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}. 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 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 in a regional Arctic configuration; and it presents
example results from coupled ocean and sea-ice adjoint-model integrations.
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}. From the perspective of coupling a
48	sea ice-model to a C-grid ocean model, the exchange of fluxes of heat
49	and fresh-water pose no difficulty for a B-grid sea-ice model
50	\citep[e.g.,][]{timmermann02a}. However, surface stress is defined at
51	velocities points and thus needs to be interpolated between a B-grid
52	sea-ice model and a C-grid ocean model. Smoothing implicitly
53	associated with this interpolation may mask grid scale noise and may
54	contribute to stabilizing the solution. On the other hand, by
55	smoothing the stress signals are damped which could lead to reduced
56	variability of the system. By choosing a C-grid for the sea-ice model,
57	we circumvent this difficulty altogether and render the stress
58	coupling as consistent as the buoyancy coupling.
59
60	A further advantage of the C-grid formulation is apparent in narrow
61	straits. In the limit of only one grid cell between coasts there is no
62	flux allowed for a B-grid (with no-slip lateral boundary counditions),
63	and models have used topographies artificially widened straits to
64	avoid this problem \citep{holloway07}. The C-grid formulation on the
65	other hand allows a flux of sea-ice through narrow passages if
66	free-slip along the boundaries is allowed. We demonstrate this effect
67	in the Candian archipelago.
68
69	Talk about problems that make the sea-ice-ocean code very sensitive and
70	changes in the code that reduce these sensitivities.
71
72	This paper describes the MITgcm sea ice
73	model; it presents example Arctic and Antarctic results from a realistic,
74	eddy-permitting, global ocean and sea-ice configuration; it compares B-grid
75	and C-grid dynamic solvers in a regional Arctic configuration; and it presents
76	example results from coupled ocean and sea-ice adjoint-model integrations.