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revision 1.10 by mlosch, Tue Mar 4 20:33:07 2008 UTC revision 1.11 by mlosch, Sat Mar 8 20:40:47 2008 UTC
# Line 6  ice simulations that exercise various ca Line 6  ice simulations that exercise various ca
6  model.  The first set of results is from a global, eddy-permitting, ocean and  model.  The first set of results is from a global, eddy-permitting, ocean and
7  sea ice configuration.  The second set of results is from a regional Arctic  sea ice configuration.  The second set of results is from a regional Arctic
8  configuration, which is used to compare the B-grid and C-grid dynamic solvers  configuration, which is used to compare the B-grid and C-grid dynamic solvers
9  and various other capabilities of the MITgcm sea ice model.  The third set of  and various other capabilities of the MITgcm sea ice model.  
10    %
11    \ml{[do we really want to do this?:] The third set of
12  results is from a yet smaller regional domain, which is used to illustrate  results is from a yet smaller regional domain, which is used to illustrate
13  treatment of sea ice open boundary condition sin the MITgcm.  treatment of sea ice open boundary condition in the MITgcm.}
14    
15  \subsection{Global Ocean and Sea Ice Simulation}  \subsection{Global Ocean and Sea Ice Simulation}
16  \label{sec:global}  \label{sec:global}
# Line 37  used. Line 39  used.
39    
40  The ocean model is coupled to the sea-ice model discussed in  The ocean model is coupled to the sea-ice model discussed in
41  \refsec{model} using the following specific options.  The  \refsec{model} using the following specific options.  The
42  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is used to  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is
43  compute sea ice thickness and concentration.  Snow cover and sea ice salinity  used to compute sea ice thickness and concentration.  Snow cover and
44  are prognostic.  Open water, dry ice, wet ice, dry snow, and wet snow albedo  sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry
45  are, respectively, 0.15, 0.88, 0.79, 0.97, and 0.83. Ice mechanics follow the  snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,
46  viscous plastic rheology of \citet{hibler79} and the ice momentum equation is  and 0.83. Ice mechanics follow the viscous plastic rheology of
47  solved numerically using the C-grid implementation of the \citet{zhang97} LSR  \citet{hibler79} and the ice momentum equation is solved numerically
48  dynamics model discussed hereinabove.  The ice is coupled to the ocean using  using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
49  the rescaled vertical coordinate system, z$^\ast$, of  model discussed hereinabove.  The ice is coupled to the ocean using
50  \citet{cam08}, that is, sea ice does not float above the ocean model but  the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
51  rather deforms the ocean's model surface level.  that is, sea ice does not float above the ocean model but rather
52    deforms the ocean's model surface level.
53    
54  This particular ECCO2 simulation is initialized from temperature and salinity  This particular ECCO2 simulation is initialized from temperature and salinity
55  fields derived from the Polar science center Hydrographic Climatology (PHC)  fields derived from the Polar science center Hydrographic Climatology (PHC)
# Line 62  radiations, and precipitation are conver Line 65  radiations, and precipitation are conver
65  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
66  radiation decays exponentially as per \citet{pau77}.  Low frequency  radiation decays exponentially as per \citet{pau77}.  Low frequency
67  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
68  Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river  Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river
69  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
70  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)
71  and prepared by P. Winsor (personnal communication, 2007) is specificied.  and prepared by P. Winsor (personnal communication, 2007) is specificied.
# Line 81  advection scheme \citep{dar04} is employ Line 84  advection scheme \citep{dar04} is employ
84  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
85  the divergent flow as per \citet{kem08}.  the divergent flow as per \citet{kem08}.
86    
87    \ml{[Dimitris, here you need to either provide figures, so that I can
88      write text, or you can provide both figures and text. I guess, one
89      figure, showing the northern and southern hemisphere in summer and
90      winter is fine (four panels), as we are showing so many figures in
91      the next section.]}
92    
93    
94  \subsection{Arctic Domain with Open Boundaries}  \subsection{Arctic Domain with Open Boundaries}
95  \label{sec:arctic}  \label{sec:arctic}
96    
97  A series of forward sensitivity experiments have been carried out on an  A series of forward sensitivity experiments have been carried out on
98  Arctic Ocean domain with open boundaries.  The objective is to compare the old  an Arctic Ocean domain with open boundaries.  The objective is to
99  B-grid LSR dynamic solver with the new C-grid LSR and EVP solvers.  One  compare the old B-grid LSR dynamic solver with the new C-grid LSR and
100  additional experiment is carried out to illustrate the differences between the  EVP solvers.  Additional experiments are is carried out to illustrate
101  two main options for sea ice thermodynamics in the MITgcm.  the differences between different ice advection schemes, ocean-ice
102    stress formulations and the two main options for sea ice
103  The Arctic domain of integration is illustrated in \reffig{arctic1}.  It  thermodynamics in the MITgcm.
104  is carved out from, and obtains open boundary conditions from, the global  
105  cubed-sphere configuration described above.  The horizontal domain size is  The Arctic domain of integration is illustrated in
106  420 by 384 grid boxes.  \reffig{arctic_topog}.  It is carved out from, and obtains open
107    boundary conditions from, the global cubed-sphere configuration
108    described above.  The horizontal domain size is 420 by 384 grid boxes.
109  \begin{figure}  \begin{figure}
110  \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}  \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}
111  \caption{Bathymetry and domain boudaries of Arctic  \caption{Bathymetry and domain boudaries of Arctic
112    Domain.\label{fig:arctic1}}    Domain. The letters label sections in the Canadian Archipelago,
113      where ice transport is evaluated.
114      \label{fig:arctic_topog}}
115  \end{figure}  \end{figure}
116    
117  The main dynamic difference from cube sphere is that it does not use  The main dynamic difference from cube sphere is that it does not use
# Line 110  Open water, dry ice, wet ice, dry snow, Line 123  Open water, dry ice, wet ice, dry snow,
123  0.76, 0.94, and 0.8.  0.76, 0.94, and 0.8.
124    
125  The model is integrated from January, 1992 to March \ml{[???]}, 2000,  The model is integrated from January, 1992 to March \ml{[???]}, 2000,
126  with five different dynamical solvers:  with three different dynamical solvers and two different boundary
127    conditions:
128  \begin{description}  \begin{description}
129  \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa  \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
130    B-grid, implying no-slip lateral boundary conditions;    Arakawa B-grid, implying no-slip lateral boundary conditions
131      ($\vek{u}=0$ exactly);
132  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
133    boundary conditions;    boundary conditions (implemented via ghost-points);
134  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
135    conditions;    conditions;
136  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
# Line 150  Figure\,6]{martin07} with a Beaufort Gyr Line 165  Figure\,6]{martin07} with a Beaufort Gyr
165  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
166    
167  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)
168  is most pronounced  is most pronounced along the coastlines, where the discretization
169  along the coastlines, where the discretization differs most between B  differs most between B and C-grids: On a B-grid the tangential
170  and C-grids: On a B-grid the tangential velocity is on the boundary  velocity lies on the boundary (and thus zero per the no-slip boundary
171  (and thus zero per the no-slip boundary conditions), whereas on the  conditions), whereas on the C-grid the its half a cell width away from
172  C-grid the its half a cell width away from the boundary, thus allowing  the boundary, thus allowing more flow. The B-LSR-ns solution has less
173  more flow. The B-LSR-ns solution has less ice drift through the Fram  ice drift through the Fram Strait and especially the along Greenland's
174  Strait and especially the along Greenland's east coast; also, the flow  east coast; also, the flow through Baffin Bay and Davis Strait into
175  through Baffin Bay and Davis Strait into the Labrador Sea is reduced  the Labrador Sea is reduced with respect the C-LSR-ns solution.
176  with respect the C-LSR-ns solution. \ml{[Do we expect this? Say  \ml{[Do we expect this? Say something about that]}
   something about that]}  
177  %  %
178  Compared to the differences between B and C-grid solutions the  Compared to the differences between B and C-grid solutions,the
179  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution  C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
180  (\reffig{iceveloc}c).  As expected the differences are largest along  (\reffig{iceveloc}c).  As expected the differences are largest along
181  coastlines: because of the free-slip boundary conditions, flow is  coastlines: because of the free-slip boundary conditions, flow is
# Line 207  of year 2000. By this time of the integr Line 221  of year 2000. By this time of the integr
221  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
222  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--d, and
223  area distributions (not shown).  \ml{Compared to other solutions, for  area distributions (not shown).  \ml{Compared to other solutions, for
224    example, AOMIP the ice thickness distribution blablabal} \ml{[What    example, AOMIP the ice thickness distribution blablabal}
   can I say about effective thickness?]}  
225  \begin{figure}[htbp]  \begin{figure}[htbp]
226    \centering    \centering
227    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
# Line 225  area distributions (not shown).  \ml{Com Line 238  area distributions (not shown).  \ml{Com
238      and C-LSR-ns solutions [cm/s].}      and C-LSR-ns solutions [cm/s].}
239    \label{fig:icethick}    \label{fig:icethick}
240  \end{figure}  \end{figure}
241    %
242  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
243  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
244  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 235  the ice volume in not larger everywhere: Line 248  the ice volume in not larger everywhere:
248  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
249  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
250  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
251  differences on the \ml{luv [what is this in English?]} and the lee of  differences with more ice on the \ml{luv [what is this in English?,
252  island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which    upstream]} and less ice in the the lee of island groups, such as
253  \ml{\ldots [I find hard to interpret].}  Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along
254    coasts less easily in the B-LSR-ns solution.
255    
256  Imposing a free-slip boundary condition in C-LSR-fs leads to a much  Imposing a free-slip boundary condition in C-LSR-fs leads to a much
257  smaller differences to C-LSR-ns than the transition from the B-grid to  smaller differences to C-LSR-ns than the transition from the B-grid to
258  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
259  still reduces the effective ice thickness by up to 2\,m where the ice  still reduces the effective ice thickness by up to 2\,m where the ice
260  is thick and the straits are narrow. Everywhere else the ice volume is  is thick and the straits are narrow. Dipoles of ice thickness
261  affected only slightly by the different boundary condition.  differences can also be observed around islands, because the free-slip
262    solution allows more flow around islands than the no-slip solution.
263    Everywhere else the ice volume is affected only slightly by the
264    different boundary condition.
265  %  %
266  The C-EVP-ns solution has generally stronger drift velocities then the  The C-EVP-ns solution has generally stronger drift velocities than the
267  C-LSR-ns solution. Consequently, more ice can be moved the eastern  C-LSR-ns solution. Consequently, more ice can be moved from the eastern
268  part of the Arctic, where ice volumes are smaller, to the western  part of the Arctic, where ice volumes are smaller, to the western
269  Arctic where ice piles up along the coast (\reffig{icethick}d). Within  Arctic where ice piles up along the coast (\reffig{icethick}d). Within
270  the Canadian Archipelago, more drift leads to faster ice export and  the Canadian Archipelago, more drift leads to faster ice export and
# Line 258  different experiments has consequences f Line 275  different experiments has consequences f
275  the Arctic. Although the main export of ice goes through the Fram  the Arctic. Although the main export of ice goes through the Fram
276  Strait, a considerable amoung of ice is exported through the Canadian  Strait, a considerable amoung of ice is exported through the Canadian
277  Archipelago \citep{???}. \reffig{archipelago} shows a time series of  Archipelago \citep{???}. \reffig{archipelago} shows a time series of
278  daily averages ice transport through various straits in the Canadian  \ml{[maybe smooth to longer time scales:] daily averaged} ice
279  Archipelago and the Fram Strait for the different model solutions.  transport through various straits in the Canadian Archipelago and the
280  Generally, the C-EVP-ns solution has highest maxiumum (export out of  Fram Strait for the different model solutions.  Generally, the
281  the Artic) and minimum (import into the Artic) fluxes as the drift  C-EVP-ns solution has highest maximum (export out of the Artic) and
282  velocities area largest in this solution \ldots  minimum (import into the Artic) fluxes as the drift velocities are
283    largest in this solution \ldots
284  \begin{figure}  \begin{figure}
285  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
286  \caption{Transport through Canadian Archipelago for different solver flavors.  \caption{Transport through Canadian Archipelago for different solver
287      flavors. The letters refer to the labels of the sections in
288      \reffig{arctic_topog}.
289  \label{fig:archipelago}}  \label{fig:archipelago}}
290  \end{figure}  \end{figure}
291    
# Line 275  velocities area largest in this solution Line 295  velocities area largest in this solution
295    models are all erroneous!]}    models are all erroneous!]}
296    
297  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
298  different solutions. Compared to that the differences between  different solutions. In contrast, the differences between free-slip
299  free-slip and no-slip solutions \emph{with the same solver} are  and no-slip solutions \emph{with the same solver} are considerably
300  considerably smaller (the difference for the EVP solver is not shown,  smaller (the difference for the EVP solver is not shown, but similar
301  but comparable to that for the LSOR solver)---albeit smaller, the  to that for the LSOR solver). Albeit smaller, the differences between
302  differences between free and no-slip solutions in ice drift can lead  free and no-slip solutions in ice drift can lead to large differences
303  to large differences in ice volume over integration time. At first,  in ice volume over the integration time. At first, this observation
304  this observation appears counterintuitive, as we expect that the  seems counterintuitive, as we expect that the solution
305  solution \emph{technique} should not affect the \emph{solution} to a  \emph{technique} should not affect the \emph{solution} to a higher
306  lower degree than actually modifying the equations. A more detailed  degree than actually modifying the equations. A more detailed study on
307  study on these differences is beyond the scope of this paper, but at  these differences is beyond the scope of this paper, but at this point
308  this point we may speculate, that the large difference between B-grid,  we may speculate, that the large difference between B-grid, C-grid,
309  C-grid, LSOR, and EVP solutions stem from incomplete convergence of  LSOR, and EVP solutions stem from incomplete convergence of the
310  the solvers due to linearization \citep[and Bruno Tremblay, personal  solvers due to linearization and due to different methods of
311    linearization \citep[and Bruno Tremblay, personal
312  communication]{hunke01}: if the convergence of the non-linear momentum  communication]{hunke01}: if the convergence of the non-linear momentum
313  equations is not complete for all linearized solvers, then one can  equations is not complete for all linearized solvers, then one can
314  imagine that each solver stops at a different point in velocity-space  imagine that each solver stops at a different point in velocity-space
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