

Efficient Sensitivities for the Spinup Phase
incollection
  

Area General 
Author(s)
Thomas Kaminski
, Ralf Giering
, Michael Voßbeck

Published in Automatic Differentiation: Applications, Theory, and Implementations

Editor(s) H. M. Bücker, G. Corliss, P. Hovland, U. Naumann, B. Norris 
Year 2005 
Publisher Springer 
Abstract In geosciences, it is common to spin up models by integrating with annually repeated boundary conditions. adgenerated code for evaluating sensitivities of the final cyclostationary state with respect to model parameters or boundary conditions usually includes a similar iteration for the derivative statements, possibly with a reduced number of iterations. We evaluate an alternative strategy that first carries out the spinup, then evaluates the full Jacobian for the final iteration and then applies the implicit function theorem to solve for the sensitivities of the cyclostationary state. We demonstrate the benefit of the strategy for the spinup of a simple boxmodel of the atmospheric transport. We derive a heuristic inequality for this benefit, which increases with the number of iterations and decreases with the size of the state space. 
CrossReferences Bucker2005ADA 
AD Tools TAF 
AD Theory and Techniques Iteration 
BibTeX
@INCOLLECTION{
Kaminski2005ESf,
author = "Thomas Kaminski and Ralf Giering and Michael Vo{\ss}beck",
title = "Efficient Sensitivities for the Spinup Phase",
editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
Norris",
booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
year = "2005",
abstract = "In geosciences, it is common to spin up models by integrating with annually
repeated boundary conditions. ADgenerated code for evaluating sensitivities of the final
cyclostationary state with respect to model parameters or boundary conditions usually includes a
similar iteration for the derivative statements, possibly with a reduced number of iterations. We
evaluate an alternative strategy that first carries out the spinup, then evaluates the full
Jacobian for the final iteration and then applies the implicit function theorem to solve for the
sensitivities of the cyclostationary state. We demonstrate the benefit of the strategy for the
spinup of a simple boxmodel of the atmospheric transport. We derive a heuristic inequality for
this benefit, which increases with the number of iterations and decreases with the size of the state
space.",
crossref = "Bucker2005ADA",
ad_tools = "TAF",
pages = "285293",
doi = "10.1007/3540284389_25",
ad_area = "General",
ad_theotech = "Iteration",
PDF = "http://www.FastOpt.com/papers/kaminskial04b.pdf"
}
 
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