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--- MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/07/28 07:36:38	1.8
+++ MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/08/14 16:12:41	1.9
@@ -1,66 +1,45 @@
 \section{Introduction}
 \label{sec:intro}
 
-In recent years, 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, i.e.,
-filter/smoother \citep{fuk02}, Green's functions \citep{men05}, and adjoint
-\citep{sta02a}, are used to fit the Massachusetts Institute of Technology
-general circulation model
-\citep[MITgcm;][]{marshall97:_finit_volum_incom_navier_stokes} 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
+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.  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
+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 integration and automatic differentiation.
-
-Although the ECCO2 optimization problem can be expressed succinctly in
-algebra, its numerical implementation for planetary scale problems is
-enormously demanding.  First, multiple forward integrations are required to
-derive approximate filter/smoothers and to compute model Green's functions.
-Second, the derivation of the adjoint model, even with the availability of
-automatic differentiation tools, is a challenging technical task, which
-requires reformulation of some of the model physics to insure
-differentiability and the addition of numerous adjoint compiler directives to
-improve efficiency \citep{marotzke99}.  The MITgcm adjoint typically requires
-5--10 times more computations and 10--100 times more storage than the forward
-model.  Third, every evaluation of the cost function entails a full forward
-integration of the assimilation model and multiple forwards (and adjoint for
-the adjoint method) iterations are required to achieve satisfactorily
-converged solutions.  Finally, evaluating the cost function also requires
-estimating the error statistics associated with unresolved physics in the
-model and with incompatibilities between observed quantities and numerical
-model variables.  These statistics are obtained from simulations at even
-higher resolutions than the assimilation model.  For all the above reasons, it
-was decided early on that the MITgcm sea ice model would be tightly coupled
-with the ocean component as opposed to loosely coupled via a flux coupler.
-
-
-
-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
+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