ceaice_split_version/ceaice_part2/ceaice_concl.tex

\section{Discussion and conclusion}
\label{sec:concl}

In this study we have presented an extension of the MITgcm adjoint 
modeling capabilities to the coupled ocean and sea-ice system.
At the heart is the development of a dynamic and thermodynamic sea-ice model
akin to most state-of-the-art models but that is amenable to efficient,
exact, parallel adjoint code generation via automatic differentiation.
At least two natural lines of applications are made possible by the
availability of the adjoint model: (i) use of the coupled adjoint modeling
capabilities for comprehensive
sensitivity calculations of the ocean/sea-ice system at high
Northern and Southern latitudes and
(ii) extension of the ECCO state estimation infrastructure to derive
estimates that are constrained both by ocean and by sea-ice observations.

The power of the adjoint method was demonstrated through a multi-year
sensitivity calculation of solid freshwater (sea-ice and snow) 
export through Lancaster Sound in the Canadian Arctic
Archipelago (CAA). The region was chosen so as to complement the
forward-model study, presented in Part 1, which examined 
the impact of rheology and dynamics on sea-ice drift
through narrow straits.
The transient adjoint sensitivities reveal dominant pathways
of sea-ice propagation through the CAA. They clearly expose
causal, time-lagged relationships between ice export and various ocean,
sea-ice, and atmospheric variables of the coupled system.
The computational cost of establishing all these relationships through pure
forward calculations would be prohibitive.
The sensitivity pattern (and thus causal relationships) differ substantially,
depending on which lateral ice drift boundary condition
(free-slip or no-slip) is imposed.
Analyzing adjoint sensitivities of the coupled ocean/sea-ice state 
may thus help in determining which of
the lateral boundary conditions provides a more realistic 
propagation of sensitivities, and thus physical linkages.
Our results seem to indicate that for a
coarse-resolution setup such as chosen here,
free-slip boundary condition seem a preferable choice,
since they provide a swifter ice movement that mimics more
closely actual ice transport through the CAA.
Note though that this statement may no longer hold for
simulations at higher resolution.
%
%\ml{PH: So based on this, do way say we prefer free-slip since
%it mimics more closely the higher-resolution model sensitivities???}
%\ml{ML: Of course, we can't say at this point, we can only say that if
%observations support the idea of ice moving forward in all seasons, right?}

The present calculations in part confirm expected responses,
such as increase in ice export with increasing ice thickness,
or decreasing ice export with increasing sea surface temperature.
They also reveal mechanisms which, although plausible,
cannot be readily anticipated.
As an example we presented precipitation sensitivities which exhibit
a annual oscillatory behavior, with negative sensitivities prevailing
throughout the fall and early winter, and positive sensitivities from
late winter though spring. This behavior can be traced to the
different impact of snow accumulation over ice, depending
on the stage of ice evolution. For growing ice, snow accumulation
suppresses ice growth (negative sensitivity), whereas for melting ice,
snow accumulation suppresses ice melt (positive sensitivity).
A secondary effect is the snow accumulation on downstream ice export
(positive sensitivity). Differences between snow and rain seem negligible
in our case study since precipitation is through the form of snow for 
an overwhelming part of the year.

Given the automated nature of adjoint code generation, and the
nonlinearity of the problem when considered over sufficiently
long time scales, independent tests are needed to gain confidence
in the adjoint solutions. We have presented such tests in the form
of finite difference experiments (guided by the adjoint solution),
and comparing cost function differences inferred from forward
perturbation experiments with differences inferred via adjoint 
sensitivity information. We found very good quantitative agreement
for initial ice thickness, and sea surface temperature perturbations.

As described above, sensitivities to precipitation show an annual
oscillatory behavior which is confirmed by forward perturbation experiments.
In terms of amplitude, precipitation shows a larger deviation
(order of 50 \%) between adjoint-based and finite difference perturbations.
Furthermore, finite difference perturbations exhibit an asymmetry
between positive and negative perturbation (of equal size).
This points to the fact that on multi-year time scales nonlinear
effects can no longer be ignored, and indicates a limit to the usefulness
of the adjoint sensitivity information.

The results shown open up the prospect for application of the
MITgcm/sim adjoint system to a variety
of sensitivity studies of Arctic and Southern Ocean climate variability.
Another such study is that of \cite{kauk-etal:09} who attempt
to isolate dominant mechanisms responsible for the 2007 Arctic
sea-ice minimum.
Given the urgency of understanding cryospheric changes, 
efforts are now under way to employ adjoint methods also in the
context of large-scale land ice sheet models \citep{heim-bugn:09}.
The MITgcm/sim adjoint system has matured to a stage where coupled
ocean/sea-ice estimation becomes feasible.
A coupled ocean/sea-ice estimate of the Labrador Sea for the
mid-1990s and mid-2000s has recently successfully been conducted by
\cite{fent:09} and will be reported elsewhere.
Steps both toward a regional Arctic and a full global system are now
within reach.
The prospect of using observations of one component
(e.g. daily sea-ice concentration) to constrain the other component
(near-surface ocean properties) through the information propagation
of the adjoint holds promise in deriving better, dynamically consistent
estimates of the polar environments. 


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1	heimbach	1.1	\section{Discussion and conclusion}
2			\label{sec:concl}
3
4	heimbach	1.3	In this study we have presented an extension of the MITgcm adjoint
5	dimitri	1.8	modeling capabilities to the coupled ocean and sea-ice system.
6			At the heart is the development of a dynamic and thermodynamic sea-ice model
7			akin to most state-of-the-art models but that is amenable to efficient,
8	heimbach	1.3	exact, parallel adjoint code generation via automatic differentiation.
9	dimitri	1.8	At least two natural lines of applications are made possible by the
10			availability of the adjoint model: (i) use of the coupled adjoint modeling
11			capabilities for comprehensive
12	heimbach	1.3	sensitivity calculations of the ocean/sea-ice system at high
13	dimitri	1.8	Northern and Southern latitudes and
14			(ii) extension of the ECCO state estimation infrastructure to derive
15			estimates that are constrained both by ocean and by sea-ice observations.
16	heimbach	1.3
17			The power of the adjoint method was demonstrated through a multi-year
18			sensitivity calculation of solid freshwater (sea-ice and snow)
19			export through Lancaster Sound in the Canadian Arctic
20	dimitri	1.8	Archipelago (CAA). The region was chosen so as to complement the
21			forward-model study, presented in Part 1, which examined
22			the impact of rheology and dynamics on sea-ice drift
23	heimbach	1.3	through narrow straits.
24			The transient adjoint sensitivities reveal dominant pathways
25			of sea-ice propagation through the CAA. They clearly expose
26	dimitri	1.8	causal, time-lagged relationships between ice export and various ocean,
27			sea-ice, and atmospheric variables of the coupled system.
28			The computational cost of establishing all these relationships through pure
29			forward calculations would be prohibitive.
30	heimbach	1.3	The sensitivity pattern (and thus causal relationships) differ substantially,
31			depending on which lateral ice drift boundary condition
32	dimitri	1.8	(free-slip or no-slip) is imposed.
33	heimbach	1.3	Analyzing adjoint sensitivities of the coupled ocean/sea-ice state
34			may thus help in determining which of
35			the lateral boundary conditions provides a more realistic
36			propagation of sensitivities, and thus physical linkages.
37	heimbach	1.6	Our results seem to indicate that for a
38			coarse-resolution setup such as chosen here,
39			free-slip boundary condition seem a preferable choice,
40	dimitri	1.8	since they provide a swifter ice movement that mimics more
41	heimbach	1.6	closely actual ice transport through the CAA.
42			Note though that this statement may no longer hold for
43			simulations at higher resolution.
44	heimbach	1.3	%
45	heimbach	1.6	%\ml{PH: So based on this, do way say we prefer free-slip since
46			%it mimics more closely the higher-resolution model sensitivities???}
47			%\ml{ML: Of course, we can't say at this point, we can only say that if
48			%observations support the idea of ice moving forward in all seasons, right?}
49	heimbach	1.3
50			The present calculations in part confirm expected responses,
51			such as increase in ice export with increasing ice thickness,
52			or decreasing ice export with increasing sea surface temperature.
53			They also reveal mechanisms which, although plausible,
54			cannot be readily anticipated.
55			As an example we presented precipitation sensitivities which exhibit
56			a annual oscillatory behavior, with negative sensitivities prevailing
57			throughout the fall and early winter, and positive sensitivities from
58			late winter though spring. This behavior can be traced to the
59			different impact of snow accumulation over ice, depending
60			on the stage of ice evolution. For growing ice, snow accumulation
61			suppresses ice growth (negative sensitivity), whereas for melting ice,
62			snow accumulation suppresses ice melt (positive sensitivity).
63			A secondary effect is the snow accumulation on downstream ice export
64			(positive sensitivity). Differences between snow and rain seem negligible
65			in our case study since precipitation is through the form of snow for
66			an overwhelming part of the year.
67
68			Given the automated nature of adjoint code generation, and the
69			nonlinearity of the problem when considered over sufficiently
70			long time scales, independent tests are needed to gain confidence
71			in the adjoint solutions. We have presented such tests in the form
72			of finite difference experiments (guided by the adjoint solution),
73			and comparing cost function differences inferred from forward
74			perturbation experiments with differences inferred via adjoint
75			sensitivity information. We found very good quantitative agreement
76			for initial ice thickness, and sea surface temperature perturbations.
77
78			As described above, sensitivities to precipitation show an annual
79			oscillatory behavior which is confirmed by forward perturbation experiments.
80			In terms of amplitude, precipitation shows a larger deviation
81			(order of 50 \%) between adjoint-based and finite difference perturbations.
82			Furthermore, finite difference perturbations exhibit an asymmetry
83			between positive and negative perturbation (of equal size).
84			This points to the fact that on multi-year time scales nonlinear
85	heimbach	1.6	effects can no longer be ignored, and indicates a limit to the usefulness
86	heimbach	1.3	of the adjoint sensitivity information.
87
88			The results shown open up the prospect for application of the
89			MITgcm/sim adjoint system to a variety
90			of sensitivity studies of Arctic and Southern Ocean climate variability.
91	heimbach	1.6	Another such study is that of \cite{kauk-etal:09} who attempt
92			to isolate dominant mechanisms responsible for the 2007 Arctic
93			sea-ice minimum.
94	heimbach	1.3	Given the urgency of understanding cryospheric changes,
95			efforts are now under way to employ adjoint methods also in the
96	heimbach	1.4	context of large-scale land ice sheet models \citep{heim-bugn:09}.
97	heimbach	1.3	The MITgcm/sim adjoint system has matured to a stage where coupled
98			ocean/sea-ice estimation becomes feasible.
99			A coupled ocean/sea-ice estimate of the Labrador Sea for the
100			mid-1990s and mid-2000s has recently successfully been conducted by
101			\cite{fent:09} and will be reported elsewhere.
102			Steps both toward a regional Arctic and a full global system are now
103			within reach.
104			The prospect of using observations of one component
105			(e.g. daily sea-ice concentration) to constrain the other component
106			(near-surface ocean properties) through the information propagation
107			of the adjoint holds promise in deriving better, dynamically consistent
108			estimates of the polar environments.
109
110
111
112
113
114	heimbach	1.1
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117	mlosch	1.7	%%% TeX-master: "ceaice_part2"
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