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

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-revision 1.9 by mlosch,
Fri Feb 29 01:29:40 2008 UTC
+revision 1.10 by mlosch,
Tue Mar  4 20:33:07 2008 UTC
 Line 36 
 variables. In the ocean, the non-linear
  used.
  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 used to
  compute sea ice thickness and concentration.  Snow cover and sea ice salinity
  are prognostic.  Open water, dry ice, wet ice, dry snow, and wet snow albedo
  are, respectively, 0.15, 0.88, 0.79, 0.97, and 0.83. Ice mechanics follow the
 Line 90 
 B-grid LSR dynamic solver with the new C
  additional experiment is carried out to illustrate the differences between the
  two main options for sea ice thermodynamics in the MITgcm.
- The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It
+ The Arctic domain of integration is illustrated in \reffig{arctic1}.  It
  is carved out from, and obtains open boundary conditions from, the global
  cubed-sphere configuration described above.  The horizontal domain size is
 by 384 grid boxes.
  \begin{figure}
- %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1}}}
+ \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}
- \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
+ \caption{Bathymetry and domain boudaries of Arctic
+   Domain.\label{fig:arctic1}}
  \end{figure}
- Difference from cube sphere is that it does not use z* coordinates nor
+ The main dynamic difference from cube sphere is that it does not use
- realfreshwater fluxes because it is not supported by open boundary code.
+ 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
+ Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
- ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
 .76, 0.94, and 0.8.
+ The model is integrated from January, 1992 to March \ml{[???]}, 2000,
+ with five different dynamical solvers:
+ \begin{description}
+ \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa
+   B-grid, implying no-slip lateral boundary conditions;
+ \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
+   boundary conditions;
+ \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
+ \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
+   boundary conditions.
+ \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 (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.
+ A principle difficulty in comparing the solutions obtained with
+ different variants of the dynamics solver 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 an 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 is on the boundary
+ (and thus zero per the no-slip boundary conditions), whereas on the
+ C-grid the its 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.
+ \begin{figure}[htbp]
+   \centering
+   \subfigure[{\footnotesize C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}
+   \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\
+   \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}
+   \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}
+   \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
+     over the first 3 months of integration [cm/s]; (b)-(d) difference
+     between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions
+     [cm/s]; color indicates speed (or differences of speed), vectors
+     indicate direction only.}
+   \label{fig:iceveloc}
+ \end{figure}
+ The C-EVP-ns solution is very different from the C-LSR-ns solution
+ (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows
+ for increased drift by over 2\,cm/s in the Beaufort Gyre and the
+ transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska
+   in the C-EVP-ns solution. [Really?]} In general, drift velocities are
+ biased towards higher values in the EVP solutions as can be seen from
+ a histogram of the differences in \reffig{drifthist}.
+ \begin{figure}[htbp]
+   \centering
+   \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}
+   \caption{Histogram of drift velocity differences for C-LSR-ns and
+     C-EVP-ns solution [cm/s].}
+   \label{fig:drifthist}
+ \end{figure}
+ \reffig{icethick}a shows the effective thickness (volume per unit
+ area) of the C-LSR-ns solution, averaged over January, February, March
+ of year 2000. By this time of the integration, the differences in the
+ ice drift velocities have led to the evolution of very different ice
+ thickness distributions, which are shown in \reffig{icethick}b--d, and
+ area distributions (not shown).  \ml{Compared to other solutions, for
+   example, AOMIP the ice thickness distribution blablabal} \ml{[What
+   can I say about effective thickness?]}
+ \begin{figure}[htbp]
+   \centering
+   \subfigure[{\footnotesize C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}
+   \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\
+   \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}
+   \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
+   {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}
+   \caption{(a) Effective thickness (volume per unit area) of the
+     C-LSR-ns solution, averaged over the months Janurary through March
+[m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,
+     and C-LSR-ns solutions [cm/s].}
+   \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 on the \ml{luv [what is this in English?]} and the lee of
+ island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which
+ \ml{\ldots [I find hard to interpret].}
+ Imposing a free-slip boundary condition in C-LSR-fs leads to a much
+ smaller differences to C-LSR-ns than the transition from the B-grid to
+ the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
+ still reduces the effective ice thickness by up to 2\,m where the ice
+ is thick and the straits are narrow. Everywhere else the ice volume is
+ affected only slightly by the different boundary condition.
+ %
+ The C-EVP-ns solution has generally stronger drift velocities then the
+ C-LSR-ns solution. Consequently, more ice can be moved the eastern
+ part of the Arctic, where ice volumes are smaller, to the western
+ Arctic where ice piles up along the coast (\reffig{icethick}d). Within
+ the Canadian Archipelago, more drift leads to faster ice export and
+ reduced effective ice thickness.
+ The difference in ice volume and ice drift velocities between the
+ different experiments has consequences for the ice transport out of
+ the Arctic. Although the main export of ice goes through the Fram
+ Strait, a considerable amoung of ice is exported through the Canadian
+ Archipelago \citep{???}. \reffig{archipelago} shows a time series of
+ daily averages ice transport through various straits in the Canadian
+ Archipelago and the Fram Strait for the different model solutions.
+ Generally, the C-EVP-ns solution has highest maxiumum (export out of
+ the Artic) and minimum (import into the Artic) fluxes as the drift
+ velocities area largest in this solution \ldots
+ \begin{figure}
+ \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ \caption{Transport through Canadian Archipelago for different solver flavors.
+ \label{fig:archipelago}}
+ \end{figure}
+ \ml{[Transport to narrow straits, area?, more runs, TEM, advection
+   schemes, Winton TD, discussion about differences in terms of model
+   error? that's tricky as it means refering to Tremblay, thus our ice
+   models are all erroneous!]}
+ In summary, we find that different dynamical solvers can yield very
+ different solutions. Compared 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 comparable to that for the LSOR solver)---albeit smaller, the
+ differences between free and no-slip solutions in ice drift can lead
+ to large differences in ice volume over integration time. At first,
+ this observation appears counterintuitive, as we expect that the
+ solution \emph{technique} should not affect the \emph{solution} to a
+ lower 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 \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 had a dramatic impact on
+ sea-ice modeling in general, and we would need to improve the solution
+ technique of dynamic sea ice model, most likely at a very high
+ compuational cost (Bruno Tremblay, personal communication).
  \begin{itemize}
  \item Configuration
  \item OBCS from cube
-Line 125 
 ice, wet ice, dry snow, and wet snow alb
+Line 317 
 ice, wet ice, dry snow, and wet snow alb
  \end{itemize}
  \begin{itemize}
- \item B-grid LSR no-slip
+ \item B-grid LSR no-slip: B-LSR-ns
- \item C-grid LSR no-slip
+ \item C-grid LSR no-slip: C-LSR-ns
- \item C-grid LSR slip
+ \item C-grid LSR slip:    C-LSR-fs
- \item C-grid EVP no-slip
+ \item C-grid EVP no-slip: C-EVP-ns
- \item C-grid EVP slip
+ \item C-grid EVP slip:    C-EVP-fs
- \item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
+ \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
- \item C-grid LSR no-slip + Winton
+   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
-Line 148 
 We anticipate small differences between
+Line 342 
 We anticipate small differences between
  \item ocean stress: different water mass properties beneath the ice
  \end{itemize}
- \begin{figure}
+ %\begin{figure}
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
- \caption{Surface sea ice velocity for different solver flavors.
+ %\caption{Surface sea ice velocity for different solver flavors.
- \label{fig:iceveloc}}
+ %\label{fig:iceveloc}}
- \end{figure}
+ %\end{figure}
- \begin{figure}
+ %\begin{figure}
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
- \caption{Transport through Canadian Archipelago for different solver flavors.
+ %\caption{Sea ice thickness for different solver flavors.
- \label{fig:archipelago}}
+ %\label{fig:icethick}}
- \end{figure}
+ %\end{figure}
- \begin{figure}
- \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
- \caption{Sea ice thickness for different solver flavors.
- \label{fig:icethick}}
- \end{figure}
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