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

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

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

-revision 1.8 by dimitri,
Fri Feb 29 01:28:05 2008 UTC
+revision 1.16 by dimitri,
Wed Jun  4 00:39:25 2008 UTC
 Line 6 
 ice simulations that exercise various ca
  model.  The first set of results is from a global, eddy-permitting, ocean and
  sea ice configuration.  The second set of results is from a regional Arctic
  configuration, which is used to compare the B-grid and C-grid dynamic solvers
- 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.
  \subsection{Global Ocean and Sea Ice Simulation}
  \label{sec:global}
-Line 26 
 relatively even grid spacing throughout
+Line 24 
 relatively even grid spacing throughout
  singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are
 vertical levels ranging in thickness from 10 m near the surface to
- 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
- 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
  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
- bathymetry. The model is integrated in a volume-conserving configuration using
+ bathymetry. Bathymetry is from the S2004 (Smith, unpublished) blend of the
+ \citet{smi97} and the General Bathymetric Charts of the Oceans (GEBCO) one
+ arc-minute bathymetric grid (see Fig.~\ref{fig:CubeBathymetry}).
+ The model is integrated in a volume-conserving configuration using
  a finite volume discretization with C-grid staggering of the prognostic
  variables. In the ocean, the non-linear equation of state of \citet{jac95} is
  used.
+ \begin{figure}[h]
+   \centering
+   \includegraphics[width=\textwidth]{\fpath/CubeBathymetry}
+   \caption{Bathymetry of the global cubed sphere model configuration.  The
+     solid lines indicate domain boundaries for the regional Arctic
+     configuration discussed in Section~\ref{sec:arctic}.}
+   \label{fig:CubeBathymetry}
+ \end{figure}
  The ocean model is coupled to the sea-ice model discussed in
- Section~\ref{sec:model} using the following specific options.  The
+ \refsec{model} using the following specific options.  The
- zero-heat-capacity thermodynamics formulation of \citet{hib80} is used to
+ zero-heat-capacity thermodynamics formulation of \citet{hibler80} is
- compute sea ice thickness and concentration.  Snow cover and sea ice salinity
+ used to compute sea ice thickness and concentration.  Snow cover and
- 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
- 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,
- viscous plastic rheology of \citet{hibler79} and the ice momentum equation is
+ and 0.83. Ice mechanics follow the viscous plastic rheology of
- solved numerically using the C-grid implementation of the \citet{zhang97} LSR
+ \citet{hibler79} and the ice momentum equation is solved numerically
- dynamics model discussed hereinabove.  The ice is coupled to the ocean using
+ using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
- the rescaled vertical coordinate system, z$^\ast$, of
+ model discussed hereinabove.  The ice is coupled to the ocean using
- \citet{cam08}, that is, sea ice does not float above the ocean model but
+ the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
- rather deforms the ocean's model surface level.
+ that is, sea ice does not float above the ocean model but rather
+ deforms the ocean's model surface level.
  This particular ECCO2 simulation is initialized from temperature and salinity
  fields derived from the Polar science center Hydrographic Climatology (PHC)
-Line 62 
 radiations, and precipitation are conver
+Line 72 
 radiations, and precipitation are conver
  stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
  radiation decays exponentially as per \citet{pau77}.  Low frequency
  precipitation has been adjusted using the pentad (5-day) data from the Global
- Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river
+ Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river
  run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
  where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
  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
  diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
  the divergent flow as per \citet{kem08}.
+ \ml{[Dimitris, here you need to either provide figures, so that I can
+   write text, or you can provide both figures and text. I guess, one
+   figure, showing the northern and southern hemisphere in summer and
+   winter is fine (four panels), as we are showing so many figures in
+   the next section.]}
  \subsection{Arctic Domain with Open Boundaries}
  \label{sec:arctic}
- A series of forward sensitivity experiments have been carried out on an
+ A series of forward sensitivity experiments have been carried out on
- Arctic Ocean domain with open boundaries.  The objective is to compare the old
+ an Arctic Ocean domain with open boundaries.  The objective is to
- 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
- additional experiment is carried out to illustrate the differences between the
+ EVP solvers.  Additional experiments are carried out to illustrate
- two main options for sea ice thermodynamics in the MITgcm.
+ the differences between different ice advection schemes, ocean-ice
+ stress formulations and the two main options for sea ice
- The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It
+ thermodynamics in the MITgcm.
- is carved out from, and obtains open boundary conditions from, the global
- cubed-sphere configuration described above.  The horizontal domain size is
+ The Arctic domain of integration is illustrated in
-by 384 grid boxes.
+ \reffig{arctic_topog}.  It is carved out from, and obtains open
+ boundary conditions from, the global cubed-sphere configuration
- \begin{figure}
+ described above.  The horizontal domain size is 420 by 384 grid boxes.
- %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1}}}
+ \begin{figure*}
- \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
+ %\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography}
+ %\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography}
+ \includegraphics*[width=0.44\linewidth]{\fpath/topography}
+ \includegraphics*[width=0.46\linewidth]{\fpath/archipelago}
+ \caption{Left: Bathymetry and domain boudaries of Arctic
+   Domain; the dashed line marks the boundaries of the inset on the
+   right hand side. The letters in the inset label sections in the
+   Canadian Archipelago, where ice transport is evaluated:
+   A: Nares Strait; %
+   B: \ml{Meighen Island}; %
+   C: Prince Gustaf Adolf Sea; %
+   D: \ml{Brock Island}; %
+   E: M'Clure Strait; %
+   F: Amundsen Gulf; %
+   G: Lancaster Sound; %
+   H: Barrow Strait \ml{W.}; %
+   I: Barrow Strait \ml{E.}; %
+   J: Barrow Strait \ml{N.}. %
+   The sections A through F comprise the total inflow into the Canadian
+   Archipelago. \ml{[May still need to check the geography.]}
+   \label{fig:arctic_topog}}
+ \end{figure*}
+ The main dynamic difference from cube sphere is that the Arctic domain
+ configuration does not use rescaled vertical coordinates (z$^\ast$)
+ and the surface boundary conditions for freshwater input are
+ different, because those features are not supported by the open
+ boundary code.
+ %
+ Open water, dry ice, wet ice, dry snow, and wet snow albedo are,
+ respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
+ The model is integrated from Jan~01, 1992 to Mar~31, 2000,
+ with three different dynamical solvers, two different boundary
+ conditions, different stress coupling, rheology, and advection
+ schemes. \reftab{experiments} gives an overview over the experiments
+ discussed in this section.
+ \begin{table}[htbp]
+   \begin{tabular}{p{.3\linewidth}p{.65\linewidth}}
+     experiment name & description \\ \hline
+     B-LSR-ns       &  the original LSOR solver of \citet{zhang97} on an
+   Arakawa B-grid, implying no-slip lateral boundary conditions
+   ($\vek{u}=0$ exactly) \\
+     C-LSR-ns       &  the LSOR solver discretized on a C-grid with no-slip lateral
+   boundary conditions (implemented via ghost-points) \\
+     C-LSR-fs       &  the LSOR solver on a C-grid with free-slip lateral boundary
+   conditions \\
+     C-EVP-ns       &  the EVP solver of \citet{hunke01} on a C-grid with
+   no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+\text{\,s}$ \\
+     C-EVP-ns10     &  the EVP solver of \citet{hunke01} on a C-grid with
+   no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+\text{\,s}$ \\
+     C-LSR-ns HB87  &  C-LSR-ns with ocean-ice stress coupling according
+   to \citet{hibler87}\\
+     C-LSR-ns TEM   &  C-LSR-ns with a truncated ellispe method (TEM)
+   rheology \citep{hibler97} \\
+     C-LSR-ns WTD   &   C-LSR-ns with 3-layer thermodynamics following
+   \citet{winton00} \\
+     C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited
+   direct-space-time advection scheme for thermodynamic variables
+   \citep{hundsdorfer94}
+   \end{tabular}
+   \caption{Overview over model simulations in \refsec{arctic}.
+     \label{tab:experiments}}
+ \end{table}
+ %\begin{description}
+ %\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
+ %  Arakawa B-grid, implying no-slip lateral boundary conditions
+ %  ($\vek{u}=0$ exactly);
+ %\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
+ %  boundary conditions (implemented via ghost-points);
+ %\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
+ %  conditions;
+ %\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
+ %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+ %  150\text{\,s}$;
+ %\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
+ %  boundary conditions  and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$;
+ %\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited
+ %  direct-space-time advection scheme \citep{hundsdorfer94};
+ %\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM)
+ %  rheology \citep{hibler97};
+ %\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according
+ %  to \citet{hibler87};
+ %\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following
+ %  \citet{winton00};
+ %%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small
+ %%  scale noise \citep{hunke01};
+ %\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with
+ %  no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} =
+ %  10\text{\,s}$.
+ %\end{description}
+ Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
+ that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
+ interpreted as pure model error. Lateral boundary conditions on a
+ coarse grid (coarse compared to the roughness of the true coast line) are
+ unclear, so that comparing the no-slip solutions to the free-slip
+ solutions gives another measure of uncertainty in sea ice modeling.
+ The remaining experiments explore further sensitivities of the system
+ to different physics (change in rheology, advection and diffusion
+ properties, stress coupling, and thermodynamics) and different time
+ steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps
+ for the EVP solution. We use two interpretations of this choice where
+ the EVP model is subcycled 120 times within a (short) model timestep
+ of 1200\,s resulting in a very long and expensive integration
+ ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 120 times within the
+ forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$).
+ A principle difficulty in comparing the solutions obtained with
+ different realizations of the model dynamics lies in the non-linear
+ feedback of the ice dynamics and thermodynamics. Already after a few
+ months the solutions have diverged so far from each other that
+ comparing velocities only makes sense within the first 3~months of the
+ integration while the ice distribution is still close to the initial
+ conditions. At the end of the integration, the differences between the
+ model solutions can be interpreted as cumulated model uncertainties.
+ \reffig{iceveloc} shows ice velocities averaged over Janunary,
+ February, and March (JFM) of 1992 for the C-LSR-ns solution; also
+ shown are the differences between B-grid and C-grid, LSR and EVP, and
+ no-slip and free-slip solution. The velocity field of the C-LSR-ns
+ solution (\reffig{iceveloc}a) roughly resembles the drift velocities
+ of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
+ models in a cyclonic circulation regime (CCR) \citep[their
+ Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
+ shifted eastwards towards Alaska.
+ The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
+ is most pronounced along the coastlines, where the discretization
+ differs most between B and C-grids: On a B-grid the tangential
+ velocity lies on the boundary (and is thus zero through the no-slip
+ boundary conditions), whereas on the C-grid it is half a cell width
+ away from the boundary, thus allowing more flow. The B-LSR-ns solution
+ has less ice drift through the Fram Strait and especially the along
+ Greenland's east coast; also, the flow through Baffin Bay and Davis
+ Strait into the Labrador Sea is reduced with respect the C-LSR-ns
+ solution.  \ml{[Do we expect this? Say something about that]}
+ %
+ Compared to the differences between B and C-grid solutions,the
+ C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
+ (\reffig{iceveloc}c).  As expected the differences are largest along
+ coastlines: because of the free-slip boundary conditions, flow is
+ faster in the C-LSR-fs solution, for example, along the east coast
+ of Greenland, the north coast of Alaska, and the east Coast of Baffin
+ Island.
+ %\newcommand{\subplotwidth}{0.44\textwidth}
+ \newcommand{\subplotwidth}{0.3\textwidth}
+ \begin{figure}[htbp]
+   \centering
+   \subfigure[{\footnotesize C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-ns}}
+   \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}
+   \\
+   \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}}
+   \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_C-EVP-ns150-C-LSR-ns}}
+   \\
+   \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_TEM-C-LSR-ns}}
+   \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_HB87-C-LSR-ns}}
+   \\
+   \subfigure[{\footnotesize  C-LSR-ns WTD $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_ThSIce-C-LSR-ns}}
+   \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMuv_adv33-C-LSR-ns}}
+   \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
+     over the first 3 months of integration [cm/s]; (b)-(h) difference
+     between solutions with B-grid, free lateral slip, EVP-solver,
+     truncated ellipse method (TEM), different ice-ocean stress
+     formulation (HB87), different thermodynamics (WTD), different
+     advection for thermodynamic variables (DST3FL) and the C-LSR-ns
+     reference solution [cm/s]; color indicates speed (or differences
+     of speed), vectors indicate direction only.}
+   \label{fig:iceveloc}
  \end{figure}
- Difference from cube sphere is that it does not use z* coordinates nor
+ The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is
- realfreshwater fluxes because it is not supported by open boundary code.
+ very different from the C-LSR-ns solution (\reffig{iceveloc}d). The
+ EVP-approximation of the VP-dynamics allows for increased drift by
- Open water, dry
+ over 2\,cm/s in the Beaufort Gyre and the transarctic drift.
- ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
+ %\ml{Also the Beaufort Gyre is moved towards Alaska in the C-EVP-ns
-.76, 0.94, and 0.8.
+ %solution. [Really?, No]}
+ In general, drift velocities are biased towards higher values in the
- \begin{itemize}
+ EVP solutions.
- \item Configuration
+ % as can be seen from a histogram of the differences in
- \item OBCS from cube
+ %\reffig{drifthist}.
- \item forcing
+ %\begin{figure}[htbp]
- \item 1/2 and full resolution
+ %  \centering
- \item with a few JFM figs from C-grid LSR no slip
+ %  \includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns}
-   ice transport through Canadian Archipelago
+ %  \caption{Histogram of drift velocity differences for C-LSR-ns and
-   thickness distribution
+ %    C-EVP-ns solution [cm/s].}
-   ice velocity and transport
+ %  \label{fig:drifthist}
- \end{itemize}
+ %\end{figure}
- \begin{itemize}
+ \reffig{icethick}a shows the effective thickness (volume per unit
- \item Arctic configuration
+ area) of the C-LSR-ns solution, averaged over January, February, March
- \item ice transport through straits and near boundaries
+ of year 2000. By this time of the integration, the differences in the
- \item focus on narrow straits in the Canadian Archipelago
+ ice drift velocities have led to the evolution of very different ice
- \end{itemize}
+ thickness distributions, which are shown in \reffig{icethick}b--d, and
+ concentrations (not shown).
- \begin{itemize}
+ \begin{figure}[htbp]
- \item B-grid LSR no-slip
+   \centering
- \item C-grid LSR no-slip
+   \subfigure[{\footnotesize C-LSR-ns}]
- \item C-grid LSR slip
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}}
- \item C-grid EVP no-slip
+   \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
- \item C-grid EVP slip
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}}
- \item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
+   \\
- \item C-grid LSR no-slip + Winton
+   \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
- \item  speed-performance-accuracy (small)
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}}
-   ice transport through Canadian Archipelago differences
+   \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
-   thickness distribution differences
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}}
-   ice velocity and transport differences
+   \\
- \end{itemize}
+   \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}]
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}}
- We anticipate small differences between the different models due to:
+   \subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}]
- \begin{itemize}
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}}
- \item advection schemes: along the ice-edge and regions with large
+   \\
-   gradients
+   \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}]
- \item C-grid: less transport through narrow straits for no slip
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}}
-   conditons, more for free slip
+   \subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}]
- \item VP vs.\ EVP: speed performance, accuracy?
+   {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
- \item ocean stress: different water mass properties beneath the ice
+   \caption{(a) Effective thickness (volume per unit area) of the
- \end{itemize}
+     C-LSR-ns solution, averaged over the months Janurary through March
+[m]; (b)-(d) difference between solutions with B-grid, free
- \begin{figure}
+     lateral slip, EVP-solver, truncated ellipse method (TEM),
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
+     different ice-ocean stress formulation (HB87), different
- \caption{Surface sea ice velocity for different solver flavors.
+     thermodynamics (WTD), different advection for thermodynamic
- \label{fig:iceveloc}}
+     variables (DST3FL) and the C-LSR-ns reference solution [m].}
+   \label{fig:icethick}
  \end{figure}
+ %
+ The generally weaker ice drift velocities in the B-LSR-ns solution,
+ when compared to the C-LSR-ns solution, in particular through the
+ narrow passages in the Canadian Archipelago, lead to a larger build-up
+ of ice north of Greenland and the Archipelago by 2\,m effective
+ thickness and more in the B-grid solution (\reffig{icethick}b). But
+ the ice volume in not larger everywhere: further west, there are
+ patches of smaller ice volume in the B-grid solution, most likely
+ because the Beaufort Gyre is weaker and hence not as effective in
+ transporting ice westwards. There are also dipoles of ice volume
+ differences with more ice on the upstream side of island groups and
+ less ice in their lee, such as Franz-Josef-Land and
+ Severnaya Semlya\ml{/or Nordland?},
+ because ice tends to flow along coasts less easily in the B-LSR-ns
+ solution.
+ Imposing a free-slip boundary condition in C-LSR-fs leads to a much
+ smaller differences to C-LSR-ns in the central Arctic than the
+ transition from the B-grid to the C-grid (\reffig{icethick}c), except
+ in the Canadian Archipelago. There it reduces the effective ice
+ thickness by 2\,m and more where the ice is thick and the straits are
+ narrow.  Dipoles of ice thickness differences can also be observed
+ around islands, because the free-slip solution allows more flow around
+ islands than the no-slip solution.  Everywhere else the ice volume is
+ affected only slightly by the different boundary condition.
+ %
+ The C-EVP-ns solution has generally stronger drift velocities than the
+ C-LSR-ns solution. Consequently, more ice can be moved from the
+ eastern part of the Arctic, where ice volumes are smaller, to the
+ western Arctic (\reffig{icethick}d). Within the Canadian Archipelago,
+ more drift leads to faster ice export and reduced effective ice
+ thickness. With a shorter time step of
+ $\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution seems to
+ converge to the LSOR solution (not shown). Only in the narrow straits
+ in the Archipelago the ice thickness is not affected by the shorter
+ time step and the ice is still thinner by 2\,m and more, as in the EVP
+ solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
+ The observed difference of order 2\,m and less are smaller than the
+ differences that were observed between different hindcast and climate
+ models in \citet{gerdes07}. There the range of sea ice volume of
+ different sea ice-ocean models (which shared very similar forcing
+ fields) was on the order of $10,000\text{km$^{3}$}$; this range was
+ even larger for coupled climate models. Here, the range (and the
+ averaging period) is smaller than $4,000\text{km$^{3}$}$ except for
+ the run \mbox{C-LSR-ns~WTD} where the more complicated thermodynamics
+ leads to generally thicker ice (\reffig{icethick} and
+ \reftab{icevolume}).
+ \begin{table}[htbp]
+   \begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r}
+     model run & ice volume
+     & \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std.,
+         km$^{3}$\,y$^{-1}$}$]}\\
+     & [$\text{km$^{3}$}$]
+     & \multicolumn{2}{c}{FS}
+     & \multicolumn{2}{c}{NI}
+     & \multicolumn{2}{c}{LS} \\ \hline
+     B-LSR-ns       & 23,824 & 2126 & 1278 &   34 &  122 &   43 &   76 \\
+     C-LSR-ns       & 24,769 & 2196 & 1253 &   70 &  224 &   77 &  110 \\
+     C-LSR-fs       & 23,286 & 2236 & 1289 &   80 &  276 &   91 &   85 \\
+     C-EVP-ns       & 27,056 & 3050 & 1652 &  352 &  735 &  256 &  151 \\
+     C-EVP-ns10     & 22,633 & 2174 & 1260 &  186 &  496 &  133 &  128 \\
+     C-LSR-ns HB87  & 23,060 & 2256 & 1327 &   64 &  230 &   77 &  114 \\
+     C-LSR-ns TEM   & 23,529 & 2222 & 1258 &   60 &  242 &   87 &  112 \\
+     C-LSR-ns WTD   & 31,634 & 2761 & 1563 &   23 &  140 &   94 &   63 \\
+     C-LSR-ns DST3FL& 24,023 & 2191 & 1261 &   88 &  251 &   84 &  129
+   \end{tabular}
+   \caption{Arctic ice volume averaged over Jan--Mar 2000, in
+     $\text{km$^{3}$}$. Mean ice transport and standard deviation for the
+     period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the
+     total northern inflow into the Canadian Archipelago (NI), and the
+     export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$.}
+   \label{tab:icevolume}
+ \end{table}
+ The difference in ice volume and ice drift velocities between the
+ different experiments has consequences for the ice transport out of
+ the Arctic. Although by far the most exported ice drifts through the
+ Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a
+ considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is
+ exported through the Canadian Archipelago \citep[and references
+ therein]{serreze06}. Note, that ice transport estimates are associated
+ with large uncertainties; also note that tuning an Arctic sea
+ ice-ocean model to reproduce observations is not our goal, but we use
+ the published numbers as an orientation.
+ \reffig{archipelago} shows a time series of daily averaged, smoothed
+ with monthly running means, ice transports through various straits in
+ the Canadian Archipelago and the Fram Strait for the different model
+ solutions and \reftab{icevolume} summarizes the time series. The
+ export through Fram Strait agrees with the observations in all model
+ solutions (annual averages range from $2110$ to
+ $2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with
+ $2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long
+ time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$),
+ while the export through the Candian Archipelago is smaller than
+ generally thought. For example, the ice transport through Lancaster
+ Sound is lower (annual averages are $43$ to
+ $256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an
+ inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but
+ a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further
+ upstream in Barrow Strait in the 1970ies from satellite images.
+ Generally, the EVP solutions have the highest maximum (export out of
+ the Artic) and lowest minimum (import into the Artic) fluxes as the
+ drift velocities are largest in these solutions.  In the extreme of
+ the Nares Strait, which is only a few grid points wide in our
+ configuration, both B- and C-grid LSOR solvers lead to practically no
+ ice transport, while the C-EVP solutions allow up to
+ $600\text{\,km$^3$\,y$^{-1}$}$ in summer; \citet{tang04} report $300$
+ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
+ the Candian Archipelago is larger in all EVP solutions
+ %(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$)
+ than in the LSOR solutions.
+ %get the order of magnitude right (range: $132$ to
+ %$165\text{\,km$^3$\,y$^{-1}$}$);
+ The B-LSR-ns solution is even smaller by another factor of two than the
+ C-LSR solutions (an exception is the WTD solution, where larger ice thickness
+ tends to block the transport).
+ %underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$.
  \begin{figure}
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
- \caption{Transport through Canadian Archipelago for different solver flavors.
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
+ \centerline{{\includegraphics*[width=\linewidth]{\fpath/ice_export}}}
+ \caption{Transport through Canadian Archipelago for different solver
+   flavors. The letters refer to the labels of the sections in
+   \reffig{arctic_topog}; positive values are flux out of the Arctic;
+   legend abbreviations are explained in \reftab{experiments}.
  \label{fig:archipelago}}
  \end{figure}
- \begin{figure}
+ %\ml{[Transport to narrow straits, area?, more runs, TEM, advection
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
+ %  schemes, Winton TD, discussion about differences in terms of model
- \caption{Sea ice thickness for different solver flavors.
+ %  error? that's tricky as it means refering to Tremblay, thus our ice
- \label{fig:icethick}}
+ %  models are all erroneous!]}
- \end{figure}
+ In summary, we find that different dynamical solvers can yield very
+ different solutions. In constrast to that, the differences between
+ free-slip and no-slip solutions \emph{with the same solver} are
+ considerably smaller (the difference for the EVP solver is not shown,
+ but similar to that for the LSOR solver). Albeit smaller, the
+ differences between free and no-slip solutions in ice drift can lead
+ to equally large differences in ice volume, especially in the Canadian
+ Archipelago over the integration time. At first, this observation
+ seems counterintuitive, as we expect that the solution
+ \emph{technique} should not affect the \emph{solution} to a higher
+ degree than actually modifying the equations. A more detailed study on
+ these differences is beyond the scope of this paper, but at this point
+ we may speculate, that the large difference between B-grid, C-grid,
+ LSOR, and EVP solutions stem from incomplete convergence of the
+ solvers due to linearization and due to different methods of
+ linearization \citep[and Bruno Tremblay, personal
+ communication]{hunke01}: if the convergence of the non-linear momentum
+ equations is not complete for all linearized solvers, then one can
+ imagine that each solver stops at a different point in velocity-space
+ thus leading to different solutions for the ice drift velocities. If
+ this were true, this tantalizing circumstance would have a dramatic
+ impact on sea-ice modeling in general, and we would need to improve
+ the solution techniques for dynamic sea ice models, most likely at a very
+ high compuational cost (Bruno Tremblay, personal communication). Further,
+ we observe that the EVP solutions tends to produce effectively
+ ``weaker'' ice that yields more easily to stress. The fast response to
+ changing wind was also observed by \citet{hunke99}, their Fig.\,10--12,
+ where the EVP model adjusts quickly to a cyclonic wind pattern, while
+ the LSOR solution does not. This property of the EVP solutions allows
+ larger ice transports through narrow straits, where the implicit
+ solver LSOR forms rigid ice. The underlying reasons for this striking
+ difference need further exploration.
+ % THIS is now almost all in the text:
+ %\begin{itemize}
+ %\item Configuration
+ %\item OBCS from cube
+ %\item forcing
+ %\item 1/2 and full resolution
+ %\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: B-LSR-ns
+ %\item C-grid LSR no-slip: C-LSR-ns
+ %\item C-grid LSR slip:    C-LSR-fs
+ %\item C-grid EVP no-slip: C-EVP-ns
+ %\item C-grid EVP slip:    C-EVP-fs
+ %\item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
+ %  new flag): C-LSR-ns+TEM
+ %\item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
+ %\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}
+ %%% Local Variables:
+ %%% mode: latex
+ %%% TeX-master: "ceaice"
+ %%% End:

 Legend:



Removed from v.1.8
 


changed lines


 
Added in v.1.16
 Legend:



Removed from v.1.8
 


changed lines


 
Added in v.1.16
-Removed from v.1.8
+Added in v.1.16

	ViewVC Help
Powered by ViewVC 1.1.22