--- MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex 2008/06/04 13:34:41 1.4 +++ MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex 2008/07/25 15:01:19 1.5 @@ -1,4 +1,4 @@ -\section{Adjoint sensiivities of the MITsim} +\section{Adjoint sensitivities of the MITsim} \label{sec:adjoint} \subsection{The adjoint of MITsim} @@ -65,305 +65,407 @@ \subsection{An example: sensitivities of sea-ice export through -the Lancaster and Jones Sound} +the Lancaster Sound} -We demonstrate the power of the adjoint method -in the context of investigating sea-ice export sensitivities through -Lancaster and Jones Sound. The rationale for doing so is to complement -the analysis of sea-ice dynamics in the presence of narrow straits. -Lancaster Sound is one of the main outflow paths of sea-ice flowing -through the Canadian Arctic Archipelago (CAA). -Export sensitivities reflect dominant -pathways through the CAA as resolved by the model. -Sensitivity maps can shed a very detailed light on various quantities -affecting the sea-ice export (and thus the underlying pathways). -Note that while the dominant circulation through Lancaster Sound is -toward the East, there is a small Westward flow to the North, -hugging the coast of Devon Island [ARE WE RESOLVING THIS?], -see e.g. \cite{mell:02, mich-etal:06,muen-etal:06}. +We demonstrate the power of the adjoint method in the context of +investigating sea-ice export sensitivities through Lancaster Sound. +The rationale for doing so is to complement the analysis of sea-ice +dynamics in the presence of narrow straits. Lancaster Sound is one of +the main outflow paths of sea-ice flowing through the Canadian Arctic +Archipelago (CAA). Export sensitivities reflect dominant pathways +through the CAA as resolved by the model. Sensitivity maps can shed a +very detailed light on various quantities affecting the sea-ice export +(and thus the underlying pathways). Note that while the dominant +circulation through Lancaster Sound is toward the East, there is a +small Westward flow to the North, hugging the coast of Devon Island +\citep{mell:02, mich-etal:06,muen-etal:06}, which is not resolved in +our simulation. The model domain is a coarsened version of the Arctic face of the high-resolution cubed-sphere configuration of the ECCO2 project -\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 -North Atlantic current to sea-ice variability and export. -The horizontal resolution varies between XX and YY km -with 50 unevenly spaced vertical levels. -The adjoint models run efficiently on 80 processors -(benchmarks have been performed both on an SGI Altix as well as an -IBM SP5 at NASA/ARC). - -Following a 3-year spinup, the model has been integrated for four -years and five months between January 1989 and May 1993. -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 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. - -The adjoint model computes sensitivities -to sea-ice export back in time from 1993 to 1989 along this -trajectory. In principle all adjoint model variable (i.e., Lagrange -multipliers) of the coupled ocean/sea-ice model -as well as the surface atmospheric state are available to -analyze the transient sensitivity behaviour. -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. +\citep{menemenlis05} as described in \refsec{forward}. The horizontal +resolution is half of that in \refsec{forward} while the vertical grid +is the same. \ml{[Is this important? Do we need to be more specific?: + ]} The adjoint models run efficiently on 80 processors (as validated +by benchmarks on both an SGI Altix and an IBM SP5 at NASA/ARC). + +Following a 3-year spinup, the model is integrated for four +years and five months between January 1989 and September 1993. +\ml{[Patrick: to what extent is this different from section 3?]} +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}. The air-sea fluxes in the presence of +%sea-ice are handled by the ice model as described in \refsec{model}. +The objective function $J$ is chosen as the ``solid'' fresh water +export, that is the export of ice and snow converted to units of fresh +water $(\rho_{i} h_{i}c + \rho_{s} h_{s}c)\,u$, through Lancaster +Sound at approximately 82\degW\ (cross-section G in +\reffig{arctic_topog}) averaged over a 12-month period between October +1992 and September 1993. + +The forward trajectory of the model integration resembles broadly that +of the model in \refsec{forward}. Many details are different, owning +to different resolution and integration period; for example, the solid +fresh water transport through Lancaster Sound is +$116\pm101\text{\,km$^{3}$\,y$^{-1}$}$ for a free slip simulation with +the C-LSOR solver, but only $39\pm64\text{\,km$^{3}$\,y$^{-1}$}$ for a +no slip simulation. + +The adjoint model computes sensitivities of this export back in time +from 1993 to 1989 along this trajectory. In principle all adjoint +model variable (i.e., Lagrange multipliers) of the coupled +ocean/sea-ice model as well as the surface atmospheric state are +available to analyze the transient sensitivity behavior. 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. DISCUSS FORWARD STATE, INCLUDING SOME NUMBERS ON SEA-ICE EXPORT -\subsection{Sensitivities to the sea-ice state} +\subsubsection{Adjoint sensitivities} -\paragraph{Sensitivities to the sea-ice thickness} - -The most readily interpretable ice-export sensitivity is that -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\ml{ in accordance with expectations/as expected}: - -(*) -Dominant pattern (for the free-slip run) is that of positive sensitivities, i.e. -a unit increase in sea-ice thickness in most places upstream -of Lancaster Sound will increase sea-ice export through Lancaster Sound. -The dominant pathway follows (backward in time) through Barrow Strait -into Viscount Melville Sound, and from there trough M'Clure Strait -into the Arctic Ocean (the "Northwest Passage"). -Secondary paths are Northward from -Viscount Melville Sound through Byam Martin Channel into -Prince Gustav Adolf Sea and through Penny Strait into MacLean Strait. - -(*) -As expected, at any given time the -region of influence is larger for the free-slip than no-slip simulation. -For the no-slip run, the region of influence is confined, after four years, -to just West of Barrow Strait (North of Prince of Wales Island), -and to the South of Penny Strait. -In contrast, sensitivities of the free-slip run extend -all the way to the Arctic interior both to the West -(M'Clure St.) and to the North (Ballantyne St., Prince Gustav Adolf Sea, -Massey Sound). - -(*) -sensitivities seem to spread out in "pulses" (seasonal cycle) -[PLOT A TIME SERIES OF ADJheff in Barrow Strait) - -(*) -The sensitivity in Baffin Bay are more complex. -The pattern evolves along the Western boundary, connecting -the Lancaster Sound Polynya, the Coburg Island Polynya, and the -North Water Polynya, and reaches into Nares Strait and the Kennedy Channel. -The sign of sensitivities has an oscillatory character -[AT FREQUENCY OF SEASONAL CYCLE?]. -First, we need to establish whether forward perturbation runs -corroborate the oscillatory behaviour. -Then, several possible explanations: -(i) connection established through Nares Strait throughflow -which extends into Western boundary current in Northern Baffin Bay. -(ii) sea-ice concentration there is seasonal, i.e. partly -ice-free during the year. Seasonal cycle in sensitivity likely -connected to ice-free vs. ice-covered parts of the year. -Negative sensitivities can potentially be attributed -to blocking of Lancaster Sound ice export by Western boundary ice -in Baffin Bay. -(iii) Alternatively to (ii), flow reversal in Lancaster Sound is a possibility -(in reality there's a Northern counter current hugging the coast of -Devon Island which we probably don't resolve). - -Remote control of Kennedy Channel on Lancaster Sound ice export -seems a nice test for appropriateness of free-slip vs. no-slip BCs. - -\paragraph{Sensitivities to the sea-ice area} - -Fig. XXX depcits transient sea-ice export sensitivities -to changes in sea-ice concentration - $\partial J / \partial area$ 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. -Contrary to the steady patterns seen for thickness sensitivities, -the ice-concentration sensitivities exhibit a strong seasonal cycle -in large parts of the domain (but synchronized on large scale). -The following discussion is w.r.t. free-slip run. - -(*) -Months, during which sensitivities are negative: -\\ -0 to 5 Db=N/A, Dr=5 (May-Jan) \\ -10 to 17 Db=7, Dr=5 (Jul-Jan) \\ -22 to 29 Db=7, Dr=5 (Jul-Jan) \\ -34 to 41 Db=7, Dr=5 (Jul-Jan) \\ -46 to 49 D=N/A \\ -% -These negative sensitivities seem to be connected to months -during which main parts of the CAA are essentially entirely ice-covered. -This means that increase in ice concentration during this period -will likely reduce ice export due to blocking -[NEED TO EXPLAIN WHY THIS IS NOT THE CASE FOR dJ/dHEFF]. -Only during periods where substantial parts of the CAA are -ice free (i.e. sea-ice concentration is less than one in larger parts of -the CAA) will an increase in ice-concentration increase ice export. - -(*) -Sensitivities peak about 2-3 months before sign reversal, i.e. -max. negative sensitivities are expected end of July -[DOUBLE CHECK THIS]. - -(*) -Peaks/bursts of sensitivities for months -14-17, 19-21, 27-29, 30-33, 38-40, 42-45 - -(*) -Spatial "anti-correlation" (in sign) between main sensitivity branch -(essentially Northwest Passage and immediate connecting channels), -and remote places. -For example: month 20, 28, 31.5, 40, 43. -The timings of max. sensitivity extent are similar between -free-slip and no-slip run; and patterns are similar within CAA, -but differ in the Arctic Ocean interior. - -(*) -Interesting (but real?) patterns in Arctic Ocean interior. - -\paragraph{Sensitivities to the sea-ice velocity} - -(*) -Patterns of ADJuice at almost any point in time are rather complicated -(in particular with respect to spatial structure of signs). -Might warrant perturbation tests. -Patterns of ADJvice, on the other hand, are more spatially coherent, -but still hard to interpret (or even counter-intuitive -in many places). - -(*) -"Growth in extent of sensitivities" goes in clear pulses: -almost no change between months: 0-5, 10-20, 24-32, 36-44 -These essentially correspond to months of - - -\subsection{Sensitivities to the oceanic state} - -\paragraph{Sensitivities to theta} - -\textit{Sensitivities at the surface (z = 5 m)} - -(*) -mabye redo with caxmax=0.02 or even 0.05 - -(*) -Core of negative sensitivities spreading through the CAA as -one might expect [TEST]: -Increase in SST will decrease ice thickness and therefore ice export. - -(*) -What's maybe unexpected is patterns of positive sensitivities -at the fringes of the "core", e.g. in the Southern channels -(Bellot St., Peel Sound, M'Clintock Channel), and to the North -(initially MacLean St., Prince Gustav Adolf Sea, Hazen St., -then shifting Northward into the Arctic interior). - -(*) -Marked sensitivity from the Arctic interior roughly along 60$^{\circ}$W -propagating into Lincoln Sea, then -entering Nares Strait and Smith Sound, periodically -warming or cooling[???] the Lancaster Sound exit. - -\textit{Sensitivities at depth (z = 200 m)} - -(*) -Negative sensitivities almost everywhere, as might be expected. - -(*) -Sensitivity patterns between free-slip and no-slip BCs -are quite similar, except in Lincoln Sea (North of Nares St), -where the sign is reversed (but pattern remains similar). - -\paragraph{Sensitivities to salt} - -T.B.D. - -\paragraph{Sensitivities to velocity} - -T.B.D. - -\subsection{Sensitivities to the atmospheric state} - -\begin{itemize} -% -\item -plot of ATEMP for 12, 24, 36, 48 months -% -\item -plot of HEFF for 12, 24, 36, 48 months -% -\end{itemize} - - - -\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. -\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, -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}] -{\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]{\fpath/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}} -} -% -\caption{Sensitivity of sea-ice export through Fram Strait in December 2005 to -sea-ice thickness at various prior times. -\label{fig:4yradjheff}} -\end{figure} +The most readily interpretable ice-export sensitivity is that to +effective ice thickness, $\partial{J} / \partial{(hc)}$. +\reffig{adjheff} shows transient $\partial{J} / \partial{(hc)}$ using +free-slip (left column) and no-slip (right column) boundary +conditions. Sensitivity snapshots are depicted for 12 months prior to +September 1993 (at the beginning of the averaging period for the objective +function $J$, top) and at the beginning of the integration in January +1989 (bottom). +\begin{figure*}[t] + \includegraphics*[width=\textwidth]{\fpath/adjheff} + \caption{Sensitivity $\partial{J}/\partial{(hc)}$ in + m$^2$\,s$^{-1}$/m for two different times (rows) and two different + boundary conditions for sea ice drift. The color scale is chosen + to illustrate the patterns of the sensitivities; the maximum and + minimum values are given above the figures. + \label{fig:adjheff}} +\end{figure*} + +At the beginning of October 1992, the positive sensitivities in +the Lancaster Sound mean that an increase of ice volume increase the +solid fresh water export. The negative sensivities to the East and to the +West can be explained by indirect effects: less ice to the East means +less resistance to eastward drift and thus more export; similarly, less ice to +the West means that more ice can be moved eastwards from the Barrow Strait +into the Lancaster Sound leading to more ice export. The sensitivities +are similar for both no slip and free slip solutions with a slightly larger +area covered by non-zero sensitivities in the free slip solution. At +the beginning of the integration (the end of the backward adjoint +integration) the free and no slip solutions are very different. The +sensitivities of the free slip solution extend through the enitre +Canadian Archipelago and into the Arctic while in the no slip solution +they still are confined to the Lancaster Sound and the Barrow +Strait. This implies that in the free slip solution ice can drift more +easily through the narrow straits of the Canadian Archipelago, so that +a positive ice volume anomaly anywhere in the Canadian Archipelago is +moved through the Lancaster Sound within 4 years thus increasing the +ice export. + +The temporal evolution of several sensitivities along the zonal axis +Lancaster Sound-Barrow Strait-Melville Sound are shown in +\reffig{lancaster}. +\begin{figure*} + \includegraphics*[height=.8\textheight]{\fpath/lancaster_adj} + \caption{Hovermoeller diagrams of sensitivities (derivatives) of the + ``solid'' fresh water (i.e., ice and snow) export $J$ through Lancaster sound + (\reffig{arctic_topog}, cross-section G) with respect to effective + ice thickness ($hc$), ocean surface temperature (SST) and + precipitation ($p$) for two runs with free slip and no slip boundary + conditions for the sea ice drift. Also shown it the normalized ice + strengh $P/P^*=(hc)\,\exp[-C\,(1-c)]$ (bottom panel); each plot is + overlaid with the contours 1 and 3 of the normalized ice strength + for orientation. + \label{fig:lancaster}} +\end{figure*} +\reffig{lancaster} shows the sensitivities of ``solid'' fresh water +export, that is ice and snow, through Lancaster sound (cross-section G +in \reffig{arctic_topog}) with respect to effective ice thickness +($hc$), ocean surface temperature (SST) and precipitation ($p$) for +two runs with free slip and no slip boundary conditions for the sea +ice drift. The Hovmoeller diagrams of sensitivities (derivatives) with +respect to effective ice thickness (top) and ocean surface temperature +(second from top) are coherent: more ice in the Lancaster Sound leads +to more export and one way to get more ice is by colder surface +temperatures (less melting from below). In the free slip case the +sensitivities can propagate westwards (backwards in time) when the ice +strength is low in late summer. In the no slip case the (normalized) +ice strength does not fall below 1 during the winters of 1991 to 1993 +(mainly because the ice concentrations remain nearly 100\%, not +shown), so that ice is blocked and cannot drift eastwards (forward in +time) in the Melville Sound-Barrow Strait-Lancaster Sound channel. +Consequently the sensitivies do not propagate westwards (backwards in +time) and the export through Lancaster Sound is only affected by +local ice formation and melting. + +The sensitivities to precipitation are negative (more precipitation +leads to less export) before January and mostly positive after +January. Further they are mostly positive for normalized ice strengths +over 3. Assuming that most precipation is snow in this area---in the +current implementation the model differentiates between snow and rain +depending on the thermodynamic growth rate; when it is cold enough for +ice to grow, all precipitation is assumed to be snow---the +sensitivities can be interpreted in terms of the model physics. Short +wave radiation cannot penetrate a snow cover and has a higer albedo +than ice (0.85 for dry snow and 0.75 for dry ice in our case); thus it +protects the ice against melting in spring (after January). On the +other hand, snow reduces the effective conductivity and thus the heat +flux through the ice. This insulating effect slows down the cooling of +the surface water underneath the ice and limits the ice growth from +below, so that less snow in the ice-growing season leads to more new +ice and thus more ice export. + +%Und jetzt weiss ich nicht mehr weiter, aber nun kann folgendes passiert sein: +%1. snow insulates against melting from above during spring: more precip (snow) -> more export +%2. less snow during fall -> more ice -> more export +%3. precip is both snow and rain, depending on the sign of "FICE" (thermodynamic growth rate), with probably different implications + + +\subsubsection{Forward sensitivities} + +\ml{[Here we need for integrations to show that the adjoint + sensitivites are not just academic. I suggest to perturb HEFF + and THETA initial conditions, and PRECIP somewhere in the Melville + Sound and then produce plots similar to reffig{lancaster}. For + PRECIP it would be great to have two perturbation experiments, one + where ADJprecip is posivite and one where ADJprecip is negative]} +%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. +%a unit increase in sea-ice thickness in most places upstream +%of Lancaster Sound will increase sea-ice export through Lancaster Sound. +%The dominant pathway follows (backward in time) through Barrow Strait +%into Viscount Melville Sound, and from there trough M'Clure Strait +%into the Arctic Ocean (the "Northwest Passage"). +%Secondary paths are Northward from +%Viscount Melville Sound through Byam Martin Channel into +%Prince Gustav Adolf Sea and through Penny Strait into MacLean Strait. + +%(*) +%As expected, at any given time the +%region of influence is larger for the free-slip than no-slip simulation. +%For the no-slip run, the region of influence is confined, after four years, +%to just West of Barrow Strait (North of Prince of Wales Island), +%and to the South of Penny Strait. +%In contrast, sensitivities of the free-slip run extend +%all the way to the Arctic interior both to the West +%(M'Clure St.) and to the North (Ballantyne St., Prince Gustav Adolf Sea, +%Massey Sound). + +%(*) +%sensitivities seem to spread out in "pulses" (seasonal cycle) +%[PLOT A TIME SERIES OF ADJheff in Barrow Strait) + +%(*) +%The sensitivity in Baffin Bay are more complex. +%The pattern evolves along the Western boundary, connecting +%the Lancaster Sound Polynya, the Coburg Island Polynya, and the +%North Water Polynya, and reaches into Nares Strait and the Kennedy Channel. +%The sign of sensitivities has an oscillatory character +%[AT FREQUENCY OF SEASONAL CYCLE?]. +%First, we need to establish whether forward perturbation runs +%corroborate the oscillatory behaviour. +%Then, several possible explanations: +%(i) connection established through Nares Strait throughflow +%which extends into Western boundary current in Northern Baffin Bay. +%(ii) sea-ice concentration there is seasonal, i.e. partly +%ice-free during the year. Seasonal cycle in sensitivity likely +%connected to ice-free vs. ice-covered parts of the year. +%Negative sensitivities can potentially be attributed +%to blocking of Lancaster Sound ice export by Western boundary ice +%in Baffin Bay. +%(iii) Alternatively to (ii), flow reversal in Lancaster Sound is a possibility +%(in reality there's a Northern counter current hugging the coast of +%Devon Island which we probably don't resolve). + +%Remote control of Kennedy Channel on Lancaster Sound ice export +%seems a nice test for appropriateness of free-slip vs. no-slip BCs. + +%\paragraph{Sensitivities to the sea-ice area} + +%Fig. XXX depcits transient sea-ice export sensitivities +%to changes in sea-ice concentration +% $\partial J / \partial area$ 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. +%Contrary to the steady patterns seen for thickness sensitivities, +%the ice-concentration sensitivities exhibit a strong seasonal cycle +%in large parts of the domain (but synchronized on large scale). +%The following discussion is w.r.t. free-slip run. + +%(*) +%Months, during which sensitivities are negative: +%\\ +%0 to 5 Db=N/A, Dr=5 (May-Jan) \\ +%10 to 17 Db=7, Dr=5 (Jul-Jan) \\ +%22 to 29 Db=7, Dr=5 (Jul-Jan) \\ +%34 to 41 Db=7, Dr=5 (Jul-Jan) \\ +%46 to 49 D=N/A \\ +%% +%These negative sensitivities seem to be connected to months +%during which main parts of the CAA are essentially entirely ice-covered. +%This means that increase in ice concentration during this period +%will likely reduce ice export due to blocking +%[NEED TO EXPLAIN WHY THIS IS NOT THE CASE FOR dJ/dHEFF]. +%Only during periods where substantial parts of the CAA are +%ice free (i.e. sea-ice concentration is less than one in larger parts of +%the CAA) will an increase in ice-concentration increase ice export. + +%(*) +%Sensitivities peak about 2-3 months before sign reversal, i.e. +%max. negative sensitivities are expected end of July +%[DOUBLE CHECK THIS]. + +%(*) +%Peaks/bursts of sensitivities for months +%14-17, 19-21, 27-29, 30-33, 38-40, 42-45 + +%(*) +%Spatial "anti-correlation" (in sign) between main sensitivity branch +%(essentially Northwest Passage and immediate connecting channels), +%and remote places. +%For example: month 20, 28, 31.5, 40, 43. +%The timings of max. sensitivity extent are similar between +%free-slip and no-slip run; and patterns are similar within CAA, +%but differ in the Arctic Ocean interior. + +%(*) +%Interesting (but real?) patterns in Arctic Ocean interior. + +%\paragraph{Sensitivities to the sea-ice velocity} + +%(*) +%Patterns of ADJuice at almost any point in time are rather complicated +%(in particular with respect to spatial structure of signs). +%Might warrant perturbation tests. +%Patterns of ADJvice, on the other hand, are more spatially coherent, +%but still hard to interpret (or even counter-intuitive +%in many places). + +%(*) +%"Growth in extent of sensitivities" goes in clear pulses: +%almost no change between months: 0-5, 10-20, 24-32, 36-44 +%These essentially correspond to months of + + +%\subsection{Sensitivities to the oceanic state} + +%\paragraph{Sensitivities to theta} + +%\textit{Sensitivities at the surface (z = 5 m)} + +%(*) +%mabye redo with caxmax=0.02 or even 0.05 + +%(*) +%Core of negative sensitivities spreading through the CAA as +%one might expect [TEST]: +%Increase in SST will decrease ice thickness and therefore ice export. + +%(*) +%What's maybe unexpected is patterns of positive sensitivities +%at the fringes of the "core", e.g. in the Southern channels +%(Bellot St., Peel Sound, M'Clintock Channel), and to the North +%(initially MacLean St., Prince Gustav Adolf Sea, Hazen St., +%then shifting Northward into the Arctic interior). + +%(*) +%Marked sensitivity from the Arctic interior roughly along 60$^{\circ}$W +%propagating into Lincoln Sea, then +%entering Nares Strait and Smith Sound, periodically +%warming or cooling[???] the Lancaster Sound exit. + +%\textit{Sensitivities at depth (z = 200 m)} + +%(*) +%Negative sensitivities almost everywhere, as might be expected. + +%(*) +%Sensitivity patterns between free-slip and no-slip BCs +%are quite similar, except in Lincoln Sea (North of Nares St), +%where the sign is reversed (but pattern remains similar). + +%\paragraph{Sensitivities to salt} + +%T.B.D. + +%\paragraph{Sensitivities to velocity} + +%T.B.D. + +%\subsection{Sensitivities to the atmospheric state} + +%\begin{itemize} +%% +%\item +%plot of ATEMP for 12, 24, 36, 48 months +%% +%\item +%plot of HEFF for 12, 24, 36, 48 months +%% +%\end{itemize} + + + +%\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. +%\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, +%the circulation around Svalbard, and ... + + +%%\begin{figure}[t!] +%%\centerline{ +%%\subfigure[{\footnotesize -12 months}] +%%{\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]{\fpath/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}} +%%} +%% +%%\caption{Sensitivity of sea-ice export through Fram Strait in December 2005 to +%%sea-ice thickness at various prior times. +%%\label{fig:4yradjheff}} +%%\end{figure} + + +%\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. %%% Local Variables: