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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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NASA NTRS1980

Numerical simulation of stratospheric sudden warmings with a primitive equation spectral model

A 26-level primitive equation spherical harmonic spectral model allowing for wave-wave and wave-zonal flow interactions is presented for the study of stratospheric sudden warmings. The warmings are simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere. In the case involving both wave-wave and wave-zonal flow interactions, this was manifested by the split in the initial polar vortex into a quasi-wave number 2 pattern. In the cases at 60 deg N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. The linear cases exhibit warmings which are more shallow and more intense at 30 km than the nonlinear cases.

Lordi, N. J.↗
NASA NTRS1985

Variability simulations with a steady, linearized primitive equations model

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

Kinter, J. L., III↗
NASA NTRS1985

Diagnosis of ageostrophic circulations in a two-dimensional primitive equation model of frontogenesis

A two-dimensional primitive equation frontogenesis model is applied to the identification of dynamical mechanisms which contribute to transverse ageostrophic circulation in warm and cold advection situations. Attention is focused on conditions conducive to significant alongfront ageostrophic flow with divergence confined to the transverse plane. The circulation is partitioned as a function of forcing mechanisms accompanied by confluence, horizontal shear and the alongfront component of the ageostrophic wind. A series of diagnostic equations is defined for the transverse geostrophic circulation and instantaneous contribution from each partitioned component of the circulation are quantified. In the cold advection case, results are obtained which are consistent with positive feedback between the subsidence pattern and forcing by horizontal shear.

Keyser, D.↗
NASA NTRS1983

On error detection in the dynamics part of primitive equation models

Rossby-Haurwitz waves have been commonly employed as initial conditions for testing the dynamics part of global atmospheric models. Difficulties arise in connection with the primitive equation (PE) model. Chao and Geller (1982) have suggested that it would be better if normal mode solutions of the linearized primitive equations would be used as initial conditions. However, tests involving normal mode conditions are not adequate for the detection of errors in the nonlinear terms. The present investigation has the objective to review the study conducted by Chao and Geller and to provide tests for the nonlinear terms.

Chao, W. C.↗
NASA NTRS1982

Utilization of normal mode initial conditions for detecting errors in the dynamics part of primitive equation global models

When a global atmospheric basic state has constant angular velocity and its temperature varies with altitude only, there exist normal mode solutions to the linearized global primitive equations. The use of these normal modes, which have known behavior in time, is superior to the use of the Rossby-Haurwitz wave as initial conditions for detecting errors in the dynamics part of primitive equation global models. With these initial conditions, integration through only one time step is sufficient to detect many formulation and coding errors. Other tests are still required for detecting problems of nonlinear instability and conservation of integral properties, however.

Chao, W. C.↗
NASA NTRS1984

Fully Implicit Numerical Methods for the Baroclinic Primitive Equations

A fully implicit code was developed to solve the three-dimensional primitive equations of atmospheric flow. The scheme is second order accurate in time and fourth order accurate in the horizontal and vertical directions. Furthermore, as a result of being fully implicit, the time step is not restricted by the mesh spacing near the poles, nor by the speed of inertia-gravity waves. Rather, the time step, deltat is determined simply by the requirement that it be small enough to adequately resolve the atmospheric flow of interest. The accuracy and efficiency of current models for fine grids should be significantly improved.

Cohn, S. E.↗
NASA NTRS1985

A two-dimensional primitive equation model of frontogenesis forced by confluence and horizontal shear

A two-dimensional primitive equation model of frontogenesis is presented. The model treats confluence and horizontal shear in combination. The structure and evolution of model frontal zones forced by confluence are described for a control case featuring a zero alongfront thermal gradient and positive and negative thermal gradients, facing downstream. A comparison is made with Miller's (1948) equation for the zero gradient situation to illustrate the significance of horizontal and vertical motions for the structure of the upper level frontal zone. Finally, the effects of ageostrophic circulations on the evolutionary and structural differences of frontal formations are studied.

Keyser, D.↗
NASA NTRS1979

A comparison of limited-area energetic processes between observations and primitive equation model predictions

Energetic analyses of the NMC initial conditions and NMC six-layer primitive equation operational prediction model 12-hr forecast for a developing cyclone are presented. Consideration is given to the total kinetic energy, the energetics of the divergent and nondivergent flows and the baroclinic (vertical shear flow) and barotropic (vertical mean flow) components of the kinetic energy. It is found that the model initial conditions lose 10-15% of the kinetic energy at various levels compared to a limited-area multivariate statistical analysis of the observational data, leading to a decrease in the horizontal kinetic energy flux, a misrepresentation of the synoptic scale wave system in the 12-hr forecast. Similar results are obtained for the nondivergent flow, while the divergent flow energetics are not reproduced accurately by the model. The horizontal flux terms of the vertical mean and vertical shear energetics are also not found to be reproduced in the upper levels, although horizontal flux contributions to the baroclinic component are improved at middle and lower levels. Finally, vertical shear kinetic energy generation is found to be well represented in the model prediction, however kinetic energy conversion between vertical shear and mean flow is not reproduced in the lower layer.

Alpert, J. C.↗
NASA NTRS1985

A note on the finite differencing of the linearized primitive equations' lower boundary condition

This note examines the accuracy of finite difference solutions of the midlatitude primitive equations and the quasi-geostrophic equation. First order accurate forward differencing of the equations' lower boundary condition is shown to poorly simulate the radiating wave response to midlatitude heating. Forward differencing always exaggerates the magnitude of the radiating response. For a realistic heating height scale and for a reasonable mesh size this exaggeration is on the order of 50 percent. Central differencing of the lower boundary condition gives an error of only about 3 percent.

Jacqmin, D.↗
NASA NTRS1984

Using exact solutions to develop an implicit scheme for the baroclinic primitive equations

The exact solutions presently obtained by means of a novel method for nonlinear initial value problems are used in the development of numerical schemes for the computer solution of these problems. The method is applied to a new, fully implicit scheme on a vertical slice of the isentropic baroclinic equations. It was not possible to find a global scale phenomenon that could be simulated by the baroclinic primitive equations on a vertical slice.

Marchesin, D.↗
NASA NTRS1981

Alterations of the climate of a primitive equation model produced by filtering approximations and subsequent tuning and stochastic forcing

A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.

Hoffman, R. N.↗
NASA NTRS1984

Memory efficient solution of the primitive equations for numerical weather prediction on the CYBER 205

Numerical Weather Prediction (NWP), for both operational and research purposes, requires only fast computational speed but also large memory. A technique for solving the Primitive Equations for atmospheric motion on the CYBER 205, as implemented in the Mesoscale Atmospheric Simulation System, which is fully vectorized and requires substantially less memory than other techniques such as the Leapfrog or Adams-Bashforth Schemes is discussed. The technique presented uses the Euler-Backard time marching scheme. Also discussed are several techniques for reducing computational time of the model by replacing slow intrinsic routines by faster algorithms which use only hardware vector instructions.

Tuccillo, J. J.↗
NASA NTRS1986

Diagnosis of the role of vertical deformation in a two-dimensional primitive equation model of upper-level frontogenesis

In the present equations for the temporal rates of change of the magnitudes of potential temperature and absolute momentum vector gradients that are projected onto vertical planes transverse to straight frontal zones, the terms involving the transverse ageostrophic circulation are of the same mathematical form, and in a kinematic sense are also analogous to, the divergence and deformation terms that involve the horizontal wind field in Pettersen's (1936) classic equation for frontogenesis in the potential temperature field. The proposed frontogenesis equation form for the magnitude of the potential temperature gradient in the transverse plane is illustrated with the results of two simulations from an idealized, two-dimensional primitive equation model in which upper level frontogenesis proceeds by very different mechanisms.

Keyser, D.↗
NASA NTRS1994

The use of stellite scatterometer winds to drive a primitive equation model of the Indian Ocean: The impact of bandlike sampling

The aim of this study is to evaluate the impact of the bandlike sampling of spaceborne scatterometers on the ability of scatterometer winds to successfully force the mean flow and seasonal cycle of an ocean model in the context of equatorial and tropical dynamics. The equatorial ocean is simulated with a four-layer, primitive equation, reduced gravity model of the Indian Ocean. The variable wind stress used in this study is derived from one year (1988) of 6-hour analyses of the 10-m wind vector over the Indian Ocean performed at the European Centre for Medium-Range Weather Forecasts (ECMWF). It is applied as a forcing at every grid point of the model to drive a reference circulation. Scatterometer winds are simulated from ECMWF winds, using the nominal configurations and orbital parameters of the European Remote Sensing 1 (ERS-1) and NASA Scatterometer (NSCAT) missions. The model is forced in real time under swaths with the raw scatterometer winds of ERS-1 and NSCAT, with a persistence condition (i.e., the wind is kept constsnt until the next passage of the satellite provides a new value). The circulation obtained for each of the scatterometer experiments is compared with the reference circulation. The seasonal circulation of the Indian Ocean with NSCAT winds is very similar to the reference. The perturbations introduced by the bandlike sampling and the persistance condition have an impact similar to that of a small uncorrelated noise added to the reference forcing. The persistence condition for ERS-1 does not give results which are as good as those obtained for NSCAT.

Barnier, Bernard↗
NASA NTRS1975

Initialization procedures for primitive equation models

A linear analysis and comparison of the damping properties of six dynamic initialization schemes is presented, indicating that the Okamura-Rivas scheme has the most efficient damping properties over the whole frequency range, and suggesting that it should be faster than the other methods and given more stable results. The results obtained with a nonlinear shallow water equations model agree well with the linear analysis. The Okamura-Rivas scheme attains complete balance in the equivalent of 5 to 6 hours of leapfrog forecasting, and requires in this model an order of magnitude less computation than the balance equation solution.

Grant, W. K. F.↗
NASA NTRS1976

High-latitude truncation errors of box-type primitive equation models

The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.

Kalnay-Rivas, E.↗
NASA NTRS1976

PECHCV, PECHFV, PEFHCV and PEFHFV: A set of atmospheric, primitive equation forecast models for the Northern Hemisphere, volume 3

As part of the SEASAT program of NASA, a set of four hemispheric, atmospheric prediction models were developed. The models, which use a polar stereographic grid in the horizontal and a sigma coordinate in the vertical, are: (1) PECHCV - five sigma layers and a 63 x 63 horizontal grid, (2) PECHFV - ten sigma layers and a 63 x 63 horizontal grid, (3) PEFHCV - five sigma layers and a 187 x 187 horizontal grid, and (4) PEFHFV - ten sigma layers and a 187 x 187 horizontal grid. The models and associated computer programs are described.

Wellck, R. E.↗
NASA NTRS1979

Development of a severe local storm prediction system: A 60-day test of a mesoscale primitive equation model

The progress and problems associated with the dynamical forecast system which was developed to predict severe storms are examined. The meteorological problem of severe convective storm forecasting is reviewed. The cascade hypothesis which forms the theoretical core of the nested grid dynamical numerical modelling system is described. The dynamical and numerical structure of the model used during the 1978 test period is presented and a preliminary description of a proposed multigrid system for future experiments and tests is provided. Six cases from the spring of 1978 are discussed to illustrate the model's performance and its problems. Potential solutions to the problems are examined.

Paine, D. A.↗