster Sound; %  
   H: Barrow Strait \ml{W.}; %  
   I: Barrow Strait \ml{E.}; %  
   J: Barrow Strait \ml{N.}. %  
   \label{fig:arctic_topog}}  
 \end{figure*}  
   
 The main dynamic difference from cube sphere is that it does not use  
 rescaled vertical coordinates (z$^\ast$) and the surface boundary  
 conditions for freshwater input are different, because those features  
 are not supported by the open boundary code.  
   
 Open water, dry ice, wet ice, dry snow, and wet snow albedo are,  
 respectively, 0.15, 0.85, 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  
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  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral    central difference scheme plus explicit diffusion for stability \\
108    boundary conditions (implemented via ghost-points);      C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
109  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary    boundary conditions (implemented via ghost-points) \\
110    conditions;      C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
111  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with    conditions \\
112    no-slip lateral boundary conditions; and      C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
113  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
114    boundary conditions.    150\text{\,s}$ \\
115  \end{description}      C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
116      no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
117      10\text{\,s}$ \\
118        C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
119      to \citet{hibler87}\\
120        C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
121      rheology \citep{hibler97} \\
122        C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
123      \citet{winton00} \\
124        C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
125      direct-space-time advection scheme for thermodynamic variables
126      \citep{hundsdorfer94}
127      \end{tabular}
128    \end{table}
129    %\begin{description}
130    %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
131    %  Arakawa B-grid, implying no-slip lateral boundary conditions
132    %  ($\vek{u}=0$ exactly);
133    %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
134    %  boundary conditions (implemented via ghost-points);
135    %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
136    %  conditions;
137    %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
138    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
139    %  150\text{\,s}$;
140    %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
141    %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
142    %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
143    %  direct-space-time advection scheme \citep{hundsdorfer94};
144    %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
145    %  rheology \citep{hibler97};
146    %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
147    %  to \citet{hibler87};
148    %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
149    %  \citet{winton00};
150    %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
151    %%  scale noise \citep{hunke01};
152    %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
153    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
154    %  10\text{\,s}$.
155    %\end{description}
156  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
157  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
158  interpreted as pure model error. Lateral boundary conditions on a  interpreted as pure model error. Lateral boundary conditions on a
159  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
160  unclear, so that comparing the no-slip solutions to the free-slip  unclear, so that comparing the no-slip solutions to the free-slip
161  solutions gives another measure of uncertainty in sea ice modeling.  solutions gives another measure of uncertainty in sea ice modeling.
162    The remaining experiments explore further sensitivities of the system
163  A principle difficulty in comparing the solutions obtained with  to different physics (change in rheology, advection and diffusion
164  different variants of the dynamics solver lies in the non-linear  properties, stress coupling, and thermodynamics) and different time
165  feedback of the ice dynamics and thermodynamics. Already after a few  steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
166  months the solutions have diverged so far from each other that  for the EVP solution. We use two interpretations of this choice where
167  comparing velocities only makes sense within the first 3~months of the  the EVP model is subcycled 120 times within a (short) model timestep
168    of 1200\,s resulting in a very long and expensive integration
169    ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 144 times within the
170    forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
171    
172    \subsection{Results}
173    \label{sec:arcticresults}
174    
175    Comparing the solutions obtained with different realizations of the
176    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  \reffig{iceveloc} shows ice velocities averaged over Janunary,  \subsubsection{Ice velocities in JFM 1992}
185    
186    \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 an 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.
195    %
196    \newcommand{\subplotwidth}{0.47\textwidth}
197    %\newcommand{\subplotwidth}{0.3\textwidth}
198    \begin{figure}[tp]
199      \centering
200      \subfigure[{\footnotesize C-LSR-ns}]
201      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-ns}}
202      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
203      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_B-LSR-ns-C-LSR-ns}}
204      \\
205      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
206      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-fs-C-LSR-ns}}
207      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
208      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-EVP-ns150-C-LSR-ns}}
209    %  \\
210    %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
211    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
212    %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
213    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
214    %  \\
215    %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
216    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
217    %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
218    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
219      \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
221        between solutions with B-grid, free lateral slip, EVP-solver,
222        truncated ellipse method (TEM), different ice-ocean stress
223        formulation (HB87), different thermodynamics (WTD), different
224        advection for thermodynamic variables (DST3FL) and the C-LSR-ns
225        reference solution [cm/s]; color indicates speed (or differences
226        of speed), vectors indicate direction only.}
227      \label{fig:iceveloc}
228    \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)  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
245  is most pronounced along the coastlines, where the discretization  is most pronounced along the coastlines, where the discretization
246  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
247  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
248  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
249  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
250  ice drift through the Fram Strait and especially the along Greenland's  has less ice drift through the Fram Strait and along
251  east coast; also, the flow through Baffin Bay and Davis Strait into  Greenland's east coast; also, the flow through Baffin Bay and Davis
252  the Labrador Sea is reduced with respect the C-LSR-ns solution.  Strait into the Labrador Sea is reduced with respect to the C-LSR-ns
253  \ml{[Do we expect this? Say something about that]}  solution.  \ml{[Do we expect this? Say something about that]}
254  %  %
255  Compared to the differences between B and C-grid solutions,the  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  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  (\reffig{iceveloc}c).  As expected the differences are largest along
258  coastlines: because of the free-slip boundary conditions, flow is  coastlines: because of the free-slip boundary conditions, flow is
259  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
260  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
261  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}  
262    
263  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
264  (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
265  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
266  transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska  to 8\,cm/s in the Beaufort Gyre and the transarctic drift.  In
267    in the C-EVP-ns solution. [Really?]} In general, drift velocities are  general, drift velocities are strongly biased towards higher values in
268  biased towards higher values in the EVP solutions as can be seen from  the EVP solutions.
269  a histogram of the differences in \reffig{drifthist}.  
270  \begin{figure}[htbp]  Compared to the other parameters, the ice rheology TEM
271    \centering  (\reffig{iceveloc}e) has a very small effect on the solution. In
272    \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}  general the ice drift tends to be increased, because there is no
273    \caption{Histogram of drift velocity differences for C-LSR-ns and  tensile stress and ice can be ``pulled appart'' at no cost.
274      C-EVP-ns solution [cm/s].}  Consequently, the largest effect on drift velocity can be observed
275    \label{fig:drifthist}  near the ice edge in the Labrador Sea. In contrast, the drift is
276  \end{figure}  stronger almost everywhere in the computational domain in the run with
277    the ice-ocean stress formulation of \citet{hibler87}
278    (\reffig{iceveloc}f). The increase is mostly aligned with the general
279    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  area distributions (not shown).  \ml{Compared to other solutions, for  concentrations (not shown).
310    example, AOMIP the ice thickness distribution blablabal}  \begin{figure}[tp]
 \begin{figure}[htbp]  
311    \centering    \centering
312    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
313    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
314    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
315    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
316      \\
317    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
318    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}    {\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=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
321    \caption{(a) Effective thickness (volume per unit area) of the    \caption{(a) Effective thickness (volume per unit area) of the
322      C-LSR-ns solution, averaged over the months Janurary through March      C-LSR-ns solution, averaged over the months Janurary through March
323      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
324      and C-LSR-ns solutions [cm/s].}      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}    \label{fig:icethick}
329  \end{figure}  \end{figure}
330  %  \addtocounter{figure}{-1}
331    \setcounter{subfigure}{4}
332    \begin{figure}[tp]
333      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
334      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
335      \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
336      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
337      \\
338      \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
339      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
340      \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
341      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
342      \caption{continued}
343    \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
350  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
351  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
352  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
353  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
354    upstream]} and less ice in the the lee of island groups, such as  less ice in their lee, such as Franz-Josef-Land and
355  Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along  Severnaya Semlya\ml{/or Nordland?},
356  coasts less easily in the B-LSR-ns solution.  because ice tends to flow along coasts less easily in the B-LSR-ns
357    solution.
358  Imposing a free-slip boundary condition in C-LSR-fs leads to a much  
359  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
360  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it  smaller differences to C-LSR-ns in the central Arctic than the
361  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
362  is thick and the straits are narrow. Dipoles of ice thickness  in the Canadian Arctic Archipelago. There it reduces the effective ice
363  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
364  solution allows more flow around islands than the no-slip solution.  narrow.  Dipoles of ice thickness differences can also be observed
365  Everywhere else the ice volume is affected only slightly by the  around islands, because the free-slip solution allows more flow around
366  different boundary condition.  islands than the no-slip solution. Everywhere else the ice volume is
367    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 eastern  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).
371  part of the Arctic, where ice volumes are smaller, to the western  Within the Canadian Arctic Archipelago, more drift leads to faster ice export
372  Arctic where ice piles up along the coast (\reffig{icethick}d). Within  and reduced effective ice thickness. With a shorter time step of
373  the Canadian Archipelago, more drift leads to faster ice export and  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to
374  reduced effective ice thickness.  the LSOR solution (not shown). Only in the narrow straits in the
375    Archipelago the ice thickness is not affected by the shorter time step
376    and the ice is still thinner by 2\,m and more, as in the EVP solution
377    with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
378    
379    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
392    differences that were observed between different hindcast models and climate
393    models in \citet{gerdes07}. There the range of sea ice volume of
394    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
396    even larger for coupled climate models. Here, the range (and the
397    averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
398    the run \mbox{C-LSR-ns~WTD} where the more complete thermodynamics
399    lead to generally thicker ice (\reffig{icethick} and
400    \reftab{icevolume}).
401    \begin{table}[t]
402      \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
403        model run & ice volume
404        & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
405            km$^{3}$\,y$^{-1}$}$]}\\
406        & [$\text{km$^{3}$}$]
407        & \multicolumn{2}{c}{FS}
408        & \multicolumn{2}{c}{NI}
409        & \multicolumn{2}{c}{LS} \\ \hline
410        B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
411        C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
412        C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
413        C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
414        C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
415        C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
416        C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
417        C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
418        C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
419      \end{tabular}
420      \caption{Arctic ice volume averaged over Jan--Mar 2000, in
421        $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
422        period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
423        total northern inflow into the Canadian Arctic Archipelago (NI), and the
424        export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.
425      \label{tab:icevolume}}
426    \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 the most exported ice drifts through the Fram  the Arctic. Although by far the most exported ice drifts through the
433  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}.  \reffig{archipelago} shows a time series of  therein]{serreze06}. Note, that ice transport estimates are associated
437  \ml{[maybe smooth to different time scales:] daily averaged, smoothed  with large uncertainties and that the results presented herein have not
438    with monthly running means,} ice transports through various straits  yet been constrained by observations; we use
439  in the Canadian Archipelago and the Fram Strait for the different  the published numbers as an orientation.
440  model solutions. The export through Fram Strait is too high in all  
441  model (annual averages ranges from $3324$ to  \reffig{archipelago} shows an excerpt of a time series of daily
442  $3931\text{\,km$^3$\,y$^{-1}$}$) solutions, while the export through  averaged ice transports, smoothed with a monthly running mean, through
443  Lancaster Sound is lower (annual averages are $41$ to  various straits in the Canadian Arctic Archipelago and the Fram Strait for
444  $201\text{\,km$^3$\,y$^{-1}$}$) than compared to observations.  the different model solutions; \reftab{icevolume} summarizes the
445  Generally, the C-EVP solutions have highest maximum (export out of the  time series.
 Artic) and minimum (import into the Artic) fluxes as the drift  
 velocities are largest in this solution. In the extreme, both B- and  
 C-grid LSOR solvers have practically no ice transport through the  
 Nares Strait, which is only a few grid points wide, while the C-EVP  
 solutions allow up to 500\,km$^3$\,y$^{-1}$ in summer.  
446  \begin{figure}  \begin{figure}
447  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
448  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
449  \caption{Transport through Canadian Archipelago for different solver  %\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    flavors. The letters refer to the labels of the sections in
453    \reffig{arctic_topog}; positive values are flux out of the Arctic.    \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}}  \label{fig:archipelago}}
458  \end{figure}  \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
462    $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
463    time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
464    while the export through the Candian Arctic Archipelago is smaller than
465    generally thought. For example, the ice transport through Lancaster
466    Sound is lower (annual averages are $43$ to
467    $256\text{\,km$^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
469    a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
470    upstream in Barrow Strait in the 1970's from satellite images.
471    Generally, the EVP solutions have the highest maximum (export out of
472    the Artic) and lowest minimum (import into the Artic) fluxes as the
473    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
475    configuration, both B- and C-grid LSOR solvers lead to practically no
476    ice transport, while the C-EVP solutions allow up to
477    $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
478    report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
479    the import into the Candian Arctic Archipelago is larger in all EVP solutions
480    %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
481    than in the LSOR solutions.
482    %get the order of magnitude right (range: $132$ to
483    %$165\text{\,km$^3$\,y$^{-1}$}$);
484    The B-LSR-ns solution is even smaller by another factor of two than the
485    C-LSR solutions (an exception is the WTD solution, where larger ice thickness
486    tends to block the transport).
487    %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
488    
489    %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
490    %  schemes, Winton TD, discussion about differences in terms of model
491    %  error? that's tricky as it means refering to Tremblay, thus our ice
492    %  models are all erroneous!]}
493    
494  \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!]}  
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 contrast, the differences between free-slip  different solutions. In constrast to that, the differences between
498  and no-slip solutions \emph{with the same solver} are considerably  free-slip and no-slip solutions \emph{with the same solver} are
499  smaller (the difference for the EVP solver is not shown, but similar  considerably smaller (the difference for the EVP solver is not shown,
500  to that for the LSOR solver). Albeit smaller, the differences between  but similar to that for the LSOR solver). Albeit smaller, the
501  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
502  in ice volume over the integration time. At first, this observation  to equally large differences in ice volume, especially in the Canadian
503    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 336  communication]{hunke01}: if the converge Line 513  communication]{hunke01}: if the converge
513  equations is not complete for all linearized solvers, then one can  equations is not complete for all linearized solvers, then one can
514  imagine that each solver stops at a different point in velocity-space  imagine that each solver stops at a different point in velocity-space
515  thus leading to different solutions for the ice drift velocities. If  thus leading to different solutions for the ice drift velocities. If
516  this were true, this tantalizing circumstance had a dramatic impact on  this were true, this tantalizing circumstance would have a dramatic
517  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
518  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
519  compuational cost (Bruno Tremblay, personal communication).  high compuational cost (Bruno Tremblay, personal communication).
520    
521    Further, we observe that the EVP solutions tends to produce
522    effectively ``weaker'' ice that yields more easily to stress. This was
523  \begin{itemize}  also observed by \citet{hunke99} in a fast response to changing winds,
524  \item Configuration  their Figures\,10--12, where the EVP model adjusts quickly to a
525  \item OBCS from cube  cyclonic wind pattern, while the LSOR solution lags in time. This
526  \item forcing  property of the EVP solutions allows larger ice transports through
527  \item 1/2 and full resolution  narrow straits, where the implicit solver LSOR forms rigid ice. The
528  \item with a few JFM figs from C-grid LSR no slip  underlying reasons for this striking difference need further
529    ice transport through Canadian Archipelago  exploration.
530    thickness distribution  
531    ice velocity and transport  % THIS is now almost all in the text:
532  \end{itemize}  %\begin{itemize}
533    %\item Configuration
534  \begin{itemize}  %\item OBCS from cube
535  \item Arctic configuration  %\item forcing
536  \item ice transport through straits and near boundaries  %\item 1/2 and full resolution
537  \item focus on narrow straits in the Canadian Archipelago  %\item with a few JFM figs from C-grid LSR no slip
538  \end{itemize}  %  ice transport through Canadian Archipelago
539    %  thickness distribution
540  \begin{itemize}  %  ice velocity and transport
541  \item B-grid LSR no-slip: B-LSR-ns  %\end{itemize}
542  \item C-grid LSR no-slip: C-LSR-ns  
543  \item C-grid LSR slip:    C-LSR-fs  %\begin{itemize}
544  \item C-grid EVP no-slip: C-EVP-ns  %\item Arctic configuration
545  \item C-grid EVP slip:    C-EVP-fs  %\item ice transport through straits and near boundaries
546  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,  %\item focus on narrow straits in the Canadian Archipelago
547    new flag): C-LSR-ns+TEM  %\end{itemize}
548  \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?  
549  \item C-grid LSR no-slip + Winton:  %\begin{itemize}
550  \item  speed-performance-accuracy (small)  %\item B-grid LSR no-slip: B-LSR-ns
551    ice transport through Canadian Archipelago differences  %\item C-grid LSR no-slip: C-LSR-ns
552    thickness distribution differences  %\item C-grid LSR slip:    C-LSR-fs
553    ice velocity and transport differences  %\item C-grid EVP no-slip: C-EVP-ns
554  \end{itemize}  %\item C-grid EVP slip:    C-EVP-fs
555    %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
556  We anticipate small differences between the different models due to:  %  new flag): C-LSR-ns+TEM
557  \begin{itemize}  %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
558  \item advection schemes: along the ice-edge and regions with large  %\item C-grid LSR no-slip + Winton:
559    gradients  %\item  speed-performance-accuracy (small)
560  \item C-grid: less transport through narrow straits for no slip  %  ice transport through Canadian Archipelago differences
561    conditons, more for free slip  %  thickness distribution differences
562  \item VP vs.\ EVP: speed performance, accuracy?  %  ice velocity and transport differences
563  \item ocean stress: different water mass properties beneath the ice  %\end{itemize}
564  \end{itemize}  
565    %We anticipate small differences between the different models due to:
566  %\begin{figure}  %\begin{itemize}
567  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}  %\item advection schemes: along the ice-edge and regions with large
568  %\caption{Surface sea ice velocity for different solver flavors.  %  gradients
569  %\label{fig:iceveloc}}  %\item C-grid: less transport through narrow straits for no slip
570  %\end{figure}  %  conditons, more for free slip
571    %\item VP vs.\ EVP: speed performance, accuracy?
572  %\begin{figure}  %\item ocean stress: different water mass properties beneath the ice
573  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}  %\end{itemize}
 %\caption{Sea ice thickness for different solver flavors.  
 %\label{fig:icethick}}  
 %\end{figure}  
574    
575  %%% Local Variables:  %%% Local Variables:
576  %%% mode: latex  %%% mode: latex
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