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revision 1.11 by mlosch, Sat Mar 8 20:40:47 2008 UTC revision 1.14 by mlosch, Tue Apr 29 14:04:15 2008 UTC
# Line 106  The Arctic domain of integration is illu Line 106  The Arctic domain of integration is illu
106  \reffig{arctic_topog}.  It is carved out from, and obtains open  \reffig{arctic_topog}.  It is carved out from, and obtains open
107  boundary conditions from, the global cubed-sphere configuration  boundary conditions from, the global cubed-sphere configuration
108  described above.  The horizontal domain size is 420 by 384 grid boxes.  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}}}  \includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
111  \caption{Bathymetry and domain boudaries of Arctic  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
112    Domain. The letters label sections in the Canadian Archipelago,  \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
113    where ice transport is evaluated.  \caption{Left: Bathymetry and domain boudaries of Arctic
114      Domain; the dashed line marks the boundaries of the inset on the
115      right hand side. The letters in the inset label sections in the
116      Canadian Archipelago, where ice transport is evaluated:
117      A: Nares Strait; %
118      B: \ml{Meighen Island}; %
119      C: Prince Gustaf Adolf Sea; %
120      D: \ml{Brock Island}; %
121      E: McClure Strait; %
122      F: Amundsen Gulf; %
123      G: Lancaster Sound; %
124      H: Barrow Strait \ml{W.}; %
125      I: Barrow Strait \ml{E.}; %
126      J: Barrow Strait \ml{N.}. %
127    \label{fig:arctic_topog}}    \label{fig:arctic_topog}}
128  \end{figure}  \end{figure*}
129    
130  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
131  rescaled vertical coordinates (z$^\ast$) and the surface boundary  rescaled vertical coordinates (z$^\ast$) and the surface boundary
132  conditions for freshwater input are different, because those features  conditions for freshwater input are different, because those features
133  are not supported by the open boundary code.  are not supported by the open boundary code.
134    
135  Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,  Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
136  0.76, 0.94, and 0.8.  respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
137    
138  The model is integrated from January, 1992 to March \ml{[???]}, 2000,  The model is integrated from January, 1992 to March \ml{[???]}, 2000,
139  with three different dynamical solvers and two different boundary  with three different dynamical solvers and two different boundary
# Line 134  conditions: Line 147  conditions:
147  \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
148    conditions;    conditions;
149  \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
150    no-slip lateral boundary conditions; and    no-slip lateral boundary conditions;
151  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
152    boundary conditions.    boundary conditions;
153    \item[C-LSR-ns adv33:] C-LSR-ns with a third-order flux limited
154      direct-space-time advection scheme \citep{hundsdorfer94};
155    \item[C-LSR-ns TEM:] C-LSR-ns with a truncated
156      ellispe method (TEM) rheology \citep{hibler97};
157    \item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
158      to \citet{hibler87};
159    \item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
160      scale noise \citep{hunke01}.
161  \end{description}  \end{description}
162  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
163  that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be  that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
164  interpreted as pure model error. Lateral boundary conditions on a  interpreted as pure model error. Lateral boundary conditions on a
165  coarse grid (compared to the roughness of the true coast line) are  coarse grid (compared to the roughness of the true coast line) are
166  unclear, so that comparing the no-slip solutions to the free-slip  unclear, so that comparing the no-slip solutions to the free-slip
167  solutions gives another measure of uncertainty in sea ice modeling.  solutions gives another measure of uncertainty in sea ice
168    modeling. The remaining experiments explore further
169    sensitivities of the system to different physics (change in rheology,
170    advection and diffusion properties and stress coupling) and numerics
171    (numerical method to damp noise in the EVP solutions).
172    
173  A principle difficulty in comparing the solutions obtained with  A principle difficulty in comparing the solutions obtained with
174  different variants of the dynamics solver lies in the non-linear  different variants of the dynamics solver lies in the non-linear
# Line 167  shifted eastwards towards Alaska. Line 192  shifted eastwards towards Alaska.
192  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)
193  is most pronounced along the coastlines, where the discretization  is most pronounced along the coastlines, where the discretization
194  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
195  velocity lies on the boundary (and thus zero per the no-slip boundary  velocity lies on the boundary (and is thus zero through the no-slip
196  conditions), whereas on the C-grid the its half a cell width away from  boundary conditions), whereas on the C-grid it is half a cell width
197  the boundary, thus allowing more flow. The B-LSR-ns solution has less  away from the boundary, thus allowing more flow. The B-LSR-ns solution
198  ice drift through the Fram Strait and especially the along Greenland's  has less ice drift through the Fram Strait and especially the along
199  east coast; also, the flow through Baffin Bay and Davis Strait into  Greenland's east coast; also, the flow through Baffin Bay and Davis
200  the Labrador Sea is reduced with respect the C-LSR-ns solution.  Strait into the Labrador Sea is reduced with respect the C-LSR-ns
201  \ml{[Do we expect this? Say something about that]}  solution.  \ml{[Do we expect this? Say something about that]}
202  %  %
203  Compared to the differences between B and C-grid solutions,the  Compared to the differences between B and C-grid solutions,the
204  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
# Line 185  Island. Line 210  Island.
210  \begin{figure}[htbp]  \begin{figure}[htbp]
211    \centering    \centering
212    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
213    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}  %  {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}
214      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-LSR-ns}}
215    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
216    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\  %  {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\
217      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}\\
218    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
219    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}  %  {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}
220      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
221    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
222    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}  %  {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}
223      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-EVP-ns-C-LSR-ns}}
224    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
225      over the first 3 months of integration [cm/s]; (b)-(d) difference      over the first 3 months of integration [cm/s]; (b)-(d) difference
226      between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions      between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions
# Line 209  biased towards higher values in the EVP Line 238  biased towards higher values in the EVP
238  a histogram of the differences in \reffig{drifthist}.  a histogram of the differences in \reffig{drifthist}.
239  \begin{figure}[htbp]  \begin{figure}[htbp]
240    \centering    \centering
241    \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}    \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
242    \caption{Histogram of drift velocity differences for C-LSR-ns and    \caption{Histogram of drift velocity differences for C-LSR-ns and
243      C-EVP-ns solution [cm/s].}      C-EVP-ns solution [cm/s].}
244    \label{fig:drifthist}    \label{fig:drifthist}
# Line 248  the ice volume in not larger everywhere: Line 277  the ice volume in not larger everywhere:
277  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
278  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
279  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
280  differences with more ice on the \ml{luv [what is this in English?,  differences with more ice on the upstream side of island groups and
281    upstream]} and less ice in the the lee of island groups, such as  less ice in their lee, such as Franz-Josef-Land and \ml{IDONTKNOW},
282  Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along  because ice tends to flow along coasts less easily in the B-LSR-ns
283  coasts less easily in the B-LSR-ns solution.  solution.
284    
285  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
286  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
# Line 272  reduced effective ice thickness. Line 301  reduced effective ice thickness.
301    
302  The difference in ice volume and ice drift velocities between the  The difference in ice volume and ice drift velocities between the
303  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
304  the Arctic. Although the main export of ice goes through the Fram  the Arctic. Although by far the most exported ice drifts through the
305  Strait, a considerable amoung of ice is exported through the Canadian  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
306  Archipelago \citep{???}. \reffig{archipelago} shows a time series of  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
307  \ml{[maybe smooth to longer time scales:] daily averaged} ice  exported through the Canadian Archipelago \citep[and references
308  transport through various straits in the Canadian Archipelago and the  therein]{serreze06}.  \reffig{archipelago} shows a time series of
309  Fram Strait for the different model solutions.  Generally, the  \ml{[maybe smooth to different time scales:] daily averaged, smoothed
310  C-EVP-ns solution has highest maximum (export out of the Artic) and    with monthly running means,} ice transports through various straits
311  minimum (import into the Artic) fluxes as the drift velocities are  in the Canadian Archipelago and the Fram Strait for the different
312  largest in this solution \ldots  model solutions. The export through Fram Strait agrees with the
313    observations in all model solutions (annual averages range from $2112$
314    to $2425\text{\,km$^3$\,y$^{-1}$}$), while the export through
315    Lancaster Sound is lower (annual averages are $66$ to
316    $256\text{\,km$^3$\,y$^{-1}$}$) than observed
317    \citep[???][]{lancaster}.  Generally, the C-EVP solutions have highest
318    maximum (export out of the Artic) and minimum (import into the Artic)
319    fluxes as the drift velocities are largest in this solution.  In the
320    extreme, both B- and C-grid LSOR solvers have practically no ice
321    transport through the Nares Strait, which is only a few grid points
322    wide, while the C-EVP solutions allow up to
323    $600\text{\,km$^3$\,y$^{-1}$}$ in summer. As as consequence, the
324    import into the Candian Archipelago is overestimated in all EVP
325    solutions (range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$), while the
326    C-LSR solutions get the order of magnitude right (range: $132$ to
327    $165\text{\,km$^3$\,y$^{-1}$}$); the B-LSR-ns solution grossly
328    underestimates the ice transport with $77\text{\,km$^3$\,y$^{-1}$}$.
329  \begin{figure}  \begin{figure}
330  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
331    \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
332  \caption{Transport through Canadian Archipelago for different solver  \caption{Transport through Canadian Archipelago for different solver
333    flavors. The letters refer to the labels of the sections in    flavors. The letters refer to the labels of the sections in
334    \reffig{arctic_topog}.    \reffig{arctic_topog}; positive values are flux out of the Arctic;
335      legend abbreviations are explained in \reftab{experiments}.
336  \label{fig:archipelago}}  \label{fig:archipelago}}
337  \end{figure}  \end{figure}
338    
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