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}\ml{, although there are sea ice only
  models diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
    lemieux09}}. 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.

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1	dimitri	1.1	\section{Introduction}
2			\label{sec:intro}
3
4	dimitri	1.2	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	dimitri	1.1	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	mlosch	1.3	kreyscher00, zhang98, hunke97}\ml{, although there are sea ice only
48	mlosch	1.4	models diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
49	mlosch	1.3	lemieux09}}. From the perspective of coupling a sea ice-model to a
50			C-grid ocean model, the exchange of fluxes of heat and fresh-water
51			pose no difficulty for a B-grid sea-ice model
52	dimitri	1.1	\citep[e.g.,][]{timmermann02a}. However, surface stress is defined at
53			velocities points and thus needs to be interpolated between a B-grid
54			sea-ice model and a C-grid ocean model. Smoothing implicitly
55			associated with this interpolation may mask grid scale noise and may
56			contribute to stabilizing the solution. On the other hand, by
57			smoothing the stress signals are damped which could lead to reduced
58			variability of the system. By choosing a C-grid for the sea-ice model,
59			we circumvent this difficulty altogether and render the stress
60			coupling as consistent as the buoyancy coupling.
61
62			A further advantage of the C-grid formulation is apparent in narrow
63			straits. In the limit of only one grid cell between coasts there is no
64			flux allowed for a B-grid (with no-slip lateral boundary counditions),
65			and models have used topographies artificially widened straits to
66			avoid this problem \citep{holloway07}. The C-grid formulation on the
67			other hand allows a flux of sea-ice through narrow passages if
68			free-slip along the boundaries is allowed. We demonstrate this effect
69			in the Candian archipelago.
70
71			Talk about problems that make the sea-ice-ocean code very sensitive and
72			changes in the code that reduce these sensitivities.
73
74			This paper describes the MITgcm sea ice
75			model; it presents example Arctic and Antarctic results from a realistic,
76			eddy-permitting, global ocean and sea-ice configuration; it compares B-grid
77			and C-grid dynamic solvers in a regional Arctic configuration; and it presents
78			example results from coupled ocean and sea-ice adjoint-model integrations.
79	mlosch	1.3
80			%%% Local Variables:
81			%%% mode: latex
82			%%% TeX-master: "ceaice"
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