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1  \section{Forward sensitivity experiments}  \section{Forward sensitivity experiments}
2  \label{sec:forward}  \label{sec:forward}
3    
4  A second series of forward sensitivity experiments have been carried out on an  This section presents results from global and regional coupled ocean and sea
5  Arctic Ocean domain with open boundaries.  Once again the objective is to  ice simulations that exercise various capabilities of the MITgcm sea ice
6  compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP  model.  The first set of results is from a global, eddy-permitting, ocean and
7  solvers.  One additional experiment is carried out to illustrate the  sea ice configuration.  The second set of results is from a regional Arctic
8  differences between the two main options for sea ice thermodynamics in the MITgcm.  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
10    results is from a yet smaller regional domain, which is used to illustrate
11    treatment of sea ice open boundary condition sin the MITgcm.
12    
13    \subsection{Global Ocean and Sea Ice Simulation}
14    \label{sec:global}
15    
16    The global ocean and sea ice results presented below were carried out as part
17    of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
18    project.  ECCO2 aims to produce increasingly accurate syntheses of all
19    available global-scale ocean and sea-ice data at resolutions that start to
20    resolve ocean eddies and other narrow current systems, which transport heat,
21    carbon, and other properties within the ocean \citep{menemenlis05}.  The
22    particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)
23    integration, labeled cube76, which has not yet been constrained by oceanic and
24    by sea ice data.  A cube-sphere grid projection is employed, which permits
25    relatively even grid spacing throughout the domain and which avoids polar
26    singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
27    510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are
28    50 vertical levels ranging in thickness from 10 m near the surface to
29    approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from the
30    National Geophysical Data Center (NGDC) 2-minute gridded global relief data
31    (ETOPO2) and the model employs the partial-cell formulation of
32    \citet{adcroft97:_shaved_cells}, which permits accurate representation of the
33    bathymetry. The model is integrated in a volume-conserving configuration using
34    a finite volume discretization with C-grid staggering of the prognostic
35    variables. In the ocean, the non-linear equation of state of \citet{jac95} is
36    used.
37    
38    The ocean model is coupled to the sea-ice model discussed in
39    Section~\ref{sec:model} using the following specific options.  The
40    zero-heat-capacity thermodynamics formulation of \citet{hib80} is used to
41    compute sea ice thickness and concentration.  Snow cover and sea ice salinity
42    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    viscous plastic rheology of \citet{hibler79} and the ice momentum equation is
45    solved numerically using the C-grid implementation of the \citet{zhang97} LSR
46    dynamics model discussed hereinabove.  The ice is coupled to the ocean using
47    the rescaled vertical coordinate system, z$^\ast$, of
48    \citet{cam08}, that is, sea ice does not float above the ocean model but
49    rather deforms the ocean's model surface level.
50    
51    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 Fig.~\ref{fig:arctic1}.  It  The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It
94  is carved out from, and obtains open boundary conditions from, the  is carved out from, and obtains open boundary conditions from, the global
95  global cubed-sphere configuration of the Estimating the Circulation  cubed-sphere configuration described above.  The horizontal domain size is
96  and Climate of the Ocean, Phase II (ECCO2) project  420 by 384 grid boxes.
 \citet{menemenlis05}.  The domain size is 420 by 384 grid boxes  
 horizontally with mean horizontal grid spacing of 18 km.  
97    
98  \begin{figure}  \begin{figure}
99  %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}  %\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1}}}
100  \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}  \caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
101  \end{figure}  \end{figure}
102    
103  There are 50 vertical levels ranging in thickness from 10 m near the surface  Difference from cube sphere is that it does not use z* coordinates nor
104  to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from  realfreshwater fluxes because it is not supported by open boundary code.
 the National Geophysical Data Center (NGDC) 2-minute gridded global relief  
 data (ETOPO2) and the model employs the partial-cell formulation of  
 \citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The  
 model is integrated in a volume-conserving configuration using a finite volume  
 discretization with C-grid staggering of the prognostic variables. In the  
 ocean, the non-linear equation of state of \citet{jackett95}.  The ocean model is  
 coupled to a sea-ice model described hereinabove.    
   
 This particular ECCO2 simulation is initialized from rest using the  
 January temperature and salinity distribution from the World Ocean  
 Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for  
 32 years prior to the 1996--2001 period discussed in the study. Surface  
 boundary conditions are from the National Centers for Environmental  
 Prediction and the National Center for Atmospheric Research  
 (NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly  
 surface winds, temperature, humidity, downward short- and long-wave  
 radiations, and precipitation are converted to heat, freshwater, and  
 wind stress fluxes using the \citet{large81, large82} bulk formulae.  
 Shortwave radiation decays exponentially as per Paulson and Simpson  
 [1977]. Additionally the time-mean river run-off from Large and Nurser  
 [2001] is applied and there is a relaxation to the monthly-mean  
 climatological sea surface salinity values from WOA01 with a  
 relaxation time scale of 3 months. Vertical mixing follows  
 \citet{large94} with background vertical diffusivity of  
 $1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of  
 $10^{-3}\text{\,m$^{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.  
105    
106  Open water, dry  Open water, dry
107  ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,  ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
# Line 104  We anticipate small differences between Line 147  We anticipate small differences between
147  \item VP vs.\ EVP: speed performance, accuracy?  \item VP vs.\ EVP: speed performance, accuracy?
148  \item ocean stress: different water mass properties beneath the ice  \item ocean stress: different water mass properties beneath the ice
149  \end{itemize}  \end{itemize}
150    
151    \begin{figure}
152    \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
153    \caption{Surface sea ice velocity for different solver flavors.
154    \label{fig:iceveloc}}
155    \end{figure}
156    
157    \begin{figure}
158    \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
159    \caption{Transport through Canadian Archipelago for different solver flavors.
160    \label{fig:archipelago}}
161    \end{figure}
162    
163    \begin{figure}
164    \centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
165    \caption{Sea ice thickness for different solver flavors.
166    \label{fig:icethick}}
167    \end{figure}
168    
169    %%% Local Variables:
170    %%% mode: latex
171    %%% TeX-master: "ceaice"
172    %%% End:
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