articles/ceaice/ceaice_forward.tex

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

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.

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

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	A second series of forward sensitivity experiments have been carried out on an
5	Arctic Ocean domain with open boundaries. Once again the objective is to
6	compare the old B-grid LSR dynamic solver with the new C-grid LSR and EVP
7	solvers. One additional experiment is carried out to illustrate the
8	differences between the two main options for sea ice thermodynamics in the MITgcm.
9
10	\subsection{Arctic Domain with Open Boundaries}
11	\label{sec:arctic}
12
13	The Arctic domain of integration is illustrated in Fig.~\ref{fig:arctic1}. It
14	is carved out from, and obtains open boundary conditions from, the
15	global cubed-sphere configuration of the Estimating the Circulation
16	and Climate of the Ocean, Phase II (ECCO2) project
17	\citet{menemenlis05}. The domain size is 420 by 384 grid boxes
18	horizontally with mean horizontal grid spacing of 18 km.
19
20	\begin{figure}
21	%\centerline{{\includegraphics*[width=0.44\linewidth]{\fpath/arctic1.eps}}}
22	\caption{Bathymetry of Arctic Domain.\label{fig:arctic1}}
23	\end{figure}
24
25	There are 50 vertical levels ranging in thickness from 10 m near the surface
26	to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
27	the National Geophysical Data Center (NGDC) 2-minute gridded global relief
28	data (ETOPO2) and the model employs the partial-cell formulation of
29	\citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The
30	model is integrated in a volume-conserving configuration using a finite volume
31	discretization with C-grid staggering of the prognostic variables. In the
32	ocean, the non-linear equation of state of \citet{jackett95}. The ocean model is
33	coupled to a sea-ice model described hereinabove.
34
35	This particular ECCO2 simulation is initialized from rest using the
36	January temperature and salinity distribution from the World Ocean
37	Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for
38	32 years prior to the 1996--2001 period discussed in the study. Surface
39	boundary conditions are from the National Centers for Environmental
40	Prediction and the National Center for Atmospheric Research
41	(NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly
42	surface winds, temperature, humidity, downward short- and long-wave
43	radiations, and precipitation are converted to heat, freshwater, and
44	wind stress fluxes using the \citet{large81, large82} bulk formulae.
45	Shortwave radiation decays exponentially as per Paulson and Simpson
46	[1977]. Additionally the time-mean river run-off from Large and Nurser
47	[2001] is applied and there is a relaxation to the monthly-mean
48	climatological sea surface salinity values from WOA01 with a
49	relaxation time scale of 3 months. Vertical mixing follows
50	\citet{large94} with background vertical diffusivity of
51	$1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of
52	$10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time
53	advection scheme with flux limiter is employed \citep{hundsdorfer94}
54	and there is no explicit horizontal diffusivity. Horizontal viscosity
55	follows \citet{lei96} but
56	modified to sense the divergent flow as per Fox-Kemper and Menemenlis
57	[in press]. Shortwave radiation decays exponentially as per Paulson
58	and Simpson [1977]. Additionally, the time-mean runoff of Large and
59	Nurser [2001] is applied near the coastline and, where there is open
60	water, there is a relaxation to monthly-mean WOA01 sea surface
61	salinity with a time constant of 45 days.
62
63	Open water, dry
64	ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
65	0.76, 0.94, and 0.8.
66
67	\begin{itemize}
68	\item Configuration
69	\item OBCS from cube
70	\item forcing
71	\item 1/2 and full resolution
72	\item with a few JFM figs from C-grid LSR no slip
73	ice transport through Canadian Archipelago
74	thickness distribution
75	ice velocity and transport
76	\end{itemize}
77
78	\begin{itemize}
79	\item Arctic configuration
80	\item ice transport through straits and near boundaries
81	\item focus on narrow straits in the Canadian Archipelago
82	\end{itemize}
83
84	\begin{itemize}
85	\item B-grid LSR no-slip
86	\item C-grid LSR no-slip
87	\item C-grid LSR slip
88	\item C-grid EVP no-slip
89	\item C-grid EVP slip
90	\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
91	\item C-grid LSR no-slip + Winton
92	\item speed-performance-accuracy (small)
93	ice transport through Canadian Archipelago differences
94	thickness distribution differences
95	ice velocity and transport differences
96	\end{itemize}
97
98	We anticipate small differences between the different models due to:
99	\begin{itemize}
100	\item advection schemes: along the ice-edge and regions with large
101	gradients
102	\item C-grid: less transport through narrow straits for no slip
103	conditons, more for free slip
104	\item VP vs.\ EVP: speed performance, accuracy?
105	\item ocean stress: different water mass properties beneath the ice
106	\end{itemize}