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 indicate that for the coarse-resolution configuration used here
the free-slip boundary condition results in much swifter ice movement and in a
much larger region of influence than does the no-slip boundary condition.
Note though that this statement may not 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 confirm some expected responses, for example,
the increase in ice export with increasing ice thickness and
the decrease in 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
an 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 in 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 we compared objective function differences inferred from forward
perturbation experiments with differences inferred from adjoint 
sensitivity information. We found very good quantitative agreement
for initial ice thickness and for 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-based estimates of
ice and snow transport sensitivity through Lancaster Sound.
Furthermore, finite difference perturbations exhibit an asymmetry
between positive and negative perturbations of equal size.
This points to the fact that, on multi-year time scales, nonlinear
effects can no longer be ignored and it indicates a limit to the usefulness
of the adjoint sensitivity information.

Given the urgency of understanding cryospheric changes,
adjoint applications are emerging as powerful research tools,
e.g., the study of \cite{kauk-etal:09} who attempt to isolate
dominant mechanisms responsible for the 2007 Arctic sea-ice minimum,
and the study of \cite{heim-bugn:09} who demonstrate how to infer Greenland
ice sheet volume sensitivities from a large-scale ice sheet adjoint model.
The results of the present study encourage application of the
MITgcm coupled ocean/sea-ice adjoint system to a variety
of sensitivity studies of Arctic and Southern Ocean climate variability.
The system has matured to a stage where coupled
ocean/sea-ice estimation becomes feasible.
For the limited domain of the the Labrador Sea, single-year estimates 
have indeed successfully been produced  by \cite{fent:10}
for the mid-1990s and mid-2000s, and will be reported elsewhere.
Steps both toward a full Arctic and a 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	dimitri	1.9	%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			Our results indicate that for the coarse-resolution configuration used here
38			the free-slip boundary condition results in much swifter ice movement and in a
39			much larger region of influence than does the no-slip boundary condition.
40			Note though that this statement may not hold for simulations at higher
41			resolution.
42	heimbach	1.3	%
43	heimbach	1.6	%\ml{PH: So based on this, do way say we prefer free-slip since
44			%it mimics more closely the higher-resolution model sensitivities???}
45			%\ml{ML: Of course, we can't say at this point, we can only say that if
46			%observations support the idea of ice moving forward in all seasons, right?}
47	heimbach	1.3
48	dimitri	1.9	The present calculations confirm some expected responses, for example,
49			the increase in ice export with increasing ice thickness and
50			the decrease in ice export with increasing sea surface temperature.
51	heimbach	1.3	They also reveal mechanisms which, although plausible,
52			cannot be readily anticipated.
53	dimitri	1.9	As an example we presented precipitation sensitivities, which exhibit
54			an annual oscillatory behavior, with negative sensitivities prevailing
55			throughout the fall and early winter and positive sensitivities from
56	heimbach	1.3	late winter though spring. This behavior can be traced to the
57			different impact of snow accumulation over ice, depending
58	dimitri	1.9	on the stage of ice evolution. For growing ice snow accumulation
59			suppresses ice growth (negative sensitivity) whereas for melting ice
60	heimbach	1.3	snow accumulation suppresses ice melt (positive sensitivity).
61			A secondary effect is the snow accumulation on downstream ice export
62			(positive sensitivity). Differences between snow and rain seem negligible
63	dimitri	1.9	in our case study, since precipitation is in the form of snow for
64	heimbach	1.3	an overwhelming part of the year.
65
66	dimitri	1.9	Given the automated nature of adjoint code generation and the
67	heimbach	1.3	nonlinearity of the problem when considered over sufficiently
68			long time scales, independent tests are needed to gain confidence
69			in the adjoint solutions. We have presented such tests in the form
70	dimitri	1.9	of finite difference experiments, guided by the adjoint solution,
71	heimbach	1.13	and we compared objective function differences inferred from forward
72	dimitri	1.9	perturbation experiments with differences inferred from adjoint
73	heimbach	1.3	sensitivity information. We found very good quantitative agreement
74	dimitri	1.9	for initial ice thickness and for sea surface temperature perturbations.
75	heimbach	1.3
76			As described above, sensitivities to precipitation show an annual
77	dimitri	1.9	oscillatory behavior, which is confirmed by forward perturbation experiments.
78	heimbach	1.3	In terms of amplitude, precipitation shows a larger deviation
79	dimitri	1.9	(order of 50\%) between adjoint-based and finite-difference-based estimates of
80			ice and snow transport sensitivity through Lancaster Sound.
81	heimbach	1.3	Furthermore, finite difference perturbations exhibit an asymmetry
82	dimitri	1.9	between positive and negative perturbations of equal size.
83			This points to the fact that, on multi-year time scales, nonlinear
84			effects can no longer be ignored and it indicates a limit to the usefulness
85	heimbach	1.3	of the adjoint sensitivity information.
86
87	heimbach	1.12	Given the urgency of understanding cryospheric changes,
88			adjoint applications are emerging as powerful research tools,
89			e.g., the study of \cite{kauk-etal:09} who attempt to isolate
90	heimbach	1.11	dominant mechanisms responsible for the 2007 Arctic sea-ice minimum,
91	heimbach	1.12	and the study of \cite{heim-bugn:09} who demonstrate how to infer Greenland
92			ice sheet volume sensitivities from a large-scale ice sheet adjoint model.
93	heimbach	1.11	The results of the present study encourage application of the
94			MITgcm coupled ocean/sea-ice adjoint system to a variety
95			of sensitivity studies of Arctic and Southern Ocean climate variability.
96			The system has matured to a stage where coupled
97			ocean/sea-ice estimation becomes feasible.
98			For the limited domain of the the Labrador Sea, single-year estimates
99	heimbach	1.14	have indeed successfully been produced by \cite{fent:10}
100	heimbach	1.11	for the mid-1990s and mid-2000s, and will be reported elsewhere.
101			Steps both toward a full Arctic and a global system are now
102			within reach.
103			The prospect of using observations of one component
104			(e.g. daily sea-ice concentration) to constrain the other component
105			(near-surface ocean properties) through the information propagation
106			of the adjoint holds promise in deriving better, dynamically consistent
107	dimitri	1.9	estimates of the polar environments.
108	heimbach	1.11
109	heimbach	1.1
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