articles/ceaice/ceaice_intro.tex

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

In recent 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 for 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 interactive sea ice.  This limits the ability to
utilize satellite data constraints over sea-ice covered regions.  This also
limits the usefulness of the derived ocean state estimates for describing and
studying polar-subpolar interactions.  This paper is a first step towards
adding sea-ice capability to the ECCO estimates.  That is, we describe a
dynamic and thermodynamic sea ice model that has been coupled to the
Massachusetts Institute of Technology general circulation model
\citep[MITgcm][]{mar97a} and that has been modified to permit efficient and
accurate automatic differentiation.

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 MITgcm \citep{marotzke99}. 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 recent 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 for 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 interactive sea ice. This limits the ability to
15	utilize satellite data constraints over sea-ice covered regions. This also
16	limits the usefulness of the derived ocean state estimates for describing and
17	studying polar-subpolar interactions. This paper is a first step towards
18	adding sea-ice capability to the ECCO estimates. That is, we describe a
19	dynamic and thermodynamic sea ice model that has been coupled to the
20	Massachusetts Institute of Technology general circulation model
21	\citep[MITgcm][]{mar97a} and that has been modified to permit efficient and
22	accurate automatic differentiation.
23
24	The availability of an adjoint model as a powerful research tool
25	complementary to an ocean model was a major design requirement early
26	on in the development of the MITgcm \citep{marotzke99}. It
27	was recognized that the adjoint model permitted computing the
28	gradients of various scalar-valued model diagnostics, norms or,
29	generally, objective functions with respect to external or independent
30	parameters very efficiently. The information associtated with these
31	gradients is useful in at least two major contexts. First, for state
32	estimation problems, the objective function is the sum of squared
33	differences between observations and model results weighted by the
34	inverse error covariances. The gradient of such an objective function
35	can be used to reduce this measure of model-data misfit to find the
36	optimal model solution in a least-squares sense. Second, the
37	objective function can be a key oceanographic quantity such as
38	meridional heat or volume transport, ocean heat content or mean
39	surface temperature index. In this case the gradient provides a
40	complete set of sensitivities of this quantity to all independent
41	variables simultaneously. These sensitivities can be used to address
42	the cause of, say, changing net transports accurately.
43
44	References to existing sea-ice adjoint models, explaining that they are either
45	for simplified configurations, for ice-only studies, or for short-duration
46	studies to motivate the present work.
47
48	Traditionally, probably for historical reasons and the ease of
49	treating the Coriolis term, most standard sea-ice models are
50	discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
51	kreyscher00, zhang98, hunke97}, although there are sea ice models
52	diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
53	lemieux09}. %
54	\ml{[there is also MI-IM, but I only found this as a reference:
55	\url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
56	From the perspective of coupling a sea ice-model to a C-grid ocean
57	model, the exchange of fluxes of heat and fresh-water pose no
58	difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
59	However, surface stress is defined at velocities points and thus needs
60	to be interpolated between a B-grid sea-ice model and a C-grid ocean
61	model. Smoothing implicitly associated with this interpolation may
62	mask grid scale noise and may contribute to stabilizing the solution.
63	On the other hand, by smoothing the stress signals are damped which
64	could lead to reduced variability of the system. By choosing a C-grid
65	for the sea-ice model, we circumvent this difficulty altogether and
66	render the stress coupling as consistent as the buoyancy coupling.
67
68	A further advantage of the C-grid formulation is apparent in narrow
69	straits. In the limit of only one grid cell between coasts there is no
70	flux allowed for a B-grid (with no-slip lateral boundary counditions),
71	and models have used topographies with artificially widened straits to
72	avoid this problem \citep{holloway07}. The C-grid formulation on the
73	other hand allows a flux of sea-ice through narrow passages if
74	free-slip along the boundaries is allowed. We demonstrate this effect
75	in the Candian archipelago.
76
77	Talk about problems that make the sea-ice-ocean code very sensitive and
78	changes in the code that reduce these sensitivities.
79
80	This paper describes the MITgcm sea ice model; it presents example
81	Arctic and Antarctic results from a realistic, eddy-permitting, global
82	ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
83	solvers and investigates further aspects of sea ice modeling in a
84	regional Arctic configuration; and it presents example results from
85	coupled ocean and sea-ice adjoint-model integrations.
86
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