--- MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/03/04 20:31:31	1.3
+++ MITgcm_contrib/articles/ceaice/ceaice_intro.tex	2008/07/18 19:09:20	1.7
@@ -1,68 +1,72 @@
 \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.
+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.
+
+
 
 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.,][]{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.
+  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
+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
@@ -71,11 +75,12 @@
 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.
 
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