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NASA NTRS1993

Using emergent order to shape a space society

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Graps, Amara L.↗

NASA NTRS1994

Evaluating GCM land surface hydrology parameterizations by computing river discharges using a runoff routing model: Application to the Mississippi basin

To relate general circulation model (GCM) hydrologic output to readily available river hydrographic data, a runoff routing scheme that routes gridded runoffs through regional- or continental-scale river drainage basins is developed. By following the basin overland flow paths, the routing model generates river discharge hydrographs that can be compared to observed river discharges, thus allowing an analysis of the GCM representation of monthly, seasonal, and annual water balances over large regions. The runoff routing model consists of two linear reservoirs, a surface reservoir and a groundwater reservoir, which store and transport water. The water transport mechanisms operating within these two reservoirs are differentiated by their time scales; the groundwater reservoir transports water much more slowly than the surface reservior. The groundwater reservior feeds the corresponding surface store, and the surface stores are connected via the river network. The routing model is implemented over the Global Energy and Water Cycle Experiment (GEWEX) Continental-Scale International Project Mississippi River basin on a rectangular grid of 2 deg X 2.5 deg. Two land surface hydrology parameterizations provide the gridded runoff data required to run the runoff routing scheme: the variable infiltration capacity model, and the soil moisture component of the simple biosphere model. These parameterizations are driven with 4 deg X 5 deg gridded climatological potential evapotranspiration and 1979 First Global Atmospheric Research Program (GARP) Global Experiment precipitation. These investigations have quantified the importance of physically realistic soil moisture holding capacities, evaporation parameters, and runoff mechanisms in land surface hydrology formulations.

Liston, G. E.↗

NASA NTRS1993

The three-dimensional structure of cumulus clouds over the ocean. 1: Structural analysis

Thermal channel (channel 6, 10.4-12.5 micrometers) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project (ISCCP) thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter-to-area (PtA) relationship. The cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Unicellular clouds are generally smaller (less than or equal to 1 km) and have smaller PtA exponents, while multicellular clouds are larger (greater than or equal to 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. When each cell is approximated as a quadric surface using a linear least squares fit, most cells have the shape of a hyperboloid of one sheet, but about 15% of the cells are best modeled by a hyperboloid of two sheets. Less than 1% of the clouds are ellipsoidal. The number of cells in a cloud increases slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness-of-fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting the eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.

Kuo, Kwo-Sen↗

NASA NTRS1999

Variance and Predictability of Precipitation at Seasonal-to-Interannual Timescales

A series of atmospheric general circulation model (AGCM) simulations, spanning a total of several thousand years, is used to assess the impact of land-surface and ocean boundary conditions on the seasonal-to-interannual variability and predictability of precipitation in a coupled modeling system. In the first half of the analysis, which focuses on precipitation variance, we show that the contributions of ocean, atmosphere, and land processes to this variance can be characterized, to first order, with a simple linear model. This allows a clean separation of the contributions, from which we find: (1) land and ocean processes have essentially different domains of influence, i.e., the amplification of precipitation variance by land-atmosphere feedback is most important outside of the regions (mainly in the tropics) that are most affected by sea surface temperatures; and (2) the strength of land-atmosphere feedback in a given region is largely controlled by the relative availability of energy and water there. In the second half of the analysis, the potential for seasonal-to-interannual predictability of precipitation is quantified under the assumption that all relevant surface boundary conditions (in the ocean and on land) are known perfectly into the future. We find that the chaotic nature of the atmospheric circulation imposes fundamental limits on predictability in many extratropical regions. Associated with this result is an indication that soil moisture initialization or assimilation in a seasonal-to-interannual forecasting system would be beneficial mainly in transition zones between dry and humid regions.

Koster, Randal D.↗

NASA NTRS2000

Wave Driven Non-Linear Flow Oscillator for the 22-Year Solar Cycle

We propose that waves generate an oscillation in the Sun to account for the 22-year magnetic cycle. The mechanism we envision is analogous to that driving the Quasi Biennial Oscillation (QBO) observed in the terrestrial atmosphere, which is well understood in principal. Planetary waves and gravity waves deposit momentum in the background atmosphere and accelerate the flow under viscous dissipation. Analysis shows that such a momentum source represents a non-linearity of third or generally odd order, which generates also the fundamental frequency/period so that an oscillation is maintained without external time dependent forcing. For the Sun, we propose that the wave driven oscillation would occur just below the convection region, where the buoyancy frequency or convective stability becomes small to favor wave breaking and wave mean flow interaction. Using scale analysis to extrapolate from terrestrial to solar conditions, we present results from a simplified analytical model, applied to the equator, that incorporates Hines'Doppler Spread Parameterization for gravity waves (GW). Based on a parametric study, we conclude: (1) Depending on the adopted horizontal wavelengths of GW's, wave amplitudes < 10 m/s can be made to produce oscillating zonal winds of about 25 m/s that should be large enough to generate a corresponding oscillation in the main poloidal magnetic field; (2) The oscillation period can be made to be 22 years provided the buoyancy frequency (stability) is sufficiently small, which would place the oscillating wind field near the base of the convection region; (3) In this region, the turbulence associated with wave processes would be enhanced by low stability, and this also helps to produce the desired oscillation period and generate the dynamo currents that would produce the reversing magnetic field. We suggest that the above mechanism may also drive other long-period metronomes in planetary and stellar interiors.

Mayr, H. G.↗

NASA NTRS2024

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2 reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude σ8 = 0.819 ± 0.015 at 1.8% precision, S 8 ≡σ 8 (Ω m>/sub>/0.3) 0.5 = 0.840 ± 0.028, and the Hubble constant H 0 = (68.3 ± 1.1) km s −1 Mpc −1 at 1.6% precision. A joint constraint with Planck CMB lensing yields σ 8 = 0.812 ± 0.013, S 8 ≡σ 8 (Ω m>/sub>/0.3) 0.5 = 0.831 ± 0.023, and H0 = (68.1 ± 1.0) km s −1 Mpc −1 . These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find that S 8 from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probing z ∼ 0.5–5 on mostly linear scales and galaxy lensing at z ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m ν < 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys.

Cosmology↗

NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗

NASA NTRS1992

Prediction of LDEF ionizing radiation environment

The Long Duration Exposure Facility (LDEF) spacecraft flew in a 28.5 deg inclination circular orbit with an altitude in the range from 172 to 258.5 nautical miles. For this orbital altitude and inclination two components contribute most of the penetrating charge particle radiation encountered - the galactic cosmic rays and the geomagnetically trapped Van Allen protons. Where shielding is less than 1.0 g/sq cm geomagnetically trapped electrons make a significant contribution. The 'Vette' models together with the associated magnetic filed models were used to obtain the trapped electron and proton fluences. The mission proton doses were obtained from the fluence using the Burrell proton dose program. For the electron and bremsstrahlung dose we used the Marshall Space Flight Center (MSFC) electron dose program. The predicted doses were in general agreement with those measured with on-board thermoluminescent detector (TLD) dosimeters. The NRL package of programs, Cosmic Ray Effects on MicroElectronics (CREME), was used to calculate the linear energy transfer (LET) spectrum due to galactic cosmic rays (GCR) and trapped protons for comparison with LDEF measurements.

Watts, John W.↗

NASA NTRS1994

The buckling response of symmetrically laminated composite plates having a trapezoidal planform area

The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stackling sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D16 and D26 terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions.

Radloff, H. D., II↗

NASA NTRS1999

Clouds in ECMWF's 30 KM Resolution Global Atmospheric Forecast Model (TL639)

Global models of the general circulation of the atmosphere resolve a wide range of length scales, and in particular cloud structures extend from planetary scales to the smallest scales resolvable, now down to 30 km in state-of-the-art models. Even the highest resolution models do not resolve small-scale cloud phenomena seen, for example, in Landsat and other high-resolution satellite images of clouds. Unresolved small-scale disturbances often grow into larger ones through non-linear processes that transfer energy upscale. Understanding upscale cascades is of crucial importance in predicting current weather, and in parameterizing cloud-radiative processes that control long term climate. Several movie animations provide examples of the temporal and spatial variation of cloud fields produced in 4-day runs of the forecast model at the European Centre for Medium-Range Weather Forecasts (ECMWF) in Reading, England, at particular times and locations of simultaneous measurement field campaigns. model resolution is approximately 30 km horizontally (triangular truncation TL639) with 31 vertical levels from surface to stratosphere. Timestep of the model is about 10 minutes, but animation frames are 3 hours apart, at timesteps when the radiation is computed. The animations were prepared from an archive of several 4-day runs at the highest available model resolution, and archived at ECMWF. Cloud, wind and temperature fields in an approximately 1000 km X 1000 km box were retrieved from the archive, then approximately 60 Mb Vis5d files were prepared with the help of Graeme Kelly of ECMWF, and were compressed into MPEG files each less than 3 Mb. We discuss the interaction of clouds and radiation in the model, and compare the variability of cloud liquid as a function of scale to that seen in cloud observations made in intensive field campaigns. Comparison of high-resolution global runs to cloud-resolving models, and to lower resolution climate models is leading to better understanding of the upscale cascade and suggesting new cloud-radiation parameterizations for climate models.

Cahalan, R. F.↗

NASA NTRS2006

The Sensitivity of Arctic Ozone Loss to Polar Stratospheric Cloud Volume and Chlorine and Bromine Loading in a Chemistry and Transport Model

The sensitivity of Arctic ozone loss to polar stratospheric cloud volume (V(sub PSC)) and chlorine and bromine loading is explored using chemistry and transport models (CTMs). A simulation using multi-decadal output from a general circulation model (GCM) in the Goddard Space Flight Center (GSFC) CTM complements one recycling a single year s GCM output in the Global Modeling Initiative (GMI) CTM. Winter polar ozone loss in the GSFC CTM depends on equivalent effective stratospheric chlorine (EESC) and polar vortex characteristics (temperatures, descent, isolation, polar stratospheric cloud amount). Polar ozone loss in the GMI CTM depends only on changes in EESC as the dynamics repeat annually. The GSFC CTM simulation reproduces a linear relationship between ozone loss and Vpsc derived from observations for 1992 - 2003 which holds for EESC within approx.85% of its maximum (approx.1990 - 2020). The GMI simulation shows that ozone loss varies linearly with EESC for constant, high V(sub PSC).

Douglass, A. R.↗

NASA NTRS2024

The Global Mapping of Electron Precipitation and Ionospheric Conductance From Whistler-Mode Chorus Waves

Auroral precipitation is the second major energy source after solar irradiation that ionizes the Earth’s upper atmosphere. Diffuse electron aurora caused by wave-particle interaction in the inner magnetosphere (L < 8) takes over 60% of total auroral energy flux, strongly contributing to the ionospheric conductance and thus to the ionosphere-thermosphere dynamics. This paper quantifies the impact of chorus waves on the diffuse aurora and the ionospheric conductance during quiet, medium, and strong geomagnetic activities, parameterized by AE <100, 100 < AE < 300, and AE > 300, respectively. Using chorus wave statistics and inner-magnetosphere plasma conditions from Timed History Events and Macroscale Interactions during Substorms (THEMIS) observations, we directly derive the energy spectrum of diffuse electron precipitation under quasi-linear theory. We then calculate the height-integrated conductance from the wave-driven aurora spectrum using the electron impact ionization model of Fang et al. (Geophys. Res. Lett., 2010, 37) and the MSIS atmosphere model. By utilizing Fang’s ionization model, the US Naval Research Laboratory Mass Spectrometer and Incoherent Scattar Radar (NRLMSISE-00) model from 2000s for the neutral atmosphere components, and the University of California, Los Angeles (UCLA) Full Diffusion Code, we improve upon the standard generalization of Maxwellian diffuse electron precipitation patterns and their resulting ionosphere conductance. Our study of global auroral precipitation and ionospheric conductance from chorus wave statistics is the first statistical model of its kind. We show that the total electron flux and conductance pattern from our results agree with those of Ovation Prime model over the pre-midnight to post-dawn sector as geomagnetic activity increases. Our study examines the relative contributions of upper band chorus (UBC) and lower band chorus wave (LBC) driven conductance in the ionosphere. We found LBC waves drove diffuse electron precipitation significantly more than UBC waves, however it is possible that THEMIS data may have underestimated the upper chorus band wave observations for magnetic latitudes below 65 degrees. ° .

diffuse auroral precipitation↗

NASA NTRS1977

Linear radial and nonradial modes of oscillation of hot white dwarfs

Low-order linear radial and nonradial quadrupole modes of oscillation of hot white dwarfs with hydrogen envelopes are evaluated in the quasi-adiabatic approximation. Luminosities range from 10 to the 36th to 10 to the 38th power. Masses range between 0.6 and 1.4 solar masses. Models are found with unstable radial modes as high as the third harmonic. The first nonradial quadrupole gravity mode is always unstable. The results may be relevant to pulsating X-ray sources in general and are specifically applied to Cen X-3, Her X-1, and SMC X-1.

Degregoria, A. J.↗

NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗

NASA NTRS1989

Eigensolution of finite element problems in a completely connected parallel architecture

A parallel algorithm for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi)=(M)(phi)(omega), where (K) and (M) are of order N, and (omega) is of order q is presented. The parallel algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm has been successfully implemented on a tightly coupled multiple-instruction-multiple-data (MIMD) parallel processing computer, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor, or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macro-tasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18 and 3.61 are achieved on two, four, six and eight processors, respectively.

Akl, Fred A.↗

NASA NTRS2022

Wave Setup at the Minamitorishima Tide Gauge

A tide gauge situated on the western shore of Minamitorishima, a small atoll in the western Pacific, has measured sea levels significantly impacted by wave setup. Evidence for this rests with (a) strong correlations between sea level anomalies and high swell and (b) sea-level differences with satellite altimetry that display near-linear dependence on offshore swell heights (regression coefficient 30 cm per meter of swell). Setup is primarily induced by swell from the northwest. We develop models of wave setup which lead to corrected sea levels better reflecting the surrounding ocean, and thus more readily useful to studies of regional sea level and practical applications such as altimetry calibration. The wave setup is also evidently affecting measurements of the tide, with suppressed tide amplitudes in winter when swell is generally largest. In February 2020 the tide gauge was relocated to the southern shore of the island, and the wave setup is now markedly reduced.

Wave setup↗

NASA NTRS1997

Algorithmic Extensions of Low-Dispersion Scheme and Modeling Effects for Acoustic Wave Simulation

Accurate computation of acoustic wave propagation may be more efficiently performed when their dispersion relations are considered. Consequently, computational algorithms which attempt to preserve these relations have been gaining popularity in recent years. In the present paper, the extensions to one such scheme are discussed. By solving the linearized, 2-D Euler and Navier-Stokes equations with such a method for the acoustic wave propagation, several issues were investigated. Among them were higher-order accuracy, choice of boundary conditions and differencing stencils, effects of viscosity, low-storage time integration, generalized curvilinear coordinates, periodic series, their reflections and interference patterns from a flat wall and scattering from a circular cylinder. The results were found to be promising en route to the aeroacoustic simulations of realistic engineering problems.

Kaushik, Dinesh K.↗

NASA NTRS1975

Shear-flexible finite-element models of laminated composite plates and shells

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Noor, A. K.↗