--- MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex	2008/07/28 04:34:37	1.6
+++ MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex	2008/07/28 12:34:27	1.7
@@ -102,23 +102,28 @@
 %
 through Lancaster Sound at approximately 82\degW\ (cross-section G in
 \reffig{arctic_topog}) averaged \ml{PH: Maybe integrated quantity is
-more physical} over the final 12-month of the integration between October
-1992 and September 1993.
+more physical; ML: what did you actually compute? I did not scale
+anything, yet. Please insert what is actually done.} over the final
+12-month of the integration 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
 %
-\ml{PH: Martin, where did you get these numbers from?}
+\ml{PH: Martin, where did you get these numbers from?} 
+\ml{[ML: I computed hu = -sum((SIheff+SIhsnow)*SIuice*area)/sum(area) at
+$i=100,j=116:122$, and then took mean(hu) and std(hu). What are your numbers?]}
 %
 $116\pm101\text{\,km$^{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.
+no slip simulation. \ml{[Here we can say that the export through
+  Lancaster Sound is highly uncertain, making is a perfect candidate
+  for sensitivity, bla bla?]}
 
 The adjoint model is the transpose of the tangent linear (or Jacobian) model
-operator. It runs backward in time, from September 1993 to
-January 1989. Along its integration it accumulates the Lagrange multipliers
+operator. It runs backwards in time, from September 1993 to
+January 1989. During its integration it accumulates the Lagrange multipliers
 of the model subject to the objective function (solid freshwater export),
 which can be interpreted as sensitivities of the objective function
 to each control variable and each element of the intermediate 
@@ -128,7 +133,7 @@
 available for analysis of 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
+areas, the sea-ice adjoint converts surface ocean sensitivities to
 atmospheric sensitivities.
 
 DISCUSS FORWARD STATE, INCLUDING SOME NUMBERS ON SEA-ICE EXPORT
@@ -139,8 +144,8 @@
 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 beginning of October 2002,
-i.e. 12 months back in time from September 1993 
+conditions. Sensitivity snapshots are depicted for beginning of October 1992,
+that is 12 months before September 1993 
 (the beginning of the averaging period for the objective
 function $J$, top),
 and for Jannuary 1989, the beginning of the forward integration (bottom).
@@ -154,51 +159,64 @@
     \label{fig:adjheff}}
 \end{figure*}
 
-As expected, the sensitivity patterns are predominantly positive,
-an increase in ice volume in most places ``upstream'' of
+The sensitivity patterns for effective ice thickness are predominantly positive.
+An increase in ice volume in most places ``upstream'' of
 Lancaster sound increases the solid fresh water export at the exit section.
-Also obvious is the transient nature of the sensitivity patterns
-(top panels vs. bottom panels),
-i.e. as time moves backward, an increasing area upstream of Lancaster Sound 
-contributes to the export sensitivity.
-The dominant pathway (free slip case) 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.
-
-The difference between the free slip and no slip solution is evident:
-by the end of the adjoint integration, in January 1989
-the free-slip sensitivities (bottom left) extend through most of the CAA
-and all the way into the Arctic interior, both to the West (M'Clure St.) 
-and to the North 
-(Ballantyne St., Prince Gustav Adolf Sea, Massey Sound), 
-whereas the no slip sensitivities (bottom right) are overall weaker 
-and remain mostly confined to Lancaster Sound and just West of Barrow Strait.
-In the free slip solution ice can drift more
-easily through narrow straits, and
-a positive ice volume anomaly further upstream in the CAA may increase
-ice export through the Lancaster Sound within a 4 year period.
+The transient nature of the sensitivity patterns 
+(top panels vs. bottom panels) is also obvious:
+the area upstream of the Lancaster Sound that
+contributes to the export sensitivity is larger in the earlier snapshot.
+In the free slip case, the sensivity follows (backwards in time) the dominant pathway
+through the Barrow Strait
+into the Viscount Melville Sound, and from there trough the M'Clure Strait
+into the Arctic Ocean (the ``Northwest Passage''). \ml{[Is that really
+  the Northwest Passage? I thought it would turn south in Barrow
+  Strait, but I am easily convinced because it makes a nicer story.]}
+Secondary paths are northward from the
+Viscount Melville Sound through the Byam Martin Channel into
+the Prince Gustav Adolf Sea and through the Penny Strait into the
+MacLean Strait. \ml{[Patrick, all these names, if mentioned in the
+  text need to be included somewhere in a figure (i.e. fig1). Can you
+  either do this in fig1 (based on martins\_figs.m) or send me a map
+  where these names are visible so I can do this unambiguously. I
+  don't know where  Byam
+  Martin Channel, Prince Gustav Adolf Sea, Penny Strait, MacLean
+  Strait, Ballantyne St., Massey Sound are.]}
+
+There are large differences between the free slip and no slip
+solution.  By the end of the adjoint integration in January 1989, the
+no slip sensitivities (bottom right) are generally weaker than the
+free slip sensitivities and hardly reach beyond the western end of the
+Barrow Strait. In contrast, the free-slip sensitivities (bottom left)
+extend through most of the CAA and into the Arctic interior, both to
+the West (M'Clure St.)  and to the North (Ballantyne St., Prince
+Gustav Adolf Sea, Massey Sound), because in this case the ice can
+drift more easily through narrow straits, so that a positive ice
+volume anomaly anywhere upstream in the CAA increases ice export
+through the Lancaster Sound within the simulated 4 year period.
 
 One peculiar feature in the October 1992 sensitivity maps (top panels)
-are the negative sensivities to the East and to the West.
+are the negative sensivities to the East and to the West of the
+Lancaster Sound.
 These 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. 
-\ml{PH: The first explanation (East) I buy, the second (West) I don't}.
-
-The temporal evolution of several ice export sensitivities 
-(eqn. XX) along a zonal axis through
-Lancaster Sound, Barrow Strait,and  Melville Sound 
-(115\degW\ to 80\degW\ ), 
-are depicted as Hovmueller diagrams in \reffig{lancaster}.
-From top to bottom, sensitivities are with respect to effective 
-ice thickness ($hc$), 
-ocean surface temperature ($SST$) and precipitation ($p$) for free slip 
-(left column) and no slip (right column) ice drift boundary conditions.
+\ml{PH: The first explanation (East) I buy, the second (West) I
+  don't.} \ml{[ML: unfortunately, I don't have anything better to
+  offer, do you? Keep in mind that these sensitivites are very small
+  and only show up, because of the colorscale. In Fig6, they are
+  hardly visible.]}
+
+The temporal evolution of several ice export sensitivities (eqn. XX,
+\ml{[which equation do you mean?]}) along a zonal axis through
+Lancaster Sound, Barrow Strait, and Melville Sound (115\degW\ to
+80\degW, averaged across the passages) are depicted as Hovmueller
+diagrams in \reffig{lancaster}. These are, from top to bottom, the
+sensitivities with respect to effective ice thickness ($hc$), ocean
+surface temperature ($SST$) and precipitation ($p$) for free slip
+(left column) and no slip (right column) ice drift boundary
+conditions.
 %
 \begin{figure*}
   \includegraphics*[height=.8\textheight]{\fpath/lancaster_adj}
@@ -221,15 +239,16 @@
 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 spread out in "pulses" following a seasonal cycle:
-can propagate westwards (backwards in time) when the ice
-strength is low in late summer, early autumn. 
+ice can propagate eastwards (forward in time and thus sensitivites can
+propagate westwards (backwards in time) when the ice strength is low
+in late summer to early autumn.  
 In contrast, during winter, the sensitivities show little to now
-westward propagation.
+westward propagation, as the ice is frozen solid and does not move.
 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
+(mainly because the ice concentrations remain near 100\%, not
 shown). Ice is therefore blocked and cannot drift eastwards 
-(forward in time) through the 
+(forward in time) through the Viscount
 Melville Sound, Barrow Strait, Lancaster Sound channel system.
 Consequently, the sensitivities do not propagate westwards (backwards in
 time) and the export through Lancaster Sound is only affected by
@@ -240,27 +259,29 @@
 before January (more precisely, late fall) and mostly positive after January
 (more precisely, January through July). 
 Times of positive sensitivities coincide with times of
-normalized ice strengths exceeding values of 3.
+normalized ice strengths exceeding values of 3
 %
 \ml{PH: Problem is, that's not true for the first two years (backward),
-East of 95\degW\ , i.e. in Lancaster Sound.
+east of 95\degW, that is, in the Lancaster Sound.
 For example, at 90\degW\ the sensitivities are negative throughout 1992,
-and no clear correlation to ice strength is apparent there.}.
-%
-Assuming that most precipation is snow in this area
+and no clear correlation to ice strength is apparent there.}
+except between 95\degW\ and 85\degW, which is an area of
+increased snow cover in spring. \ml{[ML: and no, I cannot explain
+  that. Can you?]}
+
 %
-\footnote{
+Assuming that most precipation is snow in this area\footnote{
 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 the 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).  
-\ml{PH: what about the direct effect of accumulation of precip. as snow
-which directly increases the volume.}.
+the sensitivities can be interpreted in terms of the model physics.
+The accumulation of snow directly increases the exported volume.
+Further, short wave radiation cannot penetrate the 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
@@ -268,15 +289,18 @@
 below, so that less snow in the ice-growing season leads to more new
 ice and thus more ice export.
 \ml{PH: Should probably discuss the effect of snow vs. rain.
-To me it seems that the "rain" effect doesn't really play
+To me it seems that the "rain" effect doesn't really play a role
 because the neg. sensitivities are too late in the fall,
-probably mostly falling as snow.}.
-
-%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
-
+probably mostly falling as snow.} \ml{[ML: correct, I looked at
+NCEP/CORE air temperatures, and they are hardly above freezing in
+Jul/Aug, but otherwise below freezing, that why I can assume that most
+precip is snow. ]} \ml{[this is not very good but do you have anything
+better?:]}
+The negative sensitivities to precipitation between 95\degW\ and
+85\degW\ in spring 1992 may be explained by a similar mechanism: in an
+area of thick snow (almost 50\,cm), ice cannot melt and tends to block
+the channel so that ice coming in from the West cannot pass thus
+leading to less ice export in the next season.
 
 \subsubsection{Forward sensitivities}
 
