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/sea-ice system.
At the heart is the development of a dynamic/thermodynamic sea-ice model
akin to most state-of-the-art models that is amenable to efficient,
exact, parallel adjoint code generation via automatic differentiation.

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