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\section{Forward sensitivity experiments} |
\section{Forward Sensitivity Experiments in an Arctic Domain with Open |
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Boundaries} |
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\label{sec:forward} |
\label{sec:forward} |
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| 5 |
This section presents results from global and regional coupled ocean and sea |
This section presents results from regional coupled ocean and sea |
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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 |
| 7 |
model. The first set of results is from a global, eddy-permitting, ocean and |
model. |
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sea ice configuration. The second set of results is from a regional Arctic |
The objective is to |
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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 |
| 10 |
and various other capabilities of the MITgcm sea ice model. |
EVP solvers. Additional experiments are carried out to illustrate |
| 11 |
% |
the differences between different ice advection schemes, ocean-ice |
| 12 |
\ml{[do we really want to do this?:] The third set of |
stress formulations and the two main options for sea ice |
| 13 |
results is from a yet smaller regional domain, which is used to illustrate |
thermodynamics in the MITgcm. |
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treatment of sea ice open boundary condition in the MITgcm.} |
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\subsection{Global Ocean and Sea Ice Simulation} |
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\label{sec:global} |
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The global ocean and sea ice results presented below were carried out as part |
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of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) |
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project. ECCO2 aims to produce increasingly accurate syntheses of all |
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available global-scale ocean and sea-ice data at resolutions that start to |
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resolve ocean eddies and other narrow current systems, which transport heat, |
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carbon, and other properties within the ocean \citep{menemenlis05}. The |
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particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006) |
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integration, labeled cube76, which has not yet been constrained by oceanic and |
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by sea ice data. A cube-sphere grid projection is employed, which permits |
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relatively even grid spacing throughout the domain and which avoids polar |
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singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises |
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510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are |
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50 vertical levels ranging in thickness from 10 m near the surface to |
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approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the |
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National Geophysical Data Center (NGDC) 2-minute gridded global relief data |
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(ETOPO2) and the model employs the partial-cell formulation of |
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\citet{adcroft97:_shaved_cells}, which permits accurate representation of the |
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bathymetry. The model is integrated in a volume-conserving configuration using |
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a finite volume discretization with C-grid staggering of the prognostic |
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variables. In the ocean, the non-linear equation of state of \citet{jac95} is |
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used. |
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The ocean model is coupled to the sea-ice model discussed in |
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\refsec{model} using the following specific options. The |
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zero-heat-capacity thermodynamics formulation of \citet{hibler80} is |
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used to compute sea ice thickness and concentration. Snow cover and |
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sea ice salinity are prognostic. Open water, dry ice, wet ice, dry |
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snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97, |
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and 0.83. Ice mechanics follow the viscous plastic rheology of |
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\citet{hibler79} and the ice momentum equation is solved numerically |
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using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics |
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model discussed hereinabove. The ice is coupled to the ocean using |
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the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08}, |
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that is, sea ice does not float above the ocean model but rather |
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deforms the ocean's model surface level. |
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This particular ECCO2 simulation is initialized from temperature and salinity |
\subsection{Model configuration and experiments} |
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\label{sec:arcticmodel} |
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The Arctic model domain is illustrated in \reffig{arctic_topog}. |
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\begin{figure*} |
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%\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography} |
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%\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography} |
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%\includegraphics*[width=0.44\linewidth]{\fpath/topography} |
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%\includegraphics*[width=0.46\linewidth]{\fpath/archipelago} |
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\includegraphics*[width=\linewidth]{\fpath/topography} |
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\caption{Left: Bathymetry and domain boundaries of Arctic |
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Domain. |
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%; the dashed line marks the boundaries of the inset on the right hand side. |
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The letters in the inset label sections in the |
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Canadian Archipelago, where ice transport is evaluated: |
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A: Nares Strait; % |
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B: \ml{Meighen Island}; % |
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C: Prince Gustaf Adolf Sea; % |
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D: \ml{Brock Island}; % |
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E: M'Clure Strait; % |
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F: Amundsen Gulf; % |
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G: Lancaster Sound; % |
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H: Barrow Strait \ml{W.}; % |
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I: Barrow Strait \ml{E.}; % |
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J: Barrow Strait \ml{N.}; % |
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K: Fram Strait. % |
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The sections A through F comprise the total inflow into the Canadian |
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Archipelago. \ml{[May still need to check the geography.]} |
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\label{fig:arctic_topog}} |
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\end{figure*} |
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It has 420 by 384 grid boxes and is carved out, and obtains open boundary |
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conditions from, a global cubed-sphere \citep{adcroft04:_cubed_sphere} |
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configuration similar to that described in \citet{menemenlis05}. The |
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particular simulation from which we obtain boundary conditions is a baseline |
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integration, labeled {\em ``cube76''}. Each face of the cube comprises 510 by |
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510 grid cells for a mean horizontal grid spacing of 18\,km. There are 50 |
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vertical levels ranging in thickness from 10 m near the surface to |
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approximately 450 m at a maximum model depth of 6150 m. The model employs the |
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partial-cell formulation of \citet{adcroft97:_shaved_cells}, which permits |
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accurate representation of the bathymetry. Bathymetry is from the S2004 |
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(W.~Smith, unpublished) blend of the \citet{smi97} and the General Bathymetric |
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Charts of the Oceans (GEBCO) one arc-minute bathymetric grid. The model is |
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integrated in a volume-conserving configuration using a finite volume |
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discretization with C-grid staggering of the prognostic variables. In the |
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ocean, the non-linear equation of state of \citet{jac95} is used. The global |
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ocean model is coupled to a sea ice model in a configuration similar to the |
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case C-LSR-ns (see \reftab{experiments}). |
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The {\em cube76} simulation is initialized from temperature and salinity |
| 63 |
fields derived from the Polar science center Hydrographic Climatology (PHC) |
fields derived from the Polar science center Hydrographic Climatology (PHC) |
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3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to |
3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to |
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July 2002 are derived from the European Centre for Medium-Range Weather |
July 2002 are derived from the European Centre for Medium-Range Weather |
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Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}. Surface |
Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}. Six-hourly |
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boundary conditions after September 2002 are derived from the ECMWF |
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operational analysis. There is a one month transition period, August 2002, |
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during which the ERA-40 contribution decreases linearly from 1 to 0 and the |
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ECMWF analysis contribution increases linearly from 0 to 1. Six-hourly |
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surface winds, temperature, humidity, downward short- and long-wave |
surface winds, temperature, humidity, downward short- and long-wave |
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radiations, and precipitation are converted to heat, freshwater, and wind |
radiations, and precipitation are converted to heat, freshwater, and wind |
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stress fluxes using the \citet{large81,large82} bulk formulae. Shortwave |
stress fluxes using the \citet{large81,large82} bulk formulae. Shortwave |
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radiation decays exponentially as per \citet{pau77}. Low frequency |
radiation decays exponentially as per \citet{pau77}. Low frequency |
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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 |
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Precipitation Climatology Project \citep[GPCP][]{huf01}. The time-mean river |
Precipitation Climatology Project \citep[GPCP,][]{huf01}. The time-mean river |
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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 |
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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) |
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and prepared by P. Winsor (personnal communication, 2007) is specificied. |
and prepared by P. Winsor (personnal communication, 2007) is specificied. |
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Additionally, there is a relaxation to the monthly-mean climatological sea |
Additionally, there is a relaxation to the monthly-mean climatological sea |
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surface salinity values from PHC 3.0, a relaxation time scale of 101 days. |
surface salinity values from PHC 3.0, with a relaxation time scale of 101 days. |
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Vertical mixing follows \citet{lar94} but with meridionally and vertically |
Vertical mixing follows \citet{lar94} but with meridionally and vertically |
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varying background vertical diffusivity; at the surface, vertical diffusivity |
varying background vertical diffusivity; at the surface, vertical diffusivity |
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diffusivity. Horizontal viscosity follows \citet{lei96} but modified to sense |
diffusivity. Horizontal viscosity follows \citet{lei96} but modified to sense |
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the divergent flow as per \citet{kem08}. |
the divergent flow as per \citet{kem08}. |
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| 91 |
\ml{[Dimitris, here you need to either provide figures, so that I can |
The model configuration of {\em cube76} carries over to the Arctic domain |
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write text, or you can provide both figures and text. I guess, one |
configuration except for numerical details related to the non-linear |
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figure, showing the northern and southern hemisphere in summer and |
free surface that are not supported by the open boundary code, and the |
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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 |
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the next section.]} |
are now, respectively, 0.15, 0.85, 0.76, 0.94, and 0.8. The Arctic Ocean |
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model is integrated from Jan~01, 1992 to Mar~31, 2000. |
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\reftab{experiments} gives an overview over the experiments discussed |
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\subsection{Arctic Domain with Open Boundaries} |
in \refsec{arcticresults}. |
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\label{sec:arctic} |
\begin{table} |
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\caption{Overview over model simulations in \refsec{arcticresults}. |
| 101 |
A series of forward sensitivity experiments have been carried out on |
\label{tab:experiments}} |
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an Arctic Ocean domain with open boundaries. The objective is to |
\begin{tabular}{p{.3\linewidth}p{.65\linewidth}} |
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compare the old B-grid LSR dynamic solver with the new C-grid LSR and |
experiment name & description \\ \hline |
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EVP solvers. Additional experiments are is carried out to illustrate |
B-LSR-ns & the original LSOR solver of \citet{zhang97} on an |
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the differences between different ice advection schemes, ocean-ice |
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stress formulations and the two main options for sea ice |
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thermodynamics in the MITgcm. |
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The Arctic domain of integration is illustrated in |
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\reffig{arctic_topog}. It is carved out from, and obtains open |
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boundary conditions from, the global cubed-sphere configuration |
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described above. The horizontal domain size is 420 by 384 grid boxes. |
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\begin{figure*} |
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\includegraphics*[width=0.44\linewidth,viewport=139 210 496 606,clip]{\fpath/topography} |
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%\includegraphics*[width=0.44\linewidth,viewport=0 0 496 606,clip]{\fpath/topography} |
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\includegraphics*[width=0.46\linewidth]{\fpath/archipelago} |
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\caption{Left: Bathymetry and domain boudaries of Arctic |
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Domain; the dashed line marks the boundaries of the inset on the |
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right hand side. The letters in the inset label sections in the |
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Canadian Archipelago, where ice transport is evaluated: |
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A: Nares Strait; % |
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B: \ml{Meighen Island}; % |
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C: Prince Gustaf Adolf Sea; % |
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D: \ml{Brock Island}; % |
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E: McClure Strait; % |
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F: Amundsen Gulf; % |
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G: Lancaster Sound; % |
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H: Barrow Strait \ml{W.}; % |
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I: Barrow Strait \ml{E.}; % |
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J: Barrow Strait \ml{N.}. % |
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\label{fig:arctic_topog}} |
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\end{figure*} |
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The main dynamic difference from cube sphere is that it does not use |
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rescaled vertical coordinates (z$^\ast$) and the surface boundary |
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conditions for freshwater input are different, because those features |
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are not supported by the open boundary code. |
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Open water, dry ice, wet ice, dry snow, and wet snow albedo are, |
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respectively, 0.15, 0.85, 0.76, 0.94, and 0.8. |
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The model is integrated from January, 1992 to March \ml{[???]}, 2000, |
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with three different dynamical solvers and two different boundary |
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conditions: |
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\begin{description} |
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\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an |
|
| 105 |
Arakawa B-grid, implying no-slip lateral boundary conditions |
Arakawa B-grid, implying no-slip lateral boundary conditions |
| 106 |
($\vek{u}=0$ exactly); |
($\vek{u}=0$ exactly), advection of ice variables with a 2nd-order |
| 107 |
\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral |
central difference scheme plus explicit diffusion for stability \\ |
| 108 |
boundary conditions (implemented via ghost-points); |
C-LSR-ns & the LSOR solver discretized on a C-grid with no-slip lateral |
| 109 |
\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary |
boundary conditions (implemented via ghost-points) \\ |
| 110 |
conditions; |
C-LSR-fs & the LSOR solver on a C-grid with free-slip lateral boundary |
| 111 |
\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with |
conditions \\ |
| 112 |
no-slip lateral boundary conditions; |
C-EVP-ns & the EVP solver of \citet{hunke01} on a C-grid with |
| 113 |
\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral |
no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} = |
| 114 |
boundary conditions; |
150\text{\,s}$ \\ |
| 115 |
\item[C-LSR-ns adv33:] C-LSR-ns with a third-order flux limited |
C-EVP-ns10 & the EVP solver of \citet{hunke01} on a C-grid with |
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direct-space-time advection scheme \citep{hundsdorfer94}; |
no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} = |
| 117 |
\item[C-LSR-ns TEM:] C-LSR-ns with a truncated |
10\text{\,s}$ \\ |
| 118 |
ellispe method (TEM) rheology \citep{hibler97}; |
C-LSR-ns HB87 & C-LSR-ns with ocean-ice stress coupling according |
| 119 |
\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according |
to \citet{hibler87}\\ |
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to \citet{hibler87}; |
C-LSR-ns TEM & C-LSR-ns with a truncated ellispe method (TEM) |
| 121 |
\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small |
rheology \citep{hibler97} \\ |
| 122 |
scale noise \citep{hunke01}. |
C-LSR-ns WTD & C-LSR-ns with 3-layer thermodynamics following |
| 123 |
\end{description} |
\citet{winton00} \\ |
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C-LSR-ns DST3FL& C-LSR-ns with a third-order flux limited |
| 125 |
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direct-space-time advection scheme for thermodynamic variables |
| 126 |
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\citep{hundsdorfer94} |
| 127 |
|
\end{tabular} |
| 128 |
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\end{table} |
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%\begin{description} |
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%\item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an |
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% Arakawa B-grid, implying no-slip lateral boundary conditions |
| 132 |
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% ($\vek{u}=0$ exactly); |
| 133 |
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%\item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral |
| 134 |
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% boundary conditions (implemented via ghost-points); |
| 135 |
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%\item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary |
| 136 |
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% conditions; |
| 137 |
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%\item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with |
| 138 |
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% no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} = |
| 139 |
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% 150\text{\,s}$; |
| 140 |
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%\item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral |
| 141 |
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% boundary conditions and $\Delta{t}_\mathrm{evp} = 150\text{\,s}$; |
| 142 |
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%\item[C-LSR-ns DST3FL:] C-LSR-ns with a third-order flux limited |
| 143 |
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% direct-space-time advection scheme \citep{hundsdorfer94}; |
| 144 |
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%\item[C-LSR-ns TEM:] C-LSR-ns with a truncated ellispe method (TEM) |
| 145 |
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% rheology \citep{hibler97}; |
| 146 |
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%\item[C-LSR-ns HB87:] C-LSR-ns with ocean-ice stress coupling according |
| 147 |
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% to \citet{hibler87}; |
| 148 |
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%\item[C-LSR-ns WTD:] C-LSR-ns with 3-layer thermodynamics following |
| 149 |
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% \citet{winton00}; |
| 150 |
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%%\item[C-EVP-ns damp:] C-EVP-ns with additional damping to reduce small |
| 151 |
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%% scale noise \citep{hunke01}; |
| 152 |
|
%\item[C-EVP-ns10:] the EVP solver of \citet{hunke01} on a C-grid with |
| 153 |
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% no-slip lateral boundary conditions and $\Delta{t}_\mathrm{evp} = |
| 154 |
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% 10\text{\,s}$. |
| 155 |
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%\end{description} |
| 156 |
Both LSOR and EVP solvers solve the same viscous-plastic rheology, so |
Both LSOR and EVP solvers solve the same viscous-plastic rheology, so |
| 157 |
that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be |
that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be |
| 158 |
interpreted as pure model error. Lateral boundary conditions on a |
interpreted as pure model error. Lateral boundary conditions on a |
| 159 |
coarse grid (compared to the roughness of the true coast line) are |
coarse grid (coarse compared to the roughness of the true coast line) are |
| 160 |
unclear, so that comparing the no-slip solutions to the free-slip |
unclear, so that comparing the no-slip solutions to the free-slip |
| 161 |
solutions gives another measure of uncertainty in sea ice |
solutions gives another measure of uncertainty in sea ice modeling. |
| 162 |
modeling. The remaining experiments explore further |
The remaining experiments explore further sensitivities of the system |
| 163 |
sensitivities of the system to different physics (change in rheology, |
to different physics (change in rheology, advection and diffusion |
| 164 |
advection and diffusion properties and stress coupling) and numerics |
properties, stress coupling, and thermodynamics) and different time |
| 165 |
(numerical method to damp noise in the EVP solutions). |
steps for the EVP solutions: \citet{hunke01} uses 120 subcycling steps |
| 166 |
|
for the EVP solution. We use two interpretations of this choice where |
| 167 |
A principle difficulty in comparing the solutions obtained with |
the EVP model is subcycled 120 times within a (short) model timestep |
| 168 |
different variants of the dynamics solver lies in the non-linear |
of 1200\,s resulting in a very long and expensive integration |
| 169 |
feedback of the ice dynamics and thermodynamics. Already after a few |
($\Delta{t}_\mathrm{evp}=10\text{\,s}$) and 144 times within the |
| 170 |
months the solutions have diverged so far from each other that |
forcing timescale of 6\,h ($\Delta{t}_\mathrm{evp}=150\text{\,s}$). |
| 171 |
comparing velocities only makes sense within the first 3~months of the |
|
| 172 |
|
\subsection{Results} |
| 173 |
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\label{sec:arcticresults} |
| 174 |
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|
| 175 |
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Comparing the solutions obtained with different realizations of the |
| 176 |
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model dynamics is difficult because of the non-linear feedback of the |
| 177 |
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ice dynamics and thermodynamics. Already after a few months the |
| 178 |
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solutions have diverged so far from each other that comparing |
| 179 |
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velocities only makes sense within the first 3~months of the |
| 180 |
integration while the ice distribution is still close to the initial |
integration while the ice distribution is still close to the initial |
| 181 |
conditions. At the end of the integration, the differences between the |
conditions. At the end of the integration, the differences between the |
| 182 |
model solutions can be interpreted as cumulated model uncertainties. |
model solutions can be interpreted as cumulated model uncertainties. |
| 183 |
|
|
| 184 |
\reffig{iceveloc} shows ice velocities averaged over Janunary, |
\subsubsection{Ice velocities in JFM 1992} |
| 185 |
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|
| 186 |
|
\reffig{iceveloc} shows ice velocities averaged over January, |
| 187 |
February, and March (JFM) of 1992 for the C-LSR-ns solution; also |
February, and March (JFM) of 1992 for the C-LSR-ns solution; also |
| 188 |
shown are the differences between B-grid and C-grid, LSR and EVP, and |
shown are the differences between this reference solution and various |
| 189 |
no-slip and free-slip solution. The velocity field of the C-LSR-ns |
sensitivity experiments. The velocity field of the C-LSR-ns |
| 190 |
solution (\reffig{iceveloc}a) roughly resembles the drift velocities |
solution (\reffig{iceveloc}a) roughly resembles the drift velocities |
| 191 |
of some of the AOMIP (Arctic Ocean Model Intercomparison Project) |
of some of the AOMIP (Arctic Ocean Model Intercomparison Project) |
| 192 |
models in an cyclonic circulation regime (CCR) \citep[their |
models in a cyclonic circulation regime (CCR) \citep[their |
| 193 |
Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift |
Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift |
| 194 |
shifted eastwards towards Alaska. |
shifted eastwards towards Alaska. |
| 195 |
|
% |
| 196 |
|
\newcommand{\subplotwidth}{0.47\textwidth} |
| 197 |
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%\newcommand{\subplotwidth}{0.3\textwidth} |
| 198 |
|
\begin{figure}[tp] |
| 199 |
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\centering |
| 200 |
|
\subfigure[{\footnotesize C-LSR-ns}] |
| 201 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-ns}} |
| 202 |
|
\subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}] |
| 203 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_B-LSR-ns-C-LSR-ns}} |
| 204 |
|
\\ |
| 205 |
|
\subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}] |
| 206 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-LSR-fs-C-LSR-ns}} |
| 207 |
|
\subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}] |
| 208 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_C-EVP-ns150-C-LSR-ns}} |
| 209 |
|
% \\ |
| 210 |
|
% \subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}] |
| 211 |
|
% {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}} |
| 212 |
|
% \subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}] |
| 213 |
|
% {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}} |
| 214 |
|
% \\ |
| 215 |
|
% \subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}] |
| 216 |
|
% {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}} |
| 217 |
|
% \subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}] |
| 218 |
|
% {\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}} |
| 219 |
|
\caption{(a) Ice drift velocity of the C-LSR-ns solution averaged |
| 220 |
|
over the first 3 months of integration [cm/s]; (b)-(h) difference |
| 221 |
|
between solutions with B-grid, free lateral slip, EVP-solver, |
| 222 |
|
truncated ellipse method (TEM), different ice-ocean stress |
| 223 |
|
formulation (HB87), different thermodynamics (WTD), different |
| 224 |
|
advection for thermodynamic variables (DST3FL) and the C-LSR-ns |
| 225 |
|
reference solution [cm/s]; color indicates speed (or differences |
| 226 |
|
of speed), vectors indicate direction only.} |
| 227 |
|
\label{fig:iceveloc} |
| 228 |
|
\end{figure} |
| 229 |
|
\addtocounter{figure}{-1} |
| 230 |
|
\setcounter{subfigure}{4} |
| 231 |
|
\begin{figure}[tp] |
| 232 |
|
\subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}] |
| 233 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_TEM-C-LSR-ns}} |
| 234 |
|
\subfigure[{\footnotesize C-LSR-ns HB87 $-$ C-LSR-ns}] |
| 235 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_HB87-C-LSR-ns}} |
| 236 |
|
\\ |
| 237 |
|
\subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}] |
| 238 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_ThSIce-C-LSR-ns}} |
| 239 |
|
\subfigure[{\footnotesize C-LSR-ns DST3FL $-$ C-LSR-ns}] |
| 240 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMuv1992_adv33-C-LSR-ns}} |
| 241 |
|
\caption{continued} |
| 242 |
|
\end{figure} |
| 243 |
|
|
| 244 |
The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b) |
The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b) |
| 245 |
is most pronounced along the coastlines, where the discretization |
is most pronounced along the coastlines, where the discretization |
| 247 |
velocity lies on the boundary (and is thus zero through the no-slip |
velocity lies on the boundary (and is thus zero through the no-slip |
| 248 |
boundary conditions), whereas on the C-grid it is half a cell width |
boundary conditions), whereas on the C-grid it is half a cell width |
| 249 |
away from the boundary, thus allowing more flow. The B-LSR-ns solution |
away from the boundary, thus allowing more flow. The B-LSR-ns solution |
| 250 |
has less ice drift through the Fram Strait and especially the along |
has less ice drift through the Fram Strait and along |
| 251 |
Greenland's east coast; also, the flow through Baffin Bay and Davis |
Greenland's east coast; also, the flow through Baffin Bay and Davis |
| 252 |
Strait into the Labrador Sea is reduced with respect the C-LSR-ns |
Strait into the Labrador Sea is reduced with respect to the C-LSR-ns |
| 253 |
solution. \ml{[Do we expect this? Say something about that]} |
solution. \ml{[Do we expect this? Say something about that]} |
| 254 |
% |
% |
| 255 |
Compared to the differences between B and C-grid solutions,the |
Compared to the differences between B and C-grid solutions, the |
| 256 |
C-LSR-fs ice drift field differs much less from the C-LSR-ns solution |
C-LSR-fs ice drift field differs much less from the C-LSR-ns solution |
| 257 |
(\reffig{iceveloc}c). As expected the differences are largest along |
(\reffig{iceveloc}c). As expected the differences are largest along |
| 258 |
coastlines: because of the free-slip boundary conditions, flow is |
coastlines: because of the free-slip boundary conditions, flow is |
| 259 |
faster in the C-LSR-fs solution, for example, along the east coast |
faster in the C-LSR-fs solution, for example, along the east coast |
| 260 |
of Greenland, the north coast of Alaska, and the east Coast of Baffin |
of Greenland, the north coast of Alaska, and the east Coast of Baffin |
| 261 |
Island. |
Island. |
|
\begin{figure}[htbp] |
|
|
\centering |
|
|
\subfigure[{\footnotesize C-LSR-ns}] |
|
|
% {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}} |
|
|
{\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-LSR-ns}} |
|
|
\subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}] |
|
|
% {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\ |
|
|
{\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_B-LSR-ns-C-LSR-ns}}\\ |
|
|
\subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}] |
|
|
% {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}} |
|
|
{\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-LSR-fs-C-LSR-ns}} |
|
|
\subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}] |
|
|
% {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}} |
|
|
{\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_C-EVP-ns-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)-(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} |
|
| 262 |
|
|
| 263 |
The C-EVP-ns solution is very different from the C-LSR-ns solution |
The C-EVP-ns solution with $\Delta{t}_\mathrm{evp}=150\text{\,s}$ is |
| 264 |
(\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows |
very different from the C-LSR-ns solution (\reffig{iceveloc}d). The |
| 265 |
for increased drift by over 2\,cm/s in the Beaufort Gyre and the |
EVP-approximation of the VP-dynamics allows for increased drift by up |
| 266 |
transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska |
to 8\,cm/s in the Beaufort Gyre and the transarctic drift. In |
| 267 |
in the C-EVP-ns solution. [Really?]} In general, drift velocities are |
general, drift velocities are strongly biased towards higher values in |
| 268 |
biased towards higher values in the EVP solutions as can be seen from |
the EVP solutions. |
| 269 |
a histogram of the differences in \reffig{drifthist}. |
|
| 270 |
\begin{figure}[htbp] |
Compared to the other parameters, the ice rheology TEM |
| 271 |
\centering |
(\reffig{iceveloc}e) has a very small effect on the solution. In |
| 272 |
\includegraphics[width=\textwidth]{\fpath/drifthist_C-EVP-ns-C-LSR-ns} |
general the ice drift tends to be increased, because there is no |
| 273 |
\caption{Histogram of drift velocity differences for C-LSR-ns and |
tensile stress and ice can be ``pulled appart'' at no cost. |
| 274 |
C-EVP-ns solution [cm/s].} |
Consequently, the largest effect on drift velocity can be observed |
| 275 |
\label{fig:drifthist} |
near the ice edge in the Labrador Sea. In contrast, the drift is |
| 276 |
\end{figure} |
stronger almost everywhere in the computational domain in the run with |
| 277 |
|
the ice-ocean stress formulation of \citet{hibler87} |
| 278 |
|
(\reffig{iceveloc}f). The increase is mostly aligned with the general |
| 279 |
|
direction of the flow, implying that the different stress formulation |
| 280 |
|
reduces the deceleration of drift by the ocean. |
| 281 |
|
|
| 282 |
|
The 3-layer thermodynamics following \citet{winton00} requires |
| 283 |
|
additional information on initial conditions for enthalphy. These |
| 284 |
|
different initial conditions make a comparison of the first months |
| 285 |
|
difficult to interpret. The drift in the Beaufort Gyre is slightly |
| 286 |
|
reduced relative to the reference run C-LSR-ns, but the drift through |
| 287 |
|
the Fram Strait is increased. The drift velocities near the ice edge |
| 288 |
|
are very different, because the ice extent is already larger in |
| 289 |
|
\mbox{C-LSR-ns~WTD}; inward from the ice egde, this run has smaller |
| 290 |
|
drift velocities, because the ice motion is more contrained by a |
| 291 |
|
larger ice extent than in \mbox{C-LSR-ns}, where the ice at the same |
| 292 |
|
geographical position is nearly in free drift. |
| 293 |
|
|
| 294 |
|
A more sophisticated advection scheme (\mbox{C-LSR-ns DST3FL}, |
| 295 |
|
\reffig{iceveloc}h) has some effect along the ice edge, where |
| 296 |
|
the gradients of thickness and concentration are largest. Everywhere |
| 297 |
|
else the effect is very small and can mostly be attributed to smaller |
| 298 |
|
numerical diffusion (and to the absense of explicit diffusion that is |
| 299 |
|
required for numerical stability in a simple second order central |
| 300 |
|
differences scheme). |
| 301 |
|
|
| 302 |
|
\subsubsection{Ice volume during JFM 2000} |
| 303 |
|
|
| 304 |
\reffig{icethick}a shows the effective thickness (volume per unit |
\reffig{icethick}a shows the effective thickness (volume per unit |
| 305 |
area) of the C-LSR-ns solution, averaged over January, February, March |
area) of the C-LSR-ns solution, averaged over January, February, March |
| 306 |
of year 2000. By this time of the integration, the differences in the |
of year 2000. By this time of the integration, the differences in the |
| 307 |
ice drift velocities have led to the evolution of very different ice |
ice drift velocities have led to the evolution of very different ice |
| 308 |
thickness distributions, which are shown in \reffig{icethick}b--d, and |
thickness distributions, which are shown in \reffig{icethick}b--h, and |
| 309 |
area distributions (not shown). \ml{Compared to other solutions, for |
concentrations (not shown). |
| 310 |
example, AOMIP the ice thickness distribution blablabal} |
\begin{figure}[tp] |
|
\begin{figure}[htbp] |
|
| 311 |
\centering |
\centering |
| 312 |
\subfigure[{\footnotesize C-LSR-ns}] |
\subfigure[{\footnotesize C-LSR-ns}] |
| 313 |
{\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}} |
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-ns}} |
| 314 |
\subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}] |
\subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}] |
| 315 |
{\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\ |
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_B-LSR-ns-C-LSR-ns}} |
| 316 |
|
\\ |
| 317 |
\subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}] |
\subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}] |
| 318 |
{\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}} |
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-LSR-fs-C-LSR-ns}} |
| 319 |
\subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}] |
\subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}] |
| 320 |
{\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}} |
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_C-EVP-ns150-C-LSR-ns}} |
| 321 |
\caption{(a) Effective thickness (volume per unit area) of the |
\caption{(a) Effective thickness (volume per unit area) of the |
| 322 |
C-LSR-ns solution, averaged over the months Janurary through March |
C-LSR-ns solution, averaged over the months Janurary through March |
| 323 |
2000 [m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns, |
2000 [m]; (b)-(h) difference between solutions with B-grid, free |
| 324 |
and C-LSR-ns solutions [cm/s].} |
lateral slip, EVP-solver, truncated ellipse method (TEM), |
| 325 |
|
different ice-ocean stress formulation (HB87), different |
| 326 |
|
thermodynamics (WTD), different advection for thermodynamic |
| 327 |
|
variables (DST3FL) and the C-LSR-ns reference solution [m].} |
| 328 |
\label{fig:icethick} |
\label{fig:icethick} |
| 329 |
\end{figure} |
\end{figure} |
| 330 |
% |
\addtocounter{figure}{-1} |
| 331 |
|
\setcounter{subfigure}{4} |
| 332 |
|
\begin{figure}[tp] |
| 333 |
|
\subfigure[{\footnotesize C-LSR-ns TEM $-$ C-LSR-ns}] |
| 334 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_TEM-C-LSR-ns}} |
| 335 |
|
\subfigure[{\footnotesize C-EVP-ns HB87 $-$ C-LSR-ns}] |
| 336 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_HB87-C-LSR-ns}} |
| 337 |
|
\\ |
| 338 |
|
\subfigure[{\footnotesize C-LSR-ns WTD $-$ C-LSR-ns}] |
| 339 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_ThSIce-C-LSR-ns}} |
| 340 |
|
\subfigure[{\footnotesize C-EVP-ns DST3FL $-$ C-LSR-ns}] |
| 341 |
|
{\includegraphics[width=\subplotwidth]{\fpath/JFMheff2000_adv33-C-LSR-ns}} |
| 342 |
|
\caption{continued} |
| 343 |
|
\end{figure} |
| 344 |
The generally weaker ice drift velocities in the B-LSR-ns solution, |
The generally weaker ice drift velocities in the B-LSR-ns solution, |
| 345 |
when compared to the C-LSR-ns solution, in particular through the |
when compared to the C-LSR-ns solution, in particular through the |
| 346 |
narrow passages in the Canadian Archipelago, lead to a larger build-up |
narrow passages in the Canadian Arctic Archipelago, lead to a larger build-up |
| 347 |
of ice north of Greenland and the Archipelago by 2\,m effective |
of ice north of Greenland and the Archipelago by 2\,m effective |
| 348 |
thickness and more in the B-grid solution (\reffig{icethick}b). But |
thickness and more in the B-grid solution (\reffig{icethick}b). But |
| 349 |
the ice volume in not larger everywhere: further west, there are |
the ice volume in not larger everywhere: further west, there are |
| 351 |
because the Beaufort Gyre is weaker and hence not as effective in |
because the Beaufort Gyre is weaker and hence not as effective in |
| 352 |
transporting ice westwards. There are also dipoles of ice volume |
transporting ice westwards. There are also dipoles of ice volume |
| 353 |
differences with more ice on the upstream side of island groups and |
differences with more ice on the upstream side of island groups and |
| 354 |
less ice in their lee, such as Franz-Josef-Land and \ml{IDONTKNOW}, |
less ice in their lee, such as Franz-Josef-Land and |
| 355 |
|
Severnaya Semlya\ml{/or Nordland?}, |
| 356 |
because ice tends to flow along coasts less easily in the B-LSR-ns |
because ice tends to flow along coasts less easily in the B-LSR-ns |
| 357 |
solution. |
solution. |
| 358 |
|
|
| 359 |
Imposing a free-slip boundary condition in C-LSR-fs leads to a much |
Imposing a free-slip boundary condition in C-LSR-fs leads to much |
| 360 |
smaller differences to C-LSR-ns than the transition from the B-grid to |
smaller differences to C-LSR-ns in the central Arctic than the |
| 361 |
the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it |
transition from the B-grid to the C-grid (\reffig{icethick}c), except |
| 362 |
still reduces the effective ice thickness by up to 2\,m where the ice |
in the Canadian Arctic Archipelago. There it reduces the effective ice |
| 363 |
is thick and the straits are narrow. Dipoles of ice thickness |
thickness by 2\,m and more where the ice is thick and the straits are |
| 364 |
differences can also be observed around islands, because the free-slip |
narrow. Dipoles of ice thickness differences can also be observed |
| 365 |
solution allows more flow around islands than the no-slip solution. |
around islands, because the free-slip solution allows more flow around |
| 366 |
Everywhere else the ice volume is affected only slightly by the |
islands than the no-slip solution. Everywhere else the ice volume is |
| 367 |
different boundary condition. |
affected only slightly by the different boundary condition. |
| 368 |
% |
% |
| 369 |
The C-EVP-ns solution has generally stronger drift velocities than the |
The C-EVP-ns solution has much thicker ice in the central Arctic Ocean |
| 370 |
C-LSR-ns solution. Consequently, more ice can be moved from the eastern |
than the C-LSR-ns solution (\reffig{icethick}d, note the color scale). |
| 371 |
part of the Arctic, where ice volumes are smaller, to the western |
Within the Canadian Arctic Archipelago, more drift leads to faster ice export |
| 372 |
Arctic where ice piles up along the coast (\reffig{icethick}d). Within |
and reduced effective ice thickness. With a shorter time step of |
| 373 |
the Canadian Archipelago, more drift leads to faster ice export and |
$\Delta{t}_\mathrm{evp}=10\text{\,s}$ the EVP solution converges to |
| 374 |
reduced effective ice thickness. |
the LSOR solution (not shown). Only in the narrow straits in the |
| 375 |
|
Archipelago the ice thickness is not affected by the shorter time step |
| 376 |
|
and the ice is still thinner by 2\,m and more, as in the EVP solution |
| 377 |
|
with $\Delta{t}_\mathrm{evp}=150\text{\,s}$. |
| 378 |
|
|
| 379 |
|
In year 2000, there is more ice everywhere in the domain in |
| 380 |
|
C-LSR-ns~WTD (\reffig{icethick}g, note the color scale). |
| 381 |
|
This difference, which is even more pronounced in summer (not shown), |
| 382 |
|
can be attributed to direct effects of the different thermodynamics in |
| 383 |
|
this run. The remaining runs have the largest differences in effective |
| 384 |
|
ice thickness along the north coasts of Greenland and Ellesmere Island. |
| 385 |
|
Although the effects of TEM and \citet{hibler87}'s ice-ocean stress |
| 386 |
|
formulation are so different on the initial ice velocities, both runs |
| 387 |
|
have similarly reduced ice thicknesses in this area. The 3rd-order |
| 388 |
|
advection scheme has an opposite effect of similar magnitude, pointing |
| 389 |
|
towards more implicit lateral stress with this numerical scheme. |
| 390 |
|
|
| 391 |
|
The observed difference of order 2\,m and less are smaller than the |
| 392 |
|
differences that were observed between different hindcast models and climate |
| 393 |
|
models in \citet{gerdes07}. There the range of sea ice volume of |
| 394 |
|
different sea ice-ocean models (which shared very similar forcing |
| 395 |
|
fields) was on the order of $10,000\text{km$^{3}$}$; this range was |
| 396 |
|
even larger for coupled climate models. Here, the range (and the |
| 397 |
|
averaging period) is smaller than $4,000\text{km$^{3}$}$ except for |
| 398 |
|
the run \mbox{C-LSR-ns~WTD} where the more complete thermodynamics |
| 399 |
|
lead to generally thicker ice (\reffig{icethick} and |
| 400 |
|
\reftab{icevolume}). |
| 401 |
|
\begin{table}[t] |
| 402 |
|
\begin{tabular}{lr@{\hspace{5ex}}r@{$\pm$}rr@{$\pm$}rr@{$\pm$}r} |
| 403 |
|
model run & ice volume |
| 404 |
|
& \multicolumn{6}{c}{ice transport [$\text{flux$\pm$ std., |
| 405 |
|
km$^{3}$\,y$^{-1}$}$]}\\ |
| 406 |
|
& [$\text{km$^{3}$}$] |
| 407 |
|
& \multicolumn{2}{c}{FS} |
| 408 |
|
& \multicolumn{2}{c}{NI} |
| 409 |
|
& \multicolumn{2}{c}{LS} \\ \hline |
| 410 |
|
B-LSR-ns & 23,824 & 2126 & 1278 & 34 & 122 & 43 & 76 \\ |
| 411 |
|
C-LSR-ns & 24,769 & 2196 & 1253 & 70 & 224 & 77 & 110 \\ |
| 412 |
|
C-LSR-fs & 23,286 & 2236 & 1289 & 80 & 276 & 91 & 85 \\ |
| 413 |
|
C-EVP-ns & 27,056 & 3050 & 1652 & 352 & 735 & 256 & 151 \\ |
| 414 |
|
C-EVP-ns10 & 22,633 & 2174 & 1260 & 186 & 496 & 133 & 128 \\ |
| 415 |
|
C-LSR-ns HB87 & 23,060 & 2256 & 1327 & 64 & 230 & 77 & 114 \\ |
| 416 |
|
C-LSR-ns TEM & 23,529 & 2222 & 1258 & 60 & 242 & 87 & 112 \\ |
| 417 |
|
C-LSR-ns WTD & 31,634 & 2761 & 1563 & 23 & 140 & 94 & 63 \\ |
| 418 |
|
C-LSR-ns DST3FL& 24,023 & 2191 & 1261 & 88 & 251 & 84 & 129 |
| 419 |
|
\end{tabular} |
| 420 |
|
\caption{Arctic ice volume averaged over Jan--Mar 2000, in |
| 421 |
|
$\text{km$^{3}$}$. Mean ice transport and standard deviation for the |
| 422 |
|
period Jan 1992 -- Dec 1999 through the Fram Strait (FS), the |
| 423 |
|
total northern inflow into the Canadian Arctic Archipelago (NI), and the |
| 424 |
|
export through Lancaster Sound (LS), in $\text{km$^{3}$\,y$^{-1}$}$. |
| 425 |
|
\label{tab:icevolume}} |
| 426 |
|
\end{table} |
| 427 |
|
|
| 428 |
|
\subsubsection{Ice transports} |
| 429 |
|
|
| 430 |
The difference in ice volume and ice drift velocities between the |
The difference in ice volume and ice drift velocities between the |
| 431 |
different experiments has consequences for the ice transport out of |
different experiments has consequences for the ice transport out of |
| 432 |
the Arctic. Although by far the most exported ice drifts through the |
the Arctic. Although by far the most exported ice drifts through the |
| 433 |
Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a |
Fram Strait (approximately $2300\pm610\text{\,km$^3$\,y$^{-1}$}$), a |
| 434 |
considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) ice is |
considerable amount (order $160\text{\,km$^3$\,y$^{-1}$}$) of ice is |
| 435 |
exported through the Canadian Archipelago \citep[and references |
exported through the Canadian Arctic Archipelago \citep[and references |
| 436 |
therein]{serreze06}. \reffig{archipelago} shows a time series of |
therein]{serreze06}. Note, that ice transport estimates are associated |
| 437 |
\ml{[maybe smooth to different time scales:] daily averaged, smoothed |
with large uncertainties and that the results presented herein have not |
| 438 |
with monthly running means,} ice transports through various straits |
yet been constrained by observations; we use |
| 439 |
in the Canadian Archipelago and the Fram Strait for the different |
the published numbers as an orientation. |
| 440 |
model solutions. The export through Fram Strait agrees with the |
|
| 441 |
observations in all model solutions (annual averages range from $2112$ |
\reffig{archipelago} shows an excerpt of a time series of daily |
| 442 |
to $2425\text{\,km$^3$\,y$^{-1}$}$), while the export through |
averaged ice transports, smoothed with a monthly running mean, through |
| 443 |
Lancaster Sound is lower (annual averages are $66$ to |
various straits in the Canadian Arctic Archipelago and the Fram Strait for |
| 444 |
$256\text{\,km$^3$\,y$^{-1}$}$) than observed |
the different model solutions; \reftab{icevolume} summarizes the |
| 445 |
\citep[???][]{lancaster}. Generally, the C-EVP solutions have highest |
time series. |
|
maximum (export out of the Artic) and minimum (import into the Artic) |
|
|
fluxes as the drift velocities are largest in this solution. In the |
|
|
extreme, both B- and C-grid LSOR solvers have practically no ice |
|
|
transport through the Nares Strait, which is only a few grid points |
|
|
wide, while the C-EVP solutions allow up to |
|
|
$600\text{\,km$^3$\,y$^{-1}$}$ in summer. As as consequence, the |
|
|
import into the Candian Archipelago is overestimated in all EVP |
|
|
solutions (range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$), while the |
|
|
C-LSR solutions get the order of magnitude right (range: $132$ to |
|
|
$165\text{\,km$^3$\,y$^{-1}$}$); the B-LSR-ns solution grossly |
|
|
underestimates the ice transport with $77\text{\,km$^3$\,y$^{-1}$}$. |
|
| 446 |
\begin{figure} |
\begin{figure} |
| 447 |
%\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}} |
%\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}} |
| 448 |
\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}} |
%\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/ice_export}}} |
| 449 |
\caption{Transport through Canadian Archipelago for different solver |
%\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export}}} |
| 450 |
|
\centerline{{\includegraphics[width=\linewidth]{\fpath/ice_export1996}}} |
| 451 |
|
\caption{Transport through Canadian Arctic Archipelago for different solver |
| 452 |
flavors. The letters refer to the labels of the sections in |
flavors. The letters refer to the labels of the sections in |
| 453 |
\reffig{arctic_topog}; positive values are flux out of the Arctic; |
\reffig{arctic_topog}; positive values are flux out of the Arctic; |
| 454 |
legend abbreviations are explained in \reftab{experiments}. |
legend abbreviations are explained in \reftab{experiments}. The mean |
| 455 |
|
range of the different model solution is taken over the period Jan |
| 456 |
|
1992 to Dec 1999. |
| 457 |
\label{fig:archipelago}} |
\label{fig:archipelago}} |
| 458 |
\end{figure} |
\end{figure} |
| 459 |
|
The export through Fram Strait agrees with the observations in all |
| 460 |
|
model solutions (annual averages range from $2110$ to |
| 461 |
|
$2300\text{\,km$^3$\,y$^{-1}$}$, except for \mbox{C-LSR-ns~WTD} with |
| 462 |
|
$2760\text{\,km$^3$\,y$^{-1}$}$ and the EVP solution with the long |
| 463 |
|
time step of 150\,s with nearly $3000\text{\,km$^3$\,y$^{-1}$}$), |
| 464 |
|
while the export through the Candian Arctic Archipelago is smaller than |
| 465 |
|
generally thought. For example, the ice transport through Lancaster |
| 466 |
|
Sound is lower (annual averages are $43$ to |
| 467 |
|
$256\text{\,km$^3$\,y$^{-1}$}$) than in \citet{dey81} who estimates an |
| 468 |
|
inflow into Baffin Bay of $370$ to $537\text{\,km$^3$\,y$^{-1}$}$, but |
| 469 |
|
a flow of only $102$ to $137\text{\,km$^3$\,y$^{-1}$}$ further |
| 470 |
|
upstream in Barrow Strait in the 1970's from satellite images. |
| 471 |
|
Generally, the EVP solutions have the highest maximum (export out of |
| 472 |
|
the Artic) and lowest minimum (import into the Artic) fluxes as the |
| 473 |
|
drift velocities are largest in these solutions. In the extreme of |
| 474 |
|
the Nares Strait, which is only a few grid points wide in our |
| 475 |
|
configuration, both B- and C-grid LSOR solvers lead to practically no |
| 476 |
|
ice transport, while the C-EVP solutions allow up to |
| 477 |
|
$600\text{\,km$^3$\,y$^{-1}$}$ in summer (not shown); \citet{tang04} |
| 478 |
|
report $300$ to $350\text{\,km$^3$\,y$^{-1}$}$. As as consequence, |
| 479 |
|
the import into the Candian Arctic Archipelago is larger in all EVP solutions |
| 480 |
|
%(range: $539$ to $773\text{\,km$^3$\,y$^{-1}$}$) |
| 481 |
|
than in the LSOR solutions. |
| 482 |
|
%get the order of magnitude right (range: $132$ to |
| 483 |
|
%$165\text{\,km$^3$\,y$^{-1}$}$); |
| 484 |
|
The B-LSR-ns solution is even smaller by another factor of two than the |
| 485 |
|
C-LSR solutions (an exception is the WTD solution, where larger ice thickness |
| 486 |
|
tends to block the transport). |
| 487 |
|
%underestimates the ice transport with $34\text{\,km$^3$\,y$^{-1}$}$. |
| 488 |
|
|
| 489 |
|
%\ml{[Transport to narrow straits, area?, more runs, TEM, advection |
| 490 |
|
% schemes, Winton TD, discussion about differences in terms of model |
| 491 |
|
% error? that's tricky as it means refering to Tremblay, thus our ice |
| 492 |
|
% models are all erroneous!]} |
| 493 |
|
|
| 494 |
\ml{[Transport to narrow straits, area?, more runs, TEM, advection |
\subsubsection{Discussion} |
|
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!]} |
|
| 495 |
|
|
| 496 |
In summary, we find that different dynamical solvers can yield very |
In summary, we find that different dynamical solvers can yield very |
| 497 |
different solutions. In contrast, the differences between free-slip |
different solutions. In constrast to that, the differences between |
| 498 |
and no-slip solutions \emph{with the same solver} are considerably |
free-slip and no-slip solutions \emph{with the same solver} are |
| 499 |
smaller (the difference for the EVP solver is not shown, but similar |
considerably smaller (the difference for the EVP solver is not shown, |
| 500 |
to that for the LSOR solver). Albeit smaller, the differences between |
but similar to that for the LSOR solver). Albeit smaller, the |
| 501 |
free and no-slip solutions in ice drift can lead to large differences |
differences between free and no-slip solutions in ice drift can lead |
| 502 |
in ice volume over the integration time. At first, this observation |
to equally large differences in ice volume, especially in the Canadian |
| 503 |
|
Arctic Archipelago over the integration time. At first, this observation |
| 504 |
seems counterintuitive, as we expect that the solution |
seems counterintuitive, as we expect that the solution |
| 505 |
\emph{technique} should not affect the \emph{solution} to a higher |
\emph{technique} should not affect the \emph{solution} to a higher |
| 506 |
degree than actually modifying the equations. A more detailed study on |
degree than actually modifying the equations. A more detailed study on |
| 513 |
equations is not complete for all linearized solvers, then one can |
equations is not complete for all linearized solvers, then one can |
| 514 |
imagine that each solver stops at a different point in velocity-space |
imagine that each solver stops at a different point in velocity-space |
| 515 |
thus leading to different solutions for the ice drift velocities. If |
thus leading to different solutions for the ice drift velocities. If |
| 516 |
this were true, this tantalizing circumstance had a dramatic impact on |
this were true, this tantalizing circumstance would have a dramatic |
| 517 |
sea-ice modeling in general, and we would need to improve the solution |
impact on sea-ice modeling in general, and we would need to improve |
| 518 |
technique of dynamic sea ice model, most likely at a very high |
the solution techniques for dynamic sea ice models, most likely at a very |
| 519 |
compuational cost (Bruno Tremblay, personal communication). |
high compuational cost (Bruno Tremblay, personal communication). |
| 520 |
|
|
| 521 |
|
Further, we observe that the EVP solutions tends to produce |
| 522 |
|
effectively ``weaker'' ice that yields more easily to stress. This was |
| 523 |
\begin{itemize} |
also observed by \citet{hunke99} in a fast response to changing winds, |
| 524 |
\item Configuration |
their Figures\,10--12, where the EVP model adjusts quickly to a |
| 525 |
\item OBCS from cube |
cyclonic wind pattern, while the LSOR solution lags in time. This |
| 526 |
\item forcing |
property of the EVP solutions allows larger ice transports through |
| 527 |
\item 1/2 and full resolution |
narrow straits, where the implicit solver LSOR forms rigid ice. The |
| 528 |
\item with a few JFM figs from C-grid LSR no slip |
underlying reasons for this striking difference need further |
| 529 |
ice transport through Canadian Archipelago |
exploration. |
| 530 |
thickness distribution |
|
| 531 |
ice velocity and transport |
% THIS is now almost all in the text: |
| 532 |
\end{itemize} |
%\begin{itemize} |
| 533 |
|
%\item Configuration |
| 534 |
\begin{itemize} |
%\item OBCS from cube |
| 535 |
\item Arctic configuration |
%\item forcing |
| 536 |
\item ice transport through straits and near boundaries |
%\item 1/2 and full resolution |
| 537 |
\item focus on narrow straits in the Canadian Archipelago |
%\item with a few JFM figs from C-grid LSR no slip |
| 538 |
\end{itemize} |
% ice transport through Canadian Archipelago |
| 539 |
|
% thickness distribution |
| 540 |
\begin{itemize} |
% ice velocity and transport |
| 541 |
\item B-grid LSR no-slip: B-LSR-ns |
%\end{itemize} |
| 542 |
\item C-grid LSR no-slip: C-LSR-ns |
|
| 543 |
\item C-grid LSR slip: C-LSR-fs |
%\begin{itemize} |
| 544 |
\item C-grid EVP no-slip: C-EVP-ns |
%\item Arctic configuration |
| 545 |
\item C-grid EVP slip: C-EVP-fs |
%\item ice transport through straits and near boundaries |
| 546 |
\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, |
%\item focus on narrow straits in the Canadian Archipelago |
| 547 |
new flag): C-LSR-ns+TEM |
%\end{itemize} |
| 548 |
\item C-grid LSR with different advection scheme: 33 vs 77, vs. default? |
|
| 549 |
\item C-grid LSR no-slip + Winton: |
%\begin{itemize} |
| 550 |
\item speed-performance-accuracy (small) |
%\item B-grid LSR no-slip: B-LSR-ns |
| 551 |
ice transport through Canadian Archipelago differences |
%\item C-grid LSR no-slip: C-LSR-ns |
| 552 |
thickness distribution differences |
%\item C-grid LSR slip: C-LSR-fs |
| 553 |
ice velocity and transport differences |
%\item C-grid EVP no-slip: C-EVP-ns |
| 554 |
\end{itemize} |
%\item C-grid EVP slip: C-EVP-fs |
| 555 |
|
%\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, |
| 556 |
We anticipate small differences between the different models due to: |
% new flag): C-LSR-ns+TEM |
| 557 |
\begin{itemize} |
%\item C-grid LSR with different advection scheme: 33 vs 77, vs. default? |
| 558 |
\item advection schemes: along the ice-edge and regions with large |
%\item C-grid LSR no-slip + Winton: |
| 559 |
gradients |
%\item speed-performance-accuracy (small) |
| 560 |
\item C-grid: less transport through narrow straits for no slip |
% ice transport through Canadian Archipelago differences |
| 561 |
conditons, more for free slip |
% thickness distribution differences |
| 562 |
\item VP vs.\ EVP: speed performance, accuracy? |
% ice velocity and transport differences |
| 563 |
\item ocean stress: different water mass properties beneath the ice |
%\end{itemize} |
| 564 |
\end{itemize} |
|
| 565 |
|
%We anticipate small differences between the different models due to: |
| 566 |
%\begin{figure} |
%\begin{itemize} |
| 567 |
%\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}} |
%\item advection schemes: along the ice-edge and regions with large |
| 568 |
%\caption{Surface sea ice velocity for different solver flavors. |
% gradients |
| 569 |
%\label{fig:iceveloc}} |
%\item C-grid: less transport through narrow straits for no slip |
| 570 |
%\end{figure} |
% conditons, more for free slip |
| 571 |
|
%\item VP vs.\ EVP: speed performance, accuracy? |
| 572 |
%\begin{figure} |
%\item ocean stress: different water mass properties beneath the ice |
| 573 |
%\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}} |
%\end{itemize} |
|
%\caption{Sea ice thickness for different solver flavors. |
|
|
%\label{fig:icethick}} |
|
|
%\end{figure} |
|
| 574 |
|
|
| 575 |
%%% Local Variables: |
%%% Local Variables: |
| 576 |
%%% mode: latex |
%%% mode: latex |
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