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OpenAD/F: A Modular, OpenSource Tool for Automatic Differentiation of Fortran Codes
"... 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 ..."
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Cited by 27 (13 self)
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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 languageindependent fashion. It uses code analysis results implemented in the OpenAnalysis component. The interface to the languageindependent transformation engine is an XMLbased format, specified through an XML schema. The implemented transformation algorithms allow efficient derivative computations using locally optimized crosscountry sequences
2006: Efficiency of reducedorder, timedependent adjoint data assimilation approaches
 J. Oceanogr
"... Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reducedorder optimization methods that reduce the size of the control vector ..."
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Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reducedorder optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show that such order reduction can indeed speed up the initial convergence rate of an assimilation effort in the eastern subtropical North Atlantic using in situ and satellite data as constraints. However, an improved performance of the optimization was only obtained with a hybrid approach where the optimization is started in a reduced subspace but is continued subsequently using the full control space. In such an experiment about 50 % of the computational cost can be saved as compared to the optimization in the full control space. Although several orderreduction approaches seem feasible, the best result was obtained by projecting the control vector onto Empirical Orthogonal Functions (EOFs) computed from a set of adjusted control vectors estimated previously from an optimization using the same model configuration.
2005), Estimating eddy stresses by fitting dynamics to observations using a residual‐mean ocean circulation model and its adjoint
 J. Phys. Oceanogr
"... A global ocean circulation model is formulated in terms of the “residual mean ” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the threedimensional eddy stress field that minimizes the departure of the coarseresolution model from climatological observations of ..."
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Cited by 27 (9 self)
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A global ocean circulation model is formulated in terms of the “residual mean ” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the threedimensional eddy stress field that minimizes the departure of the coarseresolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residualmean circulation yield a wealth of information about the role of eddies in largescale ocean circulation. In eddyrich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m2, and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity are inferred. The diffusivities have a welldefined largescale structure whose prominent features are 1) large values of (up to 4000 m2 s1) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of , suggestive of a dependence on the stratification N 2. It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N 2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity. 1.
Comparison of entrainment in overflows simulated by zcoordinate, isopycnal and nonhydrostatic models
, 2006
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An unstructuredgrid, finitevolume, nonhydrostatic, parallel coastal ocean simulator
 Ocean Modelling
, 2006
"... A finitevolume formulation is presented that solves the threedimensional, nonhydrostatic Navier–Stokes equations with the Boussinesq approximation on an unstructured, staggered, zlevel grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of ..."
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Cited by 24 (3 self)
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A finitevolume formulation is presented that solves the threedimensional, nonhydrostatic Navier–Stokes equations with the Boussinesq approximation on an unstructured, staggered, zlevel grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of meters. In particular, the code has been developed to simulate the nonlinear, nonhydrostatic internal wave field in the littoral ocean. The method is based on the formulation developed by Casulli, in that the freesurface and vertical diffusion are semiimplicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly with the secondorder Adams–Bashforth method, while the pressurecorrection method is employed for the nonhydrostatic pressure in order to achieve overall secondorder temporal accuracy. Advection of momentum is accomplished with an Eulerian discretization which conserves momentum in cells that do not contain the free surface, and scalar advection is discretized in a way that ensures consistency with continuity, thereby ensuring local and global mass conservation using a velocity field that conserves volume on a local and global basis. The nonhydrostatic pressure field is solved efficiently using a blockJacobi preconditioner, and while stability is limited by the internal gravity wave speed and vertical advection of momentum, applications requiring relatively small time steps due to accuracy or stability constraints are run efficiently on parallel computers, since the present formulation is written entirely with the messagepassing interface (MPI). The ParMETIS libraries are employed in order to achieve a loadbalanced parallel partitioning that minimizes interprocessor
Decadal Trends in Sea Level Patterns: 1993–2004
, 2007
"... Estimates of regional patterns of global sea level change are obtained from a 1 ° horizontal resolution general circulation model constrained by least squares to about 100 million ocean observations and many more meteorological estimates during the period 1993–2004. The data include not only altimet ..."
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Cited by 23 (5 self)
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Estimates of regional patterns of global sea level change are obtained from a 1 ° horizontal resolution general circulation model constrained by least squares to about 100 million ocean observations and many more meteorological estimates during the period 1993–2004. The data include not only altimetric variability, but most of the modern hydrography, Argo float profiles, sea surface temperature, and other observations. Spatialmean trends in altimetric data are explicitly suppressed to isolate global average longterm changes required by the in situ data alone. On large scales, some regions display strong signals although few individual points have statistically significant trends. In the regional patterns, thermal, salinity, and mass redistribution contributions are all important, showing that regional sea level change is tied directly to the general circulation. Contributions below about 900 m are significant, but not dominant, and are expected to grow with time as the abyssal ocean shifts. Estimates made here produce a global mean of about 1.6 mm yr �1, or about 60 % of the pure altimetric estimate, of which about 70 % is from the addition of freshwater. Interannual global variations may be dominated by the freshwater changes rather than by heating changes. The widely quoted altimetric global average values may well be correct, but the accuracies being inferred in the literature are not testable by existing in situ observations. Useful estimation of the global averages is extremely difficult given the realities of space–time sampling and model approximations. Systematic errors are likely to dominate most estimates of global average change: published values and error bars should be used very cautiously. 1.
Bottom topography as a control variable in an ocean model
, 2003
"... The possibility of using topography in a state estimation context as a control parameter is explored in a linear barotropic shallow water model. Along with its adjoint, the model is used to systematically assess the influence of the depth field on the modeled circulation in a steady state. Sensitivi ..."
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Cited by 22 (6 self)
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The possibility of using topography in a state estimation context as a control parameter is explored in a linear barotropic shallow water model. Along with its adjoint, the model is used to systematically assess the influence of the depth field on the modeled circulation in a steady state. Sensitivity of the flow field to the topography is greater in a partially blocked zonal channel than in a subtropical gyre. Hypothetical surface elevations are used to represent the types of data actually available. In neither case can all the details of the topography be recovered, showing that the relationship between topography and elevation does not have a unique inverse, and that many details of the topography are irrelevant to the particular physics under consideration. 1.
A new treatment of the Coriolis terms in Cgrid models at both high and low resolutions, Monthly Weather Review 127
, 1999
"... Numerical models of the ocean typically employ gridpoint techniques in which the dynamical variables defining the state of the ocean are held on a staggered grid. One common arrangement of the variables, known as the Arakawa Cgrid, is particularly prone to gridscale noise that is due to spatial ave ..."
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Cited by 22 (2 self)
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Numerical models of the ocean typically employ gridpoint techniques in which the dynamical variables defining the state of the ocean are held on a staggered grid. One common arrangement of the variables, known as the Arakawa Cgrid, is particularly prone to gridscale noise that is due to spatial averaging of Coriolis terms and that is manifest when the grid resolution is coarse with respect to the deformation radius. Here, the authors analyze the problem in the context of linear inertia–gravity waves and discuss the reason for the prevalence of noise. They suggest a solution to the problem in which the Cgrid model variables are augmented with Dgrid velocity variables. An analysis of the resulting C–D grid indicates favorable behavior and numerical results are presented to demonstrate this. Finally, they discuss the similarity in nature between the C–D grid and the Zgrid, to explain why the C–D grid works well at both high and low resolution. 1.
Can Eddies Set Ocean Stratification
 J. Phys. Oceanogr
, 2002
"... Abstract. A simple theory is presented for the buoyancy anomaly and depth of penetration of a warm lens created by a surface buoyancy flux and Ekman pumping in an initially homogeneous, rotating fluid. It is assumed that the overturning of isopycnals induced by pumping and differential heating balan ..."
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Abstract. A simple theory is presented for the buoyancy anomaly and depth of penetration of a warm lens created by a surface buoyancy flux and Ekman pumping in an initially homogeneous, rotating fluid. It is assumed that the overturning of isopycnals induced by pumping and differential heating balances the counteroverturning tendency of baroclinic instability. Baroclinic eddies not only develop on the stratified lens, but play a fundamental role in setting its stratification. The theory is successfully tested against numerical and laboratory experiments in which the mechanicallyinduced deepening of a buoyant lens is arrested by its baroclinic instability. Finally we discuss the possibility that the eddy transfer process studied here might play a role in setting the stratification and depth of the main thermocline in the ocean. 1.
2007: Tropical cyclone–induced upperocean mixing and climate: Application to equable climates
 J. Climate
"... Tropical cyclones instigate an isolated blast of vigorous mixing in the upper tropical oceans, stirring warm surface water with cooler water in the thermocline. Previous work suggests that the frequency, intensity, and lifetime of these storms may be functions of the climate state, implying that tra ..."
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Cited by 20 (1 self)
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Tropical cyclones instigate an isolated blast of vigorous mixing in the upper tropical oceans, stirring warm surface water with cooler water in the thermocline. Previous work suggests that the frequency, intensity, and lifetime of these storms may be functions of the climate state, implying that transient tropical mixing could have been stronger during warmer equable climates with higher concentrations of carbon dioxide. Stronger mixing of the tropical oceans can force the oceans ’ meridional heat flux to increase, cooling tropical latitudes while warming higher ones. This response differs significantly from previous modeling studies of equable climates that used static mixing; coupling mixing to climate changes the dynamic response. A parameterization of mixing from tropical cyclones is developed, and including it leads to a cooling of tropical oceans and a warming of subtropical waters compared with control cases with fixed mixing. The mixing penetration depth regulates the magnitude of the response. 1.