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revision 1.2 by dimitri, Wed Feb 27 21:50:42 2008 UTC revision 1.10 by mlosch, Tue Mar 4 20:33:07 2008 UTC
# Line 36  variables. In the ocean, the non-linear Line 36  variables. In the ocean, the non-linear
36  used.  used.
37    
38  The ocean model is coupled to the sea-ice model discussed in  The ocean model is coupled to the sea-ice model discussed in
39  Section~\ref{sec:model} with the following specific options.  The  \refsec{model} using the following specific options.  The
40  zero-heat-capacity thermodynamics formulation of \citet{hib80} is used to  zero-heat-capacity thermodynamics formulation of \citet{hibler80} is used to
41  compute sea ice thickness and concentration.  Snow cover and sea ice salinity  compute sea ice thickness and concentration.  Snow cover and sea ice salinity
42  are prognostic.    are prognostic.  Open water, dry ice, wet ice, dry snow, and wet snow albedo
43    are, respectively, 0.15, 0.88, 0.79, 0.97, and 0.83. Ice mechanics follow the
44  Ice mechanics follow the viscous plastic rheology of  viscous plastic rheology of \citet{hibler79} and the ice momentum equation is
45  \citet{hibler79} and the ice momentum equation is solved numerically using the  solved numerically using the C-grid implementation of the \citet{zhang97} LSR
46  C-grid implementation of the \citet{zha97} LSR dyanmics model discussed  dynamics model discussed hereinabove.  The ice is coupled to the ocean using
47  hereinabove.  the rescaled vertical coordinate system, z$^\ast$, of
48    \citet{cam08}, that is, sea ice does not float above the ocean model but
49  Open water, dry  rather deforms the ocean's model surface level.
50  ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,  
51  0.76, 0.94, and 0.8.  This particular ECCO2 simulation is initialized from temperature and salinity
52    fields derived from the Polar science center Hydrographic Climatology (PHC)
53    3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to
54    July 2002 are derived from the European Centre for Medium-Range Weather
55    Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}.  Surface
56    boundary conditions after September 2002 are derived from the ECMWF
57    operational analysis.  There is a one month transition period, August 2002,
58    during which the ERA-40 contribution decreases linearly from 1 to 0 and the
59    ECMWF analysis contribution increases linearly from 0 to 1.  Six-hourly
60    surface winds, temperature, humidity, downward short- and long-wave
61    radiations, and precipitation are converted to heat, freshwater, and wind
62    stress fluxes using the \citet{large81,large82} bulk formulae.  Shortwave
63    radiation decays exponentially as per \citet{pau77}.  Low frequency
64    precipitation has been adjusted using the pentad (5-day) data from the Global
65    Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river
66    run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
67    where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
68    and prepared by P. Winsor (personnal communication, 2007) is specificied.
69    Additionally, there is a relaxation to the monthly-mean climatological sea
70    surface salinity values from PHC 3.0, a relaxation time scale of 101 days.
71    
72    Vertical mixing follows \citet{lar94} but with meridionally and vertically
73    varying background vertical diffusivity; at the surface, vertical diffusivity
74    is $4.4\times 10^{-6}$~m$^2$~s$^{-1}$ at the Equator, $3.6\times
75    10^{-6}$~m$^2$~s$^{-1}$ north of 70$^\circ$N, and $1.9\times
76    10^{-5}$~m$^2$~s$^{-1}$ south of 30$^\circ$S and between 30$^\circ$N and
77    60$^\circ$N , with sinusoidally varying values in between these latitudes;
78    vertically, diffusivity increases to $1.1\times 10^{-4}$~m$^2$~s$^{-1}$ at a a
79    depth of 6150 m as per \citet{bry79}.  A high order monotonicity-preserving
80    advection scheme \citep{dar04} is employed and there is no explicit horizontal
81    diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
82    the divergent flow as per \citet{kem08}.
83    
84  \subsection{Arctic Domain with Open Boundaries}  \subsection{Arctic Domain with Open Boundaries}
85  \label{sec:arctic}  \label{sec:arctic}
86    
87    A series of forward sensitivity experiments have been carried out on an
88    Arctic Ocean domain with open boundaries.  The objective is to compare the old
89    B-grid LSR dynamic solver with the new C-grid LSR and EVP solvers.  One
90    additional experiment is carried out to illustrate the differences between the
91    two main options for sea ice thermodynamics in the MITgcm.
92    
93    The Arctic domain of integration is illustrated in \reffig{arctic1}.  It
94    is carved out from, and obtains open boundary conditions from, the global
95    cubed-sphere configuration described above.  The horizontal domain size is
96    420 by 384 grid boxes.
97    
98  \subsection{Arctic Domain with Open Boundaries}  \begin{figure}
99  \label{sec:arctic}  \centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/topography}}}
100    \caption{Bathymetry and domain boudaries of Arctic
101      Domain.\label{fig:arctic1}}
102    \end{figure}
103    
104    The main dynamic difference from cube sphere is that it does not use
105    rescaled vertical coordinates (z$^\ast$) and the surface boundary
106    conditions for freshwater input are different, because those features
107    are not supported by the open boundary code.
108    
109    Open water, dry ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
110    0.76, 0.94, and 0.8.
111    
112    The model is integrated from January, 1992 to March \ml{[???]}, 2000,
113    with five different dynamical solvers:
114    \begin{description}
115    \item[B-LSR-ns:] the original LSOR solver of \citet{zhang97} on an Arakawa
116      B-grid, implying no-slip lateral boundary conditions;
117    \item[C-LSR-ns:] the LSOR solver discretized on a C-grid with no-slip lateral
118      boundary conditions;
119    \item[C-LSR-fs:] the LSOR solver on a C-grid with free-slip lateral boundary
120      conditions;
121    \item[C-EVP-ns:] the EVP solver of \citet{hunke01} on a C-grid with
122      no-slip lateral boundary conditions; and
123    \item[C-EVP-fs:] the EVP solver on a C-grid with free-slip lateral
124      boundary conditions.
125    \end{description}
126    Both LSOR and EVP solvers solve the same viscous-plastic rheology, so
127    that differences between runs B-LSR-ns, C-LSR-ns, and C-EVP-ns can be
128    interpreted as pure model error. Lateral boundary conditions on a
129    coarse grid (compared to the roughness of the true coast line) are
130    unclear, so that comparing the no-slip solutions to the free-slip
131    solutions gives another measure of uncertainty in sea ice modeling.
132    
133    A principle difficulty in comparing the solutions obtained with
134    different variants of the dynamics solver lies in the non-linear
135    feedback of the ice dynamics and thermodynamics. Already after a few
136    months the solutions have diverged so far from each other that
137    comparing velocities only makes sense within the first 3~months of the
138    integration while the ice distribution is still close to the initial
139    conditions. At the end of the integration, the differences between the
140    model solutions can be interpreted as cumulated model uncertainties.
141    
142    \reffig{iceveloc} shows ice velocities averaged over Janunary,
143    February, and March (JFM) of 1992 for the C-LSR-ns solution; also
144    shown are the differences between B-grid and C-grid, LSR and EVP, and
145    no-slip and free-slip solution. The velocity field of the C-LSR-ns
146    solution (\reffig{iceveloc}a) roughly resembles the drift velocities
147    of some of the AOMIP (Arctic Ocean Model Intercomparison Project)
148    models in an cyclonic circulation regime (CCR) \citep[their
149    Figure\,6]{martin07} with a Beaufort Gyre and a transpolar drift
150    shifted eastwards towards Alaska.
151    
152    The difference beween runs C-LSR-ns and B-LSR-ns (\reffig{iceveloc}b)
153    is most pronounced
154    along the coastlines, where the discretization differs most between B
155    and C-grids: On a B-grid the tangential velocity is on the boundary
156    (and thus zero per the no-slip boundary conditions), whereas on the
157    C-grid the its half a cell width away from the boundary, thus allowing
158    more flow. The B-LSR-ns solution has less ice drift through the Fram
159    Strait and especially the along Greenland's east coast; also, the flow
160    through Baffin Bay and Davis Strait into the Labrador Sea is reduced
161    with respect the C-LSR-ns solution. \ml{[Do we expect this? Say
162      something about that]}
163    %
164    Compared to the differences between B and C-grid solutions the
165    C-LSR-fs ice drift field differs much less from the C-LSR-ns solution
166    (\reffig{iceveloc}c).  As expected the differences are largest along
167    coastlines: because of the free-slip boundary conditions, flow is
168    faster in the C-LSR-fs solution, for example, along the east coast
169    of Greenland, the north coast of Alaska, and the east Coast of Baffin
170    Island.
171    \begin{figure}[htbp]
172      \centering
173      \subfigure[{\footnotesize C-LSR-ns}]
174      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_noslip}}
175      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
176      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_bgrid-lsr_noslip}}\\
177      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
178      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_lsr_slip-lsr_noslip}}
179      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
180      {\includegraphics[width=0.44\textwidth]{\fpath/JFMuv_evp_noslip-lsr_noslip}}
181      \caption{(a) Ice drift velocity of the C-LSR-ns solution averaged
182        over the first 3 months of integration [cm/s]; (b)-(d) difference
183        between B-LSR-ns, C-LSR-fs, C-EVP-ns, and C-LSR-ns solutions
184        [cm/s]; color indicates speed (or differences of speed), vectors
185        indicate direction only.}
186      \label{fig:iceveloc}
187    \end{figure}
188    
189    The C-EVP-ns solution is very different from the C-LSR-ns solution
190    (\reffig{iceveloc}d). The EVP-approximation of the VP-dynamics allows
191    for increased drift by over 2\,cm/s in the Beaufort Gyre and the
192    transarctic drift. \ml{Also the Beaufort Gyre is moved towards Alaska
193      in the C-EVP-ns solution. [Really?]} In general, drift velocities are
194    biased towards higher values in the EVP solutions as can be seen from
195    a histogram of the differences in \reffig{drifthist}.
196    \begin{figure}[htbp]
197      \centering
198      \includegraphics[width=\textwidth]{\fpath/drifthist_evp_noslip-lsr_noslip}
199      \caption{Histogram of drift velocity differences for C-LSR-ns and
200        C-EVP-ns solution [cm/s].}
201      \label{fig:drifthist}
202    \end{figure}
203    
204  A second series of forward sensitivity experiments have been carried out on an  \reffig{icethick}a shows the effective thickness (volume per unit
205  Arctic Ocean domain with open boundaries.  Once again the objective is to  area) of the C-LSR-ns solution, averaged over January, February, March
206  compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP  of year 2000. By this time of the integration, the differences in the
207  solvers.  One additional experiment is carried out to illustrate the  ice drift velocities have led to the evolution of very different ice
208  differences between the two main options for sea ice thermodynamics in the MITgcm.  thickness distributions, which are shown in \reffig{icethick}b--d, and
209    area distributions (not shown).  \ml{Compared to other solutions, for
210  The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It    example, AOMIP the ice thickness distribution blablabal} \ml{[What
211  is carved out from, and obtains open boundary conditions from, the    can I say about effective thickness?]}
212  global cubed-sphere configuration of the Estimating the Circulation  \begin{figure}[htbp]
213  and Climate of the Ocean, Phase II (ECCO2) project    \centering
214  \citet{menemenlis05}.  The domain size is 420 by 384 grid boxes    \subfigure[{\footnotesize C-LSR-ns}]
215  horizontally with mean horizontal grid spacing of 18 km.    {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_noslip}}
216      \subfigure[{\footnotesize B-LSR-ns $-$ C-LSR-ns}]
217      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_bgrid-lsr_noslip}}\\
218      \subfigure[{\footnotesize C-LSR-fs $-$ C-LSR-ns}]
219      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_lsr_slip-lsr_noslip}}
220      \subfigure[{\footnotesize C-EVP-ns $-$ C-LSR-ns}]
221      {\includegraphics[width=0.44\textwidth]{\fpath/JFMheff2000_evp_noslip-lsr_noslip}}
222      \caption{(a) Effective thickness (volume per unit area) of the
223        C-LSR-ns solution, averaged over the months Janurary through March
224        2000 [m]; (b)-(d) difference between B-LSR-ns, C-LSR-fs, C-EVP-ns,
225        and C-LSR-ns solutions [cm/s].}
226      \label{fig:icethick}
227    \end{figure}
228    
229    The generally weaker ice drift velocities in the B-LSR-ns solution,
230    when compared to the C-LSR-ns solution, in particular through the
231    narrow passages in the Canadian Archipelago, lead to a larger build-up
232    of ice north of Greenland and the Archipelago by 2\,m effective
233    thickness and more in the B-grid solution (\reffig{icethick}b). But
234    the ice volume in not larger everywhere: further west, there are
235    patches of smaller ice volume in the B-grid solution, most likely
236    because the Beaufort Gyre is weaker and hence not as effective in
237    transporting ice westwards. There are also dipoles of ice volume
238    differences on the \ml{luv [what is this in English?]} and the lee of
239    island groups, such as Franz-Josef-Land and \ml{IDONTKNOW}, which
240    \ml{\ldots [I find hard to interpret].}
241    
242    Imposing a free-slip boundary condition in C-LSR-fs leads to a much
243    smaller differences to C-LSR-ns than the transition from the B-grid to
244    the C-grid (\reffig{icethick}c), but in the Canadian Archipelago it
245    still reduces the effective ice thickness by up to 2\,m where the ice
246    is thick and the straits are narrow. Everywhere else the ice volume is
247    affected only slightly by the different boundary condition.
248    %
249    The C-EVP-ns solution has generally stronger drift velocities then the
250    C-LSR-ns solution. Consequently, more ice can be moved the eastern
251    part of the Arctic, where ice volumes are smaller, to the western
252    Arctic where ice piles up along the coast (\reffig{icethick}d). Within
253    the Canadian Archipelago, more drift leads to faster ice export and
254    reduced effective ice thickness.
255    
256    The difference in ice volume and ice drift velocities between the
257    different experiments has consequences for the ice transport out of
258    the Arctic. Although the main export of ice goes through the Fram
259    Strait, a considerable amoung of ice is exported through the Canadian
260    Archipelago \citep{???}. \reffig{archipelago} shows a time series of
261    daily averages ice transport through various straits in the Canadian
262    Archipelago and the Fram Strait for the different model solutions.
263    Generally, the C-EVP-ns solution has highest maxiumum (export out of
264    the Artic) and minimum (import into the Artic) fluxes as the drift
265    velocities area largest in this solution \ldots
266  \begin{figure}  \begin{figure}
267  %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}  \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
268  \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}  \caption{Transport through Canadian Archipelago for different solver flavors.
269    \label{fig:archipelago}}
270  \end{figure}  \end{figure}
271    
272  There are 50 vertical levels ranging in thickness from 10 m near the surface  \ml{[Transport to narrow straits, area?, more runs, TEM, advection
273  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
274  the National Geophysical Data Center (NGDC) 2-minute gridded global relief    error? that's tricky as it means refering to Tremblay, thus our ice
275  data (ETOPO2) and the model employs the partial-cell formulation of    models are all erroneous!]}
276  \citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The  
277  model is integrated in a volume-conserving configuration using a finite volume  In summary, we find that different dynamical solvers can yield very
278  discretization with C-grid staggering of the prognostic variables. In the  different solutions. Compared to that the differences between
279  ocean, the non-linear equation of state of \citet{jackett95}.  The ocean model is  free-slip and no-slip solutions \emph{with the same solver} are
280  coupled to a sea-ice model described hereinabove.    considerably smaller (the difference for the EVP solver is not shown,
281    but comparable to that for the LSOR solver)---albeit smaller, the
282  This particular ECCO2 simulation is initialized from rest using the  differences between free and no-slip solutions in ice drift can lead
283  January temperature and salinity distribution from the World Ocean  to large differences in ice volume over integration time. At first,
284  Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for  this observation appears counterintuitive, as we expect that the
285  32 years prior to the 1996--2001 period discussed in the study. Surface  solution \emph{technique} should not affect the \emph{solution} to a
286  boundary conditions are from the National Centers for Environmental  lower degree than actually modifying the equations. A more detailed
287  Prediction and the National Center for Atmospheric Research  study on these differences is beyond the scope of this paper, but at
288  (NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly  this point we may speculate, that the large difference between B-grid,
289  surface winds, temperature, humidity, downward short- and long-wave  C-grid, LSOR, and EVP solutions stem from incomplete convergence of
290  radiations, and precipitation are converted to heat, freshwater, and  the solvers due to linearization \citep[and Bruno Tremblay, personal
291  wind stress fluxes using the \citet{large81, large82} bulk formulae.  communication]{hunke01}: if the convergence of the non-linear momentum
292  Shortwave radiation decays exponentially as per Paulson and Simpson  equations is not complete for all linearized solvers, then one can
293  [1977]. Additionally the time-mean river run-off from Large and Nurser  imagine that each solver stops at a different point in velocity-space
294  [2001] is applied and there is a relaxation to the monthly-mean  thus leading to different solutions for the ice drift velocities. If
295  climatological sea surface salinity values from WOA01 with a  this were true, this tantalizing circumstance had a dramatic impact on
296  relaxation time scale of 3 months. Vertical mixing follows  sea-ice modeling in general, and we would need to improve the solution
297  \citet{large94} with background vertical diffusivity of  technique of dynamic sea ice model, most likely at a very high
298  $1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of  compuational cost (Bruno Tremblay, personal communication).
299  $10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time  
 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.  
300    
 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.  
301    
302  \begin{itemize}  \begin{itemize}
303  \item Configuration  \item Configuration
# Line 135  ice, wet ice, dry snow, and wet snow alb Line 317  ice, wet ice, dry snow, and wet snow alb
317  \end{itemize}  \end{itemize}
318    
319  \begin{itemize}  \begin{itemize}
320  \item B-grid LSR no-slip  \item B-grid LSR no-slip: B-LSR-ns
321  \item C-grid LSR no-slip  \item C-grid LSR no-slip: C-LSR-ns
322  \item C-grid LSR slip  \item C-grid LSR slip:    C-LSR-fs
323  \item C-grid EVP no-slip  \item C-grid EVP no-slip: C-EVP-ns
324  \item C-grid EVP slip  \item C-grid EVP slip:    C-EVP-fs
325  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)  \item C-grid LSR + TEM (truncated ellipse method, no tensile stress,
326  \item C-grid LSR no-slip + Winton    new flag): C-LSR-ns+TEM
327    \item C-grid LSR with different advection scheme: 33 vs 77, vs. default?
328    \item C-grid LSR no-slip + Winton:
329  \item  speed-performance-accuracy (small)  \item  speed-performance-accuracy (small)
330    ice transport through Canadian Archipelago differences    ice transport through Canadian Archipelago differences
331    thickness distribution differences    thickness distribution differences
# Line 157  We anticipate small differences between Line 341  We anticipate small differences between
341  \item VP vs.\ EVP: speed performance, accuracy?  \item VP vs.\ EVP: speed performance, accuracy?
342  \item ocean stress: different water mass properties beneath the ice  \item ocean stress: different water mass properties beneath the ice
343  \end{itemize}  \end{itemize}
344    
345    %\begin{figure}
346    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
347    %\caption{Surface sea ice velocity for different solver flavors.
348    %\label{fig:iceveloc}}
349    %\end{figure}
350    
351    %\begin{figure}
352    %\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
353    %\caption{Sea ice thickness for different solver flavors.
354    %\label{fig:icethick}}
355    %\end{figure}
356    
357    %%% Local Variables:
358    %%% mode: latex
359    %%% TeX-master: "ceaice"
360    %%% End:
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