--- MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex	2008/03/25 22:04:31	1.3
+++ MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex	2008/06/04 13:34:41	1.4
@@ -3,57 +3,53 @@
 
 \subsection{The adjoint of MITsim}
 
-
-The ability to generate tangent linear and adjoint components
-of a coupled ocean sea-ice system was one of the main drivers
-behind the MITsim development.
-For the ocean the adjoint capability has proven to be an
-invaluable tool for sensitivity analysis as well as state estimation,
-as evidenced by various adjoint-based studies
-(for a recent summary, see \cite{heim:08}).
-
-The adjoint model operator (ADM) is the transpose of the tangent linear 
-model operator (TLM)
-of the full (in general nonlinear) forward model, i.e. the MITsim.
-It enables very efficient computation of gradients
-of scalar-valued model diagnostics 
-(so-called cost function or objective function)
-with respect to many model inputs (so-called independent or control variables).
-These inputs can be two- or three-dimensional fields of initial 
-conditions of the ocean or sea-ice state, model parameters such as 
-mixing coefficients, or time-varying surface or lateral (open) boundary conditions.
-When combined, these variables span a potentially high-dimensional
-(e.g. O(10$^8$)) so-called control space. Performing parameter perturbations
-to assess model sensitivities quickly becomes prohibitive at these scales.
-Alternatively, transient sensitivities of the objective function 
-to any element of the  control and model state space can be computed 
-very efficiently in  one single adjoint 
-model integration, provided an efficient adjoint model is available.
-
-Following closely the development and maintenance of the
-TLM and ADM components of the MITgcm we have relied heavily on the
-autmomatic differentiation (AD) tool
-"Transformation of Algorithms in Fortran" (TAF)
-developed by Fastopt \citep{gier-kami:98}.
-to derive TLM and ADM code of the MITsim
-(for details see \cite{maro-etal:99}, \cite{heim-etal:05}).
-Briefly, the nonlinear parent model is fed to the AD tool which produces 
-derivative code for the specified control space and objective function.
-Apart from its evident success, advantages of this approach have been 
-pointed out, e.g. by \cite{gier-kami:98}.
-
-Many issues underlying the efficient exact adjoint sea-ice code generation
-are similar to those arising for the ocean model's adjoint.
-Linearizing the model around the exact nonlinear model trajectory,
-as we do, is a crucial aspect in the presence of different
-regimes (e.g. effect of the seaice growth term at or away from the
-freezing point of the ocean surface).
-Adjusting the (parent) model code to support the AD tool in
-providing exact and efficient adjoint code is the main initial work.
-This may be substantial for legacy code, but fairly straightforward
-when coding with "AD application in mind".
-Once in place, an adjoint model of a new model configuration
-may be derived in about 10 minutes.
+The adjoint model of the MITgcm has become an invaluable
+tool for sensitivity analysis as well as state estimation \citep[for a
+recent summary, see][]{heim:08}. The code has been developed and
+tailored to be readily used with automatic differentiation tools for
+adjoint code generation. This route was also taken in developing and
+adapting the sea-ice compontent MITsim, so that tangent linear and
+adjoint components can be obtained and kept up to date without
+excessive effort.
+
+The adjoint model operator (ADM) is the transpose of the tangent
+linear model operator (TLM) of the full (in general nonlinear) forward
+model, in this case the MITsim. This operator computes the gradients
+of scalar-valued model diagnostics (so-called cost function or
+objective function) with respect to many model inputs (so-called
+independent or control variables).  These inputs can be two- or
+three-dimensional fields of initial conditions of the ocean or sea-ice
+state, model parameters such as mixing coefficients, or time-varying
+surface or lateral (open) boundary conditions.  When combined, these
+variables span a potentially high-dimensional (e.g.  O(10$^8$))
+so-called control space. At this problem dimension, perturbing
+individual parameters to assess model sensitivities quickly becomes
+prohibitive. By contrast, transient sensitivities of the objective
+function to any element of the control and model state space can be
+computed very efficiently in one single adjoint model integration,
+provided an adjoint model is available.
+
+In anology to the TLM and ADM components of the MITgcm we rely on the
+autmomatic differentiation (AD) tool ``Transformation of Algorithms in
+Fortran'' (TAF) developed by Fastopt \citep{gier-kami:98} to generate
+TLM and ADM code of the MITsim \citep[for details see][]{maro-etal:99,
+  heim-etal:05}.  In short, the AD tool uses the nonlinear parent
+model code to generate derivative code for the specified control space
+and objective function. Advantages of this approach have been pointed
+out, for example by \cite{gier-kami:98}.
+
+Many issues of generating efficient exact adjoint sea-ice code are
+similar to those for the ocean model's adjoint.  Linearizing the model
+around the exact nonlinear model trajectory is a crucial aspect in the
+presence of different regimes (e.g., is the thermodynamic growth term
+for sea-ice evaluated near or far away from the freezing point of the
+ocean surface?). Adapting the (parent) model code to support the AD
+tool in providing exact and efficient adjoint code represents the main
+work load initially. For legacy code, this task may become
+substantial, but it is fairly straightforward when writing new code
+with an AD tool in mind. Once this initial task is completed,
+generating the adjoint code of a new model configuration takes about
+10 minutes.
 
 [HIGHLIGHT COUPLED NATURE OF THE ADJOINT!]
 
@@ -106,7 +102,7 @@
 converted into air-sea fluxes via the bulk formulae of
 \citet{large04}.  Derivation of air-sea fluxes in the presence of
 sea-ice is handled by the ice model as described in \refsec{model}.
-The objective function chosen is 
+The objective function is chosen $J$ as the
 sea-ice export through 
 Lancaster Sound at XX$^{\circ}$W
 averaged over an 8-month period between October 1992 and May 1993.  
@@ -129,12 +125,12 @@
 \paragraph{Sensitivities to the sea-ice thickness}
 
 The most readily interpretable ice-export sensitivity is that
-to ice thickness, $\partial J / \partial heff$.
-Fig. XXX depcits transient $\partial J / \partial heff$ using free-slip
+to effective ice thickness, $\partial{J} / \partial{h}$.
+Fig. XXX depcits transient $\partial{J} / \partial{h}$ using free-slip
 (left column) and no-slip (right column) boundary conditions.
 Sensitivity snapshots are depicted for (from top to bottom) 
 12, 24, 36, and 48 months prior to May 2003.
-The dominant features are in accordance with expectations:
+The dominant features are\ml{ in accordance with expectations/as expected}:
 
 (*)
 Dominant pattern (for the free-slip run) is that of positive sensitivities, i.e.
@@ -337,6 +333,23 @@
 Atlantic current which feeds into the West Spitsbergen current,
 the circulation around Svalbard, and ...
 
+
+\ml{[based on the movie series
+  zzz\_run\_export\_canarch\_freeslip\_4yr\_1989\_ADJ*:]} The ice
+export through the Canadian Archipelag is highly sensitive to the
+previous state of the ocean-ice system in the Archipelago and the
+Western Arctic. According to the \ml{(adjoint)} senstivities of the
+eastward ice transport through Lancaster Sound (\reffig{arctic_topog},
+cross-section G) with respect to ice volume (effective thickness), ocean
+surface temperature, and vertical diffusivity near the surface
+(\reffig{fouryearadj}) after 4 years of integration the following
+mechanisms can be identified: near the ``observation'' (cross-section
+G), smaller vertical diffusivities lead to lower surface temperatures
+and hence to more ice that is available for export. Further away from
+cross-section G, the sensitivity to vertical diffusivity has the
+opposite sign, but temperature and ice volume sensitivities have the
+same sign as close to the observation.
+
 \begin{figure}[t!]
 \centerline{
 \subfigure[{\footnotesize -12 months}]
