/[MITgcm]/MITgcm_contrib/articles/ceaice/ceaice_forward.tex
ViewVC logotype

Diff of /MITgcm_contrib/articles/ceaice/ceaice_forward.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.8 by dimitri, Fri Feb 29 01:28:05 2008 UTC revision 1.17 by mlosch, Wed Jun 4 13:32:05 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  Section~\ref{sec:model} using the following specific options.  The  \refsec{model} using the following specific options.  The
49  zero-heat-capacity thermodynamics formulation of \citet{hib80} 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 Fig.~\ref{fig: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/arctic1}}}  \begin{figure*}
117  \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}  %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
118    %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
119    %\includegraphics*[width=0.44\linewidth]{\fpath/topography}
120    %\includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
121    \includegraphics*[width=\linewidth]{\fpath/topography}
122    \caption{Left: Bathymetry and domain boudaries of Arctic
123      Domain; the dashed line marks the boundaries of the inset on the
124      right hand side. The letters in the inset label sections in the
125      Canadian Archipelago, where ice transport is evaluated:
126      A: Nares Strait; %
127      B: \ml{Meighen Island}; %
128      C: Prince Gustaf Adolf Sea; %
129      D: \ml{Brock Island}; %
130      E: M'Clure Strait; %
131      F: Amundsen Gulf; %
132      G: Lancaster Sound; %
133      H: Barrow Strait \ml{W.}; %
134      I: Barrow Strait \ml{E.}; %
135      J: Barrow Strait \ml{N.}; %
136      K: Fram Strait. %
137      The sections A through F comprise the total inflow into the Canadian
138      Archipelago. \ml{[May still need to check the geography.]}
139      \label{fig:arctic_topog}}
140    \end{figure*}
141    
142    The main dynamic difference from cube sphere is that the Arctic domain
143    configuration does not use rescaled vertical coordinates (z$^\ast$)
144    and the surface boundary conditions for freshwater input are
145    different, because those features are not supported by the open
146    boundary code.
147    %
148    Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
149    respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
150    
151    The model is integrated from Jan~01, 1992 to Mar~31, 2000,
152    with three different dynamical solvers, two different boundary
153    conditions, different stress coupling, rheology, and advection
154    schemes. \reftab{experiments} gives an overview over the experiments
155    discussed in this section.
156    \begin{table}[t]
157      \caption{Overview over model simulations in \refsec{arctic}.
158        \label{tab:experiments}}
159      \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
160        experiment name & description \\ \hline
161        B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
162      Arakawa B-grid, implying no-slip lateral boundary conditions
163      ($\vek{u}=0$ exactly) \\
164        C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
165      boundary conditions (implemented via ghost-points) \\
166        C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
167      conditions \\
168        C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
169      no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
170      150\text{\,s}$ \\
171        C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
172      no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
173      10\text{\,s}$ \\
174        C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
175      to \citet{hibler87}\\
176        C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
177      rheology \citep{hibler97} \\
178        C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
179      \citet{winton00} \\
180        C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
181      direct-space-time advection scheme for thermodynamic variables
182      \citep{hundsdorfer94}
183      \end{tabular}
184    \end{table}
185    %\begin{description}
186    %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
187    %  Arakawa B-grid, implying no-slip lateral boundary conditions
188    %  ($\vek{u}=0$ exactly);
189    %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
190    %  boundary conditions (implemented via ghost-points);
191    %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
192    %  conditions;
193    %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
194    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
195    %  150\text{\,s}$;
196    %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
197    %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
198    %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
199    %  direct-space-time advection scheme \citep{hundsdorfer94};
200    %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
201    %  rheology \citep{hibler97};
202    %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
203    %  to \citet{hibler87};
204    %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
205    %  \citet{winton00};
206    %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
207    %%  scale noise \citep{hunke01};
208    %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
209    %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
210    %  10\text{\,s}$.
211    %\end{description}
212    Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
213    that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
214    interpreted as pure model error. Lateral boundary conditions on a
215    coarse grid (coarse compared to the roughness of the true coast line) are
216    unclear, so that comparing the no-slip solutions to the free-slip
217    solutions gives another measure of uncertainty in sea ice modeling.
218    The remaining experiments explore further sensitivities of the system
219    to different physics (change in rheology, advection and diffusion
220    properties, stress coupling, and thermodynamics) and different time
221    steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
222    for the EVP solution. We use two interpretations of this choice where
223    the EVP model is subcycled 120 times within a (short) model timestep
224    of 1200\,s resulting in a very long and expensive integration
225    ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
226    forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
227    
228    A principle difficulty in comparing the solutions obtained with
229    different realizations of the model dynamics lies in the non-linear
230    feedback of the ice dynamics and thermodynamics. Already after a few
231    months the solutions have diverged so far from each other that
232    comparing velocities only makes sense within the first 3~months of the
233    integration while the ice distribution is still close to the initial
234    conditions. At the end of the integration, the differences between the
235    model solutions can be interpreted as cumulated model uncertainties.
236    
237    \reffig{iceveloc} shows ice velocities averaged over Janunary,
238    February, and March (JFM) of 1992 for the C-LSR-ns solution; also
239    shown are the differences between B-grid and C-grid, LSR and EVP, and
240    no-slip and free-slip solution. The velocity field of the C-LSR-ns
241    solution (\reffig{iceveloc}a) roughly resembles the drift velocities
242    of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
243    models in a cyclonic circulation regime (CCR) \citep[their
244    Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
245    shifted eastwards towards Alaska.
246    
247    \newcommand{\subplotwidth}{0.44\textwidth}
248    %\newcommand{\subplotwidth}{0.3\textwidth}
249    \begin{figure}[tp]
250      \centering
251      \subfigure[{\footnotesize C-LSR-ns}]
252      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
253      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
254      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}
255      \\
256      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
257      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
258      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
259      {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
260    %  \\
261    %  \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
262    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
263    %  \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
264    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
265    %  \\
266    %  \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
267    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
268    %  \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
269    %  {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
270      \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
271        over the first 3 months of integration [cm/s]; (b)-(h) difference
272        between solutions with B-grid, free lateral slip, EVP-solver,
273        truncated ellipse method (TEM), different ice-ocean stress
274        formulation (HB87), different thermodynamics (WTD), different
275        advection for thermodynamic variables (DST3FL) and the C-LSR-ns
276        reference solution [cm/s]; color indicates speed (or differences
277        of speed), vectors indicate direction only.}
278      \label{fig:iceveloc}
279  \end{figure}  \end{figure}
280    \addtocounter{figure}{-1}
281  Difference from cube sphere is that it does not use z* coordinates nor  \setcounter{subfigure}{4}
282  realfreshwater fluxes because it is not supported by open boundary code.  \begin{figure}[t]
283      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
284  Open water, dry    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
285  ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,    \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
286  0.76, 0.94, and 0.8.    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
287      \\
288  \begin{itemize}    \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
289  \item Configuration    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
290  \item OBCS from cube    \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
291  \item forcing    {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
292  \item 1/2 and full resolution    \caption{continued}
 \item with a few JFM figs from C-grid LSR no slip  
   ice transport through Canadian Archipelago  
   thickness distribution  
   ice velocity and transport  
 \end{itemize}  
   
 \begin{itemize}  
 \item Arctic configuration  
 \item ice transport through straits and near boundaries  
 \item focus on narrow straits in the Canadian Archipelago  
 \end{itemize}  
   
 \begin{itemize}  
 \item B-grid LSR no-slip  
 \item C-grid LSR no-slip  
 \item C-grid LSR slip  
 \item C-grid EVP no-slip  
 \item C-grid EVP slip  
 \item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)  
 \item C-grid LSR no-slip + Winton  
 \item  speed-performance-accuracy (small)  
   ice transport through Canadian Archipelago differences  
   thickness distribution differences  
   ice velocity and transport differences  
 \end{itemize}  
   
 We anticipate small differences between the different models due to:  
 \begin{itemize}  
 \item advection schemes: along the ice-edge and regions with large  
   gradients  
 \item C-grid: less transport through narrow straits for no slip  
   conditons, more for free slip  
 \item VP vs.\ EVP: speed performance, accuracy?  
 \item ocean stress: different water mass properties beneath the ice  
 \end{itemize}  
   
 \begin{figure}  
 \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}  
 \caption{Surface sea ice velocity for different solver flavors.  
 \label{fig:iceveloc}}  
293  \end{figure}  \end{figure}
294    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
295    is most pronounced along the coastlines, where the discretization
296    differs most between B and C-grids: On a B-grid the tangential
297    velocity lies on the boundary (and is thus zero through the no-slip
298    boundary conditions), whereas on the C-grid it is half a cell width
299    away from the boundary, thus allowing more flow. The B-LSR-ns solution
300    has less ice drift through the Fram Strait and especially the along
301    Greenland's east coast; also, the flow through Baffin Bay and Davis
302    Strait into the Labrador Sea is reduced with respect the C-LSR-ns
303    solution.  \ml{[Do we expect this? Say something about that]}
304    %
305    Compared to the differences between B and C-grid solutions, the
306    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
307    (\reffig{iceveloc}c).  As expected the differences are largest along
308    coastlines: because of the free-slip boundary conditions, flow is
309    faster in the C-LSR-fs solution, for example, along the east coast
310    of Greenland, the north coast of Alaska, and the east Coast of Baffin
311    Island.
312    
313    The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
314    very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
315    EVP-approximation of the VP-dynamics allows for increased drift by
316    over 2\,cm/s in the Beaufort Gyre and the transarctic drift.
317    %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns
318    %solution. [Really?, No]}
319    In general, drift velocities are biased towards higher values in the
320    EVP solutions.
321    % as can be seen from a histogram of the differences in
322    %\reffig{drifthist}.
323    %\begin{figure}[htbp]
324    %  \centering
325    %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
326    %  \caption{Histogram of drift velocity differences for C-LSR-ns and
327    %    C-EVP-ns solution [cm/s].}
328    %  \label{fig:drifthist}
329    %\end{figure}
330    
331    Compared to the other parameters, the ice rheology TEM
332    (\reffig{iceveloc}(e)) has a very small effect on the solution. In
333    general the ice drift tends to be increased, because there is no
334    tensile stress and ice can be ``pulled appart'' at no cost.
335    Consequently, the largest effect on drift velocity can be observed
336    near the ice edge in the Labrador Sea. In contrast, in the run with
337    the ice-ocean stress formulation of \citet{hibler87},
338    \reffig{iceveloc}(f) the drift is stronger almost everywhere in the
339    computational domain. The increase is mostly aligned with the general
340    direction of the flow, implying that the different stress formulation
341    reduces the deceleration of drift by the ocean.
342    
343    The 3-layer thermodynamics following \citet{winton00} requires
344    additional information on initial conditions for enthalphy. These
345    different initial conditions make a comparison of the first months
346    difficult to interpret. The drift in the Beaufort Gyre is slightly
347    reduced relative to the reference run C-LSR-ns, but the drift through
348    the Fram Strait is increased. The drift velocities near the ice edge
349    are very different, because the ice extend is already larger in
350    \mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller
351    drift velocities, because the ice motion is more contrained by a
352    larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same
353    place is drifting nearly freely.
354    
355    A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL},
356    \reffig{iceveloc}(h)) has its largest effect along the ice edge, where
357    the gradients of thickness and concentration are largest. Everywhere
358    else the effect is very small and can mostly be attributed to smaller
359    numerical diffusion (and to the absense of explicitly diffusion for
360    numerical stability).
361    
362    \reffig{icethick}a shows the effective thickness (volume per unit
363    area) of the C-LSR-ns solution, averaged over January, February, March
364    of year 2000. By this time of the integration, the differences in the
365    ice drift velocities have led to the evolution of very different ice
366    thickness distributions, which are shown in \reffig{icethick}b--d, and
367    concentrations (not shown).
368    \begin{figure}[tp]
369      \centering
370      \subfigure[{\footnotesize C-LSR-ns}]
371      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
372      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
373      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
374      \\
375      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
376      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
377      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
378      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
379      \caption{(a) Effective thickness (volume per unit area) of the
380        C-LSR-ns solution, averaged over the months Janurary through March
381        2000 [m]; (b)-(h) difference between solutions with B-grid, free
382        lateral slip, EVP-solver, truncated ellipse method (TEM),
383        different ice-ocean stress formulation (HB87), different
384        thermodynamics (WTD), different advection for thermodynamic
385        variables (DST3FL) and the C-LSR-ns reference solution [m].}
386      \label{fig:icethick}
387    \end{figure}
388    \addtocounter{figure}{-1}
389    \setcounter{subfigure}{4}
390    \begin{figure}[t]
391      \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
392      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
393      \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
394      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
395      \\
396      \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
397      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
398      \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
399      {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
400      \caption{continued}
401    \end{figure}
402    %
403    The generally weaker ice drift velocities in the B-LSR-ns solution,
404    when compared to the C-LSR-ns solution, in particular through the
405    narrow passages in the Canadian Archipelago, lead to a larger build-up
406    of ice north of Greenland and the Archipelago by 2\,m effective
407    thickness and more in the B-grid solution (\reffig{icethick}b). But
408    the ice volume in not larger everywhere: further west, there are
409    patches of smaller ice volume in the B-grid solution, most likely
410    because the Beaufort Gyre is weaker and hence not as effective in
411    transporting ice westwards. There are also dipoles of ice volume
412    differences with more ice on the upstream side of island groups and
413    less ice in their lee, such as Franz-Josef-Land and
414    Severnaya Semlya\ml{/or Nordland?},
415    because ice tends to flow along coasts less easily in the B-LSR-ns
416    solution.
417    
418    Imposing a free-slip boundary condition in C-LSR-fs leads to a much
419    smaller differences to C-LSR-ns in the central Arctic than the
420    transition from the B-grid to the C-grid (\reffig{icethick}c), except
421    in the Canadian Archipelago. There it reduces the effective ice
422    thickness by 2\,m and more where the ice is thick and the straits are
423    narrow.  Dipoles of ice thickness differences can also be observed
424    around islands, because the free-slip solution allows more flow around
425    islands than the no-slip solution. Everywhere else the ice volume is
426    affected only slightly by the different boundary condition.
427    %
428    The C-EVP-ns solution has generally stronger drift velocities than the
429    C-LSR-ns solution. Consequently, more ice can be moved from the
430    eastern part of the Arctic, where ice volumes are smaller, to the
431    western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,
432    more drift leads to faster ice export and reduced effective ice
433    thickness. With a shorter time step of
434    $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to
435    converge to the LSOR solution (not shown). Only in the narrow straits
436    in the Archipelago the ice thickness is not affected by the shorter
437    time step and the ice is still thinner by 2\,m and more, as in the EVP
438    solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
439    
440    In year 2000, there more ice everywhere in the domain in
441    \mbox{C-LSR-ns WTD}, \reffig{icethick}(g). This difference, which is
442    even more pronounced in summer (not shown), can be attributed to
443    direct effects of the different thermodynamics in this run. The
444    remaining runs have the largest differences in effective ice thickness
445    long the north coasts of Greenland and Ellesmere Island. Although the
446    effects of TEM and \citet{hibler87}'s ice-ocean stress formulation are
447    so different on the initial ice velocities, both runs have similarly
448    reduced ice thicknesses in this area. The 3rd-order advection scheme
449    has an opposite effect of similar magnitude, point towards more
450    implicit lateral stress with this numerical scheme.
451    
452    The observed difference of order 2\,m and less are smaller than the
453    differences that were observed between different hindcast models and climate
454    models in \citet{gerdes07}. There the range of sea ice volume of
455    different sea ice-ocean models (which shared very similar forcing
456    fields) was on the order of $10,000\text{km$^{3}$}$; this range was
457    even larger for coupled climate models. Here, the range (and the
458    averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
459    the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
460    leads to generally thicker ice (\reffig{icethick} and
461    \reftab{icevolume}).
462    \begin{table}[htbp]
463      \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
464        model run & ice volume
465        & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
466            km$^{3}$\,y$^{-1}$}$]}\\
467        & [$\text{km$^{3}$}$]
468        & \multicolumn{2}{c}{FS}
469        & \multicolumn{2}{c}{NI}
470        & \multicolumn{2}{c}{LS} \\ \hline
471        B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
472        C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
473        C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
474        C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
475        C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
476        C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
477        C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
478        C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
479        C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
480      \end{tabular}
481      \caption{Arctic ice volume averaged over Jan--Mar 2000, in
482        $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
483        period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
484        total northern inflow into the Canadian Archipelago (NI), and the
485        export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}
486      \label{tab:icevolume}
487    \end{table}
488    
489    The difference in ice volume and ice drift velocities between the
490    different experiments has consequences for the ice transport out of
491    the Arctic. Although by far the most exported ice drifts through the
492    Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
493    considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
494    exported through the Canadian Archipelago \citep[and references
495    therein]{serreze06}. Note, that ice transport estimates are associated
496    with large uncertainties; also note that tuning an Arctic sea
497    ice-ocean model to reproduce observations is not our goal, but we use
498    the published numbers as an orientation.
499    
500    \reffig{archipelago} shows a time series of daily averaged, smoothed
501    with monthly running means, ice transports through various straits in
502    the Canadian Archipelago and the Fram Strait for the different model
503    solutions and \reftab{icevolume} summarizes the time series. The
504    export through Fram Strait agrees with the observations in all model
505    solutions (annual averages range from $2110$ to
506    $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
507    $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
508    time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
509    while the export through the Candian Archipelago is smaller than
510    generally thought. For example, the ice transport through Lancaster
511    Sound is lower (annual averages are $43$ to
512    $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
513    inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
514    a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
515    upstream in Barrow Strait in the 1970ies from satellite images.
516    Generally, the EVP solutions have the highest maximum (export out of
517    the Artic) and lowest minimum (import into the Artic) fluxes as the
518    drift velocities are largest in these solutions.  In the extreme of
519    the Nares Strait, which is only a few grid points wide in our
520    configuration, both B- and C-grid LSOR solvers lead to practically no
521    ice transport, while the C-EVP solutions allow up to
522    $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$
523    to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
524    the Candian Archipelago is larger in all EVP solutions
525    %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
526    than in the LSOR solutions.
527    %get the order of magnitude right (range: $132$ to
528    %$165\text{\,km$^3$\,y$^{-1}$}$);
529    The B-LSR-ns solution is even smaller by another factor of two than the
530    C-LSR solutions (an exception is the WTD solution, where larger ice thickness
531    tends to block the transport).
532    %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
533  \begin{figure}  \begin{figure}
534  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
535  \caption{Transport through Canadian Archipelago for different solver flavors.  %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
536    \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
537    \caption{Transport through Canadian Archipelago for different solver
538      flavors. The letters refer to the labels of the sections in
539      \reffig{arctic_topog}; positive values are flux out of the Arctic;
540      legend abbreviations are explained in \reftab{experiments}.
541  \label{fig:archipelago}}  \label{fig:archipelago}}
542  \end{figure}  \end{figure}
543    
544  \begin{figure}  %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
545  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}  %  schemes, Winton TD, discussion about differences in terms of model
546  \caption{Sea ice thickness for different solver flavors.  %  error? that's tricky as it means refering to Tremblay, thus our ice
547  \label{fig:icethick}}  %  models are all erroneous!]}
548  \end{figure}  
549    In summary, we find that different dynamical solvers can yield very
550    different solutions. In constrast to that, the differences between
551    free-slip and no-slip solutions \emph{with the same solver} are
552    considerably smaller (the difference for the EVP solver is not shown,
553    but similar to that for the LSOR solver). Albeit smaller, the
554    differences between free and no-slip solutions in ice drift can lead
555    to equally large differences in ice volume, especially in the Canadian
556    Archipelago over the integration time. At first, this observation
557    seems counterintuitive, as we expect that the solution
558    \emph{technique} should not affect the \emph{solution} to a higher
559    degree than actually modifying the equations. A more detailed study on
560    these differences is beyond the scope of this paper, but at this point
561    we may speculate, that the large difference between B-grid, C-grid,
562    LSOR, and EVP solutions stem from incomplete convergence of the
563    solvers due to linearization and due to different methods of
564    linearization \citep[and Bruno Tremblay, personal
565    communication]{hunke01}: if the convergence of the non-linear momentum
566    equations is not complete for all linearized solvers, then one can
567    imagine that each solver stops at a different point in velocity-space
568    thus leading to different solutions for the ice drift velocities. If
569    this were true, this tantalizing circumstance would have a dramatic
570    impact on sea-ice modeling in general, and we would need to improve
571    the solution techniques for dynamic sea ice models, most likely at a very
572    high compuational cost (Bruno Tremblay, personal communication). Further,
573    we observe that the EVP solutions tends to produce effectively
574    ``weaker'' ice that yields more easily to stress. The fast response to
575    changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
576    where the EVP model adjusts quickly to a cyclonic wind pattern, while
577    the LSOR solution does not. This property of the EVP solutions allows
578    larger ice transports through narrow straits, where the implicit
579    solver LSOR forms rigid ice. The underlying reasons for this striking
580    difference need further exploration.
581    
582    % THIS is now almost all in the text:
583    %\begin{itemize}
584    %\item Configuration
585    %\item OBCS from cube
586    %\item forcing
587    %\item 1/2 and full resolution
588    %\item with a few JFM figs from C-grid LSR no slip
589    %  ice transport through Canadian Archipelago
590    %  thickness distribution
591    %  ice velocity and transport
592    %\end{itemize}
593    
594    %\begin{itemize}
595    %\item Arctic configuration
596    %\item ice transport through straits and near boundaries
597    %\item focus on narrow straits in the Canadian Archipelago
598    %\end{itemize}
599    
600    %\begin{itemize}
601    %\item B-grid LSR no-slip: B-LSR-ns
602    %\item C-grid LSR no-slip: C-LSR-ns
603    %\item C-grid LSR slip:    C-LSR-fs
604    %\item C-grid EVP no-slip: C-EVP-ns
605    %\item C-grid EVP slip:    C-EVP-fs
606    %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
607    %  new flag): C-LSR-ns+TEM
608    %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
609    %\item C-grid LSR no-slip + Winton:
610    %\item  speed-performance-accuracy (small)
611    %  ice transport through Canadian Archipelago differences
612    %  thickness distribution differences
613    %  ice velocity and transport differences
614    %\end{itemize}
615    
616    %We anticipate small differences between the different models due to:
617    %\begin{itemize}
618    %\item advection schemes: along the ice-edge and regions with large
619    %  gradients
620    %\item C-grid: less transport through narrow straits for no slip
621    %  conditons, more for free slip
622    %\item VP vs.\ EVP: speed performance, accuracy?
623    %\item ocean stress: different water mass properties beneath the ice
624    %\end{itemize}
625    
626    %%% Local Variables:
627    %%% mode: latex
628    %%% TeX-master: "ceaice"
629    %%% End:
Legend:
Removed from v.1.8  
changed lines
  Added in v.1.17
  ViewVC Help
Powered by ViewVC 1.1.22