--- MITgcm_contrib/articles/ceaice/ceaice.tex	2007/11/07 17:26:13	1.3
+++ MITgcm_contrib/articles/ceaice/ceaice.tex	2008/01/18 17:33:56	1.8
@@ -1,6 +1,6 @@
 \documentclass[12pt]{article}
-\usepackage{epsfig}
-\usepackage{graphics}
+
+\usepackage[]{graphicx}
 \usepackage{subfigure}
 
 \usepackage[round,comma]{natbib}
@@ -35,7 +35,10 @@
 \newlength{\mediumfigwidth}\setlength{\mediumfigwidth}{39pc}
 %\newlength{\widefigwidth}\setlength{\widefigwidth}{39pc}
 \newlength{\widefigwidth}\setlength{\widefigwidth}{\textwidth}
-\newcommand{\fpath}{.}
+\newcommand{\fpath}{figs}
+
+% commenting scheme
+\newcommand{\ml}[1]{\textsf{\slshape #1}}
 
 \title{A Dynamic-Thermodynamic Sea ice Model for Ocean Climate
   Estimation on an Arakawa C-Grid}
@@ -127,17 +130,21 @@
     \frac{\partial{u_{i}}}{\partial{x_{j}}} +
     \frac{\partial{u_{j}}}{\partial{x_{i}}}\right).
 \end{equation*}
-The pressure $P$, a measure of ice strength, depends on both thickness
-$h$ and compactness (concentration) $c$: \[P =
-P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},\] with the constants $P^{*}$ and
-$C^{*}$. The nonlinear bulk and shear viscosities $\eta$ and $\zeta$
-are functions of ice strain rate invariants and ice strength such that
-the principal components of the stress lie on an elliptical yield
-curve with the ratio of major to minor axis $e$ equal to $2$; they are
-given by:
+The maximum ice pressure $P_{\max}$, a measure of ice strength, depends on
+both thickness $h$ and compactness (concentration) $c$:
+\begin{equation}
+  P_{\max} = P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},
+\label{icestrength}
+\end{equation}
+with the constants $P^{*}$ and $C^{*}$. The nonlinear bulk and shear
+viscosities $\eta$ and $\zeta$ are functions of ice strain rate
+invariants and ice strength such that the principal components of the
+stress lie on an elliptical yield curve with the ratio of major to
+minor axis $e$ equal to $2$; they are given by:
 \begin{align*}
-  \zeta =& \frac{P}{2\Delta} \\
-  \eta =& \frac{P}{2\Delta{e}^2} \\
+  \zeta =& \min\left(\frac{P_{\max}}{2\max(\Delta,\Delta_{\min})},
+   \zeta_{\max}\right) \\
+  \eta =& \frac{\zeta}{e^2} \\
   \intertext{with the abbreviation}
   \Delta = & \left[
     \left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right)
@@ -145,6 +152,24 @@
     2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2})
   \right]^{-\frac{1}{2}}
 \end{align*}
+The bulk viscosities are bounded above by imposing both a minimum
+$\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a
+maximum $\zeta_{\max} = P_{\max}/\Delta^*$, where
+$\Delta^*=(5\times10^{12}/2\times10^4)\text{\,s}^{-1}$. For stress
+tensor compuation the replacement pressure $P = 2\,\Delta\zeta$
+\citep{hibler95} is used so that the stress state always lies on the
+elliptic yield curve by definition.
+
+In the so-called truncated ellipse method the shear viscosity $\eta$
+is capped to suppress any tensile stress \citep{hibler97, geiger98}:
+\begin{equation}
+  \label{eq:etatem}
+  \eta = \min(\frac{\zeta}{e^2}
+  \frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}
+  {\sqrt{(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})^2
+      +4\dot{\epsilon}_{12}^2}}
+\end{equation}
+
 In the current implementation, the VP-model is integrated with the
 semi-implicit line successive over relaxation (LSOR)-solver of
 \citet{zhang98}, which allows for long time steps that, in our case,
@@ -287,23 +312,128 @@
 \section{Funnel Experiments}
 \label{sec:funnel}
 
-\begin{itemize}
-\item B-grid LSR no-slip
-\item C-grid LSR no-slip
-\item C-grid LSR slip
-\item C-grid EVP no-slip
-\item C-grid EVP slip
-\end{itemize}
-
-\subsection{B-grid vs.\ C-grid}
-Comparison between:
-\begin{itemize}
-\item B-grid, lsr, no-slip
-\item C-grid, lsr, no-slip 
-\item C-grid, evp, no-slip
-\end{itemize}
-all without ice-ocean stress, because ice-ocean stress does not work
-for B-grid.
+For a first/detailed comparison between the different variants of the
+MIT sea ice model an idealized geometry of a periodic channel,
+1000\,km long and 500\,m wide on a non-rotating plane, with converging
+walls forming a symmetric funnel and a narrow strait of 40\,km width
+is used. The horizontal resolution is 5\,km throughout the domain
+making the narrow strait 8 grid points wide. The ice model is
+initialized with a complete ice cover of 50\,cm uniform thickness. The
+ice model is driven by a constant along channel eastward ocean current
+of 25\,cm/s that does not see the walls in the domain. All other
+ice-ocean-atmosphere interactions are turned off, in particular there
+is no feedback of ice dynamics on the ocean current. All thermodynamic
+processes are turned off so that ice thickness variations are only
+caused by convergent or divergent ice flow. Ice volume (effective
+thickness) and concentration are advected with a third-order scheme
+with a flux limiter \citep{hundsdorfer94} to avoid undershoots. This
+scheme is unconditionally stable and does not require additional
+diffusion. The time step used here is 1\,h.
+
+\reffig{funnelf0} compares the dynamic fields ice concentration $c$,
+effective thickness $h_{eff} = h\cdot{c}$, and velocities $(u,v)$ for
+five different cases at steady state (after 10\,years of integration): 
+\begin{description}
+\item[B-LSRns:] LSR solver with no-slip boundary conditions on a B-grid, 
+\item[C-LSRns:] LSR solver with no-slip boundary conditions on a C-grid,
+\item[C-LSRfs:] LSR solver with free-slip boundary conditions on a C-grid,
+\item[C-EVPns:] EVP solver with no-slip boundary conditions on a C-grid,
+\item[C-EVPfs:] EVP solver with free-slip boundary conditions on a C-grid,
+\end{description}
+\ml{[We have not implemented the EVP solver on a B-grid.]}
+\begin{figure*}[htbp]
+  \includegraphics[width=\widefigwidth]{\fpath/all_086280}
+  \caption{Ice concentration, effective thickness [m], and ice
+    velocities [m/s]
+    for 5 different numerical solutions.} 
+  \label{fig:funnelf0}
+\end{figure*}
+At a first glance, the solutions look similar. This is encouraging as
+the details of discretization and numerics should not affect the
+solutions to first order. In all cases the ice-ocean stress pushes the
+ice cover eastwards, where it converges in the funnel. In the narrow
+channel the ice moves quickly (nearly free drift) and leaves the
+channel as narrow band.
+
+A close look reveals interesting differences between the B- and C-grid
+results. The zonal velocity in the narrow channel is nearly the free
+drift velocity ( = ocean velocity) of 25\,cm/s for the C-grid
+solutions, regardless of the boundary conditions, while it is just
+above 20\,cm/s for the B-grid solution. The ice accelerates to
+25\,cm/s after it exits the channel. Concentrating on the solutions
+B-LSRns and C-LSRns, the ice volume (effective thickness) along the
+boundaries in the narrow channel is larger in the B-grid case although
+the ice concentration is reduces in the C-grid case. The combined
+effect leads to a larger actual ice thickness at smaller
+concentrations in the C-grid case. However, since the effective
+thickness determines the ice strength $P$ in Eq\refeq{icestrength},
+the ice strength and thus the bulk and shear viscosities are larger in
+the B-grid case leading to more horizontal friction. This circumstance
+might explain why the no-slip boundary conditions in the B-grid case
+appear to be more effective in reducing the flow within the narrow
+channel, than in the C-grid case. Further, the viscosities are also
+sensitive to details of the velocity gradients. Via $\Delta$, these
+gradients enter the viscosities in the denominator so that large
+gradients tend to reduce the viscosities. This again favors more flow
+along the boundaries in the C-grid case: larger velocities
+(\reffig{funnelf0}) on grid points that are closer to the boundary by
+a factor $\frac{1}{2}$ than in the B-grid case because of the stagger
+nature of the C-grid lead numerically to larger tangential gradients
+across the boundary; these in turn make the viscosities smaller for
+less tangential friction and allow more tangential flow along the
+boundaries.
+
+The above argument can also be invoked to explain the small
+differences between the free-slip and no-slip solutions on the C-grid.
+Because of the non-linearities in the ice viscosities, in particular
+along the boundaries, the no-slip boundary conditions have only a small
+impact on the solution.
+
+The difference between LSR and EVP solutions is largest in the
+effective thickness and meridional velocity fields. The EVP velocity
+fields appears to be a little noisy. This noise has been address by
+\citet{hunke01}. It can be dealt with by reducing EVP's internal time
+step (increasing the number of iterations along with the computational
+cost) or by regularizing the bulk and shear viscosities. We revisit
+the latter option by reproducing some of the results of
+\citet{hunke01}, namely the experiment described in her section~4, for
+our C-grid no-slip cases: in a square domain with a few islands the
+ice model is initialized with constant ice thickness and linearly
+increasing ice concentration to the east. The model dynamics are
+forced with a constant anticyclonic ocean gyre and by variable
+atmospheric wind whose mean direction is diagnonal to the north-east
+corner of the domain; ice volume and concentration are held constant
+(no thermodynamics and no advection by ice velocity).
+\reffig{hunke01} shows the ice velocity field, its divergence, and the
+bulk viscosity $\zeta$ for the cases C-LRSns and C-EVPns, and for a
+C-EVPns case, where \citet{hunke01}'s regularization has been
+implemented; compare to Fig.\,4 in \citet{hunke01}. The regularization
+contraint limits ice strength and viscosities as a function of damping
+time scale, resolution and EVP-time step, effectively allowing the
+elastic waves to damp out more quickly \citep{hunke01}.
+\begin{figure*}[htbp]
+  \includegraphics[width=\widefigwidth]{\fpath/hun12days}
+  \caption{Ice flow, divergence and bulk viscosities of three
+    experiments with \citet{hunke01}'s test case: C-LSRns (top),
+    C-EVPns (middle), and C-EVPns with damping described in
+    \citet{hunke01} (bottom).}
+  \label{fig:hunke01}
+\end{figure*}
+
+In the far right (``east'') side of the domain the ice concentration
+is close to one and the ice should be nearly rigid. The applied wind
+tends to push ice toward the upper right corner. Because the highly
+compact ice is confined by the boundary, it resists any further
+compression and exhibits little motion in the rigid region on the
+right hand side. The C-LSRns solution (top row) allows high
+viscosities in the rigid region suppressing nearly all flow.
+\citet{hunke01}'s regularization for the C-EVPns solution (bottom row)
+clearly suppresses the noise present in $\nabla\cdot\vek{u}$ and
+$\log_{10}\zeta$ in the
+unregularized case (middle row), at the cost of reduced viscosities.
+These reduced viscosities lead to small but finite ice velocities
+which in turn can have a strong effect on solutions in the limit of
+nearly rigid regimes (arching and blocking, not shown).
 
 \subsection{C-grid}
 \begin{itemize}
@@ -350,45 +480,50 @@
 \subsection{Arctic Domain with Open Boundaries}
 \label{sec:arctic}
 
-The Arctic domain of integration is illustrated in Fig.~\ref{???}.  It is
-carved out from, and obtains open boundary conditions from, the global
-cubed-sphere configuration of the Estimating the Circulation and Climate of
-the Ocean, Phase II (ECCO2) project \cite{men05a}.  The domain size is 420 by
-384 grid boxes horizontally with mean horizontal grid spacing of 18 km.  
+The Arctic domain of integration is illustrated in Fig.~\ref{???}.  It
+is carved out from, and obtains open boundary conditions from, the
+global cubed-sphere configuration of the Estimating the Circulation
+and Climate of the Ocean, Phase II (ECCO2) project
+\citet{menemenlis05}.  The domain size is 420 by 384 grid boxes
+horizontally with mean horizontal grid spacing of 18 km.
 
 There are 50 vertical levels ranging in thickness from 10 m near the surface
 to approximately 450 m at a maximum model depth of 6150 m. Bathymetry is from
 the National Geophysical Data Center (NGDC) 2-minute gridded global relief
 data (ETOPO2) and the model employs the partial-cell formulation of
-\cite{adc97}, which permits accurate representation of the bathymetry. The
+\citet{adcroft97:_shaved_cells}, which permits accurate representation of the bathymetry. The
 model is integrated in a volume-conserving configuration using a finite volume
 discretization with C-grid staggering of the prognostic variables. In the
-ocean, the non-linear equation of state of \cite{jac95}.  The ocean model is
+ocean, the non-linear equation of state of \citet{jackett95}.  The ocean model is
 coupled to a sea-ice model described hereinabove.  
 
-This particular ECCO2 simulation is initialized from rest using the January
-temperature and salinity distribution from the World Ocean Atlas 2001 (WOA01)
-[Conkright et al., 2002] and it is integrated for 32 years prior to the
-1996-2001 period discussed in the study. Surface boundary conditions are from
-the National Centers for Environmental Prediction and the National Center for
-Atmospheric Research (NCEP/NCAR) atmospheric reanalysis [Kistler et al.,
-2001]. Six-hourly surface winds, temperature, humidity, downward short- and
-long-wave radiations, and precipitation are converted to heat, freshwater, and
-wind stress fluxes using the Large and Pond [1981, 1982] bulk
-formulae. Shortwave radiation decays exponentially as per Paulson and Simpson
-[1977]. Additionally the time-mean river run-off from Large and Nurser [2001]
-is applied and there is a relaxation to the monthly-mean climatological sea
-surface salinity values from WOA01 with a relaxation time scale of 3
-months. Vertical mixing follows Large et al. [1994] with background vertical
-diffusivity of 1.5 � 10-5 m2 s-1 and viscosity of 10-3 m2 s-1. A third order,
-direct-space-time advection scheme with flux limiter is employed and there is
-no explicit horizontal diffusivity. Horizontal viscosity follows Leith [1996]
-but modified to sense the divergent flow as per Fox-Kemper and Menemenlis [in
-press].  Shortwave radiation decays exponentially as per Paulson and Simpson
-[1977].  Additionally, the time-mean runoff of Large and Nurser [2001] is
-applied near the coastline and, where there is open water, there is a
-relaxation to monthly-mean WOA01 sea surface salinity with a time constant of
-45 days.
+This particular ECCO2 simulation is initialized from rest using the
+January temperature and salinity distribution from the World Ocean
+Atlas 2001 (WOA01) [Conkright et al., 2002] and it is integrated for
+32 years prior to the 1996--2001 period discussed in the study. Surface
+boundary conditions are from the National Centers for Environmental
+Prediction and the National Center for Atmospheric Research
+(NCEP/NCAR) atmospheric reanalysis [Kistler et al., 2001]. Six-hourly
+surface winds, temperature, humidity, downward short- and long-wave
+radiations, and precipitation are converted to heat, freshwater, and
+wind stress fluxes using the \citet{large81, large82} bulk formulae.
+Shortwave radiation decays exponentially as per Paulson and Simpson
+[1977]. Additionally the time-mean river run-off from Large and Nurser
+[2001] is applied and there is a relaxation to the monthly-mean
+climatological sea surface salinity values from WOA01 with a
+relaxation time scale of 3 months. Vertical mixing follows
+\citet{large94} with background vertical diffusivity of
+$1.5\times10^{-5}\text{\,m$^{2}$\,s$^{-1}$}$ and viscosity of
+$10^{-3}\text{\,m$^{2}$\,s$^{-1}$}$. A third order, direct-space-time
+advection scheme with flux limiter is employed \citep{hundsdorfer94}
+and there is no explicit horizontal diffusivity. Horizontal viscosity
+follows \citet{lei96} but
+modified to sense the divergent flow as per Fox-Kemper and Menemenlis
+[in press].  Shortwave radiation decays exponentially as per Paulson
+and Simpson [1977].  Additionally, the time-mean runoff of Large and
+Nurser [2001] is applied near the coastline and, where there is open
+water, there is a relaxation to monthly-mean WOA01 sea surface
+salinity with a time constant of 45 days.
 
 Open water, dry
 ice, wet ice, dry snow, and wet snow albedo are, respectively, 0.15, 0.85,
@@ -417,6 +552,7 @@
 \item C-grid LSR slip
 \item C-grid EVP no-slip
 \item C-grid EVP slip
+\item C-grid LSR + TEM (truncated ellipse method, no tensile stress, new flag)
 \item C-grid LSR no-slip + Winton
 \item  speed-performance-accuracy (small)
   ice transport through Canadian Archipelago differences
@@ -428,8 +564,8 @@
 \begin{itemize}
 \item advection schemes: along the ice-edge and regions with large
   gradients
-\item C-grid: more transport through narrow straits for no slip
-  conditons, less for free slip
+\item C-grid: less transport through narrow straits for no slip
+  conditons, more for free slip
 \item VP vs.\ EVP: speed performance, accuracy?
 \item ocean stress: different water mass properties beneath the ice
 \end{itemize}
@@ -510,7 +646,7 @@
 checkpointing loop.
 Again, an initial code adjustment is required to support TAFs 
 checkpointing capability.
-The code adjustments are sufficiently simply so as not to cause
+The code adjustments are sufficiently simple so as not to cause
 major limitations to the full nonlinear parent model.
 Once in place, an adjoint model of a new model configuration
 may be derived in about 10 minutes.
@@ -533,9 +669,10 @@
 We demonstrate the power of the adjoint method
 in the context of investigating sea-ice export sensitivities through Fram Strait
 (for details of this study see Heimbach et al., 2007).
+%\citep[for details of this study see][]{heimbach07}. %Heimbach et al., 2007).
 The domain chosen is a coarsened version of the Arctic face of the
 high-resolution cubed-sphere configuration of the ECCO2 project
-(see Menemenlis et al. 2005). It covers the entire Arctic,
+\citep[see][]{menemenlis05}. It covers the entire Arctic,
 extends into the North Pacific such as to cover the entire
 ice-covered regions, and comprises parts of the North Atlantic
 down to XXN to enable analysis of remote influences of the 
@@ -546,46 +683,41 @@
 (benchmarks have been performed both on an SGI Altix as well as an 
 IBM SP5 at NASA/ARC).
 
-Following a 1-year spinup, the model has been integrated for four years 
-between 1992 and 1995.
-It is forced using realistic 6-hourly NCEP/NCAR atmospheric state variables.
-Over the open ocean these are converted into
-air-sea fluxes via the bulk formulae of Large and Yeager (2004).
-Derivation of air-sea fluxes in the presence of sea-ice is handled
-by the ice model as described in Section XXX.
+Following a 1-year spinup, the model has been integrated for four
+years between 1992 and 1995. It is forced using realistic 6-hourly
+NCEP/NCAR atmospheric state variables. Over the open ocean these are
+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 sea-ice export through Fram Strait
-computed for December 1995
-The adjoint model computes sensitivities to sea-ice export back in time
-from 1995 to 1992 along this trajectory.
-In principle all adjoint model variable (i.e. Lagrange multipliers)
-of the coupled ocean/sea-ice model
-are available to analyze the transient sensitivity behaviour
-of the ocean and sea-ice state.
-Over the open ocean, the adjoint of the bulk formula scheme
-computes sensitivities to the time-varying atmospheric state.
-Over ice-covered parts, the sea-ice adjoint converts
-surface ocean sensitivities to atmospheric sensitivities.
-
-Fig. XXX(a--d) depict sensitivities of sea-ice export through Fram Strait
-in December 1995 to changes in sea-ice thickness 
-12, 24, 36, 48 months back in time.
-Corresponding sensitivities to ocean surface temperature are
-depicted in Fig. XXX(a--d).
-The main characteristics is consistency with expected advection
-of sea-ice over the relevant time scales considered.
-The general positive pattern means that an increase in
-sea-ice thickness at location $(x,y)$ and time $t$ will increase
-sea-ice export through Fram Strait at time $T_e$.
-Largest distances from Fram Strait indicate fastest sea-ice advection
-over the time span considered.
-The ice thickness sensitivities are in close correspondence to
-ocean surface sentivitites, but of opposite sign.
-An increase in temperature will incur ice melting, decrease in ice thickness,
-and therefore decrease in sea-ice export at time $T_e$.
+computed for December 1995.  The adjoint model computes sensitivities
+to sea-ice export back in time from 1995 to 1992 along this
+trajectory.  In principle all adjoint model variable (i.e., Lagrange
+multipliers) of the coupled ocean/sea-ice model are available to
+analyze the transient sensitivity behaviour of the ocean and sea-ice
+state.  Over the open ocean, the adjoint of the bulk formula scheme
+computes sensitivities to the time-varying atmospheric state.  Over
+ice-covered parts, the sea-ice adjoint converts surface ocean
+sensitivities to atmospheric sensitivities.
+
+\reffig{4yradjheff}(a--d) depict sensitivities of sea-ice export
+through Fram Strait in December 1995 to changes in sea-ice thickness
+12, 24, 36, 48 months back in time. Corresponding sensitivities to
+ocean surface temperature are depicted in
+\reffig{4yradjthetalev1}(a--d).  The main characteristics is
+consistency with expected advection of sea-ice over the relevant time
+scales considered.  The general positive pattern means that an
+increase in sea-ice thickness at location $(x,y)$ and time $t$ will
+increase sea-ice export through Fram Strait at time $T_e$.  Largest
+distances from Fram Strait indicate fastest sea-ice advection over the
+time span considered.  The ice thickness sensitivities are in close
+correspondence to ocean surface sentivitites, but of opposite sign.
+An increase in temperature will incur ice melting, decrease in ice
+thickness, and therefore decrease in sea-ice export at time $T_e$.
 
 The picture is fundamentally different and much more complex
 for sensitivities to ocean temperatures away from the surface.
-Fig. XXX (a--d) depicts ice export sensitivities to
+\reffig{4yradjthetalev10??}(a--d) depicts ice export sensitivities to
 temperatures at roughly 400 m depth.
 Primary features are the effect of the heat transport of the North
 Atlantic current which feeds into the West Spitsbergen current,
@@ -594,21 +726,21 @@
 \begin{figure}[t!]
 \centerline{
 \subfigure[{\footnotesize -12 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJheff_arc_lev1_tim072_cmax2.0E+02.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim072_cmax2.0E+02.eps}}
 %\includegraphics*[width=.3\textwidth]{H_c.bin_res_100_lev1.pdf}
 %
 \subfigure[{\footnotesize -24 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}}
 }
 
 \centerline{
 \subfigure[{\footnotesize
 -36 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJheff_arc_lev1_tim218_cmax2.0E+02.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim218_cmax2.0E+02.eps}}
 %
 \subfigure[{\footnotesize
 -48 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJheff_arc_lev1_tim292_cmax2.0E+02.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim292_cmax2.0E+02.eps}}
 }
 \caption{Sensitivity of sea-ice export through Fram Strait in December 2005 to
 sea-ice thickness at various prior times.
@@ -619,23 +751,23 @@
 \begin{figure}[t!]
 \centerline{
 \subfigure[{\footnotesize -12 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJtheta_arc_lev1_tim072_cmax5.0E+01.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJtheta_arc_lev1_tim072_cmax5.0E+01.eps}}
 %\includegraphics*[width=.3\textwidth]{H_c.bin_res_100_lev1.pdf}
 %
 \subfigure[{\footnotesize -24 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJtheta_arc_lev1_tim145_cmax5.0E+01.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJtheta_arc_lev1_tim145_cmax5.0E+01.eps}}
 }
 
 \centerline{
 \subfigure[{\footnotesize
 -36 months}] 
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJtheta_arc_lev1_tim218_cmax5.0E+01.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJtheta_arc_lev1_tim218_cmax5.0E+01.eps}}
 %
 \subfigure[{\footnotesize
 -48 months}]
-{\includegraphics*[width=0.44\linewidth]{figs/run_4yr_ADJtheta_arc_lev1_tim292_cmax5.0E+01.eps}}
+{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJtheta_arc_lev1_tim292_cmax5.0E+01.eps}}
 }
-\caption{Same as Fig. XXX but for sea surface temperature
+\caption{Same as \reffig{4yradjheff} but for sea surface temperature
 \label{fig:4yradjthetalev1}}
 \end{figure}
 
@@ -660,7 +792,7 @@
 
 \paragraph{Acknowledgements}
 We thank Jinlun Zhang for providing the original B-grid code and many
-helpful discussions.
+helpful discussions. ML thanks Elizabeth Hunke for multiple explanations.
 
 \bibliography{bib/journal_abrvs,bib/seaice,bib/genocean,bib/maths,bib/mitgcmuv,bib/fram}
 
@@ -670,3 +802,54 @@
 %%% mode: latex
 %%% TeX-master: t
 %%% End: 
+
+
+A Dynamic-Thermodynamic Sea ice Model for Ocean Climate
+  Estimation on an Arakawa C-Grid
+
+Introduction
+
+Ice Model:
+ Dynamics formulation.
+  B-C, LSR, EVP, no-slip, slip
+  parallellization
+ Thermodynamics formulation.
+  0-layer Hibler salinity + snow
+  3-layer Winton
+
+Idealized tests
+ Funnel Experiments
+ Downstream Island tests
+  B-grid LSR no-slip
+  C-grid LSR no-slip
+  C-grid LSR slip
+  C-grid EVP no-slip
+  C-grid EVP slip
+
+Arctic Setup
+ Configuration
+ OBCS from cube
+ forcing
+ 1/2 and full resolution
+ with a few JFM figs from C-grid LSR no slip
+  ice transport through Canadian Archipelago
+  thickness distribution
+  ice velocity and transport
+
+Arctic forward sensitivity experiments
+ B-grid LSR no-slip
+ C-grid LSR no-slip
+ C-grid LSR slip
+ C-grid EVP no-slip
+ C-grid EVP slip
+ C-grid LSR no-slip + Winton
+  speed-performance-accuracy (small)
+  ice transport through Canadian Archipelago differences
+  thickness distribution differences
+  ice velocity and transport differences
+
+Adjoint sensitivity experiment on 1/2-res setup
+ Sensitivity of sea ice volume flow through Fram Strait
+*** Sensitivity of sea ice volume flow through Canadian Archipelago
+
+Summary and conluding remarks
