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Isaacson, E.

Publications and source records attributed to Isaacson, E..

9 records
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NASA NTRS1985

A factored implicit scheme for numerical weather prediction

An implicit method is proposed to factor the nonlinear partial differential equations governing fast and slow modes of dynamic motion in numerical weather prediction schemes. The method permits separate factorization of the slow and fast modes of the implicit operator. A simple two-dimensional version of the system of three-dimensional equations governing atmospheric dynamics over shallow water was analyzed to assess the accuracy of the proposed method. It is shown that the method has a small error which is comparable to other discretization errors in the overall scheme.

Augenbaum, J. M.↗
NASA NTRS1985

A fully implicit scheme for the barotropic primitive equations

An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires, at each time step, the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Present experience indicates that this implicit method is practical for numerical simulation on fine meshes.

Cohn, S. E.↗
NASA NTRS1985

A fully implicit scheme for global numerical weather prediction

A fast-slow factored scheme is presented for use with shallow-water primitive equation numerical weather prediction models. The technique was developed to reduce the rotational mode errors which arise when the fast and slow terms of the governing differential equations are treated simultaneously. The method factors out the fast and slow terms along the coordinate directions by means of a modified Crank-Nicolson scheme. A finite-difference spatial discretization is carried out in the zonal and meridional directions to reduce the factorization error to near-zero, and that time steps of 60-90 min can be used to obtain acceptably accurate results, even in the presence of fine spatial structures in the flow.

Augenbaum, J. M.↗
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 NTRS1981

Applications of estimation theory to numerical weather prediction

Numerical weather prediction (NWP) is an initial value problem for a system of nonlinear partial differential equations in which the initial values are known only incompletely and inaccurately. Data at initial time can be supplemented, however, by observations of the system distributed over a time interval preceding it. Estimation theory was successful in approaching such problems for models governed by systems of ordinary differential equations and of linear PDEs. Estimation-theoretic methods for NWP are developed. A model exhibiting many features of large scale atmospheric flow important in NWP is the one governed by the shallow fluid equations. The estimation problem for a linearized formulation of these equations is studied. A finite difference version of the equations is used as a forecast model to simulate the numerical models used in NWP.

Cohn, S.↗
NASA NTRS1981

Optimal interpolation and the Kalman filter

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Cohn, S.↗
NASA NTRS1980

Mountain winds (revisited)

The prediction of extremely high wind speeds, at ground level on the downstream side of a mountain range, is possible by solving the initial value problem for a two-layered nonlinear shallow water model of the atmosphere. Three different numerical methods are described to find the solutions which may involve shocks: (1) the vonNeumann-Richtmyer artificial viscosity method, (2) a filtering scheme, and (3) a hybrid method.

Isaacson, E.↗
NASA NTRS1977

Integration schemes for climate prediction

To assure the conservation of total mass, momentum, energy, vorticity, etc., a method of modifying any given algorithm is presented. The modified scheme has at least the same order of accuracy as the given scheme.

Isaacson, E.↗