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Robert Sadourny

Abstract

Two simple numerical models of the shallow-water equations identical in all respects but for their con-servation properties have been tested regarding their internal mixing processes. The experiments show that violation of enstrophy conservation results in a spurious accumulation of rotational energy in the smaller scales, reflected by an unrealistic increase of enstrophy, which ultimately produces a finite rate of energy dissipation in the zero viscosity limit, thus violating the well-known dynamics of two-dimensional flow. Further, the experiments show a tendency to equipartition of the kinetic energy of the divergent part of the flow in the inviscid limit, suggesting the possibility of a divergent energy cascade in the physical system, as well as a possible influence of the energy mixing on the process of adjustment toward balanced flow.

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ROBERT SADOURNY

Abstract

A class of conservative finite-difference approximations of the primitive equations is given for quasi-uniform spherical grids derived from regular polyhedrons. The earth is split into several contiguous regions. Within each region, a coordinate system derived from central projections is used, instead of the spherical coordinate system, to avoid the use of inconsistent boundary conditions at the poles. The presence of artificial internal boundaries has no effect on the conservation properties of the approximations. Examples of conservative schemes, up to the second order in the case of a cube, are given. A selective damping operator is needed to remove the two-grid interval waves generated by the existence of internal boundaries.

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Ali Harzallah and Robert Sadourny

Abstract

The variability of atmospheric flow is analyzed by separating it into an internal part due to atmospheric dynamics only and an external (or forced) part due to the variability of sea surface temperature forcing. The two modes of variability are identified by performing an ensemble of seven independent long-term simulations of the atmospheric response to observed SST (1970–1988) with the LMD atmospheric general circulation model. The forced variability is defined from the analysis of the ensemble mean and the internal variability from the analysis of deviations from the ensemble mean. Emphasis is put on interannual variability of sea level pressure and 5OO-hPa geopotential height for the Northern Hemisphere winter. In view of the large systematic errors related to the relatively small number of realizations, unbiased variance estimators have been developed. Although statistical significance is not reached in some extratropical regions, large significant extratropical responses are found at the North Pacific-Alaska sector for SLP and over western Canada and the Aleutians for 5OO-hPa geopotential height. The influence of SST variations on internal variability is also examined by using a 7-year simulation using the climatological SST seasonal cycle. It is found that interannual SST changes strongly influence the geographical distribution of internal variability; in particular, it tends to increase it over oceans. Patterns of internal and external variability of the 5OO-hPa geopotential height are further examined by using EOF decompositions showing that the model realistically simulates the leading observed variability modes. The geographical structure of internal variability patterns is found to be similar to that of total variability, although similar modes tend to evolve rather differently in time. The zonally symmetric seesaw dominates the internal variability for both observed and climatologically prescribed SST. The Pacific-North American (PNA) and Western Pacific (WP) patterns, on the other hand, are the dominant modes associated with patterns of SST variability: the latter is related to Atlantic anomalies, while the former responds to both El Niño events and extratropical forcing.

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Augustin Vintzileos and Robert Sadourny

Abstract

In order to represent in a most adequate way the various feedback mechanisms that govern the atmosphere–ocean or atmosphere–surface couplings, a “delocalized physics” method is introduced, in which the subgrid-scale physical parameterizations of the atmospheric model are computed on a grid defined independently of the grid where adiabatic dynamics are computed. This “physical grid,” which can be irregular and time dependent, is defined by juxtaposing the surface grids constructed independently for the ocean, land, and sea-ice models. The delocalization method allows taking into account the nonlinearities of vertical fluxes due to heterogeneities in the finescale surface properties that are not resolved by the adiabatic atmospheric dynamics calculations. The impact of delocalizing the physics to fit a given higher resolution surface grid is tested first on experiments where the global atmosphere is forced by observed ocean temperatures. The comparison demonstrates a significant improvement of the predominant variability mode of the outgoing longwave radiation field, corresponding mainly to the seasonal cycle. The delocalized physics method is then tested on an experiment where the General circulation model of the Laboratoire de Météorologie Dynamique is coupled to the Laboratoire d’Océanographie Dynamique et de Climatologie tropical Pacific ocean model. Delocalized physics allow surface fluxes to respond better to fine sea surface temperatures structures like the Legekis waves produced by the ocean model.

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Robert Sadourny and Claude Basdevant

Abstract

A lateral diffusion scheme designed to efficiently parameterize the subgrid scale lures associated with barotropic and baroclinic transients is presented and tested on a quasi-geostrophic, two layer model, with law-scale thermal forcing. The scheme is based on formal energy conservation and potential enstrophy dissipation. At very coarse resolutions, where the cutoff scale is of the order of the internal radius of deformation, the diffusion scheme is shown to produce a realistic amount of potential-to-kinetic energy conversions, and realistic amplitudes of the large-scale barotropic modes.

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ROBERT SADOURNY and PIERRE MOREL

Abstract

The hexagonal grid based on a partition of the icosahedron has distinct geometrical qualities for the mapping of a sphere and also presents some indexing difficulties. The applicability of this grid to the primitive equations of fluid dynamics is demonstrated, and a finite-difference approximation of these equations is proposed. The basic variables are the mass fluxes from one hexagonal cell to the next through their common boundary. This scheme conserves the total mass, the total momentum, and the total kinetic energy of the fluid as well as the total squared vorticity of a nondivergent flow. A computational test was performed using a hexagonal grid to describe space periodic waves on a nonrotating plane. The systematic variation of total kinetic and potential energy is less than 10−5 after 1,000 time steps.

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Jean-Michel Hoyer and Robert Sadourny

Abstract

Simple second-order closure models of quasi-geostrophic turbulence are derived, applying either to two-layer flows within isentropic boundaries, or to Eady-type frontogenesis with vanishing potential vorticity; homogeneity and horizontal isotropy are used as simplifying assumptions. Long-term numerical integrations of the two models are performed to obtain the structure of regime flows under stationary large-scale baroclinic forcing. The various cascade processes and the corresponding inertial ranges are discussed and visualized, showing characteristic differences between fully developed baroclinic instability and the linear theory. Further applications of such models may include studies of truncation effects on the efficiency of baroclinic instability.

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Robert Sadourny and Jean-Michel Hoyer

Abstract

The inhibition of baroclinic instability in low-resolution quasi-geostrophic models is studied using a simplified second-order closure approximation. It is shown that this inhibition, which results in systematic overestimation of baroclinic energy and systematic underestimation of barotropic energy, is the result of spurious energy dissipation due to the use of inadequate lateral diffusion. Consequently, a possible methodology for the parameterization of baroclinic instability in low-resolution models is proposed, based on the construction of diffusion operators able to dissipate potential enstrophy while conserving energy exactly.

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Francis Codron, Augustin Vintzileos, and Robert Sadourny

Abstract

To take into account the strong nonlinearities of vertical fluxes due to small-scale heterogeneities of surface properties, more and more coupled general circulation models compute part of their atmospheric physical parameterizations, either the surface fluxes or the whole package, on the finer grid of their ocean or land model. A modification of a traditional interpolation scheme is presented to calculate the values of atmospheric variables over surface model grid points. In addition to the desirable properties of flux conservation and preservation of a constant field, the new scheme allows discontinuities in the interpolated fields at the surface model’s boundaries and orographic jumps, while remaining continuous elsewhere. It can also be tuned separately for each variable.

The modified scheme is then evaluated using the circulation model of the Laboratoire de Météorologie Dynamique coupled to the Laboratoire d’Océanographie Dynamique et de Climatologie tropical Pacific Ocean model using the delocalized physics method. The results show a large improvement of heat and humidity fluxes near the focus region of the South American coast in the southeastern equatorial Pacific, and a subsequent westward propagation of significant cold SST anomalies.

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Francis Codron, Augustin Vintzileos, and Robert Sadourny

Abstract

This study examines the response of the climate simulated by the Institut Pierre Simon Laplace tropical Pacific coupled general circulation model to two changes in parameterization: an improved coupling scheme at the coast, and the introduction of a saturation mixing ratio limiter in the water vapor advection scheme, which improves the rainfall distribution over and around orography. The main effect of these modifications is the suppression of spurious upwelling off the South American coast in Northern Hemisphere summer. Coupled feedbacks then extend this warming over the whole basin in an El Niño–like structure, with a maximum at the equator and in the eastern part of the basin. The mean precipitation pattern widens and moves equatorward as the trade winds weaken.

This warmer mean state leads to a doubling of the standard deviation of interannual SST anomalies, and to a longer ENSO period. The structure of the ENSO cycle also shifts from westward propagation in the original simulation to a standing oscillation. The simulation of El Niño thus improves when compared to recent observed events. The study of ENSO spatial structure and lagged correlations shows that these changes of El Niño characteristics are caused by both the increase of amplitude and the modification of the spatial structure of the wind stress response to SST anomalies.

These results show that both the mean state and variability of the tropical ocean can be very sensitive to biases or forcings, even geographically localized. They may also give some insight into the mechanisms responsible for the changes in ENSO characteristics due to decadal variability or climate change.

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