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1  \section{Introduction}  \section{Introduction}
2  \label{sec:intro}  \label{sec:intro}
3    
4  In the past five years, oceanographic state estimation has matured to the  In recent years, oceanographic state estimation has matured to the
5  extent that estimates of the evolving circulation of the ocean constrained by  extent that estimates of the evolving circulation of the ocean constrained by
6  in-situ and remotely sensed global observations are now routinely available  in-situ and remotely sensed global observations are now routinely available
7  and being applied to myriad scientific problems \citep{wun07}.  Ocean state  and being applied to myriad scientific problems \citep{wun07}.  Ocean state
8  estimation is the process of fitting an ocean general circulation model (GCM)  estimation is the process of fitting an ocean General Circulation Model (GCM)
9  to a multitude of observations.  As formulated by the consortium Estimating  to a multitude of observations.  As formulated by the consortium for Estimating
10  the Circulation and Climate of the Ocean (ECCO), an automatic differentiation  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  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  Lagrange multipliers is then used to render the problem one of unconstrained
13  least-squares minimization.  Although much has been achieved, the existing  least-squares minimization.  Although much has been achieved, the existing
14  ECCO estimates lack intercative sea ice.  This limits the ability of ECCO to  ECCO estimates lack interactive sea ice.  This limits the ability to
15  utilize satellite data constraints over sea-ice covered regions.  This also  utilize satellite data constraints over sea-ice covered regions.  This also
16  limits the usefulness of the ECCO ocean state estimates for describing and  limits the usefulness of the derived ocean state estimates for describing and
17  studying polar-subpolar interactions.  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  The availability of an adjoint model as a powerful research tool
25  complementary to an ocean model was a major design requirement early  complementary to an ocean model was a major design requirement early
26  on in the development of the MIT general circulation model (MITgcm)  on in the development of the MITgcm \citep{marotzke99}. It
 [Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It  
27  was recognized that the adjoint model permitted computing the  was recognized that the adjoint model permitted computing the
28  gradients of various scalar-valued model diagnostics, norms or,  gradients of various scalar-valued model diagnostics, norms or,
29  generally, objective functions with respect to external or independent  generally, objective functions with respect to external or independent
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