/[MITgcm]/MITgcm_contrib/articles/ceaice/ceaice_adjoint.tex

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-revision 1.6 by heimbach,
Mon Jul 28 04:34:37 2008 UTC
+revision 1.8 by mlosch,
Tue Jul 29 08:34:22 2008 UTC
 Line 102 
 J \, = \, (\rho_{i} h_{i}c + \rho_{s} h_
  %
  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
+ more physical; ML: what did you actually compute? I did not scale
-and September 1993.
+ anything, yet. Please insert what is actually done.} over the final
+-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{[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
+ operator. It runs backwards in time, from September 1993 to
- January 1989. Along its integration it accumulates the Lagrange multipliers
+ 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
-Line 128 
 ocean/sea-ice model state as well as the
+Line 133 
 ocean/sea-ice model state as well as the
  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
-Line 139 
 The most readily interpretable ice-expor
+Line 144 
 The most readily interpretable ice-expor
  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,
+ conditions. Sensitivity snapshots are depicted for beginning of October 1992,
- i.e. 12 months back in time from September 1993
+ 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).
-Line 154 
 and for Jannuary 1989, the beginning of
+Line 159 
 and for Jannuary 1989, the beginning of
      \label{fig:adjheff}}
  \end{figure*}
- As expected, the sensitivity patterns are predominantly positive,
+ The sensitivity patterns for effective ice thickness are predominantly positive.
- an increase in ice volume in most places ``upstream'' of
+ 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
+ The transient nature of the sensitivity patterns
- (top panels vs. bottom panels),
+ (top panels vs. bottom panels) is also obvious:
- i.e. as time moves backward, an increasing area upstream of Lancaster Sound
+ the area upstream of the Lancaster Sound that
- contributes to the export sensitivity.
+ contributes to the export sensitivity is larger in the earlier snapshot.
- The dominant pathway (free slip case) follows (backward in time)
+ In the free slip case, the sensivity follows (backwards in time) the dominant pathway
- through Barrow Strait
+ through the Barrow Strait
- into Viscount Melville Sound, and from there trough M'Clure Strait
+ into the Viscount Melville Sound, and from there trough the M'Clure Strait
- into the Arctic Ocean (the ``Northwest Passage'').
+ into the Arctic Ocean (the ``Northwest Passage''). \ml{[Is that really
- Secondary paths are Northward from
+   the Northwest Passage? I thought it would turn south in Barrow
- Viscount Melville Sound through Byam Martin Channel into
+   Strait, but I am easily convinced because it makes a nicer story.]}
- Prince Gustav Adolf Sea and through Penny Strait into MacLean Strait.
+ Secondary paths are northward from the
+ Viscount Melville Sound through the Byam Martin Channel into
- The difference between the free slip and no slip solution is evident:
+ the Prince Gustav Adolf Sea and through the Penny Strait into the
- by the end of the adjoint integration, in January 1989
+ MacLean Strait. \ml{[Patrick, all these names, if mentioned in the
- the free-slip sensitivities (bottom left) extend through most of the CAA
+   text need to be included somewhere in a figure (i.e. fig1). Can you
- and all the way into the Arctic interior, both to the West (M'Clure St.)
+   either do this in fig1 (based on martins\_figs.m) or send me a map
- and to the North
+   where these names are visible so I can do this unambiguously. I
- (Ballantyne St., Prince Gustav Adolf Sea, Massey Sound),
+   don't know where  Byam
- whereas the no slip sensitivities (bottom right) are overall weaker
+   Martin Channel, Prince Gustav Adolf Sea, Penny Strait, MacLean
- and remain mostly confined to Lancaster Sound and just West of Barrow Strait.
+   Strait, Ballantyne St., Massey Sound are.]}
- In the free slip solution ice can drift more
- easily through narrow straits, and
+ There are large differences between the free slip and no slip
- a positive ice volume anomaly further upstream in the CAA may increase
+ solution.  By the end of the adjoint integration in January 1989, the
- ice export through the Lancaster Sound within a 4 year period.
+ 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}.
+ \ml{PH: The first explanation (East) I buy, the second (West) I
+   don't.} \ml{[ML: unfortunately, I don't have anything better to
- The temporal evolution of several ice export sensitivities
+   offer, do you? Keep in mind that these sensitivites are very small
- (eqn. XX) along a zonal axis through
+   and only show up, because of the colorscale. In Fig6, they are
- Lancaster Sound, Barrow Strait,and  Melville Sound
+   hardly visible.]}
- (115\degW\ to 80\degW\ ),
- are depicted as Hovmueller diagrams in \reffig{lancaster}.
+ The temporal evolution of several ice export sensitivities (eqn. XX,
- From top to bottom, sensitivities are with respect to effective
+ \ml{[which equation do you mean?]}) along a zonal axis through
- ice thickness ($hc$),
+ Lancaster Sound, Barrow Strait, and Melville Sound (115\degW\ to
- ocean surface temperature ($SST$) and precipitation ($p$) for free slip
+\degW, averaged across the passages) are depicted as Hovmueller
- (left column) and no slip (right column) ice drift boundary conditions.
+ diagrams in \reffig{lancasteradj}. 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}
-   \caption{Hovermoeller diagrams of sensitivities (derivatives) of the
+   \caption{Hovermoeller diagrams along the axis Viscount Melville
-     ``solid'' fresh water (i.e., ice and snow) export $J$ through Lancaster sound
+     Sound/Barrow Strait/Lancaster Sound. The diagrams show the
+     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
+     precipitation ($p$) for two runs with free slip and no slip
-     conditions for the sea ice drift. Also shown it the normalized ice
+     boundary conditions for the sea ice drift. Each plot is overlaid
-     strengh $P/P^*=(hc)\,\exp[-C\,(1-c)]$ (bottom panel); each plot is
+     with the contours 1 and 3 of the normalized ice strengh
-     overlaid with the contours 1 and 3 of the normalized ice strength
+     $P/P^*=(hc)\,\exp[-C\,(1-c)]$ for orientation.
-     for orientation.
+     \label{fig:lancasteradj}}
-     \label{fig:lancaster}}
+ \end{figure*}
+ %
+ \begin{figure*}
+   \includegraphics*[height=.8\textheight]{\fpath/lancaster_fwd}
+   \caption{Hovermoeller diagrams along the axis Viscount Melville
+     Sound/Barrow Strait/Lancaster Sound of effective ice thickness
+     ($hc$), effective snow thickness ($h_{s}c$) and normalized ice
+     strengh $P/P^*=(hc)\,\exp[-C\,(1-c)]$ for two runs with free slip
+     and no slip boundary conditions for the sea ice drift. Each plot
+     is overlaid with the contours 1 and 3 of the normalized ice
+     strength for orientation.
+     \label{fig:lancasterfwd}}
  \end{figure*}
  %
-Line 221 
 more ice in the Lancaster Sound leads
+Line 252 
 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 spread out in "pulses" following a seasonal cycle:
- can propagate westwards (backwards in time) when the ice
+ ice can propagate eastwards (forward in time and thus sensitivites can
- strength is low in late summer, early autumn.
+ 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
-Line 240 
 they are negative (more precipitation le
+Line 272 
 they are negative (more precipitation le
  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.}.
+ and no clear correlation to ice strength is apparent there.}
- %
+ except between 95\degW\ and 85\degW, which is an area of
- Assuming that most precipation is snow in this area
+ 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
+ the sensitivities can be interpreted in terms of the model physics.
- wave radiation cannot penetrate the snow cover and has a higer albedo
+ The accumulation of snow directly increases the exported volume.
- than ice (0.85 for dry snow and 0.75 for dry ice in our case); thus it
+ Further, short wave radiation cannot penetrate the snow cover and has
- protects the ice against melting in spring (after January).
+ a higer albedo than ice (0.85 for dry snow and 0.75 for dry ice in our
- \ml{PH: what about the direct effect of accumulation of precip. as snow
+ case); thus it protects the ice against melting in spring (after
- which directly increases the volume.}.
+ 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
-Line 268 
 the surface water underneath the ice and
+Line 302 
 the surface water underneath the ice and
  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.}.
+ probably mostly falling as snow.} \ml{[ML: correct, I looked at
+ NCEP/CORE air temperatures, and they are hardly above freezing in
- %Und jetzt weiss ich nicht mehr weiter, aber nun kann folgendes passiert sein:
+ Jul/Aug, but otherwise below freezing, that why I can assume that most
- %1. snow insulates against melting from above during spring: more precip (snow) -> more export
+ precip is snow. ]} \ml{[this is not very good but do you have anything
- %2. less snow during fall -> more ice -> more export
+ better?:]}
- %3. precip is both snow and rain, depending on the sign of "FICE" (thermodynamic growth rate), with probably different implications
+ The negative sensitivities to precipitation between 95\degW\ and
+\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}
  \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
+   Sound and then produce plots similar to reffig{lancasteradj}. For
    PRECIP it would be great to have two perturbation experiments, one
    where ADJprecip is posivite and one where ADJprecip is negative]}

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