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revision 1.10 by mlosch, Tue Mar 4 20:33:07 2008 UTC revision 1.15 by mlosch, Mon Jun 2 13:25:40 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 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  \begin{figure}  described above.  The horizontal domain size is 420 by 384 grid boxes.
109  \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}  \begin{figure*}
110  \caption{Bathymetry and domain boudaries of Arctic  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
111    Domain.\label{fig:arctic1}}  %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
112  \end{figure}  \includegraphics*[width=0.44\linewidth]{\fpath/topography}
113    \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
114    \caption{Left: Bathymetry and domain boudaries of Arctic
115      Domain; the dashed line marks the boundaries of the inset on the
116      right hand side. The letters in the inset label sections in the
117      Canadian Archipelago, where ice transport is evaluated:
118      A: Nares Strait; %
119      B: \ml{Meighen Island}; %
120      C: Prince Gustaf Adolf Sea; %
121      D: \ml{Brock Island}; %
122      E: M'Clure Strait; %
123      F: Amundsen Gulf; %
124      G: Lancaster Sound; %
125      H: Barrow Strait \ml{W.}; %
126      I: Barrow Strait \ml{E.}; %
127      J: Barrow Strait \ml{N.}. %
128      The sections A through F comprise the total inflow into the Canadian
129      Archipelago. \ml{[May still need to check the geography.]}
130      \label{fig:arctic_topog}}
131    \end{figure*}
132    
133    The main dynamic difference from cube sphere is that the Arctic domain
134    configuration does not use rescaled vertical coordinates (z$^\ast$)
135    and the surface boundary conditions for freshwater input are
136    different, because those features are not supported by the open
137    boundary code.
138    %
139    Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
140    respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
141    
142  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,
143  rescaled vertical coordinates (z$^\ast$) and the surface boundary  with three different dynamical solvers, two different boundary
144  conditions for freshwater input are different, because those features  conditions, different stress coupling, rheology, and advection
145  are not supported by the open boundary code.  schemes. \reftab{experiments} gives an overview over the experiments
146    discussed in this section.
147  Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,  \begin{table}[htbp]
148  0.76, 0.94, and 0.8.    \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
149        experiment name & description \\ \hline
150  The model is integrated from January, 1992 to March \ml{[???]}, 2000,      B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
151  with five different dynamical solvers:    Arakawa B-grid, implying no-slip lateral boundary conditions
152  \begin{description}    ($\vek{u}=0$ exactly) \\
153  \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
154    B-grid, implying no-slip lateral boundary conditions;    boundary conditions (implemented via ghost-points) \\
155  \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
156    boundary conditions;    conditions \\
157  \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
158    conditions;    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
159  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with    150\text{\,s}$ \\
160    no-slip lateral boundary conditions; and      C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
161  \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral    no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
162    boundary conditions.    10\text{\,s}$ \\
163  \end{description}      C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
164      to \citet{hibler87}\\
165        C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
166      rheology \citep{hibler97} \\
167        C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
168      \citet{winton00} \\
169        C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
170      direct-space-time advection scheme for thermodynamic variables
171      \citep{hundsdorfer94}
172      \end{tabular}
173      \caption{Overview over model simulations in \refsec{arctic}.
174        \label{tab:experiments}}
175    \end{table}
176    %\begin{description}
177    %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
178    %  Arakawa B-grid, implying no-slip lateral boundary conditions
179    %  ($\vek{u}=0$ exactly);
180    %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
181    %  boundary conditions (implemented via ghost-points);
182    %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
183    %  conditions;
184    %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
185    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
186    %  150\text{\,s}$;
187    %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
188    %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
189    %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
190    %  direct-space-time advection scheme \citep{hundsdorfer94};
191    %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
192    %  rheology \citep{hibler97};
193    %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
194    %  to \citet{hibler87};
195    %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
196    %  \citet{winton00};
197    %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
198    %%  scale noise \citep{hunke01};
199    %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
200    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
201    %  10\text{\,s}$.
202    %\end{description}
203  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so  Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
204  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
205  interpreted as pure model error. Lateral boundary conditions on a  interpreted as pure model error. Lateral boundary conditions on a
206  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
207  unclear, so that comparing the no-slip solutions to the free-slip  unclear, so that comparing the no-slip solutions to the free-slip
208  solutions gives another measure of uncertainty in sea ice modeling.  solutions gives another measure of uncertainty in sea ice modeling.
209    The remaining experiments explore further sensitivities of the system
210    to different physics (change in rheology, advection and diffusion
211    properties, stress coupling, and thermodynamics) and different time
212    steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
213    for the EVP solution. We use two interpretations of this choice where
214    the EVP model is subcycled 120 times within a (short) model timestep
215    of 1200\,s resulting in a very long and expensive integration
216    ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
217    forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
218    
219  A principle difficulty in comparing the solutions obtained with  A principle difficulty in comparing the solutions obtained with
220  different variants of the dynamics solver lies in the non-linear  different realizations of the model dynamics lies in the non-linear
221  feedback of the ice dynamics and thermodynamics. Already after a few  feedback of the ice dynamics and thermodynamics. Already after a few
222  months the solutions have diverged so far from each other that  months the solutions have diverged so far from each other that
223  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 231  shown are the differences between B-grid
231  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
232  solution (\reffig{iceveloc}a) roughly resembles the drift velocities  solution (\reffig{iceveloc}a) roughly resembles the drift velocities
233  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)  of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
234  models in an cyclonic circulation regime (CCR) \citep[their  models in a cyclonic circulation regime (CCR) \citep[their
235  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift  Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
236  shifted eastwards towards Alaska.  shifted eastwards towards Alaska.
237    
238  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)
239  is most pronounced  is most pronounced along the coastlines, where the discretization
240  along the coastlines, where the discretization differs most between B  differs most between B and C-grids: On a B-grid the tangential
241  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
242  (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
243  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
244  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
245  Strait and especially the along Greenland's east coast; also, the flow  Greenland's east coast; also, the flow through Baffin Bay and Davis
246  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
247  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]}  
248  %  %
249  Compared to the differences between B and C-grid solutions the  Compared to the differences between B and C-grid solutions,the
250  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
251  (\reffig{iceveloc}c).  As expected the differences are largest along  (\reffig{iceveloc}c).  As expected the differences are largest along
252  coastlines: because of the free-slip boundary conditions, flow is  coastlines: because of the free-slip boundary conditions, flow is
253  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
254  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
255  Island.  Island.
256    %\newcommand{\subplotwidth}{0.44\textwidth}
257    \newcommand{\subplotwidth}{0.3\textwidth}
258  \begin{figure}[htbp]  \begin{figure}[htbp]
259    \centering    \centering
260    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
261    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
262    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
263    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}
264      \\
265    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
266    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
267    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
268    {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
269      \\
270      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
271      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
272      \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
273      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
274      \\
275      \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
276      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
277      \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
278      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
279    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged    \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
280      over the first 3 months of integration [cm/s]; (b)-(d) difference      over the first 3 months of integration [cm/s]; (b)-(h) difference
281      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,
282      [cm/s]; color indicates speed (or differences of speed), vectors      truncated ellipse method (TEM), different ice-ocean stress
283      indicate direction only.}      formulation (HB87), different thermodynamics (WTD), different
284        advection for thermodynamic variables (DST3FL) and the C-LSR-ns
285        reference solution [cm/s]; color indicates speed (or differences
286        of speed), vectors indicate direction only.}
287    \label{fig:iceveloc}    \label{fig:iceveloc}
288  \end{figure}  \end{figure}
289    
290  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
291  (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows  very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
292  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
293  transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska  over 2\,cm/s in the Beaufort Gyre and the transarctic drift.
294    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
295  biased towards higher values in the EVP solutions as can be seen from  %solution. [Really?, No]}
296  a histogram of the differences in \reffig{drifthist}.  In general, drift velocities are biased towards higher values in the
297  \begin{figure}[htbp]  EVP solutions.
298    \centering  % as can be seen from a histogram of the differences in
299    \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}  %\reffig{drifthist}.
300    \caption{Histogram of drift velocity differences for C-LSR-ns and  %\begin{figure}[htbp]
301      C-EVP-ns solution [cm/s].}  %  \centering
302    \label{fig:drifthist}  %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
303  \end{figure}  %  \caption{Histogram of drift velocity differences for C-LSR-ns and
304    %    C-EVP-ns solution [cm/s].}
305    %  \label{fig:drifthist}
306    %\end{figure}
307    
308  \reffig{icethick}a shows the effective thickness (volume per unit  \reffig{icethick}a shows the effective thickness (volume per unit
309  area) of the C-LSR-ns solution, averaged over January, February, March  area) of the C-LSR-ns solution, averaged over January, February, March
310  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
311  ice drift velocities have led to the evolution of very different ice  ice drift velocities have led to the evolution of very different ice
312  thickness distributions, which are shown in \reffig{icethick}b--d, and  thickness distributions, which are shown in \reffig{icethick}b--d, and
313  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?]}  
314  \begin{figure}[htbp]  \begin{figure}[htbp]
315    \centering    \centering
316    \subfigure[{\footnotesize C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-ns}]
317    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
318    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
319    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
320      \\
321    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
322    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
323    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]    \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
324    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
325      \\
326      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
327      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
328      \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
329      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
330      \\
331      \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
332      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
333      \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
334      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
335    \caption{(a) Effective thickness (volume per unit area) of the    \caption{(a) Effective thickness (volume per unit area) of the
336      C-LSR-ns solution, averaged over the months Janurary through March      C-LSR-ns solution, averaged over the months Janurary through March
337      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
338      and C-LSR-ns solutions [cm/s].}      lateral slip, EVP-solver, truncated ellipse method (TEM),
339        different ice-ocean stress formulation (HB87), different
340        thermodynamics (WTD), different advection for thermodynamic
341        variables (DST3FL) and the C-LSR-ns reference solution [m].}
342    \label{fig:icethick}    \label{fig:icethick}
343  \end{figure}  \end{figure}
344    %
345  The generally weaker ice drift velocities in the B-LSR-ns solution,  The generally weaker ice drift velocities in the B-LSR-ns solution,
346  when compared to the C-LSR-ns solution, in particular through the  when compared to the C-LSR-ns solution, in particular through the
347  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 351  the ice volume in not larger everywhere:
351  patches of smaller ice volume in the B-grid solution, most likely  patches of smaller ice volume in the B-grid solution, most likely
352  because the Beaufort Gyre is weaker and hence not as effective in  because the Beaufort Gyre is weaker and hence not as effective in
353  transporting ice westwards. There are also dipoles of ice volume  transporting ice westwards. There are also dipoles of ice volume
354  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
355  island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which  less ice in their lee, such as Franz-Josef-Land and
356  \ml{\ldots [I find hard to interpret].}  Severnaya Semlya\ml{/or Nordland?},
357    because ice tends to flow along coasts less easily in the B-LSR-ns
358    solution.
359    
360  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
361  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
362  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
363  still reduces the effective ice thickness by up to 2\,m where the ice  in the Canadian Archipelago. There it reduces the effective ice
364  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
365    narrow.  Dipoles of ice thickness differences can also be observed
366    around islands, because the free-slip solution allows more flow around
367    islands than the no-slip solution.  Everywhere else the ice volume is
368  affected only slightly by the different boundary condition.  affected only slightly by the different boundary condition.
369  %  %
370  The C-EVP-ns solution has generally stronger drift velocities then the  The C-EVP-ns solution has generally stronger drift velocities than the
371  C-LSR-ns solution. Consequently, more ice can be moved the eastern  C-LSR-ns solution. Consequently, more ice can be moved from the
372  part of the Arctic, where ice volumes are smaller, to the western  eastern part of the Arctic, where ice volumes are smaller, to the
373  Arctic where ice piles up along the coast (\reffig{icethick}d). Within  western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,
374  the Canadian Archipelago, more drift leads to faster ice export and  more drift leads to faster ice export and reduced effective ice
375  reduced effective ice thickness.  thickness. With a shorter time step of
376    $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to
377    converge to the LSOR solution (not shown). Only in the narrow straits
378    in the Archipelago the ice thickness is not affected by the shorter
379    time step and the ice is still thinner by 2\,m and more, as in the EVP
380    solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
381    
382    The observed difference of order 2\,m and less are smaller than the
383    differences that were observed between different hindcast and climate
384    models in \citet{gerdes07}. There the range of sea ice volume of
385    different sea ice-ocean models (which shared very similar forcing
386    fields) was on the order of $10,000\text{km$^{3}$}$; this range was
387    even larger for coupled climate models. Here, the range (and the
388    averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
389    the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
390    leads to generally thicker ice (\reffig{icethick} and
391    \reftab{icevolume}).
392    \begin{table}[htbp]
393      \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
394        model run & ice volume
395        & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
396            km$^{3}$\,y$^{-1}$}$]}\\
397        & [$\text{km$^{3}$}$]
398        & \multicolumn{2}{c}{FS}
399        & \multicolumn{2}{c}{NI}
400        & \multicolumn{2}{c}{LS} \\ \hline
401        B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
402        C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
403        C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
404        C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
405        C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
406        C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
407        C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
408        C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
409        C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
410      \end{tabular}
411      \caption{Arctic ice volume averaged over Jan--Mar 2000, in
412        $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
413        period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
414        total northern inflow into the Canadian Archipelago (NI), and the
415        export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}
416      \label{tab:icevolume}
417    \end{table}
418    
419  The difference in ice volume and ice drift velocities between the  The difference in ice volume and ice drift velocities between the
420  different experiments has consequences for the ice transport out of  different experiments has consequences for the ice transport out of
421  the Arctic. Although the main export of ice goes through the Fram  the Arctic. Although by far the most exported ice drifts through the
422  Strait, a considerable amoung of ice is exported through the Canadian  Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
423  Archipelago \citep{???}. \reffig{archipelago} shows a time series of  considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
424  daily averages ice transport through various straits in the Canadian  exported through the Canadian Archipelago \citep[and references
425  Archipelago and the Fram Strait for the different model solutions.  therein]{serreze06}. Note, that ice transport estimates are associated
426  Generally, the C-EVP-ns solution has highest maxiumum (export out of  with large uncertainties; also note that tuning an Arctic sea
427  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
428  velocities area largest in this solution \ldots  the published numbers as an orientation.
429    
430    \reffig{archipelago} shows a time series of daily averaged, smoothed
431    with monthly running means, ice transports through various straits in
432    the Canadian Archipelago and the Fram Strait for the different model
433    solutions and \reftab{icevolume} summarizes the time series. The
434    export through Fram Strait agrees with the observations in all model
435    solutions (annual averages range from $2110$ to
436    $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
437    $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
438    time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
439    while the export through the Candian Archipelago is smaller than
440    generally thought. For example, the ice transport through Lancaster
441    Sound is lower (annual averages are $43$ to
442    $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
443    inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
444    a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
445    upstream in Barrow Strait in the 1970ies from satellite images.
446    Generally, the EVP solutions have the highest maximum (export out of
447    the Artic) and lowest minimum (import into the Artic) fluxes as the
448    drift velocities are largest in these solutions.  In the extreme of
449    the Nares Strait, which is only a few grid points wide in our
450    configuration, both B- and C-grid LSOR solvers lead to practically no
451    ice transport, while the C-EVP solutions allow up to
452    $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$
453    to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
454    the Candian Archipelago is larger in all EVP solutions
455    %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
456    than in the LSOR solutions.
457    %get the order of magnitude right (range: $132$ to
458    %$165\text{\,km$^3$\,y$^{-1}$}$);
459    The B-LSR-ns solution is even smaller by another factor of two than the
460    C-LSR solutions (an exception is the WTD solution, where larger ice thickness
461    tends to block the transport).
462    %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
463  \begin{figure}  \begin{figure}
464  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
465  \caption{Transport through Canadian Archipelago for different solver flavors.  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
466    \centerline{{\includegraphics*[width=\linewidth]{\fpath/ice_export}}}
467    \caption{Transport through Canadian Archipelago for different solver
468      flavors. The letters refer to the labels of the sections in
469      \reffig{arctic_topog}; positive values are flux out of the Arctic;
470      legend abbreviations are explained in \reftab{experiments}.
471  \label{fig:archipelago}}  \label{fig:archipelago}}
472  \end{figure}  \end{figure}
473    
474  \ml{[Transport to narrow straits, area?, more runs, TEM, advection  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
475    schemes, Winton TD, discussion about differences in terms of model  %  schemes, Winton TD, discussion about differences in terms of model
476    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
477    models are all erroneous!]}  %  models are all erroneous!]}
478    
479  In summary, we find that different dynamical solvers can yield very  In summary, we find that different dynamical solvers can yield very
480  different solutions. Compared to that the differences between  different solutions. In constrast to that, the differences between
481  free-slip and no-slip solutions \emph{with the same solver} are  free-slip and no-slip solutions \emph{with the same solver} are
482  considerably smaller (the difference for the EVP solver is not shown,  considerably smaller (the difference for the EVP solver is not shown,
483  but comparable to that for the LSOR solver)---albeit smaller, the  but similar to that for the LSOR solver). Albeit smaller, the
484  differences between free and no-slip solutions in ice drift can lead  differences between free and no-slip solutions in ice drift can lead
485  to large differences in ice volume over integration time. At first,  to equally large differences in ice volume, especially in the Canadian
486  this observation appears counterintuitive, as we expect that the  Archipelago over the integration time. At first, this observation
487  solution \emph{technique} should not affect the \emph{solution} to a  seems counterintuitive, as we expect that the solution
488  lower degree than actually modifying the equations. A more detailed  \emph{technique} should not affect the \emph{solution} to a higher
489  study on these differences is beyond the scope of this paper, but at  degree than actually modifying the equations. A more detailed study on
490  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
491  C-grid, LSOR, and EVP solutions stem from incomplete convergence of  we may speculate, that the large difference between B-grid, C-grid,
492  the solvers due to linearization \citep[and Bruno Tremblay, personal  LSOR, and EVP solutions stem from incomplete convergence of the
493    solvers due to linearization and due to different methods of
494    linearization \citep[and Bruno Tremblay, personal
495  communication]{hunke01}: if the convergence of the non-linear momentum  communication]{hunke01}: if the convergence of the non-linear momentum
496  equations is not complete for all linearized solvers, then one can  equations is not complete for all linearized solvers, then one can
497  imagine that each solver stops at a different point in velocity-space  imagine that each solver stops at a different point in velocity-space
498  thus leading to different solutions for the ice drift velocities. If  thus leading to different solutions for the ice drift velocities. If
499  this were true, this tantalizing circumstance had a dramatic impact on  this were true, this tantalizing circumstance would have a dramatic
500  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
501  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
502  compuational cost (Bruno Tremblay, personal communication).  high compuational cost (Bruno Tremblay, personal communication). Further,
503    we observe that the EVP solutions tends to produce effectively
504    ``weaker'' ice that yields more easily to stress. The fast response to
505    changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
506  \begin{itemize}  where the EVP model adjusts quickly to a cyclonic wind pattern, while
507  \item Configuration  the LSOR solution does not. This property of the EVP solutions allows
508  \item OBCS from cube  larger ice transports through narrow straits, where the implicit
509  \item forcing  solver LSOR forms rigid ice. The underlying reasons for this striking
510  \item 1/2 and full resolution  difference need further exploration.
511  \item with a few JFM figs from C-grid LSR no slip  
512    ice transport through Canadian Archipelago  % THIS is now almost all in the text:
513    thickness distribution  %\begin{itemize}
514    ice velocity and transport  %\item Configuration
515  \end{itemize}  %\item OBCS from cube
516    %\item forcing
517  \begin{itemize}  %\item 1/2 and full resolution
518  \item Arctic configuration  %\item with a few JFM figs from C-grid LSR no slip
519  \item ice transport through straits and near boundaries  %  ice transport through Canadian Archipelago
520  \item focus on narrow straits in the Canadian Archipelago  %  thickness distribution
521  \end{itemize}  %  ice velocity and transport
522    %\end{itemize}
523  \begin{itemize}  
524  \item B-grid LSR no-slip: B-LSR-ns  %\begin{itemize}
525  \item C-grid LSR no-slip: C-LSR-ns  %\item Arctic configuration
526  \item C-grid LSR slip:    C-LSR-fs  %\item ice transport through straits and near boundaries
527  \item C-grid EVP no-slip: C-EVP-ns  %\item focus on narrow straits in the Canadian Archipelago
528  \item C-grid EVP slip:    C-EVP-fs  %\end{itemize}
529  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,  
530    new flag): C-LSR-ns+TEM  %\begin{itemize}
531  \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?  %\item B-grid LSR no-slip: B-LSR-ns
532  \item C-grid LSR no-slip + Winton:  %\item C-grid LSR no-slip: C-LSR-ns
533  \item  speed-performance-accuracy (small)  %\item C-grid LSR slip:    C-LSR-fs
534    ice transport through Canadian Archipelago differences  %\item C-grid EVP no-slip: C-EVP-ns
535    thickness distribution differences  %\item C-grid EVP slip:    C-EVP-fs
536    ice velocity and transport differences  %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
537  \end{itemize}  %  new flag): C-LSR-ns+TEM
538    %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
539  We anticipate small differences between the different models due to:  %\item C-grid LSR no-slip + Winton:
540  \begin{itemize}  %\item  speed-performance-accuracy (small)
541  \item advection schemes: along the ice-edge and regions with large  %  ice transport through Canadian Archipelago differences
542    gradients  %  thickness distribution differences
543  \item C-grid: less transport through narrow straits for no slip  %  ice velocity and transport differences
544    conditons, more for free slip  %\end{itemize}
545  \item VP vs.\ EVP: speed performance, accuracy?  
546  \item ocean stress: different water mass properties beneath the ice  %We anticipate small differences between the different models due to:
547  \end{itemize}  %\begin{itemize}
548    %\item advection schemes: along the ice-edge and regions with large
549  %\begin{figure}  %  gradients
550  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}  %\item C-grid: less transport through narrow straits for no slip
551  %\caption{Surface sea ice velocity for different solver flavors.  %  conditons, more for free slip
552  %\label{fig:iceveloc}}  %\item VP vs.\ EVP: speed performance, accuracy?
553  %\end{figure}  %\item ocean stress: different water mass properties beneath the ice
554    %\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}  
555    
556  %%% Local Variables:  %%% Local Variables:
557  %%% mode: latex  %%% mode: latex
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