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-revision 1.17 by mlosch,
Wed Jun  4 13:32:05 2008 UTC
+revision 1.18 by mlosch,
Thu Jul  3 18:16:22 2008 UTC
 Line 1
- \section{Forward sensitivity experiments}
+ \section{Forward Sensitivity Experiments in an Arctic Domain with Open
+ Boundaries}
  \label{sec:forward}
- This section presents results from global and regional coupled ocean and sea
+ This section presents results from regional coupled ocean and sea
- ice simulations that exercise various capabilities of the MITgcm sea ice
+ ice simulations of the Arctic Ocean that exercise various capabilities of the MITgcm sea ice
- model.  The first set of results is from a global, eddy-permitting, ocean and
+ model.
- sea ice configuration.  The second set of results is from a regional Arctic
+ The objective is to
- configuration, which is used to compare the B-grid and C-grid dynamic solvers
+ compare the old B-grid LSOR dynamic solver with the new C-grid LSOR and
- and various other capabilities of the MITgcm sea ice model.
+ EVP solvers. Additional experiments are carried out to illustrate
+ the differences between different ice advection schemes, ocean-ice
+ stress formulations and the two main options for sea ice
+ thermodynamics in the MITgcm.
- \subsection{Global Ocean and Sea Ice Simulation}
+ \subsection{Model configuration and experiments}
- \label{sec:global}
+ \label{sec:arcticmodel}
+ The Arctic model domain is illustrated in \reffig{arctic_topog}.
+ \begin{figure*}
+ %\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}
+ \includegraphics*[width=\linewidth]{\fpath/topography}
+ \caption{Left: Bathymetry and domain boundaries 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.}; %
+   K: Fram Strait. %
+   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*}
+ It has 420 by 384 grid boxes and is carved out, and obtains open
+ boundary conditions from, a global cubed-sphere configuration
+ similar to that described in \citet{menemenlis05}.
- The global ocean and sea ice results presented below were carried out as part
+ The global ocean and sea ice results presented in \citet{menemenlis05}
+ were carried out as part
  of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
  project.  ECCO2 aims to produce increasingly accurate syntheses of all
  available global-scale ocean and sea-ice data at resolutions that start to
  resolve ocean eddies and other narrow current systems, which transport heat,
  carbon, and other properties within the ocean \citep{menemenlis05}.  The
- particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)
+ particular ECCO2 simulation from which we obtain the boundary
+ conditions is a baseline 28-year (1979-2006)
  integration, labeled cube76, which has not yet been constrained by oceanic and
- by sea ice data.  A cube-sphere grid projection is employed, which permits
+ by sea ice data. A cube-sphere grid projection is employed, which permits
  relatively even grid spacing throughout the domain and which avoids polar
  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
+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. The model employs the
  partial-cell formulation of
  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
- bathymetry. Bathymetry is from the S2004 (Smith, unpublished) blend of the
+ bathymetry. Bathymetry is from the S2004 (W.~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}).
+ 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]
+ The global ocean model is coupled to a sea ice model in a
-   \centering
+ configuration similar to the case C-LSR-ns (see \reftab{experiments}),
-   \includegraphics[width=\textwidth]{\fpath/CubeBathymetry}
+ with open water, dry ice, wet ice, dry snow, and wet snow albedos of,
-   \caption{Bathymetry of the global cubed sphere model configuration.  The
+ respectively, 0.15, 0.88, 0.79, 0.97, and 0.83.
-     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
- \refsec{model} using the following specific options.  The
- 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 viscous plastic rheology of
- \citet{hibler79} and the ice momentum equation is solved numerically
- using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
- model discussed hereinabove.  The ice is coupled to the ocean using
- the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
- 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 72 
 radiations, and precipitation are conver
+Line 90 
 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 \citep[GPCP][]{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 91 
 advection scheme \citep{dar04} is employ
+Line 109 
 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
+ The model configuration of cube76 carries over to the Arctic domain
-   write text, or you can provide both figures and text. I guess, one
+ configuration except for numerical details related to the non-linear
-   figure, showing the northern and southern hemisphere in summer and
+ free surface that are not supported by the open boundary code, and the
-   winter is fine (four panels), as we are showing so many figures in
+ albedos of open water, dry ice, wet ice, dry snow, and wet snow, which
-   the next section.]}
+ are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8.
+ The model is integrated from Jan~01, 1992 to Mar~31, 2000
- \subsection{Arctic Domain with Open Boundaries}
+ \reftab{experiments} gives an overview over the experiments discussed
- \label{sec:arctic}
+ in \refsec{arcticresults}.
+ \begin{table}
- A series of forward sensitivity experiments have been carried out on
+   \caption{Overview over model simulations in \refsec{arcticresults}.
- an Arctic Ocean domain with open boundaries.  The objective is to
- compare the old B-grid LSR dynamic solver with the new C-grid LSR and
- EVP solvers.  Additional experiments are carried out to illustrate
- the differences between different ice advection schemes, ocean-ice
- stress formulations and the two main options for sea ice
- thermodynamics in the MITgcm.
- The Arctic domain of integration is illustrated in
- \reffig{arctic_topog}.  It is carved out from, and obtains open
- boundary conditions from, the global cubed-sphere configuration
- described above.  The horizontal domain size is 420 by 384 grid boxes.
- \begin{figure*}
- %\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}
- \includegraphics*[width=\linewidth]{\fpath/topography}
- \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.}; %
-   K: Fram Strait. %
-   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}[t]
-   \caption{Overview over model simulations in \refsec{arctic}.
      \label{tab:experiments}}
    \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) \\
+   ($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order
+   central difference scheme plus explicit diffusion for stability \\
      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
-Line 225 
 of 1200\,s resulting in a very long and
+Line 191 
 of 1200\,s resulting in a very long and
  ($\Delta{t}_\mathrm{evp}=10\text{\,s}$) 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
+ \subsection{Results}
- different realizations of the model dynamics lies in the non-linear
+ \label{sec:arcticresults}
- feedback of the ice dynamics and thermodynamics. Already after a few
- months the solutions have diverged so far from each other that
+ Comparing the solutions obtained with different realizations of the
- comparing velocities only makes sense within the first 3~months of the
+ model dynamics is difficult because of 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.
+ \subsubsection{Ice velocities in JFM 1992}
  \reffig{iceveloc} shows ice velocities averaged over Janunary,
  February, and March (JFM) of 1992 for the C-LSR-ns solution; also
-Line 359 
 else the effect is very small and can mo
+Line 330 
 else the effect is very small and can mo
  numerical diffusion (and to the absense of explicitly diffusion for
  numerical stability).
+ \subsubsection{Ice volume during JFM 2000}
  \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
-Line 399 
 concentrations (not shown).
+Line 372 
 concentrations (not shown).
    {\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}}
    \caption{continued}
  \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
-Line 437 
 in the Archipelago the ice thickness is
+Line 409 
 in the Archipelago the ice thickness is
  time step and the ice is still thinner by 2\,m and more, as in the EVP
  solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$.
- In year 2000, there more ice everywhere in the domain in
+ In year 2000, there is more ice everywhere in the domain in
  \mbox{C-LSR-ns WTD}, \reffig{icethick}(g). This difference, which is
  even more pronounced in summer (not shown), can be attributed to
  direct effects of the different thermodynamics in this run. The
-Line 497 
 with large uncertainties; also note that
+Line 469 
 with large uncertainties; also note that
  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
+ \subsubsection{Ice transports}
- with monthly running means, ice transports through various straits in
- the Canadian Archipelago and the Fram Strait for the different model
+ \reffig{archipelago} shows an excerpt of a time series of daily
- solutions and \reftab{icevolume} summarizes the time series. The
+ averaged, smoothed with monthly running means, ice transports through
- export through Fram Strait agrees with the observations in all model
+ various straits in the Canadian Archipelago and the Fram Strait for
- solutions (annual averages range from $2110$ to
+ the different model solutions and \reftab{icevolume} summarizes the
+ time series.
+ \begin{figure}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
+ %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}}
+ %\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}}
+ \centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}}
+ \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}. The mean
+   range of the different model solution is taken over the period Jan
+to Dec 1999.
+ \label{fig:archipelago}}
+ \end{figure}
+ 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}$}$),
-Line 519 
 drift velocities are largest in these so
+Line 507 
 drift velocities are largest in these so
  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 $300$
+ $600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04}
- to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence, the import into
+ report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$.  As as consequence,
- the Candian Archipelago is larger in all EVP solutions
+ 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
-Line 530 
 The B-LSR-ns solution is even smaller by
+Line 518 
 The B-LSR-ns solution is even smaller by
  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/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}
  %\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!]}
+ \subsubsection{Discussion}
  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

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