--- MITgcm_contrib/articles/ceaice/ceaice.tex 2007/11/07 14:35:09 1.1 +++ MITgcm_contrib/articles/ceaice/ceaice.tex 2008/01/21 08:06:00 1.9 @@ -1,10 +1,12 @@ +% $Header: /home/ubuntu/mnt/e9_copy/MITgcm_contrib/articles/ceaice/ceaice.tex,v 1.9 2008/01/21 08:06:00 mlosch Exp $ +% $Name: $ \documentclass[12pt]{article} -\usepackage{epsfig} -\usepackage{graphics} + +\usepackage[]{graphicx} \usepackage{subfigure} \usepackage[round,comma]{natbib} -\bibliographystyle{agu04} +\bibliographystyle{bib/agu04} \usepackage{amsmath,amssymb} \newcommand\bmmax{10} \newcommand\hmmax{10} @@ -35,7 +37,10 @@ \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 +132,21 @@ \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{eq: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 +154,24 @@ 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 +314,139 @@ \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). + +\ml{[Say something about performance? This is tricky, as the + perfomance depends strongly on the configuration. A run with slowly + changing forcing is favorable for LSR, because then only very few + iterations are required for convergences while EVP uses its fixed + number of internal timesteps. If the forcing in changing fast, LSR + needs far more iterations while EVP still uses the fixed number of + internal timesteps. I have produces runs where for slow forcing LSR + is much faster than EVP and for fast forcing, LSR is much slower + than EVP. EVP is certainly more efficient in terms of vectorization + and MFLOPS on our SX8, but is that a criterion?]} \subsection{C-grid} \begin{itemize} @@ -350,45 +493,50 @@ \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 +565,7 @@ \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 @@ -428,18 +577,12 @@ \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} -\section{Adjoint sensitivity experiment} -\label{sec:adjoint} - -Adjoint sensitivity experiment on 1/2-res setup - Sensitivity of sea ice volume flow through Fram Strait - \section{Adjoint sensiivities of the MITsim} \subsection{The adjoint of MITsim} @@ -516,7 +659,7 @@ 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. @@ -539,9 +682,10 @@ 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 @@ -552,46 +696,41 @@ (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, @@ -600,21 +739,21 @@ \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. @@ -625,23 +764,23 @@ \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} @@ -666,7 +805,7 @@ \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} @@ -676,3 +815,54 @@ %%% 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