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revision 1.19 by mlosch, Fri Jul 4 11:51:09 2008 UTC revision 1.21 by mlosch, Mon Jul 28 07:38:27 2008 UTC
# Line 215  of some of the AOMIP (Arctic Ocean Model Line 215  of some of the AOMIP (Arctic Ocean Model
215  models in a cyclonic circulation regime (CCR) \citep[their  models in a cyclonic circulation regime (CCR) \citep[their
216  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
217  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
218    %
219  \newcommand{\subplotwidth}{0.44\textwidth}  \newcommand{\subplotwidth}{0.47\textwidth}
220  %\newcommand{\subplotwidth}{0.3\textwidth}  %\newcommand{\subplotwidth}{0.3\textwidth}
221  \begin{figure}[tp]  \begin{figure}[tp]
222    \centering    \centering
223    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
224    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-ns}}
225    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
226    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_B-LSR-ns-C-LSR-ns}}
227    \\    \\
228    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
229    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-fs-C-LSR-ns}}
230    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
231    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-EVP-ns150-C-LSR-ns}}
232  %  \\  %  \\
233  %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
234  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
235  %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
236  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
237  %  \\  %  \\
238  %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
239  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
240  %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]  %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
241  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}  %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
242    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
243      over the first 3 months of integration [cm/s]; (b)-(h) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
244      between solutions with B-grid, free lateral slip, EVP-solver,      between solutions with B-grid, free lateral slip, EVP-solver,
# Line 251  shifted eastwards towards Alaska. Line 251  shifted eastwards towards Alaska.
251  \end{figure}  \end{figure}
252  \addtocounter{figure}{-1}  \addtocounter{figure}{-1}
253  \setcounter{subfigure}{4}  \setcounter{subfigure}{4}
254  \begin{figure}[t]  \begin{figure}[tp]
255    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
256    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}}
257    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
258    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}}
259    \\    \\
260    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
261    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}}
262    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
263    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}}
264    \caption{continued}    \caption{continued}
265  \end{figure}  \end{figure}
266    
267  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)  The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
268  is most pronounced along the coastlines, where the discretization  is most pronounced along the coastlines, where the discretization
269  differs most between B and C-grids: On a B-grid the tangential  differs most between B and C-grids: On a B-grid the tangential
# Line 284  Island. Line 285  Island.
285    
286  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
287  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
288  EVP-approximation of the VP-dynamics allows for increased drift by  EVP-approximation of the VP-dynamics allows for increased drift by up
289  over 2\,cm/s in the Beaufort Gyre and the transarctic drift.  to 8\,cm/s in the Beaufort Gyre and the transarctic drift.  In
290  %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns  general, drift velocities are strongly biased towards higher values in
291  %solution. [Really?, No]}  the EVP solutions.
 In general, drift velocities are biased towards higher values in the  
 EVP solutions.  
 % as can be seen from a histogram of the differences in  
 %\reffig{drifthist}.  
 %\begin{figure}[htbp]  
 %  \centering  
 %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}  
 %  \caption{Histogram of drift velocity differences for C-LSR-ns and  
 %    C-EVP-ns solution [cm/s].}  
 %  \label{fig:drifthist}  
 %\end{figure}  
292    
293  Compared to the other parameters, the ice rheology TEM  Compared to the other parameters, the ice rheology TEM
294  (\reffig{iceveloc}e) has a very small effect on the solution. In  (\reffig{iceveloc}e) has a very small effect on the solution. In
# Line 325  larger ice extent than in \mbox{C-LSR-ns Line 315  larger ice extent than in \mbox{C-LSR-ns
315  geographical position is nearly in free drift.  geographical position is nearly in free drift.
316    
317  A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},  A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
318  \reffig{iceveloc}h) has its largest effect along the ice edge, where  \reffig{iceveloc}h) has some effect along the ice edge, where
319  the gradients of thickness and concentration are largest. Everywhere  the gradients of thickness and concentration are largest. Everywhere
320  else the effect is very small and can mostly be attributed to smaller  else the effect is very small and can mostly be attributed to smaller
321  numerical diffusion (and to the absense of explicit diffusion for  numerical diffusion (and to the absense of explicit diffusion that is
322  numerical stability).  requird for numerical stability in a simple second order central
323    differences scheme).
324    
325  \subsubsection{Ice volume during JFM 2000}  \subsubsection{Ice volume during JFM 2000}
326    
# Line 361  concentrations (not shown). Line 352  concentrations (not shown).
352  \end{figure}  \end{figure}
353  \addtocounter{figure}{-1}  \addtocounter{figure}{-1}
354  \setcounter{subfigure}{4}  \setcounter{subfigure}{4}
355  \begin{figure}[t]  \begin{figure}[tp]
356    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
357    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
358    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
# Line 375  concentrations (not shown). Line 366  concentrations (not shown).
366  \end{figure}  \end{figure}
367  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
368  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
369  narrow passages in the Canadian Archipelago, lead to a larger build-up  narrow passages in the Canadian Arctic Archipelago, lead to a larger build-up
370  of ice north of Greenland and the Archipelago by 2\,m effective  of ice north of Greenland and the Archipelago by 2\,m effective
371  thickness and more in the B-grid solution (\reffig{icethick}b). But  thickness and more in the B-grid solution (\reffig{icethick}b). But
372  the ice volume in not larger everywhere: further west, there are  the ice volume in not larger everywhere: further west, there are
# Line 391  solution. Line 382  solution.
382  Imposing a free-slip boundary condition in C-LSR-fs leads to much  Imposing a free-slip boundary condition in C-LSR-fs leads to much
383  smaller differences to C-LSR-ns in the central Arctic than the  smaller differences to C-LSR-ns in the central Arctic than the
384  transition from the B-grid to the C-grid (\reffig{icethick}c), except  transition from the B-grid to the C-grid (\reffig{icethick}c), except
385  in the Canadian Archipelago. There it reduces the effective ice  in the Canadian Arctic Archipelago. There it reduces the effective ice
386  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
387  narrow.  Dipoles of ice thickness differences can also be observed  narrow.  Dipoles of ice thickness differences can also be observed
388  around islands, because the free-slip solution allows more flow around  around islands, because the free-slip solution allows more flow around
389  islands than the no-slip solution. Everywhere else the ice volume is  islands than the no-slip solution. Everywhere else the ice volume is
390  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
391  %  %
392  The C-EVP-ns solution has generally stronger drift velocities than the  The C-EVP-ns solution has much thicker ice in the central Arctic Ocean
393  C-LSR-ns solution. Consequently, more ice can be moved from the  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).
394  eastern part of the Arctic, where ice volumes are smaller, to the  Within the Canadian Arctic Archipelago, more drift leads to faster ice export
395  western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,  and reduced effective ice thickness. With a shorter time step of
396  more drift leads to faster ice export and reduced effective ice  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to
397  thickness. With a shorter time step of  the LSOR solution (not shown). Only in the narrow straits in the
398  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to  Archipelago the ice thickness is not affected by the shorter time step
399  converge to the LSOR solution (not shown). Only in the narrow straits  and the ice is still thinner by 2\,m and more, as in the EVP solution
400  in the Archipelago the ice thickness is not affected by the shorter  with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
 time step and the ice is still thinner by 2\,m and more, as in the EVP  
 solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.  
401    
402  In year 2000, there is more ice everywhere in the domain in  In year 2000, there is more ice everywhere in the domain in
403  C-LSR-ns~WTD (\reffig{icethick}g). This difference, which is  C-LSR-ns~WTD (\reffig{icethick}g, note the color scale).
404  even more pronounced in summer (not shown), can be attributed to  This difference, which is even more pronounced in summer (not shown),
405  direct effects of the different thermodynamics in this run. The  can be attributed to direct effects of the different thermodynamics in
406  remaining runs have the largest differences in effective ice thickness  this run. The remaining runs have the largest differences in effective
407  long the north coasts of Greenland and Ellesmere Island. Although the  ice thickness long the north coasts of Greenland and Ellesmere Island.
408  effects of TEM and \citet{hibler87}'s ice-ocean stress formulation are  Although the effects of TEM and \citet{hibler87}'s ice-ocean stress
409  so different on the initial ice velocities, both runs have similarly  formulation are so different on the initial ice velocities, both runs
410  reduced ice thicknesses in this area. The 3rd-order advection scheme  have similarly reduced ice thicknesses in this area. The 3rd-order
411  has an opposite effect of similar magnitude, pointing towards more  advection scheme has an opposite effect of similar magnitude, pointing
412  implicit lateral stress with this numerical scheme.  towards more implicit lateral stress with this numerical scheme.
413    
414  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
415  differences that were observed between different hindcast models and climate  differences that were observed between different hindcast models and climate
# Line 432  averaging period) is smaller than $4,000 Line 421  averaging period) is smaller than $4,000
421  the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics  the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
422  leads to generally thicker ice (\reffig{icethick} and  leads to generally thicker ice (\reffig{icethick} and
423  \reftab{icevolume}).  \reftab{icevolume}).
424  \begin{table}[htbp]  \begin{table}[t]
425    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
426      model run & ice volume      model run & ice volume
427      & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,      & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
# Line 454  leads to generally thicker ice (\reffig{ Line 443  leads to generally thicker ice (\reffig{
443    \caption{Arctic ice volume averaged over Jan--Mar 2000, in    \caption{Arctic ice volume averaged over Jan--Mar 2000, in
444      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
445      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
446      total northern inflow into the Canadian Archipelago (NI), and the      total northern inflow into the Canadian Arctic Archipelago (NI), and the
447      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.
448    \label{tab:icevolume}    \label{tab:icevolume}}
449  \end{table}  \end{table}
450    
451  \subsubsection{Ice transports}  \subsubsection{Ice transports}
# Line 466  different experiments has consequences f Line 455  different experiments has consequences f
455  the Arctic. Although by far the most exported ice drifts through the  the Arctic. Although by far the most exported ice drifts through the
456  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
457  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
458  exported through the Canadian Archipelago \citep[and references  exported through the Canadian Arctic Archipelago \citep[and references
459  therein]{serreze06}. Note, that ice transport estimates are associated  therein]{serreze06}. Note, that ice transport estimates are associated
460  with large uncertainties; also note that tuning an Arctic sea  with large uncertainties; also note that tuning an Arctic sea
461  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
# Line 474  the published numbers as an orientation. Line 463  the published numbers as an orientation.
463    
464  \reffig{archipelago} shows an excerpt of a time series of daily  \reffig{archipelago} shows an excerpt of a time series of daily
465  averaged ice transports, smoothed with a monthly running mean, through  averaged ice transports, smoothed with a monthly running mean, through
466  various straits in the Canadian Archipelago and the Fram Strait for  various straits in the Canadian Arctic Archipelago and the Fram Strait for
467  the different model solutions; \reftab{icevolume} summarizes the  the different model solutions; \reftab{icevolume} summarizes the
468  time series.  time series.
469  \begin{figure}  \begin{figure}
# Line 482  time series. Line 471  time series.
471  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
472  %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
473  \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}  \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
474  \caption{Transport through Canadian Archipelago for different solver  \caption{Transport through Canadian Arctic Archipelago for different solver
475    flavors. The letters refer to the labels of the sections in    flavors. The letters refer to the labels of the sections in
476    \reffig{arctic_topog}; positive values are flux out of the Arctic;    \reffig{arctic_topog}; positive values are flux out of the Arctic;
477    legend abbreviations are explained in \reftab{experiments}. The mean    legend abbreviations are explained in \reftab{experiments}. The mean
# Line 495  model solutions (annual averages range f Line 484  model solutions (annual averages range f
484  $2300\text{\,km$^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
485  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
486  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}$}$),
487  while the export through the Candian Archipelago is smaller than  while the export through the Candian Arctic Archipelago is smaller than
488  generally thought. For example, the ice transport through Lancaster  generally thought. For example, the ice transport through Lancaster
489  Sound is lower (annual averages are $43$ to  Sound is lower (annual averages are $43$ to
490  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
# Line 510  configuration, both B- and C-grid LSOR s Line 499  configuration, both B- and C-grid LSOR s
499  ice transport, while the C-EVP solutions allow up to  ice transport, while the C-EVP solutions allow up to
500  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
501  report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,  report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
502  the import into the Candian Archipelago is larger in all EVP solutions  the import into the Candian Arctic Archipelago is larger in all EVP solutions
503  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
504  than in the LSOR solutions.  than in the LSOR solutions.
505  %get the order of magnitude right (range: $132$ to  %get the order of magnitude right (range: $132$ to
# Line 534  considerably smaller (the difference for Line 523  considerably smaller (the difference for
523  but similar to that for the LSOR solver). Albeit smaller, the  but similar to that for the LSOR solver). Albeit smaller, the
524  differences between free and no-slip solutions in ice drift can lead  differences between free and no-slip solutions in ice drift can lead
525  to equally large differences in ice volume, especially in the Canadian  to equally large differences in ice volume, especially in the Canadian
526  Archipelago over the integration time. At first, this observation  Arctic Archipelago over the integration time. At first, this observation
527  seems counterintuitive, as we expect that the solution  seems counterintuitive, as we expect that the solution
528  \emph{technique} should not affect the \emph{solution} to a higher  \emph{technique} should not affect the \emph{solution} to a higher
529  degree than actually modifying the equations. A more detailed study on  degree than actually modifying the equations. A more detailed study on
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