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NASA NTRS1984

Effect of nonideal square-law detection on static calibration in noise-injection radiometers

The effect of nonideal square-law detection on the static calibration for a class of Dicke radiometers is examined. It is shown that fourth-order curvature in the detection characteristic adds a nonlinear term to the linear calibration relationship normally ascribed to noise-injection, balanced Dicke radiometers. The minimum error, based on an optimum straight-line fit to the calibration curve, is derived in terms of the power series coefficients describing the input-output characteristics of the detector. These coefficients can be determined by simple measurements, and detection nonlinearity is, therefore, quantitatively related to radiometric measurement error.

Hearn, C. P.↗

NASA NTRS1984

On the effect of using the Shapiro filter to smooth winds on a sphere

Spatial differencing schemes which are not enstrophy conserving nor implicitly damping require global filtering of short waves to eliminate the build-up of energy in the shortest wavelengths due to aliasing. Takacs and Balgovind (1983) have shown that filtering on a sphere with a latitude dependent damping function will cause spurious vorticity and divergence source terms to occur if care is not taken to ensure the irrotationality of the gradients of the stream function and velocity potential. Using a shallow water model with fourth-order energy-conserving spatial differencing, it is found that using a 16th-order Shapiro (1979) filter on the winds and heights to control nonlinear instability also creates spurious source terms when the winds are filtered in the meridional direction.

Takacs, L. L.↗

NASA NTRS1984

Numerical solutions of acoustic wave propagation problems using Euler computations

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Hariharan, S. I.↗

NASA NTRS1983

Effect of high latitude filtering on NWP skill

An assessment is made of the extent to which polar filtering may seriously affect the skill of latitude-longitude NWP models, such as the U.S. Navy's NOGAPS, or the GLAS fourth-order model. The limited experiments which have been completed to date with the 4 x 5-deg, 9-level version of the latter model indicate that the high latitude filter currently in operation affects its forecasting skill very little, with only one exception in which the use of the PG filter significantly improved forecasting.

Kalnay, E.↗

NASA NTRS1984

A finite difference solution for the propagation of sound in near sonic flows

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift aocustical energy to higher harmonics. With increased source strength, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at higher sound pressure level as the throat Mach number approaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory. Previously announced in STAR as N83-30167

Hariharan, S. I.↗

NASA NTRS1984

The efficient numerical calculation of condensational cloud drop growth

A modified Runge-Kutta integration technique is applied to condensational cloud droplet growth calculations, using the device of limiting dr, the growth of a droplet of radius r over the time step dt to some function of the absolute value of r(eq)-r, where r(eq) denotes the equilibrium value. The use of variable time steps to obtain an efficient choice of dt is also discussed. Results using these techniques are compared with those obtained with the standard fourth-order Runge-Kutta method, showing that the modified technique reduces the requisite computer time by a factor of about one hundred.

Robinson, N. F.↗

NASA NTRS1983

The influence of the tropics upon the prediction of the Southern Hemisphere circulation within the GLAS GCM

An examination is undertaken of the sensitivity of short term Southern Hemisphere circulation prediction to tropical wind data and tropical latent heat release. The data assimilation experiments employ the Goddard Laboratory for Atmospheric Sciences' fourth-order general circulation model. Two of the experiments are identical, but for the fact that one uses tropical wind data while the other does not. A third experiment contains the identical initial conditions of forecasts with tropical winds, while suppressing tropical latent heat release.

Baker, W. E.↗

NASA NTRS1984

Implicit Numerical Methods in Meteorology

The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.

Augenbaum, J.↗

NASA NTRS1985

Performance of the Dsa's Subcarrier Demodulation Digital Loop

The subcarrier demodulation digital loop is part of the baseband assembly. The subcarrier demodulator is a fourth-order Costas-type loop corresponding to a type 2 analog loop in terms of steady state response. The expected value and the variance of the error signal are determined as functions of the input SNR. A Nyquist sampling rate of the input signal is assumed. From the integro-difference equations a mixed s/z domain block diagram is obtained. From the loop's transfer function a set of gains for the loop filter is obtained. Also, a set of state equations is presented for future reference. Finally, the noise-equivalent bandwidths are calculated for normalized computation times of 0, 0.25 and 0.5. The subcarrier demodulator analyzed tracks a parabolic phase input with finite steady state error. Since at each update instant the loop gains are adjusted to compensate for the variations in SNR of the input signal, the noise-equivalent bandwidth is maintained constant.

Simon, M. K.↗

NASA NTRS1985

Derivation of Model Topography

The Fourth-Order model necessitates representation of the topography. The problem of the representation of the topography at grid points is addressed. The attempted was to derive an envelope topography. The TI is obtained by taking local mean plus one standard deviation at each grid point and sigma filtering it. The method was greatly influenced by large standard deviations at steep mountains. The O1 topography is the local mean. The S1 is obtained by Sigma filtering in both latitude and longitude the mean O1. The S2 is when the operation is applied twice and S3 thrice, the Q3 is the sigma filtered local mean of the upper third quantile of the source data.

Balgovind, R. C.↗

NASA NTRS1985

Sigma Filter

The GLA Fourth-Order model is needed to smooth the topography. This is to remove the Gibbs phenomenon. The Gibbs phenomenon occurs whenever we truncate a Fourier Series. The Sigma factors were introduced to reduce the Gibbs phenomenon. It is found that the smooth Fourier series is nothing but the original Fourier series with its coefficients multiplied by corresponding sigma factors. This operator can be applied many times to obtain high order sigma filtered field and is easily applicable using FFT. It is found that this filter is beneficial in deriving the topography.

Balgovind, R. C.↗

NASA NTRS1984

Numerical solutions of acoustic wave propagation problems using Euler computations

Hariharan, S. I.↗

NASA NTRS1984

Orbital stability of the unseen solar companion linked to periodic extinction events

Evidence from three-dimensional numerical modelling is presented that only cometary orbits with a limited range in inclination with respect to the galactic plane are formally stable for the length of time required to cause periodic extinction events. The calculations were done using Cowell's method employing a fourth-order Runge-Kutta integration scheme in an inertial reference frame in orbit about the Galaxy. Tidal perturbations in the radial direction due to the Galaxy and the Coriolis forces are included. The vertical component of the gravitational field of the galactic disk is superimposed on these forces. The results indicate that orbits for Nemesis that are inclined at more than 30 deg to the galactic plane are not allowed and suggests that the search for Nemesis should be concentrated toward the plane of the Galaxy. Perturbations by passing stars or molecular clouds may make even the low-inclination orbits unstable.

Torbett, M. V.↗

NASA NTRS1985

A study of the effects of numerical dissipation on the calculation of supersonic separated flows

An extensive investigation of the effect of numerical dissipation on the calculation of supersonic, separated flow over a rearward-facing step is carried out. The complete two-dimensional Navier-Stokes equations are solved by means of MacCormack's standard explicit, unsplit, time-dependent, finite difference method. A fourth-order numerical dissipation term is added explicitly. The magnitude of this term is progressively varied, and its consequences on the flowfield calculations are identified and studied. For a cold-wall, heat transfer case, numerical dissipation had a major effect on the results, particularly in the separated region. However, rather dramatically for an adiabatic wall case, numerical dissipation had virtually no effect on the results. The role of grid size on both the influence of numerical dissipation, and on the overall accuracy of the separated flow solutions is discussed.

Kuruvila, G.↗

NASA NTRS1985

The experimental results of a self tuning adaptive controller using online frequency identification

A fourth-order laboratory dynamic system featuring very low structural damping and a noncolocated actuator-sensor pair has been used to test a novel real-time adaptive controller, implemented in a minicomputer, which consists of a state estimator, a set of state feedback gains, and a frequency-locked loop for real-time parameter identification. The adaptation algorithm employed can correct controller error and stabilize the system for more than 50 percent variation in the plant's natural frequency, compared with a 10 percent stability margin in frequency variation for a fixed gain controller having the same performance as the nominal plant condition. The very rapid convergence achievable by this adaptive system is demonstrated experimentally, and proven with simple, root-locus methods.

Chiang, W.-W.↗

NASA NTRS1985

A comparison of observed and forecast energetics over North America

The observed kinetic energy balance is calculated over North America and compared with that computed from forecast fields for the 13-15 January 1979 cyclone. The FGGE upper-air rawinsonde network serves as the observational database while the forecast energetics are derived from a numerical integration with the GLAS fourth-order general circulation model initialized at 00 GMT 13 January. Maps of the observed and predicted kinetic energy and eddy conversion are in good qualitative agreement, although the model eddy conversion tends to be 2 to 3 times stronger than the observed values. Both the forecast and observations exhibit the lower and upper tropospheric maxima in vertical profiles of kinetic energy generation and dissipation typically found in cyclonic disturbances. An interesting time lag is noted in the observational analysis with the maximum observed kinetic energy occurring 12 h later than the maximum eddy conversion over the same region.

Baker, W. E.↗

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

New analytical results for AOTV guidance

Minimum energy-loss turns of an Aero-assisted, Orbital Transfer Vehicle (AOTV) performing the atmospheric portion of an orbital-plane-change maneuver are developed using the heading angle as the independent variable. Because the heading angle is monotonic, several difficulties previously encountered using the flight path angle, which is not monotonic, as the independent variable are eliminated. In addition, the solution of the optimal control problem reduces to the solution of a fourth-order polynomial which can be accomplished analytically.

Hull, D. G.↗