/pdf/scalable-molecular-dynamics-with-namd-3j7xyc70g4.pdf

Scalable Molecular Dynamics with NAMD

The NCEP Climate Forecast System Reanalysis (CFSR) was completed for the 31-yr period from 1979 to 2009, in January 2010. The CFSR was designed and executed as a global, high-resolution coupled atmosphere–ocean–land surface–sea ice system to provide the best estimate of the state of these coupled domains over this period. The current CFSR will be extended as an operational, real-time product into the future. New features of the CFSR include 1) coupling of the atmosphere and ocean during the generation of the 6-h guess field, 2) an interactive sea ice model, and 3) assimilation of satellite radiances by the Gridpoint Statistical Interpolation (GSI) scheme over the entire period. The CFSR global atmosphere resolution is ~38 km (T382) with 64 levels extending from the surface to 0.26 hPa. The global ocean's latitudinal spacing is 0.25° at the equator, extending to a global 0.5° beyond the tropics, with 40 levels to a depth of 4737 m. The global land surface model has four soil levels and the global sea ice m...

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The NCEP Climate Forecast System Reanalysis

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the three- dimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is "fast," competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address small- scale processes. A "finite-volume" approach is employed to discretize the model in space in which property fluxes are defined normal to faces that delineate the volumes. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be "shaved" to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical columns of ocean to each processing unit. The resulting model, which can handle arbitrarily complex geometry, is efficient and scalable and has been mapped on to massively parallel multiprocessors such as the Connection Machine (CM5) using data-parallel FORTRAN and the Massachusetts Institute of Technology data-flow machine MONSOON using the implicitly parallel language Id. Details of the numerical implementation of a model which has been designed for the study of dynamical processes in the ocean from the convective, through the geostrophic eddy, up to global scale are set out. The "kernel" algorithm solves the incompressible Navier Stokes equations on the sphere, in a geometry as complicated as that of the ocean basins with ir- regular coastlines and islands. (Here we use the term "Navier Stokes" to signify that the full nonhydrostatic equations are being employed; it does not imply a particular constitutive relation. The relevant equations for modeling the full complex- ity of the ocean include, as here, active tracers such as tem- perature and salt.) It builds on ideas developed in the compu- tational fluid community. The numerical challenge is to ensure that the evolving velocity field remains nondivergent. Most

/pdf/a-finite-volume-incompressible-navier-stokes-model-for-2d0vnt2c1s.pdf

A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers

Microbes are dominant drivers of biogeochemical processes, yet drawing a global picture of functional diversity, microbial community structure, and their ecological determinants remains a grand challenge. We analyzed 7.2 terabases of metagenomic data from 243 Tara Oceans samples from 68 locations in epipelagic and mesopelagic waters across the globe to generate an ocean microbial reference gene catalog with >40 million nonredundant, mostly novel sequences from viruses, prokaryotes, and picoeukaryotes. Using 139 prokaryote-enriched samples, containing >35,000 species, we show vertical stratification with epipelagic community composition mostly driven by temperature rather than other environmental factors or geography. We identify ocean microbial core functionality and reveal that >73% of its abundance is shared with the human gut microbiome despite the physicochemical differences between these two ecosystems.

/pdf/structure-and-function-of-the-global-ocean-microbiome-4ylafdtr3j.pdf

Structure and function of the global ocean microbiome

Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of small-scale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1- to 10-km scale, and simulations of the global circulation of the ocean.

/pdf/hydrostatic-quasi-hydrostatic-and-nonhydrostatic-ocean-2d84528m1a.pdf

Hydrostatic, quasi‐hydrostatic, and nonhydrostatic ocean modeling

Height coordinate ocean models commonly represent topography as a ‘‘staircase’’ of discontinuous steps that are fitted to the model grid. Here the ramifications of an alternative approach are studied in which ‘‘shaved cells’’ are used to represent irregular topography. The problem is formulated using the finite-volume method and care is taken to ensure that the discrete forms have appropriate conservation properties. Two representations of topography, ‘‘partial step’’ and ‘‘piecewise linear,’’ are considered and compared with the staircase approach in some standard problems such as the topographic b effect and flow over a Gaussian bump. It is shown that shaved cells are clearly more accurate than the conventional staircase representation. The use of partial steps, although not as accurate as the piecewise linear approach, is seen to be superior to the staircase approach. Moreover, partial steps can be readily implemented in existing height coordinate models.

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Representation of Topography by Shaved Cells in a Height Coordinate Ocean Model

The architecture of the earth system modeling framework

[1] A three-dimensional oceanic state is estimated for the period 1992–1997 as it results from combining large-scale ocean data sets with a general circulation model. At the cost of increased computational load, the estimation (assimilation) method is chosen specifically so that the resulting state estimate is consistent with the model equations, having no artificial sources or sinks. To bring the model into close agreement with observations, its initial temperature and salinity conditions are permitted to change, as are the time-dependent surface fluxes of momentum, heat and freshwater. Resulting changes of these “control vectors” are largely consistent with accepted uncertainties in the hydrographic climatology and meteorological analyses. The assimilation procedure is able to correct for many of the traditional shortcomings of the flow field by changing the surface boundary conditions. Changes in the resulting flow field are predominantly on the gyre scale and affect many features that are often poorly simulated in traditional numerical simulations, such as the strengths of the Gulf Stream and its extension, the Azores Current and the anticyclonic circulation associated with the Labrador Sea. Tests of the results and their consistency with prior error assumptions show that the constrained model has moved considerably closer to the observations imposed as constraints, but has also moved closer to independent data from the World Ocean Circulation Experiment not used in the assimilation procedure. In some regions where the comparisons remain indeterminate, not enough ocean observations are available, and it is difficult to ascribe the residuals to either the model or the observations. Although problems remain, a useful first solution to the global time-dependent ocean state estimation problem has been found. The estimates will continue to improve through the evolution of numerical models, computer power increases, more data, and more efficient estimation methods.

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Chris Hill

Papers

A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers

Hydrostatic, quasi‐hydrostatic, and nonhydrostatic ocean modeling

Representation of Topography by Shaved Cells in a Height Coordinate Ocean Model

The architecture of the earth system modeling framework

Global ocean circulation during 1992-1997, estimated from ocean observations and a general circulation model