articles/ceaice/ceaice_forward.tex

\section{Forward sensitivity experiments}
\label{sec:forward}

This section presents results from global and regional coupled ocean and sea
ice simulations that exercise various capabilities of the MITgcm sea ice
model.  The first set of results is from a global, eddy-permitting, ocean and
sea ice configuration.  The second set of results is from a regional Arctic
configuration, which is used to compare the B-grid and C-grid dynamic solvers
and various other capabilities of the MITgcm sea ice model.  The third set of
results is from a yet smaller regional domain, which is used to illustrate
treatment of sea ice open boundary condition sin the MITgcm.

\subsection{Global Ocean and Sea Ice Simulation}
\label{sec:global}

The global ocean and sea ice results presented below were carried out as part
of the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
project.  ECCO2 aims to produce increasingly accurate syntheses of all
available global-scale ocean and sea-ice data at resolutions that start to
resolve ocean eddies and other narrow current systems, which transport heat,
carbon, and other properties within the ocean \citep{menemenlis05}.  The
particular ECCO2 simulation discussed next is a baseline 28-year (1979-2006)
integration, labeled cube76, which has not yet been constrained by oceanic and
by sea ice data.  A cube-sphere grid projection is employed, which permits
relatively even grid spacing throughout the domain and which avoids polar
singularities \citep{adcroft04:_cubed_sphere}. Each face of the cube comprises
510 by 510 grid cells for a mean horizontal grid spacing of 18 km. There are
50 vertical levels ranging in thickness from 10 m near the surface to
approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from 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{jac95} is
used.

The ocean model is coupled to the sea-ice model discussed in
Section~\ref{sec:model} with the following specific options.  The
zero-heat-capacity thermodynamics formulation of \citet{hib80} is used to
compute sea ice thickness and concentration.  Snow cover and sea ice salinity
are prognostic.  Open water, dry ice, wet ice, dry snow, and wet snow albedo
are, respectively, 0.15, 0.88, 0.79, 0.97, and 0.83. Ice mechanics follow the
viscous plastic rheology of \citet{hibler79} and the ice momentum equation is
solved numerically using the C-grid implementation of the \citet{zha97} LSR
dynamics model discussed hereinabove.

This particular ECCO2 simulation is initialized from temperature and salinity
fields derived from the 


\subsection{Arctic Domain with Open Boundaries}
\label{sec:arctic}

A second series of forward sensitivity experiments have been carried out on an
Arctic Ocean domain with open boundaries.  Once again the objective is to
compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP
solvers.  One additional experiment is carried out to illustrate the
differences between the two main options for sea ice thermodynamics in the MITgcm.

The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}.  It
is carved out from, and obtains open boundary conditions from, the
global cubed-sphere configuration of the Estimating the Circulation
and Climate of the Ocean, Phase II (ECCO2) project
\citet{menemenlis05}.  The domain size is 420 by 384 grid boxes
horizontally with mean horizontal grid spacing of 18 km.

\begin{figure}
%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}
\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
\end{figure}

There are 50 vertical levels ranging in thickness from 10 m near the surface
to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
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.

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.

\begin{itemize}
\item Configuration
\item OBCS from cube
\item forcing
\item 1/2 and full resolution
\item with a few JFM figs from C-grid LSR no slip
  ice transport through Canadian Archipelago
  thickness distribution
  ice velocity and transport
\end{itemize}

\begin{itemize}
\item Arctic configuration
\item ice transport through straits and near boundaries
\item focus on narrow straits in the Canadian Archipelago
\end{itemize}

\begin{itemize}
\item B-grid LSR no-slip
\item C-grid LSR no-slip
\item C-grid LSR slip
\item C-grid EVP no-slip
\item C-grid EVP slip
\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
\item C-grid LSR no-slip + Winton
\item  speed-performance-accuracy (small)
  ice transport through Canadian Archipelago differences
  thickness distribution differences
  ice velocity and transport differences
\end{itemize}

We anticipate small differences between the different models due to:
\begin{itemize}
\item advection schemes: along the ice-edge and regions with large
  gradients
\item C-grid: less transport through narrow straits for no slip
  conditons, more for free slip
\item VP vs.\ EVP: speed performance, accuracy?
\item ocean stress: different water mass properties beneath the ice
\end{itemize}
1	dimitri	1.1	\section{Forward sensitivity experiments}
2			\label{sec:forward}
3
4	dimitri	1.2	This section presents results from global and regional coupled ocean and sea
5			ice simulations that exercise various capabilities of the MITgcm sea ice
6			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
8			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} with 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	dimitri	1.3	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{zha97} LSR
46			dynamics model discussed hereinabove.
47	dimitri	1.2
48	dimitri	1.3	This particular ECCO2 simulation is initialized from temperature and salinity
49			fields derived from the
50	dimitri	1.2
51
52
53			\subsection{Arctic Domain with Open Boundaries}
54			\label{sec:arctic}
55
56	dimitri	1.1	A second series of forward sensitivity experiments have been carried out on an
57			Arctic Ocean domain with open boundaries. Once again the objective is to
58			compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP
59			solvers. One additional experiment is carried out to illustrate the
60			differences between the two main options for sea ice thermodynamics in the MITgcm.
61
62			The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}. It
63			is carved out from, and obtains open boundary conditions from, the
64			global cubed-sphere configuration of the Estimating the Circulation
65			and Climate of the Ocean, Phase II (ECCO2) project
66			\citet{menemenlis05}. The domain size is 420 by 384 grid boxes
67			horizontally with mean horizontal grid spacing of 18 km.
68
69			\begin{figure}
70			%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}
71			\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
72			\end{figure}
73
74			There are 50 vertical levels ranging in thickness from 10 m near the surface
75			to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
76			the National Geophysical Data Center (NGDC) 2-minute gridded global relief
77			data (ETOPO2) and the model employs the partial-cell formulation of
78			\citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The
79			model is integrated in a volume-conserving configuration using a finite volume
80			discretization with C-grid staggering of the prognostic variables. In the
81			ocean, the non-linear equation of state of \citet{jackett95}. The ocean model is
82			coupled to a sea-ice model described hereinabove.
83
84			This particular ECCO2 simulation is initialized from rest using the
85			January temperature and salinity distribution from the World Ocean
86			Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for
87			32 years prior to the 1996--2001 period discussed in the study. Surface
88			boundary conditions are from the National Centers for Environmental
89			Prediction and the National Center for Atmospheric Research
90			(NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly
91			surface winds, temperature, humidity, downward short- and long-wave
92			radiations, and precipitation are converted to heat, freshwater, and
93			wind stress fluxes using the \citet{large81, large82} bulk formulae.
94			Shortwave radiation decays exponentially as per Paulson and Simpson
95			[1977]. Additionally the time-mean river run-off from Large and Nurser
96			[2001] is applied and there is a relaxation to the monthly-mean
97			climatological sea surface salinity values from WOA01 with a
98			relaxation time scale of 3 months. Vertical mixing follows
99			\citet{large94} with background vertical diffusivity of
100			$1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of
101			$10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time
102			advection scheme with flux limiter is employed \citep{hundsdorfer94}
103			and there is no explicit horizontal diffusivity. Horizontal viscosity
104			follows \citet{lei96} but
105			modified to sense the divergent flow as per Fox-Kemper and Menemenlis
106			[in press]. Shortwave radiation decays exponentially as per Paulson
107			and Simpson [1977]. Additionally, the time-mean runoff of Large and
108			Nurser [2001] is applied near the coastline and, where there is open
109			water, there is a relaxation to monthly-mean WOA01 sea surface
110			salinity with a time constant of 45 days.
111
112			Open water, dry
113			ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
114			0.76, 0.94, and 0.8.
115
116			\begin{itemize}
117			\item Configuration
118			\item OBCS from cube
119			\item forcing
120			\item 1/2 and full resolution
121			\item with a few JFM figs from C-grid LSR no slip
122			ice transport through Canadian Archipelago
123			thickness distribution
124			ice velocity and transport
125			\end{itemize}
126
127			\begin{itemize}
128			\item Arctic configuration
129			\item ice transport through straits and near boundaries
130			\item focus on narrow straits in the Canadian Archipelago
131			\end{itemize}
132
133			\begin{itemize}
134			\item B-grid LSR no-slip
135			\item C-grid LSR no-slip
136			\item C-grid LSR slip
137			\item C-grid EVP no-slip
138			\item C-grid EVP slip
139			\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
140			\item C-grid LSR no-slip + Winton
141			\item speed-performance-accuracy (small)
142			ice transport through Canadian Archipelago differences
143			thickness distribution differences
144			ice velocity and transport differences
145			\end{itemize}
146
147			We anticipate small differences between the different models due to:
148			\begin{itemize}
149			\item advection schemes: along the ice-edge and regions with large
150			gradients
151			\item C-grid: less transport through narrow straits for no slip
152			conditons, more for free slip
153			\item VP vs.\ EVP: speed performance, accuracy?
154			\item ocean stress: different water mass properties beneath the ice
155			\end{itemize}