Engineering topics

Navon, I. M.

Publications and source records attributed to Navon, I. M..

13 records

NASA NTRS1993

An adjoint sensitivity study of blocking in a two-layer isentropic model

This paper presents a new methodology for adjoint sensitivity analysis, previously developed in general terms by Cacuci, into a form directly applicable 10 meteorological problems. This technique is illustrated by examining the sensitivity of a blocking index in a two-layer isentropic model. The index represents a response function for the sensitivity analysis that unlike previous meteorological applications, is an operator and not a functional, and thus extends the scope of adjoint sensitivity to general operator-type responses depending on time and/or space. The sensitivity of the blocking index to perturbations introduced into the model atmosphere, as well as to model parameters, is discussed. The methodology of generalized adjoint sensitivity analysis described in this paper constitutes a prototype for further applications in the atmospheric and/or oceanic sciences.

Zou, X.↗

NASA NTRS1993

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Li, Y.↗

NASA NTRS1992

A comparison of the impact of two time-differencing schemes on the NASA-GLAS climate model

Evidence is presented of the sensitivity of a GCM to the time-differencing scheme employed when the physical parameterizations and space discretization are not changed. Two-time marching schemes, the leapfrog and the Matsuno schemes, are analyzed and tested on the NASA-Goddard Laboratory for Atmospheric Studies fourth-order GCM in terms of the behavior and stability of two-month-averaged fields. Linear analysis indicates that Rossby waves are slightly accelerated and slightly damped when the Matsuno scheme is utilized and that these effects are scale selective, being smallest for the longest waves.

Pfeffer, Richard L.↗

NASA NTRS1990

Finite-element schemes for extended integrations of atmospheric models

Of the two finite-element models presently used to investigate the effect of the conservation of integral invariants, by means of finite-element discretization schemes of the shallow-water equations, in order to serve as a paradigm of long-term atmospheric-model integrations, the first employs rectangular elements and conserves total energy, while the second uses triangular elements and a high-accuracy two-stage Numerov-Galerkin method. Attention is given to critical times for numerical nonlinear instability, as well as to the determination of the critical degree of dissipation entailed by the achievement of stable long-term integrations. Relative computational efficiency and accuracy comparisons are presented for the two finite-element schemes.

Steppeler, J.↗

NASA NTRS1989

Objective analysis of pseudostress over the Indian Ocean using a direct-minimization approach

A technique not previously used in objective analysis of meteorological data is used here to produce monthly average surface pseudostress data over the Indian Ocean. An initial guess field is derived and a cost functional is constructed with five terms: approximation to initial guess, approximation to climatology, a smoothness parameter, and two kinematic terms. The functional is minimized using a conjugate-gradient technique, and the weight for the climatology term controls the overall balance of influence between the climatology and the initial guess. Results from various weight combinations are presented for January and July 1984. Quantitative and qualitative comparisons to the subject analysis are made to find which weight combination provides the best results. The weight on the approximation to climatology is found to balance the influence of the original field and climatology.

Legler, David M.↗

NASA NTRS1986

A comparison of the bounded derivative and the normal-mode initialization methods using real data

Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.

Semazzi, F. H. M.↗

NASA NTRS1985

High-Latitude Filtering in a Global Grid-Point Model Using Model Normal Modes

The aim of high-latitude filtering in the vicinity of the poles is to avoid the excessively short time steps imposed on an explicit time-differencing scheme by linear stability due to fast moving inertia-gravity waves near the poles. The model normal mode expansion toward the problem of high-latitude filtering in a global shallow water model using the same philosophy as that used by Daley for the problem for large timesteps in P.E. models with explicit time integration schemes was applied.

Takacs, L. L.↗

NASA NTRS1985

A Comparison of the Bounded Derivative and the Normal Mode Initialization Methods Using Real Data

Browning et al. (1980) proposed an initialization method called the bounded derivative method (BDI). They used analytical data to test the new method. Kasahara (1982) theoretically demonstrated the equivalence between BDI and the well known nonlinear normal mode initialization method (NMI). The purposes of this study are the extension of the application of BDI to real data and comparison with NMI. The unbalanced initial state (UBD) is data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLAS GCM to the 300 mb surface. The global barotropic model described by Takacs and Balgovind (1983) is used. Orographic forcing is explicitly included in the model. Many comparisons are performed between various quantities. However, we only present a comparison of the time evolution at two grid points A(50 S, 90 E) and B(10 S, 20 E) which represent low and middle latitude locations. To facilitate a more complete comparison an initialization experiment based on the classical balance equation (CBE) was also included.

Semazzi, F. H. M.↗

NASA NTRS1985

A comparison of the bounded derivative and the normal mode initialization methods using real data

A bounded derivative initialization method (BDI) formerly used only in theoretical studies to balance gravitational wave influences is extended to a real world data set and the results are compared with those from a normal mode initialization (NMI). BDI proceeds by defining the characteristic scales of motion of interest and then constraining the time derivatives to match motions on a slow scale. A global barotropic model which considers orographic forcing is initialized by the scaled balance equations of the BDI scheme, which uses vorticity alone to achieve an initial balanced state. An external mode projector is employed to realize the NMI scheme, and five Machenhauer iterations reduce the total balance by four orders of magnitude. The initial states generated with both schemes are essentially equivalent, including the time evolution of a height field and divergence behavior being centered around regions of high orographic elevation.

Semazzi, F. H. M.↗

NASA NTRS1985

Computational modes and the Machenauer N.L.N.M.I. of the GLAS 4th order model

An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.

Navon, I. M.↗

NASA NTRS1985

High-latitude filtering in a global grid-point model using model normal modes

A normal modes expansion technique is applied to perform high latitude filtering in the GLAS fourth order global shallow water model with orography. The maximum permissible time step in the solution code is controlled by the frequency of the fastest propagating mode, which can be a gravity wave. Numerical methods are defined for filtering the data to identify the number of gravity modes to be included in the computations in order to obtain the appropriate zonal wavenumbers. The performances of the model with and without the filter, and with a time tendency and a prognostic field filter are tested with simulations of the Northern Hemisphere winter. The normal modes expansion technique is shown to leave the Rossby modes intact and permit 3-5 day predictions, a range not possible with the other high-latitude filters.

Takacs, L. L.↗

NASA NTRS1984

Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM

Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.

Navon, I. M.↗

NASA NTRS1984

Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization

A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.

Navon, I. M.↗