--- MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/06/28 15:44:39	1.6
+++ MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/07/18 19:09:20	1.7
@@ -1,49 +1,47 @@
 \section{Introduction}
 \label{sec:intro}
 
-In recent 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 for 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 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 model that has been coupled to the
-Massachusetts Institute of Technology general circulation model
-\citep[MITgcm][]{mar97a} and that has been modified to permit efficient and
-accurate automatic differentiation.
+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
+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
+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.
 
-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 MITgcm \citep{marotzke99}. 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