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Martin Losch and Patrick Heimbach

approaches but requires a separate (tedious) code development effort. Before the advent and increasing sophistication of algorithmic/automatic differentiation (AD) tools during the 1990s, this development inevitably was inexact (e.g., Sirkes and Tzipermann 1997 ) and lagged behind the forward code development. Early OGCM studies based on handwritten adjoints include those of Tziperman and Thacker (1989) , Sheinbaum and Anderson (1990) , and Marotzke and Wunsch (1993) . Carl Wunsch’s foresight at the

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Reiner Schlitzer

linear equations, which all have the same coefficient matrix 𝗧 and only differ in the right-hand-side q . Solutions are most efficiently obtained by applying a sparse 𝗟𝗨 factorization algorithm ( Harwell 1995 ) on 𝗧, and then using the factorization and the different right-hand sides for computationally cheap solution steps. The availability of the 𝗟𝗨 factor matrices also allows efficient solving of the associated adjoint equations involving the transpose of the transport matrix 𝗧 T (see

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Nelson G. Hogg and Daniel E. Frye

and led to changes in the transducer and data processing algorithms (see section 3 ). At 4000-m depth there was no reference instrument and the RCM11 and 3D-ACM measured speeds that were consistently different, with the 3D-ACM recording speeds more than 50% higher on average than the RCM11 throughout the measurement range. The overall energy levels recorded by the RCM11 were similar to those seen at 2000 m and by other instruments that have been moored in this area (see, e.g., McKee et al. 1981

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Ichiro Fukumori, Dimitris Menemenlis, and Tong Lee

. Océanogr. , 17 , 15 – 32 . Csanady , G. T. , 1982 : Circulation in the Coastal Ocean . D. Reidel, 279 pp . da Silva , A. M. , C. C. Young , and S. Levitus , 1994 : Algorithms and Procedures. 1 , Atlas of Surface Marine Data 1994, NOAA Atlas NESDIS 6, . 83 . Dickey , J. O. , S. L. Marcus , O. de Viron , and I. Fukumori , 2002 : Recent Earth oblateness variations: Unraveling climate and postglacial rebound effects. Science , 298 , 1975 – 1977 . Dorman , C. E. , R. C

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A. Köhl, D. Stammer, and B. Cornuelle

. Assoc. Comput. Mach. Trans. Math. Software , 24 , 437 – 474 . Gilbert , J. C. , and C. Lemaréchal , 1989 : Some numerical experiments with variable-storage quasi-Newton algorithms. Math. Programm. , 45 , 407 – 435 . Häkkinen , S. , and P. B. Rhines , 2004 : Decline of subpolar North Atlantic circulation during the 1990s. Science , 304 , 555 – 559 . Kalnay , E. , and Coauthors , 1996 : The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc. , 77 , 437 – 471

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Dimitris Menemenlis, Ichiro Fukumori, and Tong Lee

other oceanographic processes in the Mediterranean Sea. Fieguth et al. (1998) used a multiresolution optimal interpolation algorithm to estimate the error budget of Mediterranean altimeter data. For barometrically corrected Ocean Topography Experiment (TOPEX)/Poseidon data, they estimate low-wavenumber errors to have a standard deviation of 2.5 cm during the summer months and of 4–8 cm during the winter. If it were possible to explain and to predict some substantial fraction of these errors, more

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Peter Huybers, Geoffrey Gebbie, and Olivier Marchal

and a smaller J d , this is not always the case, presumably owing to the model nonlinearities. Second, minimization of the cost function can result in a local rather than global minimum. To address these complications, a simulated annealing algorithm (e.g., Press et al. 1999 ) is used to search for the state requiring the smallest adjustment to the tracer field. The search begins by assigning an initial tracer uncertainty, μ o , and inverting for the transport field. For simplicity, the tracer

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