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 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} 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}
85	\label{sec:arctic}
86
87	A second series of forward sensitivity experiments have been carried out on an
88	Arctic Ocean domain with open boundaries. Once again the objective is to
89	compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP
90	solvers. One additional experiment is carried out to illustrate the
91	differences between the 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
94	is carved out from, and obtains open boundary conditions from, the
95	global cubed-sphere configuration of the Estimating the Circulation
96	and Climate of the Ocean, Phase II (ECCO2) project
97	\citet{menemenlis05}. The domain size is 420 by 384 grid boxes
98	horizontally with mean horizontal grid spacing of 18 km.
99
100	\begin{figure}
101	%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}
102	\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
103	\end{figure}
104
105	There are 50 vertical levels ranging in thickness from 10 m near the surface
106	to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
107	the National Geophysical Data Center (NGDC) 2-minute gridded global relief
108	data (ETOPO2) and the model employs the partial-cell formulation of
109	\citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The
110	model is integrated in a volume-conserving configuration using a finite volume
111	discretization with C-grid staggering of the prognostic variables. In the
112	ocean, the non-linear equation of state of \citet{jackett95}. The ocean model is
113	coupled to a sea-ice model described hereinabove.
114
115	This particular ECCO2 simulation is initialized from rest using the
116	January temperature and salinity distribution from the World Ocean
117	Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for
118	32 years prior to the 1996--2001 period discussed in the study. Surface
119	boundary conditions are from the National Centers for Environmental
120	Prediction and the National Center for Atmospheric Research
121	(NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly
122	surface winds, temperature, humidity, downward short- and long-wave
123	radiations, and precipitation are converted to heat, freshwater, and
124	wind stress fluxes using the \citet{large81, large82} bulk formulae.
125	Shortwave radiation decays exponentially as per Paulson and Simpson
126	[1977]. Additionally the time-mean river run-off from Large and Nurser
127	[2001] is applied and there is a relaxation to the monthly-mean
128	climatological sea surface salinity values from WOA01 with a
129	relaxation time scale of 3 months. Vertical mixing follows
130	\citet{large94} with background vertical diffusivity of
131	$1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of
132	$10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time
133	advection scheme with flux limiter is employed \citep{hundsdorfer94}
134	and there is no explicit horizontal diffusivity. Horizontal viscosity
135	follows \citet{lei96} but
136	modified to sense the divergent flow as per Fox-Kemper and Menemenlis
137	[in press]. Shortwave radiation decays exponentially as per Paulson
138	and Simpson [1977]. Additionally, the time-mean runoff of Large and
139	Nurser [2001] is applied near the coastline and, where there is open
140	water, there is a relaxation to monthly-mean WOA01 sea surface
141	salinity with a time constant of 45 days.
142
143	Open water, dry
144	ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
145	0.76, 0.94, and 0.8.
146
147	\begin{itemize}
148	\item Configuration
149	\item OBCS from cube
150	\item forcing
151	\item 1/2 and full resolution
152	\item with a few JFM figs from C-grid LSR no slip
153	ice transport through Canadian Archipelago
154	thickness distribution
155	ice velocity and transport
156	\end{itemize}
157
158	\begin{itemize}
159	\item Arctic configuration
160	\item ice transport through straits and near boundaries
161	\item focus on narrow straits in the Canadian Archipelago
162	\end{itemize}
163
164	\begin{itemize}
165	\item B-grid LSR no-slip
166	\item C-grid LSR no-slip
167	\item C-grid LSR slip
168	\item C-grid EVP no-slip
169	\item C-grid EVP slip
170	\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
171	\item C-grid LSR no-slip + Winton
172	\item speed-performance-accuracy (small)
173	ice transport through Canadian Archipelago differences
174	thickness distribution differences
175	ice velocity and transport differences
176	\end{itemize}
177
178	We anticipate small differences between the different models due to:
179	\begin{itemize}
180	\item advection schemes: along the ice-edge and regions with large
181	gradients
182	\item C-grid: less transport through narrow straits for no slip
183	conditons, more for free slip
184	\item VP vs.\ EVP: speed performance, accuracy?
185	\item ocean stress: different water mass properties beneath the ice
186	\end{itemize}