Engineering topics

Ghil, M.

Publications and source records attributed to Ghil, M..

At least 37 records · Page 2

NASA NTRS1989

Transition to two-dimensional turbulent convection in a rapidly rotating annulus

Convection in a rapidly rotating, differentially heated annulus with sloping top and bottom lids is investigated using a semianalytical model. A relatively simple two-dimensional structure is preserved in the experimentally observed flow under rapid rotation, with temporal complexity increasing with the Rayleigh number. The model is, therefore, two-dimensional and exibits a sequence of bifurcations from steadily drifting, azimuthally periodic convection columns (thermal Rossby waves) through vacillation and a period-doubling cascade, to aperiodic weakly turbulent solutions. The results obtained here agree to within a few percent with an earlier limited-resolution two-dimensional model.

Lin, R.-Q.↗

NASA NTRS1986

Global surface wind and flux fields from model assimilation of Seasat data

Procedures for dealiasing Seasat data and developing global surface wind and latent and sensible heat flux fields are discussed. Seasat data from September 20, 1978 was dealiased using the Goddard Laboratory for Atmospheres (GLA) analysis/forecast system. The wind data obtained with the objective GLA forecast model are compared to the data subjectively dealiased by Peteherych et al. (1984) and Hoffman (1982, 1984). The GLA procedure is also verified using simulated Seasat data. The areas of high and low heat fluxes and cyclonic and anticyclonic wind stresses detected in the generated fields are analyzed and compared to climatological fields. It is observed that there is good correlation between the time-averaged analyses of wind stress obtained subjectively and objectively, and the monthly mean wind stress and latent fluxes agree with climatological fields and atmospheric and oceanic features.

Atlas, R.↗

NASA NTRS1986

Sequential estimation and satellite data assimilation in meteorology and oceanography

The central theme of this review article is the role that dynamics plays in estimating the state of the atmosphere and of the ocean from incomplete and noisy data. Objective analysis and inverse methods represent an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Four-dimensional data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric or oceanic model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and oceanic sciences, namely, mesoscale meteorology, medium and long-range forecasting, and upper-ocean dynamics.

Ghil, M.↗

NASA NTRS1986

Sequential estimation and satellite data assimilation in meteorology and oceanography

The role of dynamics in estimating the state of the atmosphere and ocean from incomplete and noisy data is discussed and the classical applications of four-dimensional data assimilation to large-scale atmospheric dynamics are presented. It is concluded that sequential updating of a forecast model with continuously incoming conventional and remote-sensing data is the most natural way of extracting the maximum amount of information from the imperfectly known dynamics, on the one hand, and the inaccurate and incomplete observations, on the other.

Ghil, M.↗

NASA NTRS1985

An efficient algorithm for estimating noise covariances in distributed systems

An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Dee, D. P.↗

NASA NTRS1985

Future possibilities in objective analysis and data assimilation for atmospheric dynamics

The role that dynamics plays in estimating the state of the atmosphere from incomplete and noisy data is reviewed. Objective analysis represents an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and related sciences, namely, mesoscale meteorology, long range forecasting, and upper ocean dynamics. Possibilities offered by judicious data assimilation in understanding barotropic adjustment, a phenomenon that appears to play a crucial role in atmospheric behavior on the scale of weeks to months, and hence in long range forecasting are addressed.

Ghil, M.↗

NASA NTRS1985

Persistent anomalies, blocking and variations in atmospheric predictability

The fully nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography, is the model used in the present consideration of low frequency variability regimes in large scale atmospheric dynamics. The solutions obtained are studied as a function of the nondimensional intensity of the forcing and dissipation. The number of modes retained in the analysis allows the multiple equilibria thus obtained, which exhibit blocked and zonal flow patterns very similar to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows, to appear for realistic values of the forcing. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.

Legras, B.↗

NASA NTRS1985

Systematic estimation of forecast and observation error covariances in four-dimensional data assimilation

A two-part algorithm is presented for reliably computing weather forecast model and observational error covariances during data assimilation. Data errors arise from instrumental inaccuracies and sub-grid scale variability, whereas forecast errors occur because of modeling errors and the propagation of previous analysis errors. A Kalman filter is defined as the primary algorithm for estimating the forecast and analysis error convariance matrices. A second algorithm is described for quantifying the noise covariance matrices of any degree to obtain accurate values for the observational error covariances. Numerical results are provided from a linearized one-dimensional shallow-water model. The results cover observational noise covariances, initial instrumental errors and erroneous model values.

Dee, D. P.↗

NASA NTRS1984

Applications of Sequential Estimation to Numerical Weather Prediction

The main objective of this cooperative research with NASA's Goddard Laboratory for Atmospheric Sciences (GLAS) is to use information about the atmosphere acquired from new types of observations, especially from satellites, in order to deepen our understanding of its behavior on time scales from hours to years. This is achieved by: (1) improving the methods for processing point observations into complete fields in space and time, using sequential estimation theory; and (2) analyzing low-frequency atmospheric variability by the methods of dynamical system theory, suitably modified to enhance practical predictability.

Ghil, M.↗

NASA NTRS1984

Boolean difference equations. I - Formulation and dynamic behavior

In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. It is suggested that delay-difference equations for Boolean-valued variables are an appropriate mathematical framework for such situations: the feedback thresholds result in the discrete, on-off character of the variables, and the interaction time scales of the feedbacks are expressed as delays. The initial-value problem for Boolean delay equations (B-Delta-Es) is formulated, and shown to have unique solutions for all times. Examples of periodic and aperiodic solutions are given. Aperiodic solutions have increasing complexity which depends on time t roughly as t to the l-1 power, l being the number of delays. Stability of solutions is defined, and some examples of stability analysis are given; additional stability questions are raised. The present formulation of (B-Delta-Es) is compared with related work and generalizations are suggested.

Dee, D.↗

NASA NTRS1983

A stochastic-dynamic model for the spatial structure of forecast error statistics

The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.

Balgovind, R.↗

NASA NTRS1983

Steady, periodic, and aperiodic atmospheric flows

Atmospheric weather patterns usually occur on scales of a 1000 km or 5000 km and greater, and quasisteady situations can be caused by the appearance of high pressure, blocking zones. Attention is given to the wave-wave interactions and their effects on atmospheric flows on the large scale. The discussion is performed with the beta-plane model for a spherical geometry and a large number of degrees of freedom. The barotropic potential vorticity equation is defined, and discretization of the topography of the sphere results in a spectral truncation with 25 components. The solutions are generated as a function of a forcing and a dissipative parameter. The model yields steady, periodic, and aperiodic solutions, which are shown to be analogous to zonal and blocked atmospheric flows.

Legras, B.↗

NASA NTRS1982

Internal variability of an energy-balance model with delayed albedo effects

A simple, deterministic energy-balance model with possible relevance to climatic variations on the time scale of glaciation cycles, is presented. The lag between ice-sheet extent and zonally-averaged temperature is modeled as a time delay in the ice-albedo feedback. The model exhibits self-sustained oscillations which are quasi-periodic or aperiodic in character. Fourier spectra of solutions have the features of many paleoclimatic records: peaks of variable height and width superimposed on a continuous, red-noise type background.

Bhattacharya, K.↗

NASA NTRS1982

The effect of model resolution and satellite sounding data on GLAS model forecasts

The effect of horizontal model resolution on satellite data impact has been studied for two versions of the GLAS second-order general circulation model: the C-model with a 4-deg latitude by 5-deg longitude resolution and the F-model with a 2.5-deg latitude and 3-deg longitude resolution. It is found that the 48-72 h forecast skill of the GLAS model was significantly improved by the increased resolution. Initial state differences between the SAT and NOSAT cycles using the F-model were on the average smaller than the corresponding differences with the C-model. However, the F-model cycle differences exhibited a smaller scale structure and, in some cases, larger gradients.

Atlas, R.↗

NASA NTRS1981

The relative contributions of increased resolution in the data assimilation and in the forecast model to satellite data impact

Assimilation cycles were carried out with two versions of the GLAS second order GCM: a coarse version with 4 deg latitude by 5 deg longitude resolution, called the C model, and a fine version with 2.5 deg latitude by 3 deg longitude resolution called the F model. For the two DST-6 cases where the combined influence of satellite data and model resolution are at a maximum at sea level, the relative contributions of increased resolution in the data assimilation and in the forecast models were evaluated. F model forecasts were generated from the C model SAT assimilation interpolated by the F grid, and C model forecasts were generated from the F model SAT assimilation interpolated to the C grid. These forecasts were then compared with the corresponding forecasts which had utilized the same grid resolution in the data assimilation and forecast models, CS and FS.

Atlas, R.↗

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

A stochastic-dynamic model for global atmospheric mass-field statistics

Global atmospheric mass field error correlations based on satellite observations and on numerical forecasts show strong and systematic latitude dependence. A model for the latitude dependent spatial correlation structure of mass field forecast errors is derived from dynamical considerations. Three methods of solution were tested. In the first method, the equation was solved by expansion in spherical harmonics, and the correlation function was computed analytically using the expansion coefficients. In the second method, the finite difference equivalent of the equation was solved using a fast poisson solver. The correlation function was computed using stratified sampling of the individual realizations. In the third method, a higher order equation was derived, and solved directly in finite differences by two successive applications of the fast poisson solver. The three methods were compared for accuracy and efficiency, and the third method was chosen as clearly superior.

Ghil, M.↗

NASA NTRS1981

A climate model with cryodynamics and geodynamics

A simplified, zero-dimensional model of the climatic system is presented which attempts to incorporate mechanisms important on the time scale of glaciation cycles: 10,000 to 100,000 years. The ocean-atmosphere radiation balance, continental ice sheet plastic flow, and upper mantle viscous flow are taken into account, with stress on the interaction between the ice sheets and the upper mantle. The model exhibits free, self-sustained oscillations of an amplitude and period comparable to those found in the paleoclimatic record of glaciations, offering mild support for the idea that unforced oscillations can actually exist in the real climatic system itself. The careful study of the interplay between internal mechanisms and external forcing is held to represent an interesting challenge to the theory of ice ages.

Ghil, M.↗