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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 1.5 kreyscher00, zhang98, hunke97}, although there are sea ice models
48     diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
49     lemieux09}. %
50     \ml{[there is also MI-IM, but I only found this as a reference:
51     \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
52     From the perspective of coupling a sea ice-model to a C-grid ocean
53     model, the exchange of fluxes of heat and fresh-water pose no
54     difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
55     However, surface stress is defined at velocities points and thus needs
56     to be interpolated between a B-grid sea-ice model and a C-grid ocean
57     model. Smoothing implicitly associated with this interpolation may
58     mask grid scale noise and may contribute to stabilizing the solution.
59     On the other hand, by smoothing the stress signals are damped which
60     could lead to reduced variability of the system. By choosing a C-grid
61     for the sea-ice model, we circumvent this difficulty altogether and
62     render the stress coupling as consistent as the buoyancy coupling.
63 dimitri 1.1
64     A further advantage of the C-grid formulation is apparent in narrow
65     straits. In the limit of only one grid cell between coasts there is no
66     flux allowed for a B-grid (with no-slip lateral boundary counditions),
67 mlosch 1.5 and models have used topographies with artificially widened straits to
68 dimitri 1.1 avoid this problem \citep{holloway07}. The C-grid formulation on the
69     other hand allows a flux of sea-ice through narrow passages if
70     free-slip along the boundaries is allowed. We demonstrate this effect
71     in the Candian archipelago.
72    
73     Talk about problems that make the sea-ice-ocean code very sensitive and
74     changes in the code that reduce these sensitivities.
75    
76 mlosch 1.5 This paper describes the MITgcm sea ice model; it presents example
77     Arctic and Antarctic results from a realistic, eddy-permitting, global
78     ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
79     solvers and investigates further aspects of sea ice modeling in a
80     regional Arctic configuration; and it presents example results from
81     coupled ocean and sea-ice adjoint-model integrations.
82 mlosch 1.3
83     %%% Local Variables:
84     %%% mode: latex
85     %%% TeX-master: "ceaice"
86     %%% End:

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