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revision 1.20 by mlosch, Sat Jul 5 10:39:16 2008 UTC revision 1.22 by dimitri, Thu Aug 14 16:12:41 2008 UTC
# Line 41  The Arctic model domain is illustrated i Line 41  The Arctic model domain is illustrated i
41    Archipelago. \ml{[May still need to check the geography.]}    Archipelago. \ml{[May still need to check the geography.]}
42    \label{fig:arctic_topog}}    \label{fig:arctic_topog}}
43  \end{figure*}  \end{figure*}
44  It has 420 by 384 grid boxes and is carved out, and obtains open  It has 420 by 384 grid boxes and is carved out, and obtains open boundary
45  boundary conditions from, a global cubed-sphere configuration  conditions from, a global cubed-sphere \citep{adcroft04:_cubed_sphere}
46  similar to that described in \citet{menemenlis05}.  configuration similar to that described in \citet{menemenlis05}. The
47    particular simulation from which we obtain boundary conditions is a baseline
48  \ml{[Some of this could be part of the introduction?]}%  integration, labeled {\em ``cube76''}. Each face of the cube comprises 510 by
49  The global ocean and sea ice results presented in \citet{menemenlis05}  510 grid cells for a mean horizontal grid spacing of 18\,km. There are 50
50  were carried out as part  vertical levels ranging in thickness from 10 m near the surface to
 of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)  
 project.  ECCO2 aims to produce increasingly accurate syntheses of all  
 available global-scale ocean and sea-ice data at resolutions that start to  
 resolve ocean eddies and other narrow current systems, which transport heat,  
 carbon, and other properties within the ocean \citep{menemenlis05}.  The  
 particular ECCO2 simulation from which we obtain the boundary  
 conditions is a baseline 28-year (1979-2006)  
 integration, labeled cube76, which has not yet been constrained by oceanic and  
 by sea ice data. A cube-sphere grid projection is employed, which permits  
 relatively even grid spacing throughout the domain and which avoids polar  
 singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises  
 510 by 510 grid cells for a mean horizontal grid spacing of 18\,km. There are  
 50 vertical levels ranging in thickness from 10 m near the surface to  
51  approximately 450 m at a maximum model depth of 6150 m. The model employs the  approximately 450 m at a maximum model depth of 6150 m. The model employs the
52  partial-cell formulation of  partial-cell formulation of \citet{adcroft97:_shaved_cells}, which permits
53  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the  accurate representation of the bathymetry. Bathymetry is from the S2004
54  bathymetry. Bathymetry is from the S2004 (W.~Smith, unpublished) blend of the  (W.~Smith, unpublished) blend of the \citet{smi97} and the General Bathymetric
55  \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one  Charts of the Oceans (GEBCO) one arc-minute bathymetric grid.  The model is
56  arc-minute bathymetric grid. % (see Fig.~\ref{fig:CubeBathymetry}).  integrated in a volume-conserving configuration using a finite volume
57  The model is integrated in a volume-conserving configuration using  discretization with C-grid staggering of the prognostic variables. In the
58  a finite volume discretization with C-grid staggering of the prognostic  ocean, the non-linear equation of state of \citet{jac95} is used.  The global
59  variables. In the ocean, the non-linear equation of state of \citet{jac95} is  ocean model is coupled to a sea ice model in a configuration similar to the
60  used.  case C-LSR-ns (see \reftab{experiments}).
 %  
 The global ocean model is coupled to a sea ice model in a  
 configuration similar to the case C-LSR-ns (see \reftab{experiments}),  
 with open water, dry ice, wet ice, dry snow, and wet snow albedos of,  
 respectively, 0.15, 0.88, 0.79, 0.97, and 0.83.  
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
# Line 96  run-off from \citet{lar01} is applied gl Line 74  run-off from \citet{lar01} is applied gl
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 110  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  The model configuration of cube76 carries over to the Arctic domain  The model configuration of {\em cube76} carries over to the Arctic domain
92  configuration except for numerical details related to the non-linear  configuration except for numerical details related to the non-linear
93  free surface that are not supported by the open boundary code, and the  free surface that are not supported by the open boundary code, and the
94  albedos of open water, dry ice, wet ice, dry snow, and wet snow, which  albedos of open water, dry ice, wet ice, dry snow, and wet snow, which
95  are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.  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.
 The model is integrated from Jan~01, 1992 to Mar~31, 2000.  
97  \reftab{experiments} gives an overview over the experiments discussed  \reftab{experiments} gives an overview over the experiments discussed
98  in \refsec{arcticresults}.  in \refsec{arcticresults}.
99  \begin{table}  \begin{table}
# Line 206  model solutions can be interpreted as cu Line 183  model solutions can be interpreted as cu
183    
184  \subsubsection{Ice velocities in JFM 1992}  \subsubsection{Ice velocities in JFM 1992}
185    
186  \reffig{iceveloc} shows ice velocities averaged over Janunary,  \reffig{iceveloc} shows ice velocities averaged over January,
187  February, and March (JFM) of 1992 for the C-LSR-ns solution; also  February, and March (JFM) of 1992 for the C-LSR-ns solution; also
188  shown are the differences between this reference solution and various  shown are the differences between this reference solution and various
189  sensitivity experiments. The velocity field of the C-LSR-ns  sensitivity experiments. The velocity field of the C-LSR-ns
# Line 272  boundary conditions), whereas on the C-g Line 249  boundary conditions), whereas on the C-g
249  away from the boundary, thus allowing more flow. The B-LSR-ns solution  away from the boundary, thus allowing more flow. The B-LSR-ns solution
250  has less ice drift through the Fram Strait and along  has less ice drift through the Fram Strait and along
251  Greenland's east coast; also, the flow through Baffin Bay and Davis  Greenland's east coast; also, the flow through Baffin Bay and Davis
252  Strait into the Labrador Sea is reduced with respect the C-LSR-ns  Strait into the Labrador Sea is reduced with respect to the C-LSR-ns
253  solution.  \ml{[Do we expect this? Say something about that]}  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
# Line 308  different initial conditions make a comp Line 285  different initial conditions make a comp
285  difficult to interpret. The drift in the Beaufort Gyre is slightly  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  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  the Fram Strait is increased. The drift velocities near the ice edge
288  are very different, because the ice extend is already larger in  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  \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  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  larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
# Line 319  A more sophisticated advection scheme (\ Line 296  A more sophisticated advection scheme (\
296  the gradients of thickness and concentration are largest. Everywhere  the gradients of thickness and concentration are largest. Everywhere
297  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
298  numerical diffusion (and to the absense of explicit diffusion that is  numerical diffusion (and to the absense of explicit diffusion that is
299  requird for numerical stability in a simple second order central  required for numerical stability in a simple second order central
300  differences scheme).  differences scheme).
301    
302  \subsubsection{Ice volume during JFM 2000}  \subsubsection{Ice volume during JFM 2000}
# Line 366  concentrations (not shown). Line 343  concentrations (not shown).
343  \end{figure}  \end{figure}
344  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
345  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
346  narrow passages in the Canadian Archipelago, lead to a larger build-up  narrow passages in the Canadian Arctic Archipelago, lead to a larger build-up
347  of ice north of Greenland and the Archipelago by 2\,m effective  of ice north of Greenland and the Archipelago by 2\,m effective
348  thickness and more in the B-grid solution (\reffig{icethick}b). But  thickness and more in the B-grid solution (\reffig{icethick}b). But
349  the ice volume in not larger everywhere: further west, there are  the ice volume in not larger everywhere: further west, there are
# Line 382  solution. Line 359  solution.
359  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
360  smaller differences to C-LSR-ns in the central Arctic than the  smaller differences to C-LSR-ns in the central Arctic than the
361  transition from the B-grid to the C-grid (\reffig{icethick}c), except  transition from the B-grid to the C-grid (\reffig{icethick}c), except
362  in the Canadian Archipelago. There it reduces the effective ice  in the Canadian Arctic Archipelago. There it reduces the effective ice
363  thickness by 2\,m and more where the ice is thick and the straits are  thickness by 2\,m and more where the ice is thick and the straits are
364  narrow.  Dipoles of ice thickness differences can also be observed  narrow.  Dipoles of ice thickness differences can also be observed
365  around islands, because the free-slip solution allows more flow around  around islands, because the free-slip solution allows more flow around
# Line 391  affected only slightly by the different Line 368  affected only slightly by the different
368  %  %
369  The C-EVP-ns solution has much thicker ice in the central Arctic Ocean  The C-EVP-ns solution has much thicker ice in the central Arctic Ocean
370  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).  than the C-LSR-ns solution (\reffig{icethick}d, note the color scale).
371  Within the Canadian Archipelago, more drift leads to faster ice export  Within the Canadian Arctic Archipelago, more drift leads to faster ice export
372  and reduced effective ice thickness. With a shorter time step of  and reduced effective ice thickness. With a shorter time step of
373  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to  $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to
374  the LSOR solution (not shown). Only in the narrow straits in the  the LSOR solution (not shown). Only in the narrow straits in the
# Line 404  C-LSR-ns~WTD (\reffig{icethick}g, note t Line 381  C-LSR-ns~WTD (\reffig{icethick}g, note t
381  This difference, which is even more pronounced in summer (not shown),  This difference, which is even more pronounced in summer (not shown),
382  can be attributed to direct effects of the different thermodynamics in  can be attributed to direct effects of the different thermodynamics in
383  this run. The remaining runs have the largest differences in effective  this run. The remaining runs have the largest differences in effective
384  ice thickness long the north coasts of Greenland and Ellesmere Island.  ice thickness along the north coasts of Greenland and Ellesmere Island.
385  Although the effects of TEM and \citet{hibler87}'s ice-ocean stress  Although the effects of TEM and \citet{hibler87}'s ice-ocean stress
386  formulation are so different on the initial ice velocities, both runs  formulation are so different on the initial ice velocities, both runs
387  have similarly reduced ice thicknesses in this area. The 3rd-order  have similarly reduced ice thicknesses in this area. The 3rd-order
# Line 418  different sea ice-ocean models (which sh Line 395  different sea ice-ocean models (which sh
395  fields) was on the order of $10,000\text{km$^{3}$}$; this range was  fields) was on the order of $10,000\text{km$^{3}$}$; this range was
396  even larger for coupled climate models. Here, the range (and the  even larger for coupled climate models. Here, the range (and the
397  averaging period) is smaller than $4,000\text{km$^{3}$}$ except for  averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
398  the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics  the run \mbox{C-LSR-ns~WTD} where the more complete thermodynamics
399  leads to generally thicker ice (\reffig{icethick} and  lead to generally thicker ice (\reffig{icethick} and
400  \reftab{icevolume}).  \reftab{icevolume}).
401  \begin{table}[t]  \begin{table}[t]
402    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}    \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
# Line 443  leads to generally thicker ice (\reffig{ Line 420  leads to generally thicker ice (\reffig{
420    \caption{Arctic ice volume averaged over Jan--Mar 2000, in    \caption{Arctic ice volume averaged over Jan--Mar 2000, in
421      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the      $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
422      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the      period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
423      total northern inflow into the Canadian Archipelago (NI), and the      total northern inflow into the Canadian Arctic Archipelago (NI), and the
424      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.      export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.
425    \label{tab:icevolume}}    \label{tab:icevolume}}
426  \end{table}  \end{table}
# Line 454  The difference in ice volume and ice dri Line 431  The difference in ice volume and ice dri
431  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
432  the Arctic. Although by far the most exported ice drifts through the  the Arctic. Although by far the most exported ice drifts through the
433  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
434  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) of ice is
435  exported through the Canadian Archipelago \citep[and references  exported through the Canadian Arctic Archipelago \citep[and references
436  therein]{serreze06}. Note, that ice transport estimates are associated  therein]{serreze06}. Note, that ice transport estimates are associated
437  with large uncertainties; also note that tuning an Arctic sea  with large uncertainties and that the results presented herein have not
438  ice-ocean model to reproduce observations is not our goal, but we use  yet been constrained by observations; we use
439  the published numbers as an orientation.  the published numbers as an orientation.
440    
441  \reffig{archipelago} shows an excerpt of a time series of daily  \reffig{archipelago} shows an excerpt of a time series of daily
442  averaged ice transports, smoothed with a monthly running mean, through  averaged ice transports, smoothed with a monthly running mean, through
443  various straits in the Canadian Archipelago and the Fram Strait for  various straits in the Canadian Arctic Archipelago and the Fram Strait for
444  the different model solutions; \reftab{icevolume} summarizes the  the different model solutions; \reftab{icevolume} summarizes the
445  time series.  time series.
446  \begin{figure}  \begin{figure}
# Line 471  time series. Line 448  time series.
448  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
449  %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}  %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
450  \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}  \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
451  \caption{Transport through Canadian Archipelago for different solver  \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    legend abbreviations are explained in \reftab{experiments}. The mean
# Line 484  model solutions (annual averages range f Line 461  model solutions (annual averages range f
461  $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with  $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
462  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long  $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
463  time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),  time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
464  while the export through the Candian Archipelago is smaller than  while the export through the Candian Arctic Archipelago is smaller than
465  generally thought. For example, the ice transport through Lancaster  generally thought. For example, the ice transport through Lancaster
466  Sound is lower (annual averages are $43$ to  Sound is lower (annual averages are $43$ to
467  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an  $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
468  inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but  inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
469  a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further  a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
470  upstream in Barrow Strait in the 1970ies from satellite images.  upstream in Barrow Strait in the 1970's from satellite images.
471  Generally, the EVP solutions have the highest maximum (export out of  Generally, the EVP solutions have the highest maximum (export out of
472  the Artic) and lowest minimum (import into the Artic) fluxes as the  the Artic) and lowest minimum (import into the Artic) fluxes as the
473  drift velocities are largest in these solutions.  In the extreme of  drift velocities are largest in these solutions.  In the extreme of
# Line 499  configuration, both B- and C-grid LSOR s Line 476  configuration, both B- and C-grid LSOR s
476  ice transport, while the C-EVP solutions allow up to  ice transport, while the C-EVP solutions allow up to
477  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}  $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
478  report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,  report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
479  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
480  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)  %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
481  than in the LSOR solutions.  than in the LSOR solutions.
482  %get the order of magnitude right (range: $132$ to  %get the order of magnitude right (range: $132$ to
# Line 523  considerably smaller (the difference for Line 500  considerably smaller (the difference for
500  but similar to that for the LSOR solver). Albeit smaller, the  but similar to that for the LSOR solver). Albeit smaller, the
501  differences between free and no-slip solutions in ice drift can lead  differences between free and no-slip solutions in ice drift can lead
502  to equally large differences in ice volume, especially in the Canadian  to equally large differences in ice volume, especially in the Canadian
503  Archipelago over the integration time. At first, this observation  Arctic Archipelago over the integration time. At first, this observation
504  seems counterintuitive, as we expect that the solution  seems counterintuitive, as we expect that the solution
505  \emph{technique} should not affect the \emph{solution} to a higher  \emph{technique} should not affect the \emph{solution} to a higher
506  degree than actually modifying the equations. A more detailed study on  degree than actually modifying the equations. A more detailed study on
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