--- MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/04/29 14:02:29	1.4
+++ MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/08/14 16:12:41	1.9
@@ -1,81 +1,65 @@
 \section{Introduction}
 \label{sec:intro}
 
-In the past five years, oceanographic state estimation has matured to the
-extent that estimates of the evolving circulation of the ocean constrained by
-in-situ and remotely sensed global observations are now routinely available
-and being applied to myriad scientific problems \citep{wun07}.  Ocean state
-estimation is the process of fitting an ocean general circulation model (GCM)
-to a multitude of observations.  As formulated by the consortium Estimating
-the Circulation and Climate of the Ocean (ECCO), an automatic differentiation
-tool is used to calculate the so-called adjoint code of a GCM.  The method of
-Lagrange multipliers is then used to render the problem one of unconstrained
-least-squares minimization.  Although much has been achieved, the existing
-ECCO estimates lack intercative sea ice.  This limits the ability of ECCO to
-utilize satellite data constraints over sea-ice covered regions.  This also
-limits the usefulness of the ECCO ocean state estimates for describing and
-studying polar-subpolar interactions.
-
-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}\ml{, although there are sea ice only
-  models diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
-    lemieux09}}. 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.
+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 artificially widened straits to
+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 archipelago.
+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 in a regional Arctic configuration; and it presents
-example results from coupled ocean and sea-ice adjoint-model integrations.
+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.
 
 %%% Local Variables: 
 %%% mode: latex