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Wiener filtering theory for stationary ergodic inputs with known spectral densities and optimal control transfer functions of random-input nonlinear saturating systems with random unwanted disturbances
Hart (1979) showed that the truncated spectral equations obtained by Charney and Devore (1979) could be derived merely by assuming that the cross-stream scale of the topography was large compared to the downstream scale. Since actual topography does not have the large y scales postulated by Hart, his model was modified in the current investigation to obtain equations with arbitrary zonal variations of topography by projecting all variable functions onto the first topographic cross-stream mode. The topographic heights and streamfunctions are expanded as Fourier series in the cross-stream coordinate and the series are truncated after the first term. This accomplishes Hart's results but permits more realistic y variations in the topography. The present investigation is the first in a two-part series. The second part will deal with a two-layer baroclinic channel flow, again with arbitrary zonal variations of topography.
Radiative transfer theory was used to model upwelling radiance for an orbiting sensor viewing an estuarine environment. Radiance was calculated in Tm bands 3,4, and 5 and MSS bands 4 and 5 for an optically shallow estuary of either clear or turbid water, and of three bottom types: vegetation, sand, or mud. A portion of a TM image of Chesapeake Bay was enhanced to obtain a quick look at what submerged features could be detected. The enhancements were compared with low altitude color aerial photography. The TM bands 1,2, and 3 were found to contain water and submerged features information. Band 1 contained a significant amount of noise and low contrast. Band 2 appeared to contain the most amount of bottom information. Band 3, while having the least amount of noise and best constrast, contained a lesser amount of bottom information because of increase water absorption. Several water signatures were identified which correlated with submerged vegetation shown in the aerial photography.
Relativistic shock models of gamma-ray bursts may be tested by comparing their predicted low-energy asymptotic spectral indices s to observations. Synchrotron radiation theory predicts that the instantaneous spectrum has s = 1/3, and the spectrum integrated over the radiative decay of the electrons' energies has s = 1/2 with other cases lying between these limits. We examine the spectra of 11 bursts obtained by the Large Area Detectors on BATSE. One agrees with the predicted instantaneous spectrum, as does the initial portion of a second, and three are close to the predicted integrated spectrum. All of the observed asymptotic spectral slopes lie in the predicted range. This evidence for relativistic shocks is independent of detailed models of bursts and of assumptions about their distances. Radiation observed with the predicted instantaneous spectrum has a comparatively smooth time dependence, consistent with the necessarily long radiation time, while radiation observed with the predicted integrated spectrum has a spiky time dependence, consistent with the necessarily short radiation time.
A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic harmonic oscillator equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.
Each of the two Voyager spacecraft launched in 1977 has completed a reconnaissance of the Jovian and Saturnian systems. In connection with occultation experiments, strong scintillations were observed. Further theoretical work is required before these scintillations can be interpreted. The present study is, therefore, concerned with the derivation of a theory for strong scattering during atmospheric occultation experiments, taking into account as fundamental quantity of interest the spatial spectrum (or spectral density) of intensity fluctuations. Attention is given to a theory for intensity spectra, and numerical calculations. The new formula derived for Phi-i accounts for strong scattering of electromagnetic waves during atmospheric occultations.
Confidence limit is a routine requirement for Fourier spectral analysis. But this confidence limit is established based on ergodic theory: For stationary process, temporal average equals the ensemble average. Therefore, one can divide the data into n-sections and treat each section as independent realization. Most natural processes in general, and climate data in particular, are not stationary; therefore, there is a need for the Hilbert Spectral analysis for such processes. Here ergodic theory is no longer applicable. We propose to use various adjustable parameters in the shifting processes of the Empirical Mode Decomposition (EMD) method to obtain an ensemble of Intrinsic Mode Function 0 sets. Based on such an ensemble, we introduce a statistical measure in. a form of confidence limits for the Intrinsic Mode Functions, and consequently, the Hilbert spectra. The criterion of selecting the various adjustable parameters is based on the orthogonality test of the resulting M F sets. Length-of-day data from 1962 to 2001 will be used to illustrate this new approach. Its implication in climate data analysis will also be discussed.
The concept of rotationally sampled wind speed is described. The unusual wind characteristics that result from rotationally sampling the wind are shown first for early measurements made using an 8-point ring of anemometers on a vertical plane array of meteorological towers. Quantitative characterization of the rotationally sampled wind is made in terms of the power spectral density function of the wind speed. Verification of the importance of the new concept is demonstrated with spectral analyses of the response of the MOD-OA blade flapwise root bending moment and the corresponding rotational analysis of the wind measured immediately upwind of the MOD-OA using a 12-point ring of anemometers on a 7-tower vertical plane array. The Pacific Northwest Laboratory (PNL) theory of the rotationally sampled wind speed power spectral density function is tested successfully against the wind spectrum measured at the MOD-OA vertical plane array. A single-tower empirical model of the rotationally sampled wind speed is also successfully tested against the measurements from the full vertical plane array. Rotational measurements of the wind velocity with hotfilm anemometers attached to rotating blades are shown to be accurate and practical for research on winds at the blades of wind turbines. Some measurements at the rotor blade of a MOD-2 turbine using the hotfilm technique in a pilot research program are shown. They are compared and contrasted to the expectations based upon application of the PNL theory of rotationally sampled wind to the MOD-2 size and rotation rate but without teeter, blade bending, or rotor induction accounted for. Finally, the importance of temperature layering and of wind modifications due to flow over complex terrain is demonstrated by the use of hotfilm anemometer data, and meteorological tower and acoustic doppler sounder data from the MOD-2 site at Goodnoe Hills, Washington.
The first results of observations of ion cyclotron waves by the elliptically orbiting ISEE 1 and 2 pair of spacecraft are reported. The most intense waves (8 nT) were observed in the outer plasmasphere where convection drift velocities were largest and the Alfven velocity was a minimum. Wave polarization is predominantly left-handed with propagation almost parallel to the ambient magnetic field, and the spectral slot and polarization reversal predicted by cold plasma propagation theory are identified in the wave data. Computations of the experimental wave spectra during the passage through the plasmapause show that the spectral slots relate to the local plasma parameters, possibly suggesting an ion cyclotron wave growth source near the spacecraft. A regular wave packet structure seen over the first 30 min of the event is attributed to the modulation of this energy source by the Pc 5 waves seen at the same time.
The power spectrum of phototube current from a laser Doppler velocimeter operating in the heterodyne mode has been computed. The spectrum is obtained in terms of the space time correlation function of the fluid. The spectral width and shape predicted by the theory are in agreement with experiment. For normal operating parameters the time average spectrum contains information only for times shorter than the Lagrangian integral time scale of the turbulence. To examine the long time behavior, one must use either extremely small scattering angles, much longer wavelength radiation or a different mode of signal analysis, e.g., FM detection.
The power spectrum of phototube current from a laser Doppler velocimeter operating in the heterodyne mode has been computed. The spectral width and shape predicted by the theory are in agreement with experiment. For normal operating parameters the time-average spectrum contains information only for times shorter than the Lagrangian-integral time scale of the turbulence. To examine the long-time behavior, one must use either extremely small scattering angles, much-longer-wavelength radiation, or a different mode of signal analysis, e.g., FM detection.
Collision-induced absorption in the translation-rotation band of H2 and H2-He mixtures has been measured from 20 to 900 kaysers at 77.4, 195, and 292 K. To establish the accuracy of the results, various sources of error are investigated. The zeroth and first spectral moments are evaluated from experiment and theory for H2 at the various temperatures. To obtain theoretical moments consistent with the experimental values, the quantum pair-distribution function must be used. The major portion of the experimental moments can be accounted for by quadrupole-induced dipoles in H2 pairs. The remaining portion is attributable to an anisotropic overlap interaction, although its magnitude depends on the value of the molecular parameters required to calculate the quadrupole contribution.
Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.
The theoretical basis for and experimental validation of a measurement method for separating airborne and structure borne noise radiated by aircraft type panels are presented. An extension of the two microphone, cross spectral, acoustic intensity method combined with existing theory of sound radiation of thin shell structures of various designs, is restricted to the frequency range below the coincidence frequency of the structure. Consequently, the method lends itself to low frequency noise problems such as propeller harmonics. Both an aluminum sheet and two built up aircraft panel designs (two aluminum panels with frames and stringers) with and without added damping were measured. Results indicate that the method is quick, reliable, inexpensive, and can be applied to thin shell structures of various designs.
Previous measurements of the far infrared absorption due to H2-He collisions at the temperatures of 77, 195, and 292 K are analyzed. The spectra are fitted by a semiempirical line shape representing the isotropic induced overlap component and combined anisotropic quadrupolar and overlap components. The experimental spectral moments are evaluated and compared with theory for several induced-dipole and potential models. From the isotropic contribution, the range and strength of the induced dipole is evaluated and compared with the results of ab initio calculations. Fitting parameters are obtained with physically plausible temperature dependences which allow simple and accurate representation of the spectra and of their moments at temperatures different from those of the measurements.
The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.
Reflectance spectra from several regional lunar pyroclastic deposits are presented in support of the theory that mantling units have a unique spectral signature indicative of the presence of a significant, Fe-bearing volcanic glass component. The Rime Bode region discussed is illustrative of an area in which several types of remote sensing data were used to reconstruct the geologic events associated with the emplacement of a regional pyroclastic mantling deposit. Five new areas are identified on the basis of the present data which may represent higher albedo regional pyroclastic deposits.
The contents include: 1. State space, spectral space, and observation space; 2. Variances and correlations; 3. Isotropic and anisotropic correlation modeling on the sphere; 4. Operational ozone data assimilation; and 5. Kalman filtering for trace constituents.