Tangent Linear and Adjoint Models
A typical question 'asked' of a model is:
What is the sensitivity of a large number of output
parameters with respect to one (or a small number) of input parameters?
For example the CO2 concentration in an atmospheric
model is doubled and this 'projects' on to the myriad output
parameters of the model...
But often a more useful question is to ask:
What is the sensitivity of a small number of output
parameters with respect to a large number of input variables? For
example, to what parameter in the model is the global-mean
temperature at the surface of the earth most sensitive?
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In the adjoint
method, an objective ("cost") function, J, is identified with some
measure of the model state which can be evaluated through a forward integration.
Subsequently a "backward" integration of the adjoint model returns the gradient,
or sensitivity, of the cost function, dJ/dX, with respect to a given set
of control variables, X. |
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The
former question can be answered by use of the tangent linear
model or by Monte-Carlo approaches. The latter question can be
answered using the adjoint of the tangent linear model and
involves integration of it backwards in time to yield the
sensitivity of some scalar function of the output parameters to
input parameters. While one is often more interested in the answer to the latter
question, unless the adjoint of the tangent linear model is
available, it generally involves prohibitively many forward integrations,
each one corresponding to a small change in one of the many
input parameters.CMI has put much effort in to the development of models that
can be 'automatically differentiated'. MITgcm is one of very few models that have sibling
tangent-linear and adjoint codes. Moreover, they are maintained
automatically using an automatic adjoint compiler.
Look here for technical details associated with
automatic differentiation
and MITgcm.
Applications
of our adjoint techniques can be found here.
Technical web sites on AD can be found here.
Recent CMI/Adjoint related Publications:
Heimbach, P., D. Menemenlis, M. Losch,
J.M. Campin, and C. Hill, 2010: On the
formulation of sea-ice models. Part 2:
Lessons from multi-year adjoint sea ice
export sensitivities through the Canadian
Arctic Archipelago. Ocean Modelling,
in press, doi:10.1016/j.ocemod.2010.02.002.
Losch, M., D. Menemenlis, J.M. Campin,
P. Heimbach, and C. Hill, 2010: On the
formulation of sea-ice models. Part 1:
Effects of different solver implementations
and parameterizations. Ocean Modelling,
in press, doi:10.1016/j.ocemod.2009.12.008
read
more...
2009
Utke, J., L. Harscoet, P. Heimbach, C.
Hill, P. Hovland and U. Naumann, 2009:
Toward adjointable MPI. Proceedings of
the 10th IEEE International Workshop on
Parallel and Distributed Scientific and
Engineering, PDSEC-09, Rome, Italy, pp.
1-8, doi:10.1109/IPDPS.2009.5161165.
2008
Heimbach, P., 2008: The MITgcm/ECCO
adjoint modeling infrastructure. CLIVAR
Exchanges, 13(1), January
2008, pp. 13-17.
Utke, J., U. Naumann, M. Fagan, N.
Thallent, M. Strout, P. Heimbach, C. Hill
and C. Wunsch, 2008: OpenAD/F: A modular,
open-source tool for automatic
differentiation of Fortran codes. ACM
Transactions on Mathematical Software (TOMS),
34(4), doi:10.1145/1377596.1377598
2007
Losch, M. and P. Heimbach, 2007: Adjoint
sensitivity of an ocean general circulation
model to bottom topography. J. Phys.
Oceanogr., 37(2), pp.
377-393, doi:10.1175/JPO3017.1
2006
Gebbie, G., P. Heimbach and C. Wunsch,
2006: Strategies for
nested and
eddy-resolving
state estimation.
J.
Geophys. Res.,
111,
C10073, doi:10.1029/2005JC003094
2005
Heimbach, P., C.
Hill and R. Giering,
2005: An efficient exact
adjoint of the parallel
MIT general circulation
model, generated via
automatic
differentiation. Future Generation
Computer Systems,
21(8),
1356-1371, doi:10.1016/j.future.2004.11.010.
Menemenlis D., C.
Hill, A. Adcroft, J.M.
Campin, B. Cheng, B.
Ciotti, I. Fukumori, A.
Koehl, P. Heimbach, C.
Henze, T. Lee, D.
Stammer, J. Taft, and J.
Zhang, 2005: NASA
Supercomputer Improves
Prospects for Ocean
Climate Research.
EOS Transactions AGU, 86(9),
p. 89
2003
U. Naumann
and P. Heimbach, 2003:
Coupling tangent-linear
and adjoint models.
in: V. Kumar, M.
Gavrilova, C.J.K. Tan,
P. L’Ecuyer (Eds.), Lecture
Notes in Computer
Science (LNCS), Vol.
2668, part II, pp.
105-114,
Springer-Verlag.
2002
P. Heimbach,
C. Hill and R. Giering,
2002:
Automatic Generation of
Efficient Adjoint Code
for a Parallel Navier-Stokes
Solver. in: J.J.
Dongarra, P.M.A. Sloot
and C.J.K. Tan (Eds.), Lecture
Notes in Computer
Science (LNCS), Vol.
2330, part II, pp.
1019-1028, Springer-Verlag.
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