articles/ceaice/ceaice_intro.tex

\section{Introduction}
\label{sec:intro}

In the past five years, oceanographic state estimation has matured to the
extent that estimates of the evolving circulation of the ocean constrained by
in-situ and remotely sensed global observations are now routinely available
and being applied to myriad scientific problems \citep{wun07}.  Ocean state
estimation is the process of fitting an ocean general circulation model (GCM)
to a multitude of observations.  As formulated by the consortium Estimating
the Circulation and Climate of the Ocean (ECCO), an automatic differentiation
tool is used to calculate the so-called adjoint code of a GCM.  The method of
Lagrange multipliers is then used to render the problem one of unconstrained
least-squares minimization.  Although much has been achieved, the existing
ECCO estimates lack intercative sea ice.  This limits the ability of ECCO to
utilize satellite data constraints over sea-ice covered regions.  This also
limits the usefulness of the ECCO ocean state estimates for describing and
studying polar-subpolar interactions.

The availability of an adjoint model as a powerful research tool
complementary to an ocean model was a major design requirement early
on in the development of the MIT general circulation model (MITgcm)
[Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It
was recognized that the adjoint model permitted computing the
gradients of various scalar-valued model diagnostics, norms or,
generally, objective functions with respect to external or independent
parameters very efficiently. The information associtated with these
gradients is useful in at least two major contexts. First, for state
estimation problems, the objective function is the sum of squared
differences between observations and model results weighted by the
inverse error covariances. The gradient of such an objective function
can be used to reduce this measure of model-data misfit to find the
optimal model solution in a least-squares sense.  Second, the
objective function can be a key oceanographic quantity such as
meridional heat or volume transport, ocean heat content or mean
surface temperature index. In this case the gradient provides a
complete set of sensitivities of this quantity to all independent
variables simultaneously. These sensitivities can be used to address
the cause of, say, changing net transports accurately.

References to existing sea-ice adjoint models, explaining that they are either
for simplified configurations, for ice-only studies, or for short-duration
studies to motivate the present work.

Traditionally, probably for historical reasons and the ease of
treating the Coriolis term, most standard sea-ice models are
discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
  kreyscher00, zhang98, hunke97}, although there are sea ice models
diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
  lemieux09}. %
\ml{[there is also MI-IM, but I only found this as a reference:
  \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
From the perspective of coupling a sea ice-model to a C-grid ocean
model, the exchange of fluxes of heat and fresh-water pose no
difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
However, surface stress is defined at velocities points and thus needs
to be interpolated between a B-grid sea-ice model and a C-grid ocean
model. Smoothing implicitly associated with this interpolation may
mask grid scale noise and may contribute to stabilizing the solution.
On the other hand, by smoothing the stress signals are damped which
could lead to reduced variability of the system. By choosing a C-grid
for the sea-ice model, we circumvent this difficulty altogether and
render the stress coupling as consistent as the buoyancy coupling.

A further advantage of the C-grid formulation is apparent in narrow
straits. In the limit of only one grid cell between coasts there is no
flux allowed for a B-grid (with no-slip lateral boundary counditions),
and models have used topographies with artificially widened straits to
avoid this problem \citep{holloway07}. The C-grid formulation on the
other hand allows a flux of sea-ice through narrow passages if
free-slip along the boundaries is allowed. We demonstrate this effect
in the Candian archipelago.

Talk about problems that make the sea-ice-ocean code very sensitive and
changes in the code that reduce these sensitivities.

This paper describes the MITgcm sea ice model; it presents example
Arctic and Antarctic results from a realistic, eddy-permitting, global
ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
solvers and investigates further aspects of sea ice modeling in a
regional Arctic configuration; and it presents example results from
coupled ocean and sea-ice adjoint-model integrations.

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1	\section{Introduction}
2	\label{sec:intro}
3
4	In the past five years, oceanographic state estimation has matured to the
5	extent that estimates of the evolving circulation of the ocean constrained by
6	in-situ and remotely sensed global observations are now routinely available
7	and being applied to myriad scientific problems \citep{wun07}. Ocean state
8	estimation is the process of fitting an ocean general circulation model (GCM)
9	to a multitude of observations. As formulated by the consortium Estimating
10	the Circulation and Climate of the Ocean (ECCO), an automatic differentiation
11	tool is used to calculate the so-called adjoint code of a GCM. The method of
12	Lagrange multipliers is then used to render the problem one of unconstrained
13	least-squares minimization. Although much has been achieved, the existing
14	ECCO estimates lack intercative sea ice. This limits the ability of ECCO to
15	utilize satellite data constraints over sea-ice covered regions. This also
16	limits the usefulness of the ECCO ocean state estimates for describing and
17	studying polar-subpolar interactions.
18
19	The availability of an adjoint model as a powerful research tool
20	complementary to an ocean model was a major design requirement early
21	on in the development of the MIT general circulation model (MITgcm)
22	[Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It
23	was recognized that the adjoint model permitted computing the
24	gradients of various scalar-valued model diagnostics, norms or,
25	generally, objective functions with respect to external or independent
26	parameters very efficiently. The information associtated with these
27	gradients is useful in at least two major contexts. First, for state
28	estimation problems, the objective function is the sum of squared
29	differences between observations and model results weighted by the
30	inverse error covariances. The gradient of such an objective function
31	can be used to reduce this measure of model-data misfit to find the
32	optimal model solution in a least-squares sense. Second, the
33	objective function can be a key oceanographic quantity such as
34	meridional heat or volume transport, ocean heat content or mean
35	surface temperature index. In this case the gradient provides a
36	complete set of sensitivities of this quantity to all independent
37	variables simultaneously. These sensitivities can be used to address
38	the cause of, say, changing net transports accurately.
39
40	References to existing sea-ice adjoint models, explaining that they are either
41	for simplified configurations, for ice-only studies, or for short-duration
42	studies to motivate the present work.
43
44	Traditionally, probably for historical reasons and the ease of
45	treating the Coriolis term, most standard sea-ice models are
46	discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
47	kreyscher00, zhang98, hunke97}, although there are sea ice models
48	diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
49	lemieux09}. %
50	\ml{[there is also MI-IM, but I only found this as a reference:
51	\url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
52	From the perspective of coupling a sea ice-model to a C-grid ocean
53	model, the exchange of fluxes of heat and fresh-water pose no
54	difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
55	However, surface stress is defined at velocities points and thus needs
56	to be interpolated between a B-grid sea-ice model and a C-grid ocean
57	model. Smoothing implicitly associated with this interpolation may
58	mask grid scale noise and may contribute to stabilizing the solution.
59	On the other hand, by smoothing the stress signals are damped which
60	could lead to reduced variability of the system. By choosing a C-grid
61	for the sea-ice model, we circumvent this difficulty altogether and
62	render the stress coupling as consistent as the buoyancy coupling.
63
64	A further advantage of the C-grid formulation is apparent in narrow
65	straits. In the limit of only one grid cell between coasts there is no
66	flux allowed for a B-grid (with no-slip lateral boundary counditions),
67	and models have used topographies with artificially widened straits to
68	avoid this problem \citep{holloway07}. The C-grid formulation on the
69	other hand allows a flux of sea-ice through narrow passages if
70	free-slip along the boundaries is allowed. We demonstrate this effect
71	in the Candian archipelago.
72
73	Talk about problems that make the sea-ice-ocean code very sensitive and
74	changes in the code that reduce these sensitivities.
75
76	This paper describes the MITgcm sea ice model; it presents example
77	Arctic and Antarctic results from a realistic, eddy-permitting, global
78	ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
79	solvers and investigates further aspects of sea ice modeling in a
80	regional Arctic configuration; and it presents example results from
81	coupled ocean and sea-ice adjoint-model integrations.
82
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