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} using 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{zhang97} LSR
dynamics model discussed hereinabove.  The ice is coupled to the ocean using
the rescaled vertical coordinate system, z$^\ast$, of
\citet{cam08}, that is, sea ice does not float above the ocean model but
rather deforms the ocean's model surface level.

This particular ECCO2 simulation is initialized from temperature and salinity
fields derived from the Polar science center Hydrographic Climatology (PHC)
3.0 \citep{ste01a}. Surface boundary conditions for the period January 1979 to
July 2002 are derived from the European Centre for Medium-Range Weather
Forecasts (ECMWF) 40 year re-analysis (ERA-40) \citep{upp05}.  Surface
boundary conditions after September 2002 are derived from the ECMWF
operational analysis.  There is a one month transition period, August 2002,
during which the ERA-40 contribution decreases linearly from 1 to 0 and the
ECMWF analysis contribution increases linearly from 0 to 1.  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 \citet{pau77}.  Low frequency
precipitation has been adjusted using the pentad (5-day) data from the Global
Precipitation Climatology Project (GPCP) \citep{huf01}.  The time-mean river
run-off from \citet{lar01} is applied globally, except in the Arctic Ocean
where monthly mean river runoff based on the Arctic Runoff Data Base (ARDB)
and prepared by P. Winsor (personnal communication, 2007) is specificied.
Additionally, there is a relaxation to the monthly-mean climatological sea
surface salinity values from PHC 3.0, a relaxation time scale of 101 days.

Vertical mixing follows \citet{lar94} but with meridionally and vertically
varying background vertical diffusivity; at the surface, vertical diffusivity
is $4.4\times 10^{-6}$~m$^2$~s$^{-1}$ at the Equator, $3.6\times
10^{-6}$~m$^2$~s$^{-1}$ north of 70$^\circ$N, and $1.9\times
10^{-5}$~m$^2$~s$^{-1}$ south of 30$^\circ$S and between 30$^\circ$N and
60$^\circ$N , with sinusoidally varying values in between these latitudes;
vertically, diffusivity increases to $1.1\times 10^{-4}$~m$^2$~s$^{-1}$ at a a
depth of 6150 m as per \citet{bry79}.  A high order monotonicity-preserving
advection scheme \citep{dar04} is employed and there is no explicit horizontal
diffusivity.  Horizontal viscosity follows \citet{lei96} but modified to sense
the divergent flow as per \citet{kem08}.

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

A series of forward sensitivity experiments have been carried out on an
Arctic Ocean domain with open boundaries.  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 described above.  The horizontal domain size is
420 by 384 grid boxes.

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

Difference from cube sphere is that it does not use z* coordinates nor
realfreshwater fluxes because it is not supported by open boundary code.

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}

\begin{figure}
\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
\caption{Surface sea ice velocity for different solver flavors.
\label{fig:iceveloc}}
\end{figure}

\begin{figure}
\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
\caption{Transport through Canadian Archipelago for different solver flavors.
\label{fig:archipelago}}
\end{figure}

\begin{figure}
\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
\caption{Sea ice thickness nsitivity for different solver flavors.
\label{fig:icethick}}
\end{figure}
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	dimitri	1.5	Section~\ref{sec:model} using the following specific options. The
40	dimitri	1.2	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	mlosch	1.4	solved numerically using the C-grid implementation of the \citet{zhang97} LSR
46	dimitri	1.5	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	dimitri	1.2
51	dimitri	1.3	This particular ECCO2 simulation is initialized from temperature and salinity
52	dimitri	1.5	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	dimitri	1.2
84			\subsection{Arctic Domain with Open Boundaries}
85			\label{sec:arctic}
86
87	dimitri	1.7	A series of forward sensitivity experiments have been carried out on an
88	dimitri	1.6	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	dimitri	1.1
93			The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}. It
94	dimitri	1.6	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	dimitri	1.1
98			\begin{figure}
99	dimitri	1.7	%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1}}}
100	dimitri	1.1	\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
101			\end{figure}
102
103	dimitri	1.6	Difference from cube sphere is that it does not use z* coordinates nor
104			realfreshwater fluxes because it is not supported by open boundary code.
105	dimitri	1.1
106			Open water, dry
107			ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
108			0.76, 0.94, and 0.8.
109
110			\begin{itemize}
111			\item Configuration
112			\item OBCS from cube
113			\item forcing
114			\item 1/2 and full resolution
115			\item with a few JFM figs from C-grid LSR no slip
116			ice transport through Canadian Archipelago
117			thickness distribution
118			ice velocity and transport
119			\end{itemize}
120
121			\begin{itemize}
122			\item Arctic configuration
123			\item ice transport through straits and near boundaries
124			\item focus on narrow straits in the Canadian Archipelago
125			\end{itemize}
126
127			\begin{itemize}
128			\item B-grid LSR no-slip
129			\item C-grid LSR no-slip
130			\item C-grid LSR slip
131			\item C-grid EVP no-slip
132			\item C-grid EVP slip
133			\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
134			\item C-grid LSR no-slip + Winton
135			\item speed-performance-accuracy (small)
136			ice transport through Canadian Archipelago differences
137			thickness distribution differences
138			ice velocity and transport differences
139			\end{itemize}
140
141			We anticipate small differences between the different models due to:
142			\begin{itemize}
143			\item advection schemes: along the ice-edge and regions with large
144			gradients
145			\item C-grid: less transport through narrow straits for no slip
146			conditons, more for free slip
147			\item VP vs.\ EVP: speed performance, accuracy?
148			\item ocean stress: different water mass properties beneath the ice
149			\end{itemize}
150	dimitri	1.6
151			\begin{figure}
152	dimitri	1.7	\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM1992uvice}}}
153			\caption{Surface sea ice velocity for different solver flavors.
154			\label{fig:iceveloc}}
155	dimitri	1.6	\end{figure}
156
157			\begin{figure}
158	dimitri	1.7	\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/Jan1992xport}}}
159			\caption{Transport through Canadian Archipelago for different solver flavors.
160			\label{fig:archipelago}}
161	dimitri	1.6	\end{figure}
162
163			\begin{figure}
164	dimitri	1.7	\centerline{{\includegraphics*[width=0.6\linewidth]{\fpath/JFM2000heff}}}
165			\caption{Sea ice thickness nsitivity for different solver flavors.
166			\label{fig:icethick}}
167	dimitri	1.6	\end{figure}