Comparaison de différentes techniques d'approximation de séries temporelles incertaines issues d'écoulements océaniques

International audienceThe analysis of time series is a fundamental task in many flow simulations such as oceanic and atmospheric flows. A major challenge is the construction of a faithful and accurate time-dependent surrogate with a manageable number of samples. Several techniques have been tested to handle the time-dependent aspects of the surrogate including a direct approach, low-rank decomposition, auto-regressive model and global Bayesian emulators. These techniques rely on two popular methods for uncertainty quantification, namely Polynomial chaos expansion and Gaussian processes regression. The different techniques were tested and compared on the uncertain evolution of the sea surface height forecast at two location exhibiting different levels of variance. Two ensembles sizes were considered as well as two versions of polynomial chaos (ordinary least squares or ridge regression) and Gaussian processes (exponential or Matern covariance function) to assess their impact on the results. Our conclusions focus on the advantages and the drawbacks, in terms of accuracy, flexibility and computational costs of the different techniques

An Additive Schwarz Preconditioner for the Spectral Element Ocean Model Formulation of the Shallow Water Equations

We discretize the shallow water equations with an Adams-Bashford scheme combined with the Crank-Nicholson scheme for the time derivatives and spectral elements for the discretization in space. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. This system can be solved with a preconditioned conjugate gradients, where the matrix-vector product is only implicitly given. We derive an overlapping block preconditioner based on additive Schwarz methods for preconditioning the reduced system

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.United States. Office of Naval Research (award N00014-101-0498)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099)Gulf of Mexico Research Initiative (contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C)

Mantle 3He distribution and deep circulation in the Indian Ocean

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C06012, doi:10.1029/2003JC002028.The World Ocean Circulation Experiment Indian Ocean helium isotope data are mapped and features of intermediate and deep circulation are inferred and discussed. The 3He added to the deep Indian Ocean originates from (1) a strong source on the mid-ocean ridge at about 19°S/65°E, (2) a source located in the Gulf of Aden in the northwestern Indian Ocean, (3) sources located in the convergent margins in the northeastern Indian Ocean, and (4) water imported from the Indonesian Seas. The main circulation features inferred from the 3He distribution include (1) deep (2000–3000 m) eastward flow in the central Indian Ocean, which overflows into the West Australian Basin through saddles in the Ninetyeast Ridge, (2) a deep (2000–3000 m) southwestward flow in the western Indian Ocean, and (3) influx of Banda Sea Intermediate Waters associated with the deep core (1000–1500 m) of the through flow from the Pacific Ocean. The large-scale 3He distribution is consonant with the known pathways of deep and bottom water circulation in the Indian Ocean.National Science Foundation support is acknowledged for the UM part of the work through grants OCE-9820131 and OCE-998150. Support for the LDEO portion of the work was obtained from the National Science Foundation through awards OCE 94-13162 and OCE 98-20130

Mass Transport in Wave Tank

The mass transport induced by a small amplitude progressive wave traveling in a rectangular wave tank is investigated. Attention is focused on the three-dimensional mean flow structure generated by the Stokes boundary layers near the side walls. The mass-transport problem is formulated in terms of vorticity and velocity field. A numerical scheme is developed to solve the coupled transport equation for the vorticity and the Poisson equation for the stream function. It is found that the side-wall boundary layers generate mean downstream vorticities. When the Reynolds number is small, the diffusion process dominates. Therefore, the vorticities generated from the boundary layers are diffused into the entire wave tank. On the other hand, when the Reynolds number is much larger than one, the convection process becomes as important as the diffusion process, the steady vorticities are confined within a small area adjacent to the solid boundaries. When the aspect ratio, width divided by depth, is of the order of magnitude of one, a pair of circulation cells appear on the plane perpendicular to the direction of wave propagation. As the width of the tank increases, more cells appear. The spanwise variations of the mass-transport velocity in the wave propagation direction become more significant when the aspect ratio is larger

The Spectral Element Method for the Shallow Water Equations on the Sphere

The spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models. This is the first step in evaluating the suitability of spectral elements for climate modeling. The potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed. The method requires that the sphere be tiled with rectangles, for which we make use of the gnomonic projection to map the sphere onto the cube. To measure the performance of the method relative to other models, results are presented from a standard suite of shallow water test cases for the sphere. These results confirm the spectral accuracy of the method

Mass transport in three-dimensional water waves

A spectral scheme is developed to study the mass transport in three-dimensional water waves where the steady flow is assumed to be periodic in two horizontal directions. The velocity–vorticity formulation is adopted for the numerical solution, and boundary conditions for the vorticity are derived to enforce the no-slip conditions. The numerical scheme is used to calculate the mass transport under two intersecting wave trains; the resulting flow is reminiscent of the Langmuir circulation patterns. The scheme is then applied to study the steady flow in a three-dimensional standing wave