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revision 1.16 by dimitri, Wed Jun 4 00:39:25 2008 UTC revision 1.17 by mlosch, Wed Jun 4 13:32:05 2008 UTC
# Line 116  described above.  The horizontal domain Line 116  described above.  The horizontal domain
116  \begin{figure*}  \begin{figure*}
117  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
118  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
119  \includegraphics*[width=0.44\linewidth]{\fpath/topography}  %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
120  \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}  %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
121    \includegraphics*[width=\linewidth]{\fpath/topography}
122  \caption{Left: Bathymetry and domain boudaries of Arctic  \caption{Left: Bathymetry and domain boudaries of Arctic
123    Domain; the dashed line marks the boundaries of the inset on the    Domain; the dashed line marks the boundaries of the inset on the
124    right hand side. The letters in the inset label sections in the    right hand side. The letters in the inset label sections in the
# Line 131  described above.  The horizontal domain Line 132  described above.  The horizontal domain
132    G: Lancaster Sound; %    G: Lancaster Sound; %
133    H: Barrow Strait \ml{W.}; %    H: Barrow Strait \ml{W.}; %
134    I: Barrow Strait \ml{E.}; %    I: Barrow Strait \ml{E.}; %
135    J: Barrow Strait \ml{N.}. %    J: Barrow Strait \ml{N.}; %
136      K: Fram Strait. %
137    The sections A through F comprise the total inflow into the Canadian    The sections A through F comprise the total inflow into the Canadian
138    Archipelago. \ml{[May still need to check the geography.]}    Archipelago. \ml{[May still need to check the geography.]}
139    \label{fig:arctic_topog}}    \label{fig:arctic_topog}}
# Line 151  with three different dynamical solvers, Line 153  with three different dynamical solvers,
153  conditions, different stress coupling, rheology, and advection  conditions, different stress coupling, rheology, and advection
154  schemes. \reftab{experiments} gives an overview over the experiments  schemes. \reftab{experiments} gives an overview over the experiments
155  discussed in this section.  discussed in this section.
156  \begin{table}[htbp]  \begin{table}[t]
157      \caption{Overview over model simulations in \refsec{arctic}.
158        \label{tab:experiments}}
159    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
160      experiment name & description \\ \hline      experiment name & description \\ \hline
161      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
# Line 177  discussed in this section. Line 181  discussed in this section.
181    direct-space-time advection scheme for thermodynamic variables    direct-space-time advection scheme for thermodynamic variables
182    \citep{hundsdorfer94}    \citep{hundsdorfer94}
183    \end{tabular}    \end{tabular}
   \caption{Overview over model simulations in \refsec{arctic}.  
     \label{tab:experiments}}  
184  \end{table}  \end{table}
185  %\begin{description}  %\begin{description}
186  %\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 242  models in a cyclonic circulation regime Line 244  models in a cyclonic circulation regime
244  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
245  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
246    
247  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)  \newcommand{\subplotwidth}{0.44\textwidth}
248  is most pronounced along the coastlines, where the discretization  %\newcommand{\subplotwidth}{0.3\textwidth}
249  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]  
250    \centering    \centering
251    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
252    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
# Line 273  Island. Line 257  Island.
257    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
258    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
259    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
260    \\  %  \\
261    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
262    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
263    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
264    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
265    \\  %  \\
266    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
267    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
268    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
269    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
270    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
271      over the first 3 months of integration [cm/s]; (b)-(h) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
272      between solutions with B-grid, free lateral slip, EVP-solver,      between solutions with B-grid, free lateral slip, EVP-solver,
# Line 293  Island. Line 277  Island.
277      of speed), vectors indicate direction only.}      of speed), vectors indicate direction only.}
278    \label{fig:iceveloc}    \label{fig:iceveloc}
279  \end{figure}  \end{figure}
280    \addtocounter{figure}{-1}
281    \setcounter{subfigure}{4}
282    \begin{figure}[t]
283      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
284      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
285      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
286      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
287      \\
288      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
289      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
290      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
291      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
292      \caption{continued}
293    \end{figure}
294    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
295    is most pronounced along the coastlines, where the discretization
296    differs most between B and C-grids: On a B-grid the tangential
297    velocity lies on the boundary (and is thus zero through the no-slip
298    boundary conditions), whereas on the C-grid it is half a cell width
299    away from the boundary, thus allowing more flow. The B-LSR-ns solution
300    has less ice drift through the Fram Strait and especially the along
301    Greenland's east coast; also, the flow through Baffin Bay and Davis
302    Strait into the Labrador Sea is reduced with respect the C-LSR-ns
303    solution.  \ml{[Do we expect this? Say something about that]}
304    %
305    Compared to the differences between B and C-grid solutions, the
306    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
307    (\reffig{iceveloc}c).  As expected the differences are largest along
308    coastlines: because of the free-slip boundary conditions, flow is
309    faster in the C-LSR-fs solution, for example, along the east coast
310    of Greenland, the north coast of Alaska, and the east Coast of Baffin
311    Island.
312    
313  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
314  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 312  EVP solutions. Line 328  EVP solutions.
328  %  \label{fig:drifthist}  %  \label{fig:drifthist}
329  %\end{figure}  %\end{figure}
330    
331    Compared to the other parameters, the ice rheology TEM
332    (\reffig{iceveloc}(e)) has a very small effect on the solution. In
333    general the ice drift tends to be increased, because there is no
334    tensile stress and ice can be ``pulled appart'' at no cost.
335    Consequently, the largest effect on drift velocity can be observed
336    near the ice edge in the Labrador Sea. In contrast, in the run with
337    the ice-ocean stress formulation of \citet{hibler87},
338    \reffig{iceveloc}(f) the drift is stronger almost everywhere in the
339    computational domain. The increase is mostly aligned with the general
340    direction of the flow, implying that the different stress formulation
341    reduces the deceleration of drift by the ocean.
342    
343    The 3-layer thermodynamics following \citet{winton00} requires
344    additional information on initial conditions for enthalphy. These
345    different initial conditions make a comparison of the first months
346    difficult to interpret. The drift in the Beaufort Gyre is slightly
347    reduced relative to the reference run C-LSR-ns, but the drift through
348    the Fram Strait is increased. The drift velocities near the ice edge
349    are very different, because the ice extend is already larger in
350    \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
351    drift velocities, because the ice motion is more contrained by a
352    larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
353    place is drifting nearly freely.
354    
355    A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
356    \reffig{iceveloc}(h)) has its largest effect along the ice edge, where
357    the gradients of thickness and concentration are largest. Everywhere
358    else the effect is very small and can mostly be attributed to smaller
359    numerical diffusion (and to the absense of explicitly diffusion for
360    numerical stability).
361    
362  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
363  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
364  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
365  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
366  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--d, and
367  concentrations (not shown).  concentrations (not shown).
368  \begin{figure}[htbp]  \begin{figure}[tp]
369    \centering    \centering
370    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
371    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
# Line 329  concentrations (not shown). Line 376  concentrations (not shown).
376    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
377    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
378    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
379    \\    \caption{(a) Effective thickness (volume per unit area) of the
380        C-LSR-ns solution, averaged over the months Janurary through March
381        2000 [m]; (b)-(h) difference between solutions with B-grid, free
382        lateral slip, EVP-solver, truncated ellipse method (TEM),
383        different ice-ocean stress formulation (HB87), different
384        thermodynamics (WTD), different advection for thermodynamic
385        variables (DST3FL) and the C-LSR-ns reference solution [m].}
386      \label{fig:icethick}
387    \end{figure}
388    \addtocounter{figure}{-1}
389    \setcounter{subfigure}{4}
390    \begin{figure}[t]
391    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
392    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
393    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
# Line 339  concentrations (not shown). Line 397  concentrations (not shown).
397    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
398    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
399    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
400    \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}  
401  \end{figure}  \end{figure}
402  %  %
403  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
# Line 371  in the Canadian Archipelago. There it re Line 422  in the Canadian Archipelago. There it re
422  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
423  narrow.  Dipoles of ice thickness differences can also be observed  narrow.  Dipoles of ice thickness differences can also be observed
424  around islands, because the free-slip solution allows more flow around  around islands, because the free-slip solution allows more flow around
425  islands than the no-slip solution.  Everywhere else the ice volume is  islands than the no-slip solution. Everywhere else the ice volume is
426  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
427  %  %
428  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 386  in the Archipelago the ice thickness is Line 437  in the Archipelago the ice thickness is
437  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
438  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
439    
440    In year 2000, there more ice everywhere in the domain in
441    \mbox{C-LSR-ns WTD}, \reffig{icethick}(g). This difference, which is
442    even more pronounced in summer (not shown), can be attributed to
443    direct effects of the different thermodynamics in this run. The
444    remaining runs have the largest differences in effective ice thickness
445    long the north coasts of Greenland and Ellesmere Island. Although the
446    effects of TEM and \citet{hibler87}'s ice-ocean stress formulation are
447    so different on the initial ice velocities, both runs have similarly
448    reduced ice thicknesses in this area. The 3rd-order advection scheme
449    has an opposite effect of similar magnitude, point towards more
450    implicit lateral stress with this numerical scheme.
451    
452  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
453  differences that were observed between different hindcast and climate  differences that were observed between different hindcast models and climate
454  models in \citet{gerdes07}. There the range of sea ice volume of  models in \citet{gerdes07}. There the range of sea ice volume of
455  different sea ice-ocean models (which shared very similar forcing  different sea ice-ocean models (which shared very similar forcing
456  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 470  tends to block the transport). Line 533  tends to block the transport).
533  \begin{figure}  \begin{figure}
534  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
535  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
536  \centerline{{\includegraphics*[width=\linewidth]{\fpath/ice_export}}}  \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
537  \caption{Transport through Canadian Archipelago for different solver  \caption{Transport through Canadian Archipelago for different solver
538    flavors. The letters refer to the labels of the sections in    flavors. The letters refer to the labels of the sections in
539    \reffig{arctic_topog}; positive values are flux out of the Arctic;    \reffig{arctic_topog}; positive values are flux out of the Arctic;
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