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revision 1.10 by mlosch, Tue Mar 4 20:33:07 2008 UTC revision 1.16 by dimitri, Wed Jun 4 00:39:25 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.
 results is from a yet smaller regional domain, which is used to illustrate  
 treatment of sea ice open boundary condition sin the MITgcm.  
10    
11  \subsection{Global Ocean and Sea Ice Simulation}  \subsection{Global Ocean and Sea Ice Simulation}
12  \label{sec:global}  \label{sec:global}
# Line 26  relatively even grid spacing throughout Line 24  relatively even grid spacing throughout
24  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
25  510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are  510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are
26  50 vertical levels ranging in thickness from 10 m near the surface to  50 vertical levels ranging in thickness from 10 m near the surface to
27  approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the  approximately 450 m at a maximum model depth of 6150 m. The model employs the
28  National Geophysical Data Center (NGDC) 2-minute gridded global relief data  partial-cell formulation of
 (ETOPO2) and the model employs the partial-cell formulation of  
29  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
30  bathymetry. The model is integrated in a volume-conserving configuration using  bathymetry. Bathymetry is from the S2004 (Smith, unpublished) blend of the
31    \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one
32    arc-minute bathymetric grid (see Fig.~\ref{fig:CubeBathymetry}).
33    The model is integrated in a volume-conserving configuration using
34  a finite volume discretization with C-grid staggering of the prognostic  a finite volume discretization with C-grid staggering of the prognostic
35  variables. In the ocean, the non-linear equation of state of \citet{jac95} is  variables. In the ocean, the non-linear equation of state of \citet{jac95} is
36  used.  used.
37    
38    \begin{figure}[h]
39      \centering
40      \includegraphics[width=\textwidth]{\fpath/CubeBathymetry}
41      \caption{Bathymetry of the global cubed sphere model configuration.  The
42        solid lines indicate domain boundaries for the regional Arctic
43        configuration discussed in Section~\ref{sec:arctic}.}
44      \label{fig:CubeBathymetry}
45    \end{figure}
46    
47  The ocean model is coupled to the sea-ice model discussed in  The ocean model is coupled to the sea-ice model discussed in
48  \refsec{model} using the following specific options.  The  \refsec{model} using the following specific options.  The
49  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is used to  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is
50  compute sea ice thickness and concentration.  Snow cover and sea ice salinity  used to compute sea ice thickness and concentration.  Snow cover and
51  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
52  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,
53  viscous plastic rheology of \citet{hibler79} and the ice momentum equation is  and 0.83. Ice mechanics follow the viscous plastic rheology of
54  solved numerically using the C-grid implementation of the \citet{zhang97} LSR  \citet{hibler79} and the ice momentum equation is solved numerically
55  dynamics model discussed hereinabove.  The ice is coupled to the ocean using  using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
56  the rescaled vertical coordinate system, z$^\ast$, of  model discussed hereinabove.  The ice is coupled to the ocean using
57  \citet{cam08}, that is, sea ice does not float above the ocean model but  the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
58  rather deforms the ocean's model surface level.  that is, sea ice does not float above the ocean model but rather
59    deforms the ocean's model surface level.
60    
61  This particular ECCO2 simulation is initialized from temperature and salinity  This particular ECCO2 simulation is initialized from temperature and salinity
62  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 72  radiations, and precipitation are conver
72  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
73  radiation decays exponentially as per \citet{pau77}.  Low frequency  radiation decays exponentially as per \citet{pau77}.  Low frequency
74  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
75  Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river  Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river
76  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
77  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)
78  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 91  advection scheme \citep{dar04} is employ
91  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
92  the divergent flow as per \citet{kem08}.  the divergent flow as per \citet{kem08}.
93    
94    \ml{[Dimitris, here you need to either provide figures, so that I can
95      write text, or you can provide both figures and text. I guess, one
96      figure, showing the northern and southern hemisphere in summer and
97      winter is fine (four panels), as we are showing so many figures in
98      the next section.]}
99    
100    
101  \subsection{Arctic Domain with Open Boundaries}  \subsection{Arctic Domain with Open Boundaries}
102  \label{sec:arctic}  \label{sec:arctic}
103    
104  A series of forward sensitivity experiments have been carried out on an  A series of forward sensitivity experiments have been carried out on
105  Arctic Ocean domain with open boundaries.  The objective is to compare the old  an Arctic Ocean domain with open boundaries.  The objective is to
106  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
107  additional experiment is carried out to illustrate the differences between the  EVP solvers.  Additional experiments are carried out to illustrate
108  two main options for sea ice thermodynamics in the MITgcm.  the differences between different ice advection schemes, ocean-ice
109    stress formulations and the two main options for sea ice
110  The Arctic domain of integration is illustrated in \reffig{arctic1}.  It  thermodynamics in the MITgcm.
111  is carved out from, and obtains open boundary conditions from, the global  
112  cubed-sphere configuration described above.  The horizontal domain size is  The Arctic domain of integration is illustrated in
113  420 by 384 grid boxes.  \reffig{arctic_topog}.  It is carved out from, and obtains open
114    boundary conditions from, the global cubed-sphere configuration
115  \begin{figure}  described above.  The horizontal domain size is 420 by 384 grid boxes.
116  \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}  \begin{figure*}
117  \caption{Bathymetry and domain boudaries of Arctic  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
118    Domain.\label{fig:arctic1}}  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
119  \end{figure}  \includegraphics*[width=0.44\linewidth]{\fpath/topography}
120    \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
121    \caption{Left: Bathymetry and domain boudaries of Arctic
122      Domain; the dashed line marks the boundaries of the inset on the
123      right hand side. The letters in the inset label sections in the
124      Canadian Archipelago, where ice transport is evaluated:
125      A: Nares Strait; %
126      B: \ml{Meighen Island}; %
127      C: Prince Gustaf Adolf Sea; %
128      D: \ml{Brock Island}; %
129      E: M'Clure Strait; %
130      F: Amundsen Gulf; %
131      G: Lancaster Sound; %
132      H: Barrow Strait \ml{W.}; %
133      I: Barrow Strait \ml{E.}; %
134      J: Barrow Strait \ml{N.}. %
135      The sections A through F comprise the total inflow into the Canadian
136      Archipelago. \ml{[May still need to check the geography.]}
137      \label{fig:arctic_topog}}
138    \end{figure*}
139    
140    The main dynamic difference from cube sphere is that the Arctic domain
141    configuration does not use rescaled vertical coordinates (z$^\ast$)
142    and the surface boundary conditions for freshwater input are
143    different, because those features are not supported by the open
144    boundary code.
145    %
146    Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
147    respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
148    
149  The main dynamic difference from cube sphere is that it does not use  The model is integrated from Jan~01, 1992 to Mar~31, 2000,
150  rescaled vertical coordinates (z$^\ast$) and the surface boundary  with three different dynamical solvers, two different boundary
151  conditions for freshwater input are different, because those features  conditions, different stress coupling, rheology, and advection
152  are not supported by the open boundary code.  schemes. \reftab{experiments} gives an overview over the experiments
153    discussed in this section.
154  Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,  \begin{table}[htbp]
155  0.76, 0.94, and 0.8.    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
156        experiment name & description \\ \hline
157  The model is integrated from January, 1992 to March \ml{[???]}, 2000,      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
158  with five different dynamical solvers:    Arakawa B-grid, implying no-slip lateral boundary conditions
159  \begin{description}    ($\vek{u}=0$ exactly) \\
160  \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa      C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
161    B-grid, implying no-slip lateral boundary conditions;    boundary conditions (implemented via ghost-points) \\
162  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral      C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
163    boundary conditions;    conditions \\
164  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary      C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
165    conditions;    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
166  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with    150\text{\,s}$ \\
167    no-slip lateral boundary conditions; and      C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
168  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
169    boundary conditions.    10\text{\,s}$ \\
170  \end{description}      C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
171      to \citet{hibler87}\\
172        C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
173      rheology \citep{hibler97} \\
174        C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
175      \citet{winton00} \\
176        C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
177      direct-space-time advection scheme for thermodynamic variables
178      \citep{hundsdorfer94}
179      \end{tabular}
180      \caption{Overview over model simulations in \refsec{arctic}.
181        \label{tab:experiments}}
182    \end{table}
183    %\begin{description}
184    %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
185    %  Arakawa B-grid, implying no-slip lateral boundary conditions
186    %  ($\vek{u}=0$ exactly);
187    %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
188    %  boundary conditions (implemented via ghost-points);
189    %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
190    %  conditions;
191    %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
192    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
193    %  150\text{\,s}$;
194    %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
195    %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
196    %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
197    %  direct-space-time advection scheme \citep{hundsdorfer94};
198    %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
199    %  rheology \citep{hibler97};
200    %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
201    %  to \citet{hibler87};
202    %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
203    %  \citet{winton00};
204    %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
205    %%  scale noise \citep{hunke01};
206    %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
207    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
208    %  10\text{\,s}$.
209    %\end{description}
210  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
211  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
212  interpreted as pure model error. Lateral boundary conditions on a  interpreted as pure model error. Lateral boundary conditions on a
213  coarse grid (compared to the roughness of the true coast line) are  coarse grid (coarse compared to the roughness of the true coast line) are
214  unclear, so that comparing the no-slip solutions to the free-slip  unclear, so that comparing the no-slip solutions to the free-slip
215  solutions gives another measure of uncertainty in sea ice modeling.  solutions gives another measure of uncertainty in sea ice modeling.
216    The remaining experiments explore further sensitivities of the system
217    to different physics (change in rheology, advection and diffusion
218    properties, stress coupling, and thermodynamics) and different time
219    steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
220    for the EVP solution. We use two interpretations of this choice where
221    the EVP model is subcycled 120 times within a (short) model timestep
222    of 1200\,s resulting in a very long and expensive integration
223    ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
224    forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
225    
226  A principle difficulty in comparing the solutions obtained with  A principle difficulty in comparing the solutions obtained with
227  different variants of the dynamics solver lies in the non-linear  different realizations of the model dynamics lies in the non-linear
228  feedback of the ice dynamics and thermodynamics. Already after a few  feedback of the ice dynamics and thermodynamics. Already after a few
229  months the solutions have diverged so far from each other that  months the solutions have diverged so far from each other that
230  comparing velocities only makes sense within the first 3~months of the  comparing velocities only makes sense within the first 3~months of the
# Line 145  shown are the differences between B-grid Line 238  shown are the differences between B-grid
238  no-slip and free-slip solution. The velocity field of the C-LSR-ns  no-slip and free-slip solution. The velocity field of the C-LSR-ns
239  solution (\reffig{iceveloc}a) roughly resembles the drift velocities  solution (\reffig{iceveloc}a) roughly resembles the drift velocities
240  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
241  models in an cyclonic circulation regime (CCR) \citep[their  models in a cyclonic circulation regime (CCR) \citep[their
242  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
243  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
244    
245  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)
246  is most pronounced  is most pronounced along the coastlines, where the discretization
247  along the coastlines, where the discretization differs most between B  differs most between B and C-grids: On a B-grid the tangential
248  and C-grids: On a B-grid the tangential velocity is on the boundary  velocity lies on the boundary (and is thus zero through the no-slip
249  (and thus zero per the no-slip boundary conditions), whereas on the  boundary conditions), whereas on the C-grid it is half a cell width
250  C-grid the its half a cell width away from the boundary, thus allowing  away from the boundary, thus allowing more flow. The B-LSR-ns solution
251  more flow. The B-LSR-ns solution has less ice drift through the Fram  has less ice drift through the Fram Strait and especially the along
252  Strait and especially the along Greenland's east coast; also, the flow  Greenland's east coast; also, the flow through Baffin Bay and Davis
253  through Baffin Bay and Davis Strait into the Labrador Sea is reduced  Strait into the Labrador Sea is reduced with respect the C-LSR-ns
254  with respect the C-LSR-ns solution. \ml{[Do we expect this? Say  solution.  \ml{[Do we expect this? Say something about that]}
   something about that]}  
255  %  %
256  Compared to the differences between B and C-grid solutions the  Compared to the differences between B and C-grid solutions,the
257  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
258  (\reffig{iceveloc}c).  As expected the differences are largest along  (\reffig{iceveloc}c).  As expected the differences are largest along
259  coastlines: because of the free-slip boundary conditions, flow is  coastlines: because of the free-slip boundary conditions, flow is
260  faster in the C-LSR-fs solution, for example, along the east coast  faster in the C-LSR-fs solution, for example, along the east coast
261  of Greenland, the north coast of Alaska, and the east Coast of Baffin  of Greenland, the north coast of Alaska, and the east Coast of Baffin
262  Island.  Island.
263    %\newcommand{\subplotwidth}{0.44\textwidth}
264    \newcommand{\subplotwidth}{0.3\textwidth}
265  \begin{figure}[htbp]  \begin{figure}[htbp]
266    \centering    \centering
267    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
268    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
269    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
270    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}
271      \\
272    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
273    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
274    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
275    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
276      \\
277      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
278      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
279      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
280      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
281      \\
282      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
283      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
284      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
285      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
286    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
287      over the first 3 months of integration [cm/s]; (b)-(d) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
288      between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions      between solutions with B-grid, free lateral slip, EVP-solver,
289      [cm/s]; color indicates speed (or differences of speed), vectors      truncated ellipse method (TEM), different ice-ocean stress
290      indicate direction only.}      formulation (HB87), different thermodynamics (WTD), different
291        advection for thermodynamic variables (DST3FL) and the C-LSR-ns
292        reference solution [cm/s]; color indicates speed (or differences
293        of speed), vectors indicate direction only.}
294    \label{fig:iceveloc}    \label{fig:iceveloc}
295  \end{figure}  \end{figure}
296    
297  The C-EVP-ns solution is very different from the C-LSR-ns solution  The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
298  (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
299  for increased drift by over 2\,cm/s in the Beaufort Gyre and the  EVP-approximation of the VP-dynamics allows for increased drift by
300  transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska  over 2\,cm/s in the Beaufort Gyre and the transarctic drift.
301    in the C-EVP-ns solution. [Really?]} In general, drift velocities are  %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns
302  biased towards higher values in the EVP solutions as can be seen from  %solution. [Really?, No]}
303  a histogram of the differences in \reffig{drifthist}.  In general, drift velocities are biased towards higher values in the
304  \begin{figure}[htbp]  EVP solutions.
305    \centering  % as can be seen from a histogram of the differences in
306    \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}  %\reffig{drifthist}.
307    \caption{Histogram of drift velocity differences for C-LSR-ns and  %\begin{figure}[htbp]
308      C-EVP-ns solution [cm/s].}  %  \centering
309    \label{fig:drifthist}  %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
310  \end{figure}  %  \caption{Histogram of drift velocity differences for C-LSR-ns and
311    %    C-EVP-ns solution [cm/s].}
312    %  \label{fig:drifthist}
313    %\end{figure}
314    
315  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
316  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
317  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
318  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
319  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--d, and
320  area distributions (not shown).  \ml{Compared to other solutions, for  concentrations (not shown).
   example, AOMIP the ice thickness distribution blablabal} \ml{[What  
   can I say about effective thickness?]}  
321  \begin{figure}[htbp]  \begin{figure}[htbp]
322    \centering    \centering
323    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
324    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
325    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
326    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
327      \\
328    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
329    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
330    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
331    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
332      \\
333      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
334      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
335      \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
336      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
337      \\
338      \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
339      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
340      \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
341      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
342    \caption{(a) Effective thickness (volume per unit area) of the    \caption{(a) Effective thickness (volume per unit area) of the
343      C-LSR-ns solution, averaged over the months Janurary through March      C-LSR-ns solution, averaged over the months Janurary through March
344      2000 [m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,      2000 [m]; (b)-(d) difference between solutions with B-grid, free
345      and C-LSR-ns solutions [cm/s].}      lateral slip, EVP-solver, truncated ellipse method (TEM),
346        different ice-ocean stress formulation (HB87), different
347        thermodynamics (WTD), different advection for thermodynamic
348        variables (DST3FL) and the C-LSR-ns reference solution [m].}
349    \label{fig:icethick}    \label{fig:icethick}
350  \end{figure}  \end{figure}
351    %
352  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
353  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
354  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 358  the ice volume in not larger everywhere:
358  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
359  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
360  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
361  differences on the \ml{luv [what is this in English?]} and the lee of  differences with more ice on the upstream side of island groups and
362  island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which  less ice in their lee, such as Franz-Josef-Land and
363  \ml{\ldots [I find hard to interpret].}  Severnaya Semlya\ml{/or Nordland?},
364    because ice tends to flow along coasts less easily in the B-LSR-ns
365    solution.
366    
367  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
368  smaller differences to C-LSR-ns than the transition from the B-grid to  smaller differences to C-LSR-ns in the central Arctic than the
369  the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it  transition from the B-grid to the C-grid (\reffig{icethick}c), except
370  still reduces the effective ice thickness by up to 2\,m where the ice  in the Canadian Archipelago. There it reduces the effective ice
371  is thick and the straits are narrow. Everywhere else the ice volume is  thickness by 2\,m and more where the ice is thick and the straits are
372    narrow.  Dipoles of ice thickness differences can also be observed
373    around islands, because the free-slip solution allows more flow around
374    islands than the no-slip solution.  Everywhere else the ice volume is
375  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
376  %  %
377  The C-EVP-ns solution has generally stronger drift velocities then the  The C-EVP-ns solution has generally stronger drift velocities than the
378  C-LSR-ns solution. Consequently, more ice can be moved the eastern  C-LSR-ns solution. Consequently, more ice can be moved from the
379  part of the Arctic, where ice volumes are smaller, to the western  eastern part of the Arctic, where ice volumes are smaller, to the
380  Arctic where ice piles up along the coast (\reffig{icethick}d). Within  western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,
381  the Canadian Archipelago, more drift leads to faster ice export and  more drift leads to faster ice export and reduced effective ice
382  reduced effective ice thickness.  thickness. With a shorter time step of
383    $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to
384    converge to the LSOR solution (not shown). Only in the narrow straits
385    in the Archipelago the ice thickness is not affected by the shorter
386    time step and the ice is still thinner by 2\,m and more, as in the EVP
387    solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
388    
389    The observed difference of order 2\,m and less are smaller than the
390    differences that were observed between different hindcast and climate
391    models in \citet{gerdes07}. There the range of sea ice volume of
392    different sea ice-ocean models (which shared very similar forcing
393    fields) was on the order of $10,000\text{km$^{3}$}$; this range was
394    even larger for coupled climate models. Here, the range (and the
395    averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
396    the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
397    leads to generally thicker ice (\reffig{icethick} and
398    \reftab{icevolume}).
399    \begin{table}[htbp]
400      \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
401        model run & ice volume
402        & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
403            km$^{3}$\,y$^{-1}$}$]}\\
404        & [$\text{km$^{3}$}$]
405        & \multicolumn{2}{c}{FS}
406        & \multicolumn{2}{c}{NI}
407        & \multicolumn{2}{c}{LS} \\ \hline
408        B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
409        C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
410        C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
411        C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
412        C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
413        C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
414        C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
415        C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
416        C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
417      \end{tabular}
418      \caption{Arctic ice volume averaged over Jan--Mar 2000, in
419        $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
420        period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
421        total northern inflow into the Canadian Archipelago (NI), and the
422        export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}
423      \label{tab:icevolume}
424    \end{table}
425    
426  The difference in ice volume and ice drift velocities between the  The difference in ice volume and ice drift velocities between the
427  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
428  the Arctic. Although the main export of ice goes through the Fram  the Arctic. Although by far the most exported ice drifts through the
429  Strait, a considerable amoung of ice is exported through the Canadian  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
430  Archipelago \citep{???}. \reffig{archipelago} shows a time series of  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
431  daily averages ice transport through various straits in the Canadian  exported through the Canadian Archipelago \citep[and references
432  Archipelago and the Fram Strait for the different model solutions.  therein]{serreze06}. Note, that ice transport estimates are associated
433  Generally, the C-EVP-ns solution has highest maxiumum (export out of  with large uncertainties; also note that tuning an Arctic sea
434  the Artic) and minimum (import into the Artic) fluxes as the drift  ice-ocean model to reproduce observations is not our goal, but we use
435  velocities area largest in this solution \ldots  the published numbers as an orientation.
436    
437    \reffig{archipelago} shows a time series of daily averaged, smoothed
438    with monthly running means, ice transports through various straits in
439    the Canadian Archipelago and the Fram Strait for the different model
440    solutions and \reftab{icevolume} summarizes the time series. The
441    export through Fram Strait agrees with the observations in all model
442    solutions (annual averages range from $2110$ to
443    $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
444    $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
445    time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
446    while the export through the Candian Archipelago is smaller than
447    generally thought. For example, the ice transport through Lancaster
448    Sound is lower (annual averages are $43$ to
449    $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
450    inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
451    a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
452    upstream in Barrow Strait in the 1970ies from satellite images.
453    Generally, the EVP solutions have the highest maximum (export out of
454    the Artic) and lowest minimum (import into the Artic) fluxes as the
455    drift velocities are largest in these solutions.  In the extreme of
456    the Nares Strait, which is only a few grid points wide in our
457    configuration, both B- and C-grid LSOR solvers lead to practically no
458    ice transport, while the C-EVP solutions allow up to
459    $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$
460    to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
461    the Candian Archipelago is larger in all EVP solutions
462    %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
463    than in the LSOR solutions.
464    %get the order of magnitude right (range: $132$ to
465    %$165\text{\,km$^3$\,y$^{-1}$}$);
466    The B-LSR-ns solution is even smaller by another factor of two than the
467    C-LSR solutions (an exception is the WTD solution, where larger ice thickness
468    tends to block the transport).
469    %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
470  \begin{figure}  \begin{figure}
471  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
472  \caption{Transport through Canadian Archipelago for different solver flavors.  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
473    \centerline{{\includegraphics*[width=\linewidth]{\fpath/ice_export}}}
474    \caption{Transport through Canadian Archipelago for different solver
475      flavors. The letters refer to the labels of the sections in
476      \reffig{arctic_topog}; positive values are flux out of the Arctic;
477      legend abbreviations are explained in \reftab{experiments}.
478  \label{fig:archipelago}}  \label{fig:archipelago}}
479  \end{figure}  \end{figure}
480    
481  \ml{[Transport to narrow straits, area?, more runs, TEM, advection  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
482    schemes, Winton TD, discussion about differences in terms of model  %  schemes, Winton TD, discussion about differences in terms of model
483    error? that's tricky as it means refering to Tremblay, thus our ice  %  error? that's tricky as it means refering to Tremblay, thus our ice
484    models are all erroneous!]}  %  models are all erroneous!]}
485    
486  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
487  different solutions. Compared to that the differences between  different solutions. In constrast to that, the differences between
488  free-slip and no-slip solutions \emph{with the same solver} are  free-slip and no-slip solutions \emph{with the same solver} are
489  considerably smaller (the difference for the EVP solver is not shown,  considerably smaller (the difference for the EVP solver is not shown,
490  but comparable to that for the LSOR solver)---albeit smaller, the  but similar to that for the LSOR solver). Albeit smaller, the
491  differences between free and no-slip solutions in ice drift can lead  differences between free and no-slip solutions in ice drift can lead
492  to large differences in ice volume over integration time. At first,  to equally large differences in ice volume, especially in the Canadian
493  this observation appears counterintuitive, as we expect that the  Archipelago over the integration time. At first, this observation
494  solution \emph{technique} should not affect the \emph{solution} to a  seems counterintuitive, as we expect that the solution
495  lower degree than actually modifying the equations. A more detailed  \emph{technique} should not affect the \emph{solution} to a higher
496  study on these differences is beyond the scope of this paper, but at  degree than actually modifying the equations. A more detailed study on
497  this point we may speculate, that the large difference between B-grid,  these differences is beyond the scope of this paper, but at this point
498  C-grid, LSOR, and EVP solutions stem from incomplete convergence of  we may speculate, that the large difference between B-grid, C-grid,
499  the solvers due to linearization \citep[and Bruno Tremblay, personal  LSOR, and EVP solutions stem from incomplete convergence of the
500    solvers due to linearization and due to different methods of
501    linearization \citep[and Bruno Tremblay, personal
502  communication]{hunke01}: if the convergence of the non-linear momentum  communication]{hunke01}: if the convergence of the non-linear momentum
503  equations is not complete for all linearized solvers, then one can  equations is not complete for all linearized solvers, then one can
504  imagine that each solver stops at a different point in velocity-space  imagine that each solver stops at a different point in velocity-space
505  thus leading to different solutions for the ice drift velocities. If  thus leading to different solutions for the ice drift velocities. If
506  this were true, this tantalizing circumstance had a dramatic impact on  this were true, this tantalizing circumstance would have a dramatic
507  sea-ice modeling in general, and we would need to improve the solution  impact on sea-ice modeling in general, and we would need to improve
508  technique of dynamic sea ice model, most likely at a very high  the solution techniques for dynamic sea ice models, most likely at a very
509  compuational cost (Bruno Tremblay, personal communication).  high compuational cost (Bruno Tremblay, personal communication). Further,
510    we observe that the EVP solutions tends to produce effectively
511    ``weaker'' ice that yields more easily to stress. The fast response to
512    changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
513  \begin{itemize}  where the EVP model adjusts quickly to a cyclonic wind pattern, while
514  \item Configuration  the LSOR solution does not. This property of the EVP solutions allows
515  \item OBCS from cube  larger ice transports through narrow straits, where the implicit
516  \item forcing  solver LSOR forms rigid ice. The underlying reasons for this striking
517  \item 1/2 and full resolution  difference need further exploration.
518  \item with a few JFM figs from C-grid LSR no slip  
519    ice transport through Canadian Archipelago  % THIS is now almost all in the text:
520    thickness distribution  %\begin{itemize}
521    ice velocity and transport  %\item Configuration
522  \end{itemize}  %\item OBCS from cube
523    %\item forcing
524  \begin{itemize}  %\item 1/2 and full resolution
525  \item Arctic configuration  %\item with a few JFM figs from C-grid LSR no slip
526  \item ice transport through straits and near boundaries  %  ice transport through Canadian Archipelago
527  \item focus on narrow straits in the Canadian Archipelago  %  thickness distribution
528  \end{itemize}  %  ice velocity and transport
529    %\end{itemize}
530  \begin{itemize}  
531  \item B-grid LSR no-slip: B-LSR-ns  %\begin{itemize}
532  \item C-grid LSR no-slip: C-LSR-ns  %\item Arctic configuration
533  \item C-grid LSR slip:    C-LSR-fs  %\item ice transport through straits and near boundaries
534  \item C-grid EVP no-slip: C-EVP-ns  %\item focus on narrow straits in the Canadian Archipelago
535  \item C-grid EVP slip:    C-EVP-fs  %\end{itemize}
536  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,  
537    new flag): C-LSR-ns+TEM  %\begin{itemize}
538  \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?  %\item B-grid LSR no-slip: B-LSR-ns
539  \item C-grid LSR no-slip + Winton:  %\item C-grid LSR no-slip: C-LSR-ns
540  \item  speed-performance-accuracy (small)  %\item C-grid LSR slip:    C-LSR-fs
541    ice transport through Canadian Archipelago differences  %\item C-grid EVP no-slip: C-EVP-ns
542    thickness distribution differences  %\item C-grid EVP slip:    C-EVP-fs
543    ice velocity and transport differences  %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
544  \end{itemize}  %  new flag): C-LSR-ns+TEM
545    %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
546  We anticipate small differences between the different models due to:  %\item C-grid LSR no-slip + Winton:
547  \begin{itemize}  %\item  speed-performance-accuracy (small)
548  \item advection schemes: along the ice-edge and regions with large  %  ice transport through Canadian Archipelago differences
549    gradients  %  thickness distribution differences
550  \item C-grid: less transport through narrow straits for no slip  %  ice velocity and transport differences
551    conditons, more for free slip  %\end{itemize}
552  \item VP vs.\ EVP: speed performance, accuracy?  
553  \item ocean stress: different water mass properties beneath the ice  %We anticipate small differences between the different models due to:
554  \end{itemize}  %\begin{itemize}
555    %\item advection schemes: along the ice-edge and regions with large
556  %\begin{figure}  %  gradients
557  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}  %\item C-grid: less transport through narrow straits for no slip
558  %\caption{Surface sea ice velocity for different solver flavors.  %  conditons, more for free slip
559  %\label{fig:iceveloc}}  %\item VP vs.\ EVP: speed performance, accuracy?
560  %\end{figure}  %\item ocean stress: different water mass properties beneath the ice
561    %\end{itemize}
 %\begin{figure}  
 %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}  
 %\caption{Sea ice thickness for different solver flavors.  
 %\label{fig:icethick}}  
 %\end{figure}  
562    
563  %%% Local Variables:  %%% Local Variables:
564  %%% mode: latex  %%% mode: latex
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