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The Oxford English Dictionary lists eight distinct meanings for the noun “wave” and 10 for the verb form. Physical phenomena of waves, as known by scientists and engineers, are ubiquitous and include those on water surfaces, in sound, seismology, clouds, electromagnetism, cosmic gravitational radiation, in sand, and so on. In the conventional technical sense, waves almost always have some mathematically stated connection between the wavelength (distance between crests), the phase speed (or frequency), and, sometimes, the amplitude. Various exceptions are known, including solitary waves (solitons) and shock waves. Often the waves are mere propagators of motion, but in other cases, they can transport material as well. With the evolution of the English language, the term “wave” has been invoked to describe a huge variety of phenomena ranging from waves of disease, disorder, and emotion, to hair (“permanent waves”), to crowd behavior in stadiums, to “waving” goodbye, to the World War II women's military WAVES, to the titles of novels—for example, from Virginia Woolf. [ABSTRACT FROM AUTHOR]

In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as forcings. For purposes of calculating changes in important functions of state variables such as total mass and energy, or volumetric current transports, results are sensitive to mis-representation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here toy models of a mass-spring oscillator and of a barotropic Rossby-wave equation are used to demonstrate many of the issues. Results from Kalman-filter estimates, and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in 'reanalysis' -like estimates require a full understanding of both models and observations. [ABSTRACT FROM AUTHOR]

The OpenAD/F tool allows the evaluation of derivatives of functions defined by a Fortran program. The derivative evaluation is performed by a Fortran code resulting from the analysis and transformation of the original program that defines the function of interest. OpenAD/F has been designed with a particular emphasis on modularity, flexibility, and the use of open source components. While the code transformation follows the basic principles of automatic differentiation, the tool implements new algorithmic approaches at various levels, for example, for basic block preaccumulation and call graph reversal. Unlike most other automatic differentiation tools, OpenAD/F uses components provided by the OpenAD framework, which supports a comparatively easy extension of the code transformations in a language-independent fashion. It uses code analysis results implemented in the OpenAnalysis component. The interface to the language-independent transformation engine is an XML-based format, specified through an XML schema. The implemented transformation algorithms allow efficient derivative computations using locally optimized cross-country sequences of vertex, edge, and face elimination steps. Specifically, for the generation of adjoint codes, OpenAD/F supports various code reversal schemes with hierarchical checkpointing at the subroutine level. As an example from geophysical fluid dynamics, a nonlinear time-dependent scalable, yet simple, barotropic ocean model is considered. OpenAD/F's reverse mode is applied to compute sensitivities of some of the model's transport properties with respect to gridded fields such as bottom topography as independent (control) variables. Categories and Subject Descriptors: G.1.4 [Numerical Analysis]: --Automatic differentiation; D.3.4 [Programming Languages]: --Code generation, Compilers; F.3.2 [Logics and Meanings of Program]: Semantics of Programming Languages Program analysis; G. 1.6 [Numerical Analysis]: --Gradient methods General Terms: Algorithms, Performance Additional Key Words and Phrases: Automatic differentiation, source transformation, adjoint compiler