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revision 1.15 by mlosch, Mon Jun 2 13:25:40 2008 UTC revision 1.18 by mlosch, Thu Jul 3 18:16:22 2008 UTC
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1  \section{Forward sensitivity experiments}  \section{Forward Sensitivity Experiments in an Arctic Domain with Open
2    Boundaries}
3  \label{sec:forward}  \label{sec:forward}
4    
5  This section presents results from global and regional coupled ocean and sea  This section presents results from regional coupled ocean and sea
6  ice simulations that exercise various capabilities of the MITgcm sea ice  ice simulations of the Arctic Ocean that exercise various capabilities of the MITgcm sea ice
7  model.  The first set of results is from a global, eddy-permitting, ocean and  model.
8  sea ice configuration.  The second set of results is from a regional Arctic  The objective is to
9  configuration, which is used to compare the B-grid and C-grid dynamic solvers  compare the old B-grid LSOR dynamic solver with the new C-grid LSOR and
10  and various other capabilities of the MITgcm sea ice model.    EVP solvers. Additional experiments are carried out to illustrate
11  %  the differences between different ice advection schemes, ocean-ice
12  \ml{[do we really want to do this?:] The third set of  stress formulations and the two main options for sea ice
13  results is from a yet smaller regional domain, which is used to illustrate  thermodynamics in the MITgcm.
 treatment of sea ice open boundary condition in the MITgcm.}  
14    
15  \subsection{Global Ocean and Sea Ice Simulation}  \subsection{Model configuration and experiments}
16  \label{sec:global}  \label{sec:arcticmodel}
17    The Arctic model domain is illustrated in \reffig{arctic_topog}.
18    \begin{figure*}
19    %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
20    %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
21    %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
22    %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
23    \includegraphics*[width=\linewidth]{\fpath/topography}
24    \caption{Left: Bathymetry and domain boundaries of Arctic
25      Domain.
26      %; the dashed line marks the boundaries of the inset on the right hand side.
27      The letters in the inset label sections in the
28      Canadian Archipelago, where ice transport is evaluated:
29      A: Nares Strait; %
30      B: \ml{Meighen Island}; %
31      C: Prince Gustaf Adolf Sea; %
32      D: \ml{Brock Island}; %
33      E: M'Clure Strait; %
34      F: Amundsen Gulf; %
35      G: Lancaster Sound; %
36      H: Barrow Strait \ml{W.}; %
37      I: Barrow Strait \ml{E.}; %
38      J: Barrow Strait \ml{N.}; %
39      K: Fram Strait. %
40      The sections A through F comprise the total inflow into the Canadian
41      Archipelago. \ml{[May still need to check the geography.]}
42      \label{fig:arctic_topog}}
43    \end{figure*}
44    It has 420 by 384 grid boxes and is carved out, and obtains open
45    boundary conditions from, a global cubed-sphere configuration
46    similar to that described in \citet{menemenlis05}.
47    
48  The global ocean and sea ice results presented below were carried out as part  The global ocean and sea ice results presented in \citet{menemenlis05}
49    were carried out as part
50  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
51  project.  ECCO2 aims to produce increasingly accurate syntheses of all  project.  ECCO2 aims to produce increasingly accurate syntheses of all
52  available global-scale ocean and sea-ice data at resolutions that start to  available global-scale ocean and sea-ice data at resolutions that start to
53  resolve ocean eddies and other narrow current systems, which transport heat,  resolve ocean eddies and other narrow current systems, which transport heat,
54  carbon, and other properties within the ocean \citep{menemenlis05}.  The  carbon, and other properties within the ocean \citep{menemenlis05}.  The
55  particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)  particular ECCO2 simulation from which we obtain the boundary
56    conditions is a baseline 28-year (1979-2006)
57  integration, labeled cube76, which has not yet been constrained by oceanic and  integration, labeled cube76, which has not yet been constrained by oceanic and
58  by sea ice data.  A cube-sphere grid projection is employed, which permits  by sea ice data. A cube-sphere grid projection is employed, which permits
59  relatively even grid spacing throughout the domain and which avoids polar  relatively even grid spacing throughout the domain and which avoids polar
60  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
61  510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are  510 by 510 grid cells for a mean horizontal grid spacing of 18\,km. There are
62  50 vertical levels ranging in thickness from 10 m near the surface to  50 vertical levels ranging in thickness from 10 m near the surface to
63  approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the  approximately 450 m at a maximum model depth of 6150 m. The model employs the
64  National Geophysical Data Center (NGDC) 2-minute gridded global relief data  partial-cell formulation of
 (ETOPO2) and the model employs the partial-cell formulation of  
65  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
66  bathymetry. The model is integrated in a volume-conserving configuration using  bathymetry. Bathymetry is from the S2004 (W.~Smith, unpublished) blend of the
67    \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one
68    arc-minute bathymetric grid. % (see Fig.~\ref{fig:CubeBathymetry}).
69    The model is integrated in a volume-conserving configuration using
70  a finite volume discretization with C-grid staggering of the prognostic  a finite volume discretization with C-grid staggering of the prognostic
71  variables. In the ocean, the non-linear equation of state of \citet{jac95} is  variables. In the ocean, the non-linear equation of state of \citet{jac95} is
72  used.  used.
73    %
74  The ocean model is coupled to the sea-ice model discussed in  The global ocean model is coupled to a sea ice model in a
75  \refsec{model} using the following specific options.  The  configuration similar to the case C-LSR-ns (see \reftab{experiments}),
76  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is  with open water, dry ice, wet ice, dry snow, and wet snow albedos of,
77  used to compute sea ice thickness and concentration.  Snow cover and  respectively, 0.15, 0.88, 0.79, 0.97, and 0.83.
 sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry  
 snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,  
 and 0.83. Ice mechanics follow the viscous plastic rheology of  
 \citet{hibler79} and the ice momentum equation is solved numerically  
 using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics  
 model discussed hereinabove.  The ice is coupled to the ocean using  
 the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},  
 that is, sea ice does not float above the ocean model but rather  
 deforms the ocean's model surface level.  
78    
79  This particular ECCO2 simulation is initialized from temperature and salinity  This particular ECCO2 simulation is initialized from temperature and salinity
80  fields derived from the Polar science center Hydrographic Climatology (PHC)  fields derived from the Polar science center Hydrographic Climatology (PHC)
# Line 65  radiations, and precipitation are conver Line 90  radiations, and precipitation are conver
90  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
91  radiation decays exponentially as per \citet{pau77}.  Low frequency  radiation decays exponentially as per \citet{pau77}.  Low frequency
92  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
93  Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river  Precipitation Climatology Project \citep[GPCP,][]{huf01}.  The time-mean river
94  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
95  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)
96  and prepared by P. Winsor (personnal communication, 2007) is specificied.  and prepared by P. Winsor (personnal communication, 2007) is specificied.
# Line 84  advection scheme \citep{dar04} is employ Line 109  advection scheme \citep{dar04} is employ
109  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
110  the divergent flow as per \citet{kem08}.  the divergent flow as per \citet{kem08}.
111    
112  \ml{[Dimitris, here you need to either provide figures, so that I can  The model configuration of cube76 carries over to the Arctic domain
113    write text, or you can provide both figures and text. I guess, one  configuration except for numerical details related to the non-linear
114    figure, showing the northern and southern hemisphere in summer and  free surface that are not supported by the open boundary code, and the
115    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
116    the next section.]}  are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
117    
118    The model is integrated from Jan~01, 1992 to Mar~31, 2000
119  \subsection{Arctic Domain with Open Boundaries}  \reftab{experiments} gives an overview over the experiments discussed
120  \label{sec:arctic}  in \refsec{arcticresults}.
121    \begin{table}
122  A series of forward sensitivity experiments have been carried out on    \caption{Overview over model simulations in \refsec{arcticresults}.
123  an Arctic Ocean domain with open boundaries.  The objective is to      \label{tab:experiments}}
 compare the old B-grid LSR dynamic solver with the new C-grid LSR and  
 EVP solvers.  Additional experiments are carried out to illustrate  
 the differences between different ice advection schemes, ocean-ice  
 stress formulations and the two main options for sea ice  
 thermodynamics in the MITgcm.  
   
 The Arctic domain of integration is illustrated in  
 \reffig{arctic_topog}.  It is carved out from, and obtains open  
 boundary conditions from, the global cubed-sphere configuration  
 described above.  The horizontal domain size is 420 by 384 grid boxes.  
 \begin{figure*}  
 %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}  
 %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}  
 \includegraphics*[width=0.44\linewidth]{\fpath/topography}  
 \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}  
 \caption{Left: Bathymetry and domain boudaries of Arctic  
   Domain; the dashed line marks the boundaries of the inset on the  
   right hand side. The letters in the inset label sections in the  
   Canadian Archipelago, where ice transport is evaluated:  
   A: Nares Strait; %  
   B: \ml{Meighen Island}; %  
   C: Prince Gustaf Adolf Sea; %  
   D: \ml{Brock Island}; %  
   E: M'Clure Strait; %  
   F: Amundsen Gulf; %  
   G: Lancaster Sound; %  
   H: Barrow Strait \ml{W.}; %  
   I: Barrow Strait \ml{E.}; %  
   J: Barrow Strait \ml{N.}. %  
   The sections A through F comprise the total inflow into the Canadian  
   Archipelago. \ml{[May still need to check the geography.]}  
   \label{fig:arctic_topog}}  
 \end{figure*}  
   
 The main dynamic difference from cube sphere is that the Arctic domain  
 configuration does not use rescaled vertical coordinates (z$^\ast$)  
 and the surface boundary conditions for freshwater input are  
 different, because those features are not supported by the open  
 boundary code.  
 %  
 Open water, dry ice, wet ice, dry snow, and wet snow albedo are,  
 respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.  
   
 The model is integrated from Jan~01, 1992 to Mar~31, 2000,  
 with three different dynamical solvers, two different boundary  
 conditions, different stress coupling, rheology, and advection  
 schemes. \reftab{experiments} gives an overview over the experiments  
 discussed in this section.  
 \begin{table}[htbp]  
124    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
125      experiment name & description \\ \hline      experiment name & description \\ \hline
126      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
127    Arakawa B-grid, implying no-slip lateral boundary conditions    Arakawa B-grid, implying no-slip lateral boundary conditions
128    ($\vek{u}=0$ exactly) \\    ($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order
129      central difference scheme plus explicit diffusion for stability \\
130      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
131    boundary conditions (implemented via ghost-points) \\    boundary conditions (implemented via ghost-points) \\
132      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 170  discussed in this section. Line 147  discussed in this section.
147    direct-space-time advection scheme for thermodynamic variables    direct-space-time advection scheme for thermodynamic variables
148    \citep{hundsdorfer94}    \citep{hundsdorfer94}
149    \end{tabular}    \end{tabular}
   \caption{Overview over model simulations in \refsec{arctic}.  
     \label{tab:experiments}}  
150  \end{table}  \end{table}
151  %\begin{description}  %\begin{description}
152  %\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 216  of 1200\,s resulting in a very long and Line 191  of 1200\,s resulting in a very long and
191  ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the  ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
192  forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).  forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
193    
194  A principle difficulty in comparing the solutions obtained with  \subsection{Results}
195  different realizations of the model dynamics lies in the non-linear  \label{sec:arcticresults}
196  feedback of the ice dynamics and thermodynamics. Already after a few  
197  months the solutions have diverged so far from each other that  Comparing the solutions obtained with different realizations of the
198  comparing velocities only makes sense within the first 3~months of the  model dynamics is difficult because of the non-linear feedback of the
199    ice dynamics and thermodynamics. Already after a few months the
200    solutions have diverged so far from each other that comparing
201    velocities only makes sense within the first 3~months of the
202  integration while the ice distribution is still close to the initial  integration while the ice distribution is still close to the initial
203  conditions. At the end of the integration, the differences between the  conditions. At the end of the integration, the differences between the
204  model solutions can be interpreted as cumulated model uncertainties.  model solutions can be interpreted as cumulated model uncertainties.
205    
206    \subsubsection{Ice velocities in JFM 1992}
207    
208  \reffig{iceveloc} shows ice velocities averaged over Janunary,  \reffig{iceveloc} shows ice velocities averaged over Janunary,
209  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
# Line 235  models in a cyclonic circulation regime Line 215  models in a cyclonic circulation regime
215  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
216  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
217    
218  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)  \newcommand{\subplotwidth}{0.44\textwidth}
219  is most pronounced along the coastlines, where the discretization  %\newcommand{\subplotwidth}{0.3\textwidth}
220  differs most between B and C-grids: On a B-grid the tangential  \begin{figure}[tp]
 velocity lies on the boundary (and is thus zero through the no-slip  
 boundary conditions), whereas on the C-grid it is half a cell width  
 away from the boundary, thus allowing more flow. The B-LSR-ns solution  
 has less ice drift through the Fram Strait and especially the along  
 Greenland's east coast; also, the flow through Baffin Bay and Davis  
 Strait into the Labrador Sea is reduced with respect the C-LSR-ns  
 solution.  \ml{[Do we expect this? Say something about that]}  
 %  
 Compared to the differences between B and C-grid solutions,the  
 C-LSR-fs ice drift field differs much less from the C-LSR-ns solution  
 (\reffig{iceveloc}c).  As expected the differences are largest along  
 coastlines: because of the free-slip boundary conditions, flow is  
 faster in the C-LSR-fs solution, for example, along the east coast  
 of Greenland, the north coast of Alaska, and the east Coast of Baffin  
 Island.  
 %\newcommand{\subplotwidth}{0.44\textwidth}  
 \newcommand{\subplotwidth}{0.3\textwidth}  
 \begin{figure}[htbp]  
221    \centering    \centering
222    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
223    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
# Line 266  Island. Line 228  Island.
228    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
229    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
230    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
231    \\  %  \\
232    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
233    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
234    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
235    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
236    \\  %  \\
237    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
238    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
239    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
240    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
241    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
242      over the first 3 months of integration [cm/s]; (b)-(h) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
243      between solutions with B-grid, free lateral slip, EVP-solver,      between solutions with B-grid, free lateral slip, EVP-solver,
# Line 286  Island. Line 248  Island.
248      of speed), vectors indicate direction only.}      of speed), vectors indicate direction only.}
249    \label{fig:iceveloc}    \label{fig:iceveloc}
250  \end{figure}  \end{figure}
251    \addtocounter{figure}{-1}
252    \setcounter{subfigure}{4}
253    \begin{figure}[t]
254      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
255      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
256      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
257      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
258      \\
259      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
260      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
261      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
262      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
263      \caption{continued}
264    \end{figure}
265    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
266    is most pronounced along the coastlines, where the discretization
267    differs most between B and C-grids: On a B-grid the tangential
268    velocity lies on the boundary (and is thus zero through the no-slip
269    boundary conditions), whereas on the C-grid it is half a cell width
270    away from the boundary, thus allowing more flow. The B-LSR-ns solution
271    has less ice drift through the Fram Strait and especially the along
272    Greenland's east coast; also, the flow through Baffin Bay and Davis
273    Strait into the Labrador Sea is reduced with respect the C-LSR-ns
274    solution.  \ml{[Do we expect this? Say something about that]}
275    %
276    Compared to the differences between B and C-grid solutions, the
277    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
278    (\reffig{iceveloc}c).  As expected the differences are largest along
279    coastlines: because of the free-slip boundary conditions, flow is
280    faster in the C-LSR-fs solution, for example, along the east coast
281    of Greenland, the north coast of Alaska, and the east Coast of Baffin
282    Island.
283    
284  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
285  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
# Line 305  EVP solutions. Line 299  EVP solutions.
299  %  \label{fig:drifthist}  %  \label{fig:drifthist}
300  %\end{figure}  %\end{figure}
301    
302    Compared to the other parameters, the ice rheology TEM
303    (\reffig{iceveloc}(e)) has a very small effect on the solution. In
304    general the ice drift tends to be increased, because there is no
305    tensile stress and ice can be ``pulled appart'' at no cost.
306    Consequently, the largest effect on drift velocity can be observed
307    near the ice edge in the Labrador Sea. In contrast, in the run with
308    the ice-ocean stress formulation of \citet{hibler87},
309    \reffig{iceveloc}(f) the drift is stronger almost everywhere in the
310    computational domain. The increase is mostly aligned with the general
311    direction of the flow, implying that the different stress formulation
312    reduces the deceleration of drift by the ocean.
313    
314    The 3-layer thermodynamics following \citet{winton00} requires
315    additional information on initial conditions for enthalphy. These
316    different initial conditions make a comparison of the first months
317    difficult to interpret. The drift in the Beaufort Gyre is slightly
318    reduced relative to the reference run C-LSR-ns, but the drift through
319    the Fram Strait is increased. The drift velocities near the ice edge
320    are very different, because the ice extend is already larger in
321    \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
322    drift velocities, because the ice motion is more contrained by a
323    larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
324    place is drifting nearly freely.
325    
326    A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
327    \reffig{iceveloc}(h)) has its largest effect along the ice edge, where
328    the gradients of thickness and concentration are largest. Everywhere
329    else the effect is very small and can mostly be attributed to smaller
330    numerical diffusion (and to the absense of explicitly diffusion for
331    numerical stability).
332    
333    \subsubsection{Ice volume during JFM 2000}
334    
335  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
336  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
337  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
338  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
339  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--d, and
340  concentrations (not shown).  concentrations (not shown).
341  \begin{figure}[htbp]  \begin{figure}[tp]
342    \centering    \centering
343    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
344    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
# Line 322  concentrations (not shown). Line 349  concentrations (not shown).
349    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
350    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
351    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
352    \\    \caption{(a) Effective thickness (volume per unit area) of the
353        C-LSR-ns solution, averaged over the months Janurary through March
354        2000 [m]; (b)-(h) difference between solutions with B-grid, free
355        lateral slip, EVP-solver, truncated ellipse method (TEM),
356        different ice-ocean stress formulation (HB87), different
357        thermodynamics (WTD), different advection for thermodynamic
358        variables (DST3FL) and the C-LSR-ns reference solution [m].}
359      \label{fig:icethick}
360    \end{figure}
361    \addtocounter{figure}{-1}
362    \setcounter{subfigure}{4}
363    \begin{figure}[t]
364    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
365    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
366    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
# Line 332  concentrations (not shown). Line 370  concentrations (not shown).
370    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
371    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
372    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
373    \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}  
374  \end{figure}  \end{figure}
 %  
375  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
376  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
377  narrow passages in the Canadian Archipelago, lead to a larger build-up  narrow passages in the Canadian Archipelago, lead to a larger build-up
# Line 364  in the Canadian Archipelago. There it re Line 394  in the Canadian Archipelago. There it re
394  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
395  narrow.  Dipoles of ice thickness differences can also be observed  narrow.  Dipoles of ice thickness differences can also be observed
396  around islands, because the free-slip solution allows more flow around  around islands, because the free-slip solution allows more flow around
397  islands than the no-slip solution.  Everywhere else the ice volume is  islands than the no-slip solution. Everywhere else the ice volume is
398  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
399  %  %
400  The C-EVP-ns solution has generally stronger drift velocities than the  The C-EVP-ns solution has generally stronger drift velocities than the
# Line 379  in the Archipelago the ice thickness is Line 409  in the Archipelago the ice thickness is
409  time step and the ice is still thinner by 2\,m and more, as in the EVP  time step and the ice is still thinner by 2\,m and more, as in the EVP
410  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
411    
412    In year 2000, there is more ice everywhere in the domain in
413    \mbox{C-LSR-ns WTD}, \reffig{icethick}(g). This difference, which is
414    even more pronounced in summer (not shown), can be attributed to
415    direct effects of the different thermodynamics in this run. The
416    remaining runs have the largest differences in effective ice thickness
417    long the north coasts of Greenland and Ellesmere Island. Although the
418    effects of TEM and \citet{hibler87}'s ice-ocean stress formulation are
419    so different on the initial ice velocities, both runs have similarly
420    reduced ice thicknesses in this area. The 3rd-order advection scheme
421    has an opposite effect of similar magnitude, point towards more
422    implicit lateral stress with this numerical scheme.
423    
424  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
425  differences that were observed between different hindcast and climate  differences that were observed between different hindcast models and climate
426  models in \citet{gerdes07}. There the range of sea ice volume of  models in \citet{gerdes07}. There the range of sea ice volume of
427  different sea ice-ocean models (which shared very similar forcing  different sea ice-ocean models (which shared very similar forcing
428  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
# Line 427  with large uncertainties; also note that Line 469  with large uncertainties; also note that
469  ice-ocean model to reproduce observations is not our goal, but we use  ice-ocean model to reproduce observations is not our goal, but we use
470  the published numbers as an orientation.  the published numbers as an orientation.
471    
472  \reffig{archipelago} shows a time series of daily averaged, smoothed  \subsubsection{Ice transports}
473  with monthly running means, ice transports through various straits in  
474  the Canadian Archipelago and the Fram Strait for the different model  \reffig{archipelago} shows an excerpt of a time series of daily
475  solutions and \reftab{icevolume} summarizes the time series. The  averaged, smoothed with monthly running means, ice transports through
476  export through Fram Strait agrees with the observations in all model  various straits in the Canadian Archipelago and the Fram Strait for
477  solutions (annual averages range from $2110$ to  the different model solutions and \reftab{icevolume} summarizes the
478    time series.
479    \begin{figure}
480    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
481    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
482    %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
483    \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
484    \caption{Transport through Canadian Archipelago for different solver
485      flavors. The letters refer to the labels of the sections in
486      \reffig{arctic_topog}; positive values are flux out of the Arctic;
487      legend abbreviations are explained in \reftab{experiments}. The mean
488      range of the different model solution is taken over the period Jan
489      1992 to Dec 1999.
490    \label{fig:archipelago}}
491    \end{figure}
492    The export through Fram Strait agrees with the observations in all
493    model solutions (annual averages range from $2110$ to
494  $2300\text{\,km$^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
495  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
496  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}$}$),
# Line 449  drift velocities are largest in these so Line 507  drift velocities are largest in these so
507  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
508  configuration, both B- and C-grid LSOR solvers lead to practically no  configuration, both B- and C-grid LSOR solvers lead to practically no
509  ice transport, while the C-EVP solutions allow up to  ice transport, while the C-EVP solutions allow up to
510  $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
511  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,
512  the Candian Archipelago is larger in all EVP solutions  the import into the Candian Archipelago is larger in all EVP solutions
513  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
514  than in the LSOR solutions.  than in the LSOR solutions.
515  %get the order of magnitude right (range: $132$ to  %get the order of magnitude right (range: $132$ to
# Line 460  The B-LSR-ns solution is even smaller by Line 518  The B-LSR-ns solution is even smaller by
518  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
519  tends to block the transport).  tends to block the transport).
520  %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}  
521    
522  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
523  %  schemes, Winton TD, discussion about differences in terms of model  %  schemes, Winton TD, discussion about differences in terms of model
524  %  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
525  %  models are all erroneous!]}  %  models are all erroneous!]}
526    
527    \subsubsection{Discussion}
528    
529  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
530  different solutions. In constrast to that, the differences between  different solutions. In constrast to that, the differences between
531  free-slip and no-slip solutions \emph{with the same solver} are  free-slip and no-slip solutions \emph{with the same solver} are
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