articles/ceaice/ceaice_intro.tex

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

Ocean state estimation has matured to the extent that estimates of the
time-evolving ocean circulation, constrained by a multitude of in-situ and
remotely sensed global observations, are now routinely available and being
applied to myriad scientific problems \citep[and references therein]{wun07}.
As formulated by the consortium for Estimating the Circulation and Climate of
the Ocean (ECCO), least-squares methods are used to fit the Massachusetts
Institute of Technology general circulation model \citep[MITgcm;][]{mar97a} to
the available data.  Much has been achieved but 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.  In this paper we describe a dynamic and thermodynamic sea ice
model that has been coupled to the MITgcm and that has been modified to permit
efficient and accurate forward and adjoint integration.  The forward model
borrows many components from current-generation sea ice models but these
components are reformulated on an Arakawa C grid in order to match the MITgcm
oceanic grid and they are modified in many ways to permit efficient and
accurate automatic differentiation.  To illustrate how the use of the forward and
adjoint parts together can help give insight into discrete model dynamics, we
study the interaction between littoral regions in the Canadian Arctic
Archipelago and sea-ice model dynamics.

Because early numerical ocean models were formulated on the Arakawa-B grid and
because of the easier treatment of the Coriolis term, most standard sea-ice
models are discretized on Arakawa-B grids \citep[e.g.,][]{hibler79, harder99,
  kreyscher00, zhang98, hunke97}.  As model resolution increases, more and
more ocean and sea ice models are being formulated on the Arakawa-C grid
\citep[e.g.,][]{mar97a,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 Arctic Archipelago (CAA).

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	Ocean state estimation has matured to the extent that estimates of the
5	time-evolving ocean circulation, constrained by a multitude of in-situ and
6	remotely sensed global observations, are now routinely available and being
7	applied to myriad scientific problems \citep[and references therein]{wun07}.
8	As formulated by the consortium for Estimating the Circulation and Climate of
9	the Ocean (ECCO), least-squares methods are used to fit the Massachusetts
10	Institute of Technology general circulation model \citep[MITgcm;][]{mar97a} to
11	the available data. Much has been achieved but the existing ECCO estimates
12	lack interactive sea ice. This limits the ability to utilize satellite data
13	constraints over sea-ice covered regions. This also limits the usefulness of
14	the derived ocean state estimates for describing and studying polar-subpolar
15	interactions. In this paper we describe a dynamic and thermodynamic sea ice
16	model that has been coupled to the MITgcm and that has been modified to permit
17	efficient and accurate forward and adjoint integration. The forward model
18	borrows many components from current-generation sea ice models but these
19	components are reformulated on an Arakawa C grid in order to match the MITgcm
20	oceanic grid and they are modified in many ways to permit efficient and
21	accurate automatic differentiation. To illustrate how the use of the forward and
22	adjoint parts together can help give insight into discrete model dynamics, we
23	study the interaction between littoral regions in the Canadian Arctic
24	Archipelago and sea-ice model dynamics.
25
26	Because early numerical ocean models were formulated on the Arakawa-B grid and
27	because of the easier treatment of the Coriolis term, most standard sea-ice
28	models are discretized on Arakawa-B grids \citep[e.g.,][]{hibler79, harder99,
29	kreyscher00, zhang98, hunke97}. As model resolution increases, more and
30	more ocean and sea ice models are being formulated on the Arakawa-C grid
31	\citep[e.g.,][]{mar97a,ip91,tremblay97,lemieux09}.
32	%\ml{[there is also MI-IM, but I only found this as a reference:
33	% \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
34	From the perspective of coupling a sea ice-model to a C-grid ocean model, the
35	exchange of fluxes of heat and fresh-water pose no difficulty for a B-grid
36	sea-ice model \citep[e.g.,][]{timmermann02a}. However, surface stress is
37	defined at velocities points and thus needs to be interpolated between a
38	B-grid sea-ice model and a C-grid ocean model. Smoothing implicitly associated
39	with this interpolation may mask grid scale noise and may contribute to
40	stabilizing the solution. On the other hand, by smoothing the stress signals
41	are damped which could lead to reduced variability of the system. By choosing
42	a C-grid for the sea-ice model, we circumvent this difficulty altogether and
43	render the stress 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 with 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 Arctic Archipelago (CAA).
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 model; it presents example
58	Arctic and Antarctic results from a realistic, eddy-permitting, global
59	ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
60	solvers and investigates further aspects of sea ice modeling in a
61	regional Arctic configuration; and it presents example results from
62	coupled ocean and sea-ice adjoint-model integrations.
63
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