articles/ceaice/ceaice_intro.tex

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

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	The availability of an adjoint model as a powerful research tool
5	complementary to an ocean model was a major design requirement early
6	on in the development of the MIT general circulation model (MITgcm)
7	[Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It
8	was recognized that the adjoint model permitted computing the
9	gradients of various scalar-valued model diagnostics, norms or,
10	generally, objective functions with respect to external or independent
11	parameters very efficiently. The information associtated with these
12	gradients is useful in at least two major contexts. First, for state
13	estimation problems, the objective function is the sum of squared
14	differences between observations and model results weighted by the
15	inverse error covariances. The gradient of such an objective function
16	can be used to reduce this measure of model-data misfit to find the
17	optimal model solution in a least-squares sense. Second, the
18	objective function can be a key oceanographic quantity such as
19	meridional heat or volume transport, ocean heat content or mean
20	surface temperature index. In this case the gradient provides a
21	complete set of sensitivities of this quantity to all independent
22	variables simultaneously. These sensitivities can be used to address
23	the cause of, say, changing net transports accurately.
24
25	References to existing sea-ice adjoint models, explaining that they are either
26	for simplified configurations, for ice-only studies, or for short-duration
27	studies to motivate the present work.
28
29	Traditionally, probably for historical reasons and the ease of
30	treating the Coriolis term, most standard sea-ice models are
31	discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
32	kreyscher00, zhang98, hunke97}. From the perspective of coupling a
33	sea ice-model to a C-grid ocean model, the exchange of fluxes of heat
34	and fresh-water pose no difficulty for a B-grid sea-ice model
35	\citep[e.g.,][]{timmermann02a}. However, surface stress is defined at
36	velocities points and thus needs to be interpolated between a B-grid
37	sea-ice model and a C-grid ocean model. Smoothing implicitly
38	associated with this interpolation may mask grid scale noise and may
39	contribute to stabilizing the solution. On the other hand, by
40	smoothing the stress signals are damped which could lead to reduced
41	variability of the system. By choosing a C-grid for the sea-ice model,
42	we circumvent this difficulty altogether and render the stress
43	coupling as consistent as the buoyancy coupling.
44
45	A further advantage of the C-grid formulation is apparent in narrow
46	straits. In the limit of only one grid cell between coasts there is no
47	flux allowed for a B-grid (with no-slip lateral boundary counditions),
48	and models have used topographies artificially widened straits to
49	avoid this problem \citep{holloway07}. The C-grid formulation on the
50	other hand allows a flux of sea-ice through narrow passages if
51	free-slip along the boundaries is allowed. We demonstrate this effect
52	in the Candian archipelago.
53
54	Talk about problems that make the sea-ice-ocean code very sensitive and
55	changes in the code that reduce these sensitivities.
56
57	This paper describes the MITgcm sea ice
58	model; it presents example Arctic and Antarctic results from a realistic,
59	eddy-permitting, global ocean and sea-ice configuration; it compares B-grid
60	and C-grid dynamic solvers in a regional Arctic configuration; and it presents
61	example results from coupled ocean and sea-ice adjoint-model integrations.