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.  

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 dyanmics model discussed
hereinabove.

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.

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


\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	\section{Forward sensitivity experiments}
2	\label{sec:forward}
3
4	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	are prognostic.
43
44	Ice mechanics follow the viscous plastic rheology of
45	\citet{hibler79} and the ice momentum equation is solved numerically using the
46	C-grid implementation of the \citet{zha97} LSR dyanmics model discussed
47	hereinabove.
48
49	Open water, dry
50	ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
51	0.76, 0.94, and 0.8.
52
53	\subsection{Arctic Domain with Open Boundaries}
54	\label{sec:arctic}
55
56
57	\subsection{Arctic Domain with Open Boundaries}
58	\label{sec:arctic}
59
60	A second series of forward sensitivity experiments have been carried out on an
61	Arctic Ocean domain with open boundaries. Once again the objective is to
62	compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP
63	solvers. One additional experiment is carried out to illustrate the
64	differences between the two main options for sea ice thermodynamics in the MITgcm.
65
66	The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}. It
67	is carved out from, and obtains open boundary conditions from, the
68	global cubed-sphere configuration of the Estimating the Circulation
69	and Climate of the Ocean, Phase II (ECCO2) project
70	\citet{menemenlis05}. The domain size is 420 by 384 grid boxes
71	horizontally with mean horizontal grid spacing of 18 km.
72
73	\begin{figure}
74	%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}
75	\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
76	\end{figure}
77
78	There are 50 vertical levels ranging in thickness from 10 m near the surface
79	to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
80	the National Geophysical Data Center (NGDC) 2-minute gridded global relief
81	data (ETOPO2) and the model employs the partial-cell formulation of
82	\citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The
83	model is integrated in a volume-conserving configuration using a finite volume
84	discretization with C-grid staggering of the prognostic variables. In the
85	ocean, the non-linear equation of state of \citet{jackett95}. The ocean model is
86	coupled to a sea-ice model described hereinabove.
87
88	This particular ECCO2 simulation is initialized from rest using the
89	January temperature and salinity distribution from the World Ocean
90	Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for
91	32 years prior to the 1996--2001 period discussed in the study. Surface
92	boundary conditions are from the National Centers for Environmental
93	Prediction and the National Center for Atmospheric Research
94	(NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly
95	surface winds, temperature, humidity, downward short- and long-wave
96	radiations, and precipitation are converted to heat, freshwater, and
97	wind stress fluxes using the \citet{large81, large82} bulk formulae.
98	Shortwave radiation decays exponentially as per Paulson and Simpson
99	[1977]. Additionally the time-mean river run-off from Large and Nurser
100	[2001] is applied and there is a relaxation to the monthly-mean
101	climatological sea surface salinity values from WOA01 with a
102	relaxation time scale of 3 months. Vertical mixing follows
103	\citet{large94} with background vertical diffusivity of
104	$1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of
105	$10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time
106	advection scheme with flux limiter is employed \citep{hundsdorfer94}
107	and there is no explicit horizontal diffusivity. Horizontal viscosity
108	follows \citet{lei96} but
109	modified to sense the divergent flow as per Fox-Kemper and Menemenlis
110	[in press]. Shortwave radiation decays exponentially as per Paulson
111	and Simpson [1977]. Additionally, the time-mean runoff of Large and
112	Nurser [2001] is applied near the coastline and, where there is open
113	water, there is a relaxation to monthly-mean WOA01 sea surface
114	salinity with a time constant of 45 days.
115
116	Open water, dry
117	ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
118	0.76, 0.94, and 0.8.
119
120	\begin{itemize}
121	\item Configuration
122	\item OBCS from cube
123	\item forcing
124	\item 1/2 and full resolution
125	\item with a few JFM figs from C-grid LSR no slip
126	ice transport through Canadian Archipelago
127	thickness distribution
128	ice velocity and transport
129	\end{itemize}
130
131	\begin{itemize}
132	\item Arctic configuration
133	\item ice transport through straits and near boundaries
134	\item focus on narrow straits in the Canadian Archipelago
135	\end{itemize}
136
137	\begin{itemize}
138	\item B-grid LSR no-slip
139	\item C-grid LSR no-slip
140	\item C-grid LSR slip
141	\item C-grid EVP no-slip
142	\item C-grid EVP slip
143	\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
144	\item C-grid LSR no-slip + Winton
145	\item speed-performance-accuracy (small)
146	ice transport through Canadian Archipelago differences
147	thickness distribution differences
148	ice velocity and transport differences
149	\end{itemize}
150
151	We anticipate small differences between the different models due to:
152	\begin{itemize}
153	\item advection schemes: along the ice-edge and regions with large
154	gradients
155	\item C-grid: less transport through narrow straits for no slip
156	conditons, more for free slip
157	\item VP vs.\ EVP: speed performance, accuracy?
158	\item ocean stress: different water mass properties beneath the ice
159	\end{itemize}