ceaice_split_version/ceaice_part1/ceaice_concl2.tex

\section{Conclusions}
\label{sec:concl}

We have shown that changes in discretization details, in boundary
conditions, and in sea-ice-dynamics formulation lead to considerable
differences in model results. Notably numerical formulation (for
example B-grid versus C-grid or EVP versus LSR) has as much, or even
greater, influence on solution than physical parameterizations (for
example free-slip versus no-slip boundary conditions). This is
especially true in regions of
\begin{itemize}
\item convergence as seen in the north of Greenland ice thickness in figure 4.
\item along coasts, see the eastern coast of Greenland in figure 3
(where velocity differences
are apparent).
\item in the vicinity of straits, see the Canadian Arctic Archipelago
in figures 3 and 4.
\end{itemize}
One upshot of all these experiments is that sea-ice export from the
Arctic into both the Baffin Bay and GIN (Greenland/Iceland/Norwegian) Sea
regions is highly sensitive to numerical formulation. Changes in
export in turn impact deep-water mass formation in the northern North
Atlantic and so uncertainties due to numerical formulation might
potentially have wide reaching impacts outside of the Arctic.

The relatively large differences between solutions with different
dynamical solvers is somewhat surprising. The expectation is that the
solution technique should not affect the solution to a higher degree
than actually modifying the equations.  The EVP solutions tend to
produce effectively ``weaker'' ice that yields more easily to stress
than the LSOR solutions , similar to the findings in \citet{hunke99}.
The differences between LSOR and EVP can, in part, stem from
incomplete convergence of the solvers due to linearization and due to
different methods of linearization \citep[and B. Tremblay, pers.
comm. 2008]{hunke01}.  However, we note that the EVP LSOR differences
decrease with descreasing sub-cycling time step but the difference
remains significant even at a 3 second sub-cycling period. For the
LSOR solutions we use 2 pseudo time steps, so that the convergence of
the non-linear momentum equations may not be complete
\citep{lemieux09}. However, this effect is most likely reduced and
constrained to small areas as in \citet{lemieux09} by the small time
step that we used. Whether more pseudo time steps make the LSOR
solution generate weaker ice remains unclear. Preliminary tests showed
that the viscositites even increase especially in areas of thick ice,
when the number of pseudo time steps is increased (not shown).

%[Reviewer 2: statement about robustness, against forcing, choice
%  of computational interval etc.:]
A few comments regarding the robustness of our results against choice
of forcing, integration period, and horizontal resolution follow.
Strictly speaking, our results refer to an 8-year integration with
18~km horizontal grid spacing.  We find that the differences between
the solutions have an obvious trend after the first season but that
this trend flattens out after a few seasons.  We do not expect the
differences to increase dramatically with additional integration time,
since the simulated multi-year sea ice has reached a quasi
equilibrium. Surface atmospheric conditions are specified every 6
hours. Models with weaker ice can react more quickly to a change in
wind forcing, therefore we speculate that the differences between EVP
and LSOR integrations would change with different forcing: less
variable wind forcing would lead to smaller differences, while larger
flucations in the forcing would increase them. In the same way, we
expect that with coarser grids, the ocean component is much less
variable so that in this case one will only find smaller differences
between ice models.

The MITgcm sea ice model
%makes possible,
enables, within the same code, the direct comparison of various widely
used dynamics and thermodynamics model components.  What sets apart
the MITgcm sea ice model from other current-generation sea ice models
is the ability to derive an accurate, stable, and efficient adjoint
model using automatic differentiation source transformation tools.
This capability is the topic of a companion, second paper. The adjoint
model greatly facilitates and enhances exploration of the model's
parameter space. It lays the foundation for coupled ocean and sea ice
state estimation.


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1	mlosch	1.1	\section{Conclusions}
2			\label{sec:concl}
3
4			We have shown that changes in discretization details, in boundary
5			conditions, and in sea-ice-dynamics formulation lead to considerable
6			differences in model results. Notably numerical formulation (for
7			example B-grid versus C-grid or EVP versus LSR) has as much, or even
8			greater, influence on solution than physical parameterizations (for
9			example free-slip versus no-slip boundary conditions). This is
10			especially true in regions of
11			\begin{itemize}
12			\item convergence as seen in the north of Greenland ice thickness in figure 4.
13			\item along coasts, see the eastern coast of Greenland in figure 3
14			(where velocity differences
15			are apparent).
16			\item in the vicinity of straits, see the Canadian Arctic Archipelago
17			in figures 3 and 4.
18			\end{itemize}
19			One upshot of all these experiments is that sea-ice export from the
20			Arctic into both the Baffin Bay and GIN (Greenland/Iceland/Norwegian) Sea
21			regions is highly sensitive to numerical formulation. Changes in
22			export in turn impact deep-water mass formation in the northern North
23			Atlantic and so uncertainties due to numerical formulation might
24			potentially have wide reaching impacts outside of the Arctic.
25
26			The relatively large differences between solutions with different
27			dynamical solvers is somewhat surprising. The expectation is that the
28			solution technique should not affect the solution to a higher degree
29			than actually modifying the equations. The EVP solutions tend to
30			produce effectively ``weaker'' ice that yields more easily to stress
31			than the LSOR solutions , similar to the findings in \citet{hunke99}.
32			The differences between LSOR and EVP can, in part, stem from
33			incomplete convergence of the solvers due to linearization and due to
34			different methods of linearization \citep[and B. Tremblay, pers.
35			comm. 2008]{hunke01}. However, we note that the EVP LSOR differences
36			decrease with descreasing sub-cycling time step but the difference
37			remains significant even at a 3 second sub-cycling period. For the
38			LSOR solutions we use 2 pseudo time steps, so that the convergence of
39			the non-linear momentum equations may not be complete
40			\citep{lemieux09}. However, this effect is most likely reduced and
41			constrained to small areas as in \citet{lemieux09} by the small time
42			step that we used. Whether more pseudo time steps make the LSOR
43			solution generate weaker ice remains unclear. Preliminary tests showed
44			that the viscositites even increase especially in areas of thick ice,
45			when the number of pseudo time steps is increased (not shown).
46
47			%[Reviewer 2: statement about robustness, against forcing, choice
48			% of computational interval etc.:]
49			A few comments regarding the robustness of our results against choice
50			of forcing, integration period, and horizontal resolution follow.
51			Strictly speaking, our results refer to an 8-year integration with
52			18~km horizontal grid spacing. We find that the differences between
53			the solutions have an obvious trend after the first season but that
54			this trend flattens out after a few seasons. We do not expect the
55			differences to increase dramatically with additional integration time,
56			since the simulated multi-year sea ice has reached a quasi
57			equilibrium. Surface atmospheric conditions are specified every 6
58			hours. Models with weaker ice can react more quickly to a change in
59			wind forcing, therefore we speculate that the differences between EVP
60			and LSOR integrations would change with different forcing: less
61			variable wind forcing would lead to smaller differences, while larger
62			flucations in the forcing would increase them. In the same way, we
63			expect that with coarser grids, the ocean component is much less
64			variable so that in this case one will only find smaller differences
65			between ice models.
66
67			The MITgcm sea ice model
68			%makes possible,
69			enables, within the same code, the direct comparison of various widely
70			used dynamics and thermodynamics model components. What sets apart
71			the MITgcm sea ice model from other current-generation sea ice models
72			is the ability to derive an accurate, stable, and efficient adjoint
73			model using automatic differentiation source transformation tools.
74			This capability is the topic of a companion, second paper. The adjoint
75			model greatly facilitates and enhances exploration of the model's
76			parameter space. It lays the foundation for coupled ocean and sea ice
77			state estimation.
78
79
80
81
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