| 1 |
\section{Adjoint sensiivities of the MITsim} |
\section{Adjoint sensitivities of the MITsim} |
| 2 |
\label{sec:adjoint} |
\label{sec:adjoint} |
| 3 |
|
|
| 4 |
\subsection{The adjoint of MITsim} |
\subsection{The adjoint of MITsim} |
| 65 |
|
|
| 66 |
|
|
| 67 |
\subsection{An example: sensitivities of sea-ice export through |
\subsection{An example: sensitivities of sea-ice export through |
| 68 |
the Lancaster and Jones Sound} |
the Lancaster Sound} |
| 69 |
|
|
| 70 |
We demonstrate the power of the adjoint method |
We demonstrate the power of the adjoint method in the context of |
| 71 |
in the context of investigating sea-ice export sensitivities through |
investigating sea-ice export sensitivities through Lancaster Sound. |
| 72 |
Lancaster and Jones Sound. The rationale for doing so is to complement |
The rationale for doing so is to complement the analysis of sea-ice |
| 73 |
the analysis of sea-ice dynamics in the presence of narrow straits. |
dynamics in the presence of narrow straits. Lancaster Sound is one of |
| 74 |
Lancaster Sound is one of the main outflow paths of sea-ice flowing |
the main outflow paths of sea-ice flowing through the Canadian Arctic |
| 75 |
through the Canadian Arctic Archipelago (CAA). |
Archipelago (CAA). Export sensitivities reflect dominant pathways |
| 76 |
Export sensitivities reflect dominant |
through the CAA as resolved by the model. Sensitivity maps can shed a |
| 77 |
pathways through the CAA as resolved by the model. |
very detailed light on various quantities affecting the sea-ice export |
| 78 |
Sensitivity maps can shed a very detailed light on various quantities |
(and thus the underlying pathways). Note that while the dominant |
| 79 |
affecting the sea-ice export (and thus the underlying pathways). |
circulation through Lancaster Sound is toward the East, there is a |
| 80 |
Note that while the dominant circulation through Lancaster Sound is |
small Westward flow to the North, hugging the coast of Devon Island |
| 81 |
toward the East, there is a small Westward flow to the North, |
\citep{mell:02, mich-etal:06,muen-etal:06}, which is not resolved in |
| 82 |
hugging the coast of Devon Island [ARE WE RESOLVING THIS?], |
our simulation. |
|
see e.g. \cite{mell:02, mich-etal:06,muen-etal:06}. |
|
| 83 |
|
|
| 84 |
The model domain is a coarsened version of the Arctic face of the |
The model domain is a coarsened version of the Arctic face of the |
| 85 |
high-resolution cubed-sphere configuration of the ECCO2 project |
high-resolution cubed-sphere configuration of the ECCO2 project |
| 86 |
\citep[see][]{menemenlis05}. It covers the entire Arctic, |
\citep{menemenlis05} as described in \refsec{forward}. The horizontal |
| 87 |
extends into the North Pacific such as to cover the entire |
resolution is half of that in \refsec{forward} while the vertical grid |
| 88 |
ice-covered regions, and comprises parts of the North Atlantic |
is the same. \ml{[Is this important? Do we need to be more specific?: |
| 89 |
down to XXN to enable analysis of remote influences of the |
]} The adjoint models run efficiently on 80 processors (as validated |
| 90 |
North Atlantic current to sea-ice variability and export. |
by benchmarks on both an SGI Altix and an IBM SP5 at NASA/ARC). |
| 91 |
The horizontal resolution varies between XX and YY km |
|
| 92 |
with 50 unevenly spaced vertical levels. |
Following a 3-year spinup, the model is integrated for four |
| 93 |
The adjoint models run efficiently on 80 processors |
years and five months between January 1989 and September 1993. |
| 94 |
(benchmarks have been performed both on an SGI Altix as well as an |
\ml{[Patrick: to what extent is this different from section 3?]} |
| 95 |
IBM SP5 at NASA/ARC). |
It is forced using realistic 6-hourly NCEP/NCAR atmospheric state variables. |
| 96 |
|
%Over the open ocean these are |
| 97 |
Following a 3-year spinup, the model has been integrated for four |
%converted into air-sea fluxes via the bulk formulae of |
| 98 |
years and five months between January 1989 and May 1993. |
%\citet{large04}. The air-sea fluxes in the presence of |
| 99 |
It is forced using realistic 6-hourly |
%sea-ice are handled by the ice model as described in \refsec{model}. |
| 100 |
NCEP/NCAR atmospheric state variables. Over the open ocean these are |
The objective function $J$ is chosen as the ``solid'' fresh water |
| 101 |
converted into air-sea fluxes via the bulk formulae of |
export, that is the export of ice and snow converted to units of fresh |
| 102 |
\citet{large04}. Derivation of air-sea fluxes in the presence of |
water $(\rho_{i} h_{i}c + \rho_{s} h_{s}c)\,u$, through Lancaster |
| 103 |
sea-ice is handled by the ice model as described in \refsec{model}. |
Sound at approximately 82\degW\ (cross-section G in |
| 104 |
The objective function is chosen $J$ as the |
\reffig{arctic_topog}) averaged over a 12-month period between October |
| 105 |
sea-ice export through |
1992 and September 1993. |
| 106 |
Lancaster Sound at XX$^{\circ}$W |
|
| 107 |
averaged over an 8-month period between October 1992 and May 1993. |
The forward trajectory of the model integration resembles broadly that |
| 108 |
|
of the model in \refsec{forward}. Many details are different, owning |
| 109 |
The adjoint model computes sensitivities |
to different resolution and integration period; for example, the solid |
| 110 |
to sea-ice export back in time from 1993 to 1989 along this |
fresh water transport through Lancaster Sound is |
| 111 |
trajectory. In principle all adjoint model variable (i.e., Lagrange |
$116\pm101\text{\,km$^{3}$\,y$^{-1}$}$ for a free slip simulation with |
| 112 |
multipliers) of the coupled ocean/sea-ice model |
the C-LSOR solver, but only $39\pm64\text{\,km$^{3}$\,y$^{-1}$}$ for a |
| 113 |
as well as the surface atmospheric state are available to |
no slip simulation. |
| 114 |
analyze the transient sensitivity behaviour. |
|
| 115 |
Over the open ocean, the adjoint of the bulk formula scheme |
The adjoint model computes sensitivities of this export back in time |
| 116 |
computes sensitivities to the time-varying atmospheric state. Over |
from 1993 to 1989 along this trajectory. In principle all adjoint |
| 117 |
ice-covered parts, the sea-ice adjoint converts surface ocean |
model variable (i.e., Lagrange multipliers) of the coupled |
| 118 |
sensitivities to atmospheric sensitivities. |
ocean/sea-ice model as well as the surface atmospheric state are |
| 119 |
|
available to analyze the transient sensitivity behavior. Over the |
| 120 |
|
open ocean, the adjoint of the bulk formula scheme computes |
| 121 |
|
sensitivities to the time-varying atmospheric state. Over ice-covered |
| 122 |
|
parts, the sea-ice adjoint converts surface ocean sensitivities to |
| 123 |
|
atmospheric sensitivities. |
| 124 |
|
|
| 125 |
DISCUSS FORWARD STATE, INCLUDING SOME NUMBERS ON SEA-ICE EXPORT |
DISCUSS FORWARD STATE, INCLUDING SOME NUMBERS ON SEA-ICE EXPORT |
| 126 |
|
|
| 127 |
\subsection{Sensitivities to the sea-ice state} |
\subsubsection{Adjoint sensitivities} |
| 128 |
|
|
| 129 |
\paragraph{Sensitivities to the sea-ice thickness} |
The most readily interpretable ice-export sensitivity is that to |
| 130 |
|
effective ice thickness, $\partial{J} / \partial{(hc)}$. |
| 131 |
The most readily interpretable ice-export sensitivity is that |
\reffig{adjheff} shows transient $\partial{J} / \partial{(hc)}$ using |
| 132 |
to effective ice thickness, $\partial{J} / \partial{h}$. |
free-slip (left column) and no-slip (right column) boundary |
| 133 |
Fig. XXX depcits transient $\partial{J} / \partial{h}$ using free-slip |
conditions. Sensitivity snapshots are depicted for 12 months prior to |
| 134 |
(left column) and no-slip (right column) boundary conditions. |
September 1993 (at the beginning of the averaging period for the objective |
| 135 |
Sensitivity snapshots are depicted for (from top to bottom) |
function $J$, top) and at the beginning of the integration in January |
| 136 |
12, 24, 36, and 48 months prior to May 2003. |
1989 (bottom). |
| 137 |
The dominant features are\ml{ in accordance with expectations/as expected}: |
\begin{figure*}[t] |
| 138 |
|
\includegraphics*[width=\textwidth]{\fpath/adjheff} |
| 139 |
(*) |
\caption{Sensitivity $\partial{J}/\partial{(hc)}$ in |
| 140 |
Dominant pattern (for the free-slip run) is that of positive sensitivities, i.e. |
m$^2$\,s$^{-1}$/m for two different times (rows) and two different |
| 141 |
a unit increase in sea-ice thickness in most places upstream |
boundary conditions for sea ice drift. The color scale is chosen |
| 142 |
of Lancaster Sound will increase sea-ice export through Lancaster Sound. |
to illustrate the patterns of the sensitivities; the maximum and |
| 143 |
The dominant pathway follows (backward in time) through Barrow Strait |
minimum values are given above the figures. |
| 144 |
into Viscount Melville Sound, and from there trough M'Clure Strait |
\label{fig:adjheff}} |
| 145 |
into the Arctic Ocean (the "Northwest Passage"). |
\end{figure*} |
| 146 |
Secondary paths are Northward from |
|
| 147 |
Viscount Melville Sound through Byam Martin Channel into |
At the beginning of October 1992, the positive sensitivities in |
| 148 |
Prince Gustav Adolf Sea and through Penny Strait into MacLean Strait. |
the Lancaster Sound mean that an increase of ice volume increase the |
| 149 |
|
solid fresh water export. The negative sensivities to the East and to the |
| 150 |
(*) |
West can be explained by indirect effects: less ice to the East means |
| 151 |
As expected, at any given time the |
less resistance to eastward drift and thus more export; similarly, less ice to |
| 152 |
region of influence is larger for the free-slip than no-slip simulation. |
the West means that more ice can be moved eastwards from the Barrow Strait |
| 153 |
For the no-slip run, the region of influence is confined, after four years, |
into the Lancaster Sound leading to more ice export. The sensitivities |
| 154 |
to just West of Barrow Strait (North of Prince of Wales Island), |
are similar for both no slip and free slip solutions with a slightly larger |
| 155 |
and to the South of Penny Strait. |
area covered by non-zero sensitivities in the free slip solution. At |
| 156 |
In contrast, sensitivities of the free-slip run extend |
the beginning of the integration (the end of the backward adjoint |
| 157 |
all the way to the Arctic interior both to the West |
integration) the free and no slip solutions are very different. The |
| 158 |
(M'Clure St.) and to the North (Ballantyne St., Prince Gustav Adolf Sea, |
sensitivities of the free slip solution extend through the enitre |
| 159 |
Massey Sound). |
Canadian Archipelago and into the Arctic while in the no slip solution |
| 160 |
|
they still are confined to the Lancaster Sound and the Barrow |
| 161 |
(*) |
Strait. This implies that in the free slip solution ice can drift more |
| 162 |
sensitivities seem to spread out in "pulses" (seasonal cycle) |
easily through the narrow straits of the Canadian Archipelago, so that |
| 163 |
[PLOT A TIME SERIES OF ADJheff in Barrow Strait) |
a positive ice volume anomaly anywhere in the Canadian Archipelago is |
| 164 |
|
moved through the Lancaster Sound within 4 years thus increasing the |
| 165 |
(*) |
ice export. |
| 166 |
The sensitivity in Baffin Bay are more complex. |
|
| 167 |
The pattern evolves along the Western boundary, connecting |
The temporal evolution of several sensitivities along the zonal axis |
| 168 |
the Lancaster Sound Polynya, the Coburg Island Polynya, and the |
Lancaster Sound-Barrow Strait-Melville Sound are shown in |
| 169 |
North Water Polynya, and reaches into Nares Strait and the Kennedy Channel. |
\reffig{lancaster}. |
| 170 |
The sign of sensitivities has an oscillatory character |
\begin{figure*} |
| 171 |
[AT FREQUENCY OF SEASONAL CYCLE?]. |
\includegraphics*[height=.8\textheight]{\fpath/lancaster_adj} |
| 172 |
First, we need to establish whether forward perturbation runs |
\caption{Hovermoeller diagrams of sensitivities (derivatives) of the |
| 173 |
corroborate the oscillatory behaviour. |
``solid'' fresh water (i.e., ice and snow) export $J$ through Lancaster sound |
| 174 |
Then, several possible explanations: |
(\reffig{arctic_topog}, cross-section G) with respect to effective |
| 175 |
(i) connection established through Nares Strait throughflow |
ice thickness ($hc$), ocean surface temperature (SST) and |
| 176 |
which extends into Western boundary current in Northern Baffin Bay. |
precipitation ($p$) for two runs with free slip and no slip boundary |
| 177 |
(ii) sea-ice concentration there is seasonal, i.e. partly |
conditions for the sea ice drift. Also shown it the normalized ice |
| 178 |
ice-free during the year. Seasonal cycle in sensitivity likely |
strengh $P/P^*=(hc)\,\exp[-C\,(1-c)]$ (bottom panel); each plot is |
| 179 |
connected to ice-free vs. ice-covered parts of the year. |
overlaid with the contours 1 and 3 of the normalized ice strength |
| 180 |
Negative sensitivities can potentially be attributed |
for orientation. |
| 181 |
to blocking of Lancaster Sound ice export by Western boundary ice |
\label{fig:lancaster}} |
| 182 |
in Baffin Bay. |
\end{figure*} |
| 183 |
(iii) Alternatively to (ii), flow reversal in Lancaster Sound is a possibility |
\reffig{lancaster} shows the sensitivities of ``solid'' fresh water |
| 184 |
(in reality there's a Northern counter current hugging the coast of |
export, that is ice and snow, through Lancaster sound (cross-section G |
| 185 |
Devon Island which we probably don't resolve). |
in \reffig{arctic_topog}) with respect to effective ice thickness |
| 186 |
|
($hc$), ocean surface temperature (SST) and precipitation ($p$) for |
| 187 |
Remote control of Kennedy Channel on Lancaster Sound ice export |
two runs with free slip and no slip boundary conditions for the sea |
| 188 |
seems a nice test for appropriateness of free-slip vs. no-slip BCs. |
ice drift. The Hovmoeller diagrams of sensitivities (derivatives) with |
| 189 |
|
respect to effective ice thickness (top) and ocean surface temperature |
| 190 |
\paragraph{Sensitivities to the sea-ice area} |
(second from top) are coherent: more ice in the Lancaster Sound leads |
| 191 |
|
to more export and one way to get more ice is by colder surface |
| 192 |
Fig. XXX depcits transient sea-ice export sensitivities |
temperatures (less melting from below). In the free slip case the |
| 193 |
to changes in sea-ice concentration |
sensitivities can propagate westwards (backwards in time) when the ice |
| 194 |
$\partial J / \partial area$ using free-slip |
strength is low in late summer. In the no slip case the (normalized) |
| 195 |
(left column) and no-slip (right column) boundary conditions. |
ice strength does not fall below 1 during the winters of 1991 to 1993 |
| 196 |
Sensitivity snapshots are depicted for (from top to bottom) |
(mainly because the ice concentrations remain nearly 100\%, not |
| 197 |
12, 24, 36, and 48 months prior to May 2003. |
shown), so that ice is blocked and cannot drift eastwards (forward in |
| 198 |
Contrary to the steady patterns seen for thickness sensitivities, |
time) in the Melville Sound-Barrow Strait-Lancaster Sound channel. |
| 199 |
the ice-concentration sensitivities exhibit a strong seasonal cycle |
Consequently the sensitivies do not propagate westwards (backwards in |
| 200 |
in large parts of the domain (but synchronized on large scale). |
time) and the export through Lancaster Sound is only affected by |
| 201 |
The following discussion is w.r.t. free-slip run. |
local ice formation and melting. |
| 202 |
|
|
| 203 |
(*) |
The sensitivities to precipitation are negative (more precipitation |
| 204 |
Months, during which sensitivities are negative: |
leads to less export) before January and mostly positive after |
| 205 |
\\ |
January. Further they are mostly positive for normalized ice strengths |
| 206 |
0 to 5 Db=N/A, Dr=5 (May-Jan) \\ |
over 3. Assuming that most precipation is snow in this area---in the |
| 207 |
10 to 17 Db=7, Dr=5 (Jul-Jan) \\ |
current implementation the model differentiates between snow and rain |
| 208 |
22 to 29 Db=7, Dr=5 (Jul-Jan) \\ |
depending on the thermodynamic growth rate; when it is cold enough for |
| 209 |
34 to 41 Db=7, Dr=5 (Jul-Jan) \\ |
ice to grow, all precipitation is assumed to be snow---the |
| 210 |
46 to 49 D=N/A \\ |
sensitivities can be interpreted in terms of the model physics. Short |
| 211 |
% |
wave radiation cannot penetrate a snow cover and has a higer albedo |
| 212 |
These negative sensitivities seem to be connected to months |
than ice (0.85 for dry snow and 0.75 for dry ice in our case); thus it |
| 213 |
during which main parts of the CAA are essentially entirely ice-covered. |
protects the ice against melting in spring (after January). On the |
| 214 |
This means that increase in ice concentration during this period |
other hand, snow reduces the effective conductivity and thus the heat |
| 215 |
will likely reduce ice export due to blocking |
flux through the ice. This insulating effect slows down the cooling of |
| 216 |
[NEED TO EXPLAIN WHY THIS IS NOT THE CASE FOR dJ/dHEFF]. |
the surface water underneath the ice and limits the ice growth from |
| 217 |
Only during periods where substantial parts of the CAA are |
below, so that less snow in the ice-growing season leads to more new |
| 218 |
ice free (i.e. sea-ice concentration is less than one in larger parts of |
ice and thus more ice export. |
| 219 |
the CAA) will an increase in ice-concentration increase ice export. |
|
| 220 |
|
%Und jetzt weiss ich nicht mehr weiter, aber nun kann folgendes passiert sein: |
| 221 |
(*) |
%1. snow insulates against melting from above during spring: more precip (snow) -> more export |
| 222 |
Sensitivities peak about 2-3 months before sign reversal, i.e. |
%2. less snow during fall -> more ice -> more export |
| 223 |
max. negative sensitivities are expected end of July |
%3. precip is both snow and rain, depending on the sign of "FICE" (thermodynamic growth rate), with probably different implications |
| 224 |
[DOUBLE CHECK THIS]. |
|
| 225 |
|
|
| 226 |
(*) |
\subsubsection{Forward sensitivities} |
| 227 |
Peaks/bursts of sensitivities for months |
|
| 228 |
14-17, 19-21, 27-29, 30-33, 38-40, 42-45 |
\ml{[Here we need for integrations to show that the adjoint |
| 229 |
|
sensitivites are not just academic. I suggest to perturb HEFF |
| 230 |
(*) |
and THETA initial conditions, and PRECIP somewhere in the Melville |
| 231 |
Spatial "anti-correlation" (in sign) between main sensitivity branch |
Sound and then produce plots similar to reffig{lancaster}. For |
| 232 |
(essentially Northwest Passage and immediate connecting channels), |
PRECIP it would be great to have two perturbation experiments, one |
| 233 |
and remote places. |
where ADJprecip is posivite and one where ADJprecip is negative]} |
| 234 |
For example: month 20, 28, 31.5, 40, 43. |
%The dominant features are\ml{ in accordance with expectations/as expected}: |
| 235 |
The timings of max. sensitivity extent are similar between |
|
| 236 |
free-slip and no-slip run; and patterns are similar within CAA, |
%(*) |
| 237 |
but differ in the Arctic Ocean interior. |
%Dominant pattern (for the free-slip run) is that of positive sensitivities, i.e. |
| 238 |
|
%a unit increase in sea-ice thickness in most places upstream |
| 239 |
(*) |
%of Lancaster Sound will increase sea-ice export through Lancaster Sound. |
| 240 |
Interesting (but real?) patterns in Arctic Ocean interior. |
%The dominant pathway follows (backward in time) through Barrow Strait |
| 241 |
|
%into Viscount Melville Sound, and from there trough M'Clure Strait |
| 242 |
\paragraph{Sensitivities to the sea-ice velocity} |
%into the Arctic Ocean (the "Northwest Passage"). |
| 243 |
|
%Secondary paths are Northward from |
| 244 |
(*) |
%Viscount Melville Sound through Byam Martin Channel into |
| 245 |
Patterns of ADJuice at almost any point in time are rather complicated |
%Prince Gustav Adolf Sea and through Penny Strait into MacLean Strait. |
| 246 |
(in particular with respect to spatial structure of signs). |
|
| 247 |
Might warrant perturbation tests. |
%(*) |
| 248 |
Patterns of ADJvice, on the other hand, are more spatially coherent, |
%As expected, at any given time the |
| 249 |
but still hard to interpret (or even counter-intuitive |
%region of influence is larger for the free-slip than no-slip simulation. |
| 250 |
in many places). |
%For the no-slip run, the region of influence is confined, after four years, |
| 251 |
|
%to just West of Barrow Strait (North of Prince of Wales Island), |
| 252 |
(*) |
%and to the South of Penny Strait. |
| 253 |
"Growth in extent of sensitivities" goes in clear pulses: |
%In contrast, sensitivities of the free-slip run extend |
| 254 |
almost no change between months: 0-5, 10-20, 24-32, 36-44 |
%all the way to the Arctic interior both to the West |
| 255 |
These essentially correspond to months of |
%(M'Clure St.) and to the North (Ballantyne St., Prince Gustav Adolf Sea, |
| 256 |
|
%Massey Sound). |
| 257 |
|
|
| 258 |
\subsection{Sensitivities to the oceanic state} |
%(*) |
| 259 |
|
%sensitivities seem to spread out in "pulses" (seasonal cycle) |
| 260 |
\paragraph{Sensitivities to theta} |
%[PLOT A TIME SERIES OF ADJheff in Barrow Strait) |
| 261 |
|
|
| 262 |
\textit{Sensitivities at the surface (z = 5 m)} |
%(*) |
| 263 |
|
%The sensitivity in Baffin Bay are more complex. |
| 264 |
(*) |
%The pattern evolves along the Western boundary, connecting |
| 265 |
mabye redo with caxmax=0.02 or even 0.05 |
%the Lancaster Sound Polynya, the Coburg Island Polynya, and the |
| 266 |
|
%North Water Polynya, and reaches into Nares Strait and the Kennedy Channel. |
| 267 |
(*) |
%The sign of sensitivities has an oscillatory character |
| 268 |
Core of negative sensitivities spreading through the CAA as |
%[AT FREQUENCY OF SEASONAL CYCLE?]. |
| 269 |
one might expect [TEST]: |
%First, we need to establish whether forward perturbation runs |
| 270 |
Increase in SST will decrease ice thickness and therefore ice export. |
%corroborate the oscillatory behaviour. |
| 271 |
|
%Then, several possible explanations: |
| 272 |
(*) |
%(i) connection established through Nares Strait throughflow |
| 273 |
What's maybe unexpected is patterns of positive sensitivities |
%which extends into Western boundary current in Northern Baffin Bay. |
| 274 |
at the fringes of the "core", e.g. in the Southern channels |
%(ii) sea-ice concentration there is seasonal, i.e. partly |
| 275 |
(Bellot St., Peel Sound, M'Clintock Channel), and to the North |
%ice-free during the year. Seasonal cycle in sensitivity likely |
| 276 |
(initially MacLean St., Prince Gustav Adolf Sea, Hazen St., |
%connected to ice-free vs. ice-covered parts of the year. |
| 277 |
then shifting Northward into the Arctic interior). |
%Negative sensitivities can potentially be attributed |
| 278 |
|
%to blocking of Lancaster Sound ice export by Western boundary ice |
| 279 |
(*) |
%in Baffin Bay. |
| 280 |
Marked sensitivity from the Arctic interior roughly along 60$^{\circ}$W |
%(iii) Alternatively to (ii), flow reversal in Lancaster Sound is a possibility |
| 281 |
propagating into Lincoln Sea, then |
%(in reality there's a Northern counter current hugging the coast of |
| 282 |
entering Nares Strait and Smith Sound, periodically |
%Devon Island which we probably don't resolve). |
| 283 |
warming or cooling[???] the Lancaster Sound exit. |
|
| 284 |
|
%Remote control of Kennedy Channel on Lancaster Sound ice export |
| 285 |
\textit{Sensitivities at depth (z = 200 m)} |
%seems a nice test for appropriateness of free-slip vs. no-slip BCs. |
| 286 |
|
|
| 287 |
(*) |
%\paragraph{Sensitivities to the sea-ice area} |
| 288 |
Negative sensitivities almost everywhere, as might be expected. |
|
| 289 |
|
%Fig. XXX depcits transient sea-ice export sensitivities |
| 290 |
(*) |
%to changes in sea-ice concentration |
| 291 |
Sensitivity patterns between free-slip and no-slip BCs |
% $\partial J / \partial area$ using free-slip |
| 292 |
are quite similar, except in Lincoln Sea (North of Nares St), |
%(left column) and no-slip (right column) boundary conditions. |
| 293 |
where the sign is reversed (but pattern remains similar). |
%Sensitivity snapshots are depicted for (from top to bottom) |
| 294 |
|
%12, 24, 36, and 48 months prior to May 2003. |
| 295 |
\paragraph{Sensitivities to salt} |
%Contrary to the steady patterns seen for thickness sensitivities, |
| 296 |
|
%the ice-concentration sensitivities exhibit a strong seasonal cycle |
| 297 |
T.B.D. |
%in large parts of the domain (but synchronized on large scale). |
| 298 |
|
%The following discussion is w.r.t. free-slip run. |
| 299 |
\paragraph{Sensitivities to velocity} |
|
| 300 |
|
%(*) |
| 301 |
T.B.D. |
%Months, during which sensitivities are negative: |
| 302 |
|
%\\ |
| 303 |
\subsection{Sensitivities to the atmospheric state} |
%0 to 5 Db=N/A, Dr=5 (May-Jan) \\ |
| 304 |
|
%10 to 17 Db=7, Dr=5 (Jul-Jan) \\ |
| 305 |
\begin{itemize} |
%22 to 29 Db=7, Dr=5 (Jul-Jan) \\ |
| 306 |
% |
%34 to 41 Db=7, Dr=5 (Jul-Jan) \\ |
| 307 |
\item |
%46 to 49 D=N/A \\ |
| 308 |
plot of ATEMP for 12, 24, 36, 48 months |
%% |
| 309 |
% |
%These negative sensitivities seem to be connected to months |
| 310 |
\item |
%during which main parts of the CAA are essentially entirely ice-covered. |
| 311 |
plot of HEFF for 12, 24, 36, 48 months |
%This means that increase in ice concentration during this period |
| 312 |
% |
%will likely reduce ice export due to blocking |
| 313 |
\end{itemize} |
%[NEED TO EXPLAIN WHY THIS IS NOT THE CASE FOR dJ/dHEFF]. |
| 314 |
|
%Only during periods where substantial parts of the CAA are |
| 315 |
|
%ice free (i.e. sea-ice concentration is less than one in larger parts of |
| 316 |
|
%the CAA) will an increase in ice-concentration increase ice export. |
| 317 |
\reffig{4yradjheff}(a--d) depict sensitivities of sea-ice export |
|
| 318 |
through Fram Strait in December 1995 to changes in sea-ice thickness |
%(*) |
| 319 |
12, 24, 36, 48 months back in time. Corresponding sensitivities to |
%Sensitivities peak about 2-3 months before sign reversal, i.e. |
| 320 |
ocean surface temperature are depicted in |
%max. negative sensitivities are expected end of July |
| 321 |
\reffig{4yradjthetalev1}(a--d). The main characteristics is |
%[DOUBLE CHECK THIS]. |
| 322 |
consistency with expected advection of sea-ice over the relevant time |
|
| 323 |
scales considered. The general positive pattern means that an |
%(*) |
| 324 |
increase in sea-ice thickness at location $(x,y)$ and time $t$ will |
%Peaks/bursts of sensitivities for months |
| 325 |
increase sea-ice export through Fram Strait at time $T_e$. Largest |
%14-17, 19-21, 27-29, 30-33, 38-40, 42-45 |
| 326 |
distances from Fram Strait indicate fastest sea-ice advection over the |
|
| 327 |
time span considered. The ice thickness sensitivities are in close |
%(*) |
| 328 |
correspondence to ocean surface sentivitites, but of opposite sign. |
%Spatial "anti-correlation" (in sign) between main sensitivity branch |
| 329 |
An increase in temperature will incur ice melting, decrease in ice |
%(essentially Northwest Passage and immediate connecting channels), |
| 330 |
thickness, and therefore decrease in sea-ice export at time $T_e$. |
%and remote places. |
| 331 |
|
%For example: month 20, 28, 31.5, 40, 43. |
| 332 |
The picture is fundamentally different and much more complex |
%The timings of max. sensitivity extent are similar between |
| 333 |
for sensitivities to ocean temperatures away from the surface. |
%free-slip and no-slip run; and patterns are similar within CAA, |
| 334 |
\reffig{4yradjthetalev10??}(a--d) depicts ice export sensitivities to |
%but differ in the Arctic Ocean interior. |
| 335 |
temperatures at roughly 400 m depth. |
|
| 336 |
Primary features are the effect of the heat transport of the North |
%(*) |
| 337 |
Atlantic current which feeds into the West Spitsbergen current, |
%Interesting (but real?) patterns in Arctic Ocean interior. |
| 338 |
the circulation around Svalbard, and ... |
|
| 339 |
|
%\paragraph{Sensitivities to the sea-ice velocity} |
| 340 |
|
|
| 341 |
\ml{[based on the movie series |
%(*) |
| 342 |
zzz\_run\_export\_canarch\_freeslip\_4yr\_1989\_ADJ*:]} The ice |
%Patterns of ADJuice at almost any point in time are rather complicated |
| 343 |
export through the Canadian Archipelag is highly sensitive to the |
%(in particular with respect to spatial structure of signs). |
| 344 |
previous state of the ocean-ice system in the Archipelago and the |
%Might warrant perturbation tests. |
| 345 |
Western Arctic. According to the \ml{(adjoint)} senstivities of the |
%Patterns of ADJvice, on the other hand, are more spatially coherent, |
| 346 |
eastward ice transport through Lancaster Sound (\reffig{arctic_topog}, |
%but still hard to interpret (or even counter-intuitive |
| 347 |
cross-section G) with respect to ice volume (effective thickness), ocean |
%in many places). |
| 348 |
surface temperature, and vertical diffusivity near the surface |
|
| 349 |
(\reffig{fouryearadj}) after 4 years of integration the following |
%(*) |
| 350 |
mechanisms can be identified: near the ``observation'' (cross-section |
%"Growth in extent of sensitivities" goes in clear pulses: |
| 351 |
G), smaller vertical diffusivities lead to lower surface temperatures |
%almost no change between months: 0-5, 10-20, 24-32, 36-44 |
| 352 |
and hence to more ice that is available for export. Further away from |
%These essentially correspond to months of |
| 353 |
cross-section G, the sensitivity to vertical diffusivity has the |
|
| 354 |
opposite sign, but temperature and ice volume sensitivities have the |
|
| 355 |
same sign as close to the observation. |
%\subsection{Sensitivities to the oceanic state} |
| 356 |
|
|
| 357 |
\begin{figure}[t!] |
%\paragraph{Sensitivities to theta} |
| 358 |
\centerline{ |
|
| 359 |
\subfigure[{\footnotesize -12 months}] |
%\textit{Sensitivities at the surface (z = 5 m)} |
| 360 |
{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim072_cmax2.0E+02.eps}} |
|
| 361 |
%\includegraphics*[width=.3\textwidth]{H_c.bin_res_100_lev1.pdf} |
%(*) |
| 362 |
% |
%mabye redo with caxmax=0.02 or even 0.05 |
| 363 |
\subfigure[{\footnotesize -24 months}] |
|
| 364 |
{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}} |
%(*) |
| 365 |
} |
%Core of negative sensitivities spreading through the CAA as |
| 366 |
% |
%one might expect [TEST]: |
| 367 |
\caption{Sensitivity of sea-ice export through Fram Strait in December 2005 to |
%Increase in SST will decrease ice thickness and therefore ice export. |
| 368 |
sea-ice thickness at various prior times. |
|
| 369 |
\label{fig:4yradjheff}} |
%(*) |
| 370 |
\end{figure} |
%What's maybe unexpected is patterns of positive sensitivities |
| 371 |
|
%at the fringes of the "core", e.g. in the Southern channels |
| 372 |
|
%(Bellot St., Peel Sound, M'Clintock Channel), and to the North |
| 373 |
|
%(initially MacLean St., Prince Gustav Adolf Sea, Hazen St., |
| 374 |
|
%then shifting Northward into the Arctic interior). |
| 375 |
|
|
| 376 |
|
%(*) |
| 377 |
|
%Marked sensitivity from the Arctic interior roughly along 60$^{\circ}$W |
| 378 |
|
%propagating into Lincoln Sea, then |
| 379 |
|
%entering Nares Strait and Smith Sound, periodically |
| 380 |
|
%warming or cooling[???] the Lancaster Sound exit. |
| 381 |
|
|
| 382 |
|
%\textit{Sensitivities at depth (z = 200 m)} |
| 383 |
|
|
| 384 |
|
%(*) |
| 385 |
|
%Negative sensitivities almost everywhere, as might be expected. |
| 386 |
|
|
| 387 |
|
%(*) |
| 388 |
|
%Sensitivity patterns between free-slip and no-slip BCs |
| 389 |
|
%are quite similar, except in Lincoln Sea (North of Nares St), |
| 390 |
|
%where the sign is reversed (but pattern remains similar). |
| 391 |
|
|
| 392 |
|
%\paragraph{Sensitivities to salt} |
| 393 |
|
|
| 394 |
|
%T.B.D. |
| 395 |
|
|
| 396 |
|
%\paragraph{Sensitivities to velocity} |
| 397 |
|
|
| 398 |
|
%T.B.D. |
| 399 |
|
|
| 400 |
|
%\subsection{Sensitivities to the atmospheric state} |
| 401 |
|
|
| 402 |
|
%\begin{itemize} |
| 403 |
|
%% |
| 404 |
|
%\item |
| 405 |
|
%plot of ATEMP for 12, 24, 36, 48 months |
| 406 |
|
%% |
| 407 |
|
%\item |
| 408 |
|
%plot of HEFF for 12, 24, 36, 48 months |
| 409 |
|
%% |
| 410 |
|
%\end{itemize} |
| 411 |
|
|
| 412 |
|
|
| 413 |
|
|
| 414 |
|
%\reffig{4yradjheff}(a--d) depict sensitivities of sea-ice export |
| 415 |
|
%through Fram Strait in December 1995 to changes in sea-ice thickness |
| 416 |
|
%12, 24, 36, 48 months back in time. Corresponding sensitivities to |
| 417 |
|
%ocean surface temperature are depicted in |
| 418 |
|
%\reffig{4yradjthetalev1}(a--d). The main characteristics is |
| 419 |
|
%consistency with expected advection of sea-ice over the relevant time |
| 420 |
|
%scales considered. The general positive pattern means that an |
| 421 |
|
%increase in sea-ice thickness at location $(x,y)$ and time $t$ will |
| 422 |
|
%increase sea-ice export through Fram Strait at time $T_e$. Largest |
| 423 |
|
%distances from Fram Strait indicate fastest sea-ice advection over the |
| 424 |
|
%time span considered. The ice thickness sensitivities are in close |
| 425 |
|
%correspondence to ocean surface sentivitites, but of opposite sign. |
| 426 |
|
%An increase in temperature will incur ice melting, decrease in ice |
| 427 |
|
%thickness, and therefore decrease in sea-ice export at time $T_e$. |
| 428 |
|
|
| 429 |
|
%The picture is fundamentally different and much more complex |
| 430 |
|
%for sensitivities to ocean temperatures away from the surface. |
| 431 |
|
%\reffig{4yradjthetalev10??}(a--d) depicts ice export sensitivities to |
| 432 |
|
%temperatures at roughly 400 m depth. |
| 433 |
|
%Primary features are the effect of the heat transport of the North |
| 434 |
|
%Atlantic current which feeds into the West Spitsbergen current, |
| 435 |
|
%the circulation around Svalbard, and ... |
| 436 |
|
|
| 437 |
|
|
| 438 |
|
%%\begin{figure}[t!] |
| 439 |
|
%%\centerline{ |
| 440 |
|
%%\subfigure[{\footnotesize -12 months}] |
| 441 |
|
%%{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim072_cmax2.0E+02.eps}} |
| 442 |
|
%%\includegraphics*[width=.3\textwidth]{H_c.bin_res_100_lev1.pdf} |
| 443 |
|
%% |
| 444 |
|
%%\subfigure[{\footnotesize -24 months}] |
| 445 |
|
%%{\includegraphics*[width=0.44\linewidth]{\fpath/run_4yr_ADJheff_arc_lev1_tim145_cmax2.0E+02.eps}} |
| 446 |
|
%%} |
| 447 |
|
%% |
| 448 |
|
%%\caption{Sensitivity of sea-ice export through Fram Strait in December 2005 to |
| 449 |
|
%%sea-ice thickness at various prior times. |
| 450 |
|
%%\label{fig:4yradjheff}} |
| 451 |
|
%%\end{figure} |
| 452 |
|
|
| 453 |
|
|
| 454 |
|
%\ml{[based on the movie series |
| 455 |
|
% zzz\_run\_export\_canarch\_freeslip\_4yr\_1989\_ADJ*:]} The ice |
| 456 |
|
%export through the Canadian Archipelag is highly sensitive to the |
| 457 |
|
%previous state of the ocean-ice system in the Archipelago and the |
| 458 |
|
%Western Arctic. According to the \ml{(adjoint)} senstivities of the |
| 459 |
|
%eastward ice transport through Lancaster Sound (\reffig{arctic_topog}, |
| 460 |
|
%cross-section G) with respect to ice volume (effective thickness), ocean |
| 461 |
|
%surface temperature, and vertical diffusivity near the surface |
| 462 |
|
%(\reffig{fouryearadj}) after 4 years of integration the following |
| 463 |
|
%mechanisms can be identified: near the ``observation'' (cross-section |
| 464 |
|
%G), smaller vertical diffusivities lead to lower surface temperatures |
| 465 |
|
%and hence to more ice that is available for export. Further away from |
| 466 |
|
%cross-section G, the sensitivity to vertical diffusivity has the |
| 467 |
|
%opposite sign, but temperature and ice volume sensitivities have the |
| 468 |
|
%same sign as close to the observation. |
| 469 |
|
|
| 470 |
|
|
| 471 |
%%% Local Variables: |
%%% Local Variables: |
Parent Directory
| 
Revision Log
| 
Revision Graph
| 
Patch