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revision 1.2 by dimitri, Wed Feb 27 21:50:42 2008 UTC revision 1.11 by mlosch, Sat Mar 8 20:40:47 2008 UTC
# Line 6  ice simulations that exercise various ca Line 6  ice simulations that exercise various ca
6  model.  The first set of results is from a global, eddy-permitting, ocean and  model.  The first set of results is from a global, eddy-permitting, ocean and
7  sea ice configuration.  The second set of results is from a regional Arctic  sea ice configuration.  The second set of results is from a regional Arctic
8  configuration, which is used to compare the B-grid and C-grid dynamic solvers  configuration, which is used to compare the B-grid and C-grid dynamic solvers
9  and various other capabilities of the MITgcm sea ice model.  The third set of  and various other capabilities of the MITgcm sea ice model.  
10    %
11    \ml{[do we really want to do this?:] The third set of
12  results is from a yet smaller regional domain, which is used to illustrate  results is from a yet smaller regional domain, which is used to illustrate
13  treatment of sea ice open boundary condition sin the MITgcm.  treatment of sea ice open boundary condition in the MITgcm.}
14    
15  \subsection{Global Ocean and Sea Ice Simulation}  \subsection{Global Ocean and Sea Ice Simulation}
16  \label{sec:global}  \label{sec:global}
# Line 36  variables. In the ocean, the non-linear Line 38  variables. In the ocean, the non-linear
38  used.  used.
39    
40  The ocean model is coupled to the sea-ice model discussed in  The ocean model is coupled to the sea-ice model discussed in
41  Section~\ref{sec:model} with the following specific options.  The  \refsec{model} using the following specific options.  The
42  zero-heat-capacity thermodynamics formulation of \citet{hib80} is used to  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is
43  compute sea ice thickness and concentration.  Snow cover and sea ice salinity  used to compute sea ice thickness and concentration.  Snow cover and
44  are prognostic.    sea ice salinity are prognostic.  Open water, dry ice, wet ice, dry
45    snow, and wet snow albedo are, respectively, 0.15, 0.88, 0.79, 0.97,
46  Ice mechanics follow the viscous plastic rheology of  and 0.83. Ice mechanics follow the viscous plastic rheology of
47  \citet{hibler79} and the ice momentum equation is solved numerically using the  \citet{hibler79} and the ice momentum equation is solved numerically
48  C-grid implementation of the \citet{zha97} LSR dyanmics model discussed  using the C-grid implementation of the \citet{zhang97}'s LSOR dynamics
49  hereinabove.  model discussed hereinabove.  The ice is coupled to the ocean using
50    the rescaled vertical coordinate system, z$^\ast$, of \citet{cam08},
51    that is, sea ice does not float above the ocean model but rather
52    deforms the ocean's model surface level.
53    
54    This particular ECCO2 simulation is initialized from temperature and salinity
55    fields derived from the Polar science center Hydrographic Climatology (PHC)
56    3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to
57    July 2002 are derived from the European Centre for Medium-Range Weather
58    Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}.  Surface
59    boundary conditions after September 2002 are derived from the ECMWF
60    operational analysis.  There is a one month transition period, August 2002,
61    during which the ERA-40 contribution decreases linearly from 1 to 0 and the
62    ECMWF analysis contribution increases linearly from 0 to 1.  Six-hourly
63    surface winds, temperature, humidity, downward short- and long-wave
64    radiations, and precipitation are converted to heat, freshwater, and wind
65    stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
66    radiation decays exponentially as per \citet{pau77}.  Low frequency
67    precipitation has been adjusted using the pentad (5-day) data from the Global
68    Precipitation Climatology Project \citep[GPCP][]{huf01}.  The time-mean river
69    run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
70    where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
71    and prepared by P. Winsor (personnal communication, 2007) is specificied.
72    Additionally, there is a relaxation to the monthly-mean climatological sea
73    surface salinity values from PHC 3.0, a relaxation time scale of 101 days.
74    
75    Vertical mixing follows \citet{lar94} but with meridionally and vertically
76    varying background vertical diffusivity; at the surface, vertical diffusivity
77    is $4.4\times 10^{-6}$~m$^2$~s$^{-1}$ at the Equator, $3.6\times
78    10^{-6}$~m$^2$~s$^{-1}$ north of 70$^\circ$N, and $1.9\times
79    10^{-5}$~m$^2$~s$^{-1}$ south of 30$^\circ$S and between 30$^\circ$N and
80    60$^\circ$N , with sinusoidally varying values in between these latitudes;
81    vertically, diffusivity increases to $1.1\times 10^{-4}$~m$^2$~s$^{-1}$ at a a
82    depth of 6150 m as per \citet{bry79}.  A high order monotonicity-preserving
83    advection scheme \citep{dar04} is employed and there is no explicit horizontal
84    diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
85    the divergent flow as per \citet{kem08}.
86    
87    \ml{[Dimitris, here you need to either provide figures, so that I can
88      write text, or you can provide both figures and text. I guess, one
89      figure, showing the northern and southern hemisphere in summer and
90      winter is fine (four panels), as we are showing so many figures in
91      the next section.]}
92    
 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.  
93    
94  \subsection{Arctic Domain with Open Boundaries}  \subsection{Arctic Domain with Open Boundaries}
95  \label{sec:arctic}  \label{sec:arctic}
96    
97    A series of forward sensitivity experiments have been carried out on
98    an Arctic Ocean domain with open boundaries.  The objective is to
99    compare the old B-grid LSR dynamic solver with the new C-grid LSR and
100    EVP solvers.  Additional experiments are is carried out to illustrate
101    the differences between different ice advection schemes, ocean-ice
102    stress formulations and the two main options for sea ice
103    thermodynamics in the MITgcm.
104    
105    The Arctic domain of integration is illustrated in
106    \reffig{arctic_topog}.  It is carved out from, and obtains open
107    boundary conditions from, the global cubed-sphere configuration
108    described above.  The horizontal domain size is 420 by 384 grid boxes.
109    \begin{figure}
110    \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}
111    \caption{Bathymetry and domain boudaries of Arctic
112      Domain. The letters label sections in the Canadian Archipelago,
113      where ice transport is evaluated.
114      \label{fig:arctic_topog}}
115    \end{figure}
116    
117    The main dynamic difference from cube sphere is that it does not use
118    rescaled vertical coordinates (z$^\ast$) and the surface boundary
119    conditions for freshwater input are different, because those features
120    are not supported by the open boundary code.
121    
122  \subsection{Arctic Domain with Open Boundaries}  Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
123  \label{sec:arctic}  0.76, 0.94, and 0.8.
124    
125  A second series of forward sensitivity experiments have been carried out on an  The model is integrated from January, 1992 to March \ml{[???]}, 2000,
126  Arctic Ocean domain with open boundaries.  Once again the objective is to  with three different dynamical solvers and two different boundary
127  compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP  conditions:
128  solvers.  One additional experiment is carried out to illustrate the  \begin{description}
129  differences between the two main options for sea ice thermodynamics in the MITgcm.  \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an
130      Arakawa B-grid, implying no-slip lateral boundary conditions
131  The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It    ($\vek{u}=0$ exactly);
132  is carved out from, and obtains open boundary conditions from, the  \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
133  global cubed-sphere configuration of the Estimating the Circulation    boundary conditions (implemented via ghost-points);
134  and Climate of the Ocean, Phase II (ECCO2) project  \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
135  \citet{menemenlis05}.  The domain size is 420 by 384 grid boxes    conditions;
136  horizontally with mean horizontal grid spacing of 18 km.  \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
137      no-slip lateral boundary conditions; and
138    \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
139      boundary conditions.
140    \end{description}
141    Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
142    that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
143    interpreted as pure model error. Lateral boundary conditions on a
144    coarse grid (compared to the roughness of the true coast line) are
145    unclear, so that comparing the no-slip solutions to the free-slip
146    solutions gives another measure of uncertainty in sea ice modeling.
147    
148    A principle difficulty in comparing the solutions obtained with
149    different variants of the dynamics solver lies in the non-linear
150    feedback of the ice dynamics and thermodynamics. Already after a few
151    months the solutions have diverged so far from each other that
152    comparing velocities only makes sense within the first 3~months of the
153    integration while the ice distribution is still close to the initial
154    conditions. At the end of the integration, the differences between the
155    model solutions can be interpreted as cumulated model uncertainties.
156    
157    \reffig{iceveloc} shows ice velocities averaged over Janunary,
158    February, and March (JFM) of 1992 for the C-LSR-ns solution; also
159    shown are the differences between B-grid and C-grid, LSR and EVP, and
160    no-slip and free-slip solution. The velocity field of the C-LSR-ns
161    solution (\reffig{iceveloc}a) roughly resembles the drift velocities
162    of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
163    models in an cyclonic circulation regime (CCR) \citep[their
164    Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
165    shifted eastwards towards Alaska.
166    
167    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
168    is most pronounced along the coastlines, where the discretization
169    differs most between B and C-grids: On a B-grid the tangential
170    velocity lies on the boundary (and thus zero per the no-slip boundary
171    conditions), whereas on the C-grid the its half a cell width away from
172    the boundary, thus allowing more flow. The B-LSR-ns solution has less
173    ice drift through the Fram Strait and especially the along Greenland's
174    east coast; also, the flow through Baffin Bay and Davis Strait into
175    the Labrador Sea is reduced with respect the C-LSR-ns solution.
176    \ml{[Do we expect this? Say something about that]}
177    %
178    Compared to the differences between B and C-grid solutions,the
179    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
180    (\reffig{iceveloc}c).  As expected the differences are largest along
181    coastlines: because of the free-slip boundary conditions, flow is
182    faster in the C-LSR-fs solution, for example, along the east coast
183    of Greenland, the north coast of Alaska, and the east Coast of Baffin
184    Island.
185    \begin{figure}[htbp]
186      \centering
187      \subfigure[{\footnotesize C-LSR-ns}]
188      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}
189      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
190      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\
191      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
192      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}
193      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
194      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}
195      \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
196        over the first 3 months of integration [cm/s]; (b)-(d) difference
197        between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions
198        [cm/s]; color indicates speed (or differences of speed), vectors
199        indicate direction only.}
200      \label{fig:iceveloc}
201    \end{figure}
202    
203    The C-EVP-ns solution is very different from the C-LSR-ns solution
204    (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows
205    for increased drift by over 2\,cm/s in the Beaufort Gyre and the
206    transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska
207      in the C-EVP-ns solution. [Really?]} In general, drift velocities are
208    biased towards higher values in the EVP solutions as can be seen from
209    a histogram of the differences in \reffig{drifthist}.
210    \begin{figure}[htbp]
211      \centering
212      \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}
213      \caption{Histogram of drift velocity differences for C-LSR-ns and
214        C-EVP-ns solution [cm/s].}
215      \label{fig:drifthist}
216    \end{figure}
217    
218    \reffig{icethick}a shows the effective thickness (volume per unit
219    area) of the C-LSR-ns solution, averaged over January, February, March
220    of year 2000. By this time of the integration, the differences in the
221    ice drift velocities have led to the evolution of very different ice
222    thickness distributions, which are shown in \reffig{icethick}b--d, and
223    area distributions (not shown).  \ml{Compared to other solutions, for
224      example, AOMIP the ice thickness distribution blablabal}
225    \begin{figure}[htbp]
226      \centering
227      \subfigure[{\footnotesize C-LSR-ns}]
228      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}
229      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
230      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\
231      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
232      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}
233      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
234      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}
235      \caption{(a) Effective thickness (volume per unit area) of the
236        C-LSR-ns solution, averaged over the months Janurary through March
237        2000 [m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,
238        and C-LSR-ns solutions [cm/s].}
239      \label{fig:icethick}
240    \end{figure}
241    %
242    The generally weaker ice drift velocities in the B-LSR-ns solution,
243    when compared to the C-LSR-ns solution, in particular through the
244    narrow passages in the Canadian Archipelago, lead to a larger build-up
245    of ice north of Greenland and the Archipelago by 2\,m effective
246    thickness and more in the B-grid solution (\reffig{icethick}b). But
247    the ice volume in not larger everywhere: further west, there are
248    patches of smaller ice volume in the B-grid solution, most likely
249    because the Beaufort Gyre is weaker and hence not as effective in
250    transporting ice westwards. There are also dipoles of ice volume
251    differences with more ice on the \ml{luv [what is this in English?,
252      upstream]} and less ice in the the lee of island groups, such as
253    Franz-Josef-Land and \ml{IDONTKNOW}, because ice tends to flow along
254    coasts less easily in the B-LSR-ns solution.
255    
256    Imposing a free-slip boundary condition in C-LSR-fs leads to a much
257    smaller differences to C-LSR-ns than the transition from the B-grid to
258    the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
259    still reduces the effective ice thickness by up to 2\,m where the ice
260    is thick and the straits are narrow. Dipoles of ice thickness
261    differences can also be observed around islands, because the free-slip
262    solution allows more flow around islands than the no-slip solution.
263    Everywhere else the ice volume is affected only slightly by the
264    different boundary condition.
265    %
266    The C-EVP-ns solution has generally stronger drift velocities than the
267    C-LSR-ns solution. Consequently, more ice can be moved from the eastern
268    part of the Arctic, where ice volumes are smaller, to the western
269    Arctic where ice piles up along the coast (\reffig{icethick}d). Within
270    the Canadian Archipelago, more drift leads to faster ice export and
271    reduced effective ice thickness.
272    
273    The difference in ice volume and ice drift velocities between the
274    different experiments has consequences for the ice transport out of
275    the Arctic. Although the main export of ice goes through the Fram
276    Strait, a considerable amoung of ice is exported through the Canadian
277    Archipelago \citep{???}. \reffig{archipelago} shows a time series of
278    \ml{[maybe smooth to longer time scales:] daily averaged} ice
279    transport through various straits in the Canadian Archipelago and the
280    Fram Strait for the different model solutions.  Generally, the
281    C-EVP-ns solution has highest maximum (export out of the Artic) and
282    minimum (import into the Artic) fluxes as the drift velocities are
283    largest in this solution \ldots
284  \begin{figure}  \begin{figure}
285  %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
286  \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}  \caption{Transport through Canadian Archipelago for different solver
287      flavors. The letters refer to the labels of the sections in
288      \reffig{arctic_topog}.
289    \label{fig:archipelago}}
290  \end{figure}  \end{figure}
291    
292  There are 50 vertical levels ranging in thickness from 10 m near the surface  \ml{[Transport to narrow straits, area?, more runs, TEM, advection
293  to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from    schemes, Winton TD, discussion about differences in terms of model
294  the National Geophysical Data Center (NGDC) 2-minute gridded global relief    error? that's tricky as it means refering to Tremblay, thus our ice
295  data (ETOPO2) and the model employs the partial-cell formulation of    models are all erroneous!]}
296  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The  
297  model is integrated in a volume-conserving configuration using a finite volume  In summary, we find that different dynamical solvers can yield very
298  discretization with C-grid staggering of the prognostic variables. In the  different solutions. In contrast, the differences between free-slip
299  ocean, the non-linear equation of state of \citet{jackett95}.  The ocean model is  and no-slip solutions \emph{with the same solver} are considerably
300  coupled to a sea-ice model described hereinabove.    smaller (the difference for the EVP solver is not shown, but similar
301    to that for the LSOR solver). Albeit smaller, the differences between
302  This particular ECCO2 simulation is initialized from rest using the  free and no-slip solutions in ice drift can lead to large differences
303  January temperature and salinity distribution from the World Ocean  in ice volume over the integration time. At first, this observation
304  Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for  seems counterintuitive, as we expect that the solution
305  32 years prior to the 1996--2001 period discussed in the study. Surface  \emph{technique} should not affect the \emph{solution} to a higher
306  boundary conditions are from the National Centers for Environmental  degree than actually modifying the equations. A more detailed study on
307  Prediction and the National Center for Atmospheric Research  these differences is beyond the scope of this paper, but at this point
308  (NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly  we may speculate, that the large difference between B-grid, C-grid,
309  surface winds, temperature, humidity, downward short- and long-wave  LSOR, and EVP solutions stem from incomplete convergence of the
310  radiations, and precipitation are converted to heat, freshwater, and  solvers due to linearization and due to different methods of
311  wind stress fluxes using the \citet{large81, large82} bulk formulae.  linearization \citep[and Bruno Tremblay, personal
312  Shortwave radiation decays exponentially as per Paulson and Simpson  communication]{hunke01}: if the convergence of the non-linear momentum
313  [1977]. Additionally the time-mean river run-off from Large and Nurser  equations is not complete for all linearized solvers, then one can
314  [2001] is applied and there is a relaxation to the monthly-mean  imagine that each solver stops at a different point in velocity-space
315  climatological sea surface salinity values from WOA01 with a  thus leading to different solutions for the ice drift velocities. If
316  relaxation time scale of 3 months. Vertical mixing follows  this were true, this tantalizing circumstance had a dramatic impact on
317  \citet{large94} with background vertical diffusivity of  sea-ice modeling in general, and we would need to improve the solution
318  $1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of  technique of dynamic sea ice model, most likely at a very high
319  $10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time  compuational cost (Bruno Tremblay, personal communication).
320  advection scheme with flux limiter is employed \citep{hundsdorfer94}  
 and there is no explicit horizontal diffusivity. Horizontal viscosity  
 follows \citet{lei96} but  
 modified to sense the divergent flow as per Fox-Kemper and Menemenlis  
 [in press].  Shortwave radiation decays exponentially as per Paulson  
 and Simpson [1977].  Additionally, the time-mean runoff of Large and  
 Nurser [2001] is applied near the coastline and, where there is open  
 water, there is a relaxation to monthly-mean WOA01 sea surface  
 salinity with a time constant of 45 days.  
321    
 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.  
322    
323  \begin{itemize}  \begin{itemize}
324  \item Configuration  \item Configuration
# Line 135  ice, wet ice, dry snow, and wet snow alb Line 338  ice, wet ice, dry snow, and wet snow alb
338  \end{itemize}  \end{itemize}
339    
340  \begin{itemize}  \begin{itemize}
341  \item B-grid LSR no-slip  \item B-grid LSR no-slip: B-LSR-ns
342  \item C-grid LSR no-slip  \item C-grid LSR no-slip: C-LSR-ns
343  \item C-grid LSR slip  \item C-grid LSR slip:    C-LSR-fs
344  \item C-grid EVP no-slip  \item C-grid EVP no-slip: C-EVP-ns
345  \item C-grid EVP slip  \item C-grid EVP slip:    C-EVP-fs
346  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
347  \item C-grid LSR no-slip + Winton    new flag): C-LSR-ns+TEM
348    \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
349    \item C-grid LSR no-slip + Winton:
350  \item  speed-performance-accuracy (small)  \item  speed-performance-accuracy (small)
351    ice transport through Canadian Archipelago differences    ice transport through Canadian Archipelago differences
352    thickness distribution differences    thickness distribution differences
# Line 157  We anticipate small differences between Line 362  We anticipate small differences between
362  \item VP vs.\ EVP: speed performance, accuracy?  \item VP vs.\ EVP: speed performance, accuracy?
363  \item ocean stress: different water mass properties beneath the ice  \item ocean stress: different water mass properties beneath the ice
364  \end{itemize}  \end{itemize}
365    
366    %\begin{figure}
367    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
368    %\caption{Surface sea ice velocity for different solver flavors.
369    %\label{fig:iceveloc}}
370    %\end{figure}
371    
372    %\begin{figure}
373    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
374    %\caption{Sea ice thickness for different solver flavors.
375    %\label{fig:icethick}}
376    %\end{figure}
377    
378    %%% Local Variables:
379    %%% mode: latex
380    %%% TeX-master: "ceaice"
381    %%% End:
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