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Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.
Uncertainties associated with the primitive random variables such as manufacturing process (processing temperature, fiber volume ratio, void volume ratio), constituent properties (fiber, matrix and interface), and geometric parameters (ply thickness, interphase thickness) have been simulated to quantify the scatter in the first matrix cracking strength (FMCS) and the ultimate tensile strength of SCS-6/RBSN (SiC fiber (SCS-6) reinforced reaction-bonded silicon nitride composite) ceramic matrix composite laminate at room temperature. Cumulative probability distribution function for the FMCS and ultimate tensile strength at room temperature (RT) of (0)(sub 8), (0(sub 2)/90(sub 2), and (+/-45(sub 2))(sub S) laminates have been simulated and the sensitivity of primitive variables to the respective strengths have been quantified. Computationally predicted scatter of the strengths for a uniaxial laminate have been compared with those from limited experimental data. Also the experimental procedure used in the tests has been described briefly. Results show a very good agreement between the computational simulation and the experimental data. Dominating failure modes in (0)(sub 8), (0/90)(sub s) and (+/-45)(sub S) laminates have been identified. Results indicate that the first matrix cracking strength for the (0)(sub S), and (0/90)(sub S) laminates is sensitive to the thermal properties, modulus and strengths of both the fiber and matrix whereas the ultimate tensile strength is sensitive to the fiber strength and the fiber volume ratio. In the case of a (+/-45)(sub S), laminate, both the FMCS and the ultimate tensile strengths have a small scatter range and are sensitive to the fiber tensile strength as well as the fiber volume ratio.
A statistical description of Earth's broad scale, core-source magnetic field has been developed and tested. The description features an expected, or mean, spatial magnetic power spectrum that is neither "flat" nor "while" at any depth, but is akin to spectra advanced by Stevenson and McLeod. This multipole spectrum describes the magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Natural variations of core multipole powers about their mean values are to be expected over geologic time and are described via trial probability distribution functions that neither require nor prohibit magnetic isotropy. The description is thus applicable to core-source dipole and low degree non-dipole fields despite axial dipole anisotropy. The description is combined with main field models of modem satellite and surface geomagnetic measurements to make testable predictions of: (1) the radius of Earth's core, (2) mean paleomagnetic field intensity, and (3) the mean rates and durations of both dipole power excursions and durable axial dipole reversals. The predicted core radius is 0.7% above the 3480 km seismologic value. The predicted root mean square paleointensity (35.6 mu T) and mean Virtual Axial Dipole Moment (about 6.2 lx 1022 Am(exp 2)) are within the range of various mean paleointensity estimates. The predicted mean rate of dipole power excursions, as defined by an absolute dipole moment <20% of the 1980 value, is 9.04/Myr and 14% less than obtained by analysis of a 4 Myr paleointensity record. The predicted mean rate of durable axial dipole reversals (2.26/Myr) is 2.3% more than established by the polarity time-scale for the past 84 Myr. The predicted mean duration of axial dipole reversals (5533 yr) is indistinguishable from an observational value. The accuracy of these predictions demonstrates the power and utility of the description, which is thought to merit further development and testing. It is suggested that strong stable stratification of Earth's uppermost outer core leads to a geologically long interval of no dipole reversals and a very nearly axisymmetric field outside the core. Statistical descriptions of other planetary magnetic fields are outlined.
Key questions to which SONEX was directed were the following: Can aircraft corridors be detected? Is there a unique tracer for aircraft NO(x)? Can a "background" NO(x) (or NO(y) be defined? What fraction of NO(x) measured during SONEX was from aircraft? How representative was SONEX of the North Atlantic in 1997 and how typical of other years? We attempt to answer these questions through species-species correlations, probability distribution functions (PDFs), and meteorological history. There is not a unique aircraft tracer, largely due to the high variability of air mass origins and tracer ratios, which render "average" quantities meaningless. The greatest NO and NO(y) signals were associated with lightning and convective NO sources. Well-defined background CO, NO(y) and NO(y)/ozone ratio appear in subsets of two cross-track flights with subtropical origins and five flights with predominantly mid-latitude air. Forty percent of the observations on these 7 flights showed NO(y)/ozone to be above background, evidently due to unreacted NO(x). This NO(x) is a combination of aircraft, lightning and surface pollution injected by convection. The strongly subtropical signatures in SONEX observations, confirmed by pv (potential vorticity) values along flight tracks, argues for most of the unreacted NO(x) originating from lightning. Potential vorticity statistics along SONEX flight tracks in 1992-1998, and for the North Atlantic as a whole, show the SONEX meteorological environment to be representative of the North Atlantic flight corridor in the October-November period.
A methodology is developed to simulate computationally the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain, etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, plv. laminate and structural levels. This methodology is implemented in a computer code integrated probabilistic assessment of composite structures (IPACS). A fuselage-type composite structure is analyzed to demonstrate the code's capability . The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.
A simple model of horizontal inhomogeneity and cloud fraction in cirrus clouds has been formulated on the basis that all internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of the ice water mixing ratio (and extinction) and the normalized variability of cloud depth. Using radar cloud depth data as input, the model reproduced well the in-cloud ice water mixing ratio histograms obtained from horizontal runs during the FIRE2 cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud fraction decreased to exponential distributions which peaked at the lowest nonzero ice value for cloud fractions below 90%. Cloud fractions predicted by the model were always within 28% of the observed value. The predicted average ice water mixing ratios were within 34% of the observed values. This model could be used in a GCM to produce the ice mixing ratio probability distribution function and to estimate cloud fraction. It only requires basic meteorological parameters, the depth of the saturated layer and the standard deviation of cloud depth as input.
We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.
A partial description of Earth's broad scale, core-source magnetic field has been developed and tested three ways. The description features an expected, or mean, spatial magnetic power spectrum that is approximately inversely proportional to horizontal wavenumber atop Earth's core. This multipole spectrum describes a magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Temporal variations of core multipole powers about mean values are to be expected and are described statistically, via trial probability distribution functions, instead of deterministically, via trial solution of closed transport equations. The distributions considered here are closed and neither require nor prohibit magnetic isotropy. The description is therefore applicable to, and tested against, both dipole and low degree non-dipole fields. In Part 1, a physical basis for an expectation spectrum is developed and checked. The description is then combined with main field models of twentieth century satellite and surface geomagnetic field measurements to make testable predictions of the radius of Earth's core. The predicted core radius is 0.7% above the 3480 km seismological value. Partial descriptions of other planetary dipole fields are noted.
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.
Coherent Vortex Simulation (CVS) filtering has been applied to Direct Numerical Simulation (DNS) data of forced and unforced time-developing turbulent mixing layers. CVS filtering splits the turbulent flow into two orthogonal parts, one corresponding to coherent vortices and the other to incoherent background flow. We have shown that the coherent vortices can be represented by few wavelet modes and that these modes are sufficient to reproduce the vorticity probability distribution function (PDF) and the energy spectrum over the entire inertial range. The remaining incoherent background flow is homogeneous, has small amplitude, and is uncorrelated. These results are compared with those obtained for the same compression rate using large eddy simulation (LES) filtering. In contrast to the incoherent background flow of CVS filtering, the LES subgrid scales have a much larger amplitude and are correlated, which makes their statistical modeling more difficult.
In situ observations of CO2 obtained from 1992 through 2000 using the NASA ER-2 aircraft and high-altitude balloons show that seasonal and interannual variations in CO2 mixing ratios propagate from the troposphere into the lower stratosphere via the tropical tropopause, along with the long-term trend due to fossil fuel combustion. These signals spread laterally and vertically, providing detailed quantitative information about the transport history of sampled air. We have used these data to derive age spectra and mean ages that can be compared with results from models of the stratospheric circulation. For an air parcel at a point in the stratosphere, the age spectrum is defined as the probability distribution function for transit times from the tropical tropopause for each fluid element comprising the parcel. The mean age is the average transit time, corresponding to the first moment of the age spectrum. Age spectra have been derived for altitudes below approximately 20 km for the tropics and for northern midlatitudes where there is sufficient data and where the amplitudes of the seasonal and interannual oscillations in CO2 mixing ratios are large enough to be detected. Tropical age spectra are narrow, with seasonal variation indicating faster ascent during northern winter, consistent with a circulation driven by breaking of extratropical waves. The midlatitude CO2 data are consistent with bimodal age spectra, which could result from a subtropical "barrier" to horizontal exchange over a substantial altitude region. Seasonally resolved mean ages are available with nearly pole-to-pole coverage below 20 km and in the tropics and at middle and high northern latitudes up to the maximum altitude reached by the balloons (approximately 30 km). At ER-2 altitudes, steep meridional gradients in mean age are observed in the subtropics. Between 20 and 30 km, midlatitude air is approximately 2 years older than tropical air at the same altitude. The oldest air sampled was in the Arctic polar vortex with a mean age of .5 plus or minus 0.5 years. This value is much younger than mean ages inferred from simultaneous and previous observations of SF6 in the Arctic vortex, providing evidence for a mesospheric sink for SF6. The mean age in the midlatitude middle stratosphere (approximately 25-32 km) is nearly constant with respect to altitude at 5 plus or minus 0.5 years. Comparison with earlier balloon observations of CO2 dating back to the 1970s shows that the mean age of air in this region has been relatively invariant over the last 25 years.
The NASA Orbital Debris Program Office at Johnson Space Center has developed a new computer-based orbital debris engineering model, ORDEM2000, which describes the orbital debris environment in the low Earth orbit region between 200 and 2000 km altitude. The model is appropriate for those engineering solutions requiring knowledge and estimates of the orbital debris environment (debris spatial density, flux, etc.). ORDEM2000 can also be used as a benchmark for ground-based debris measurements and observations. We incorporated a large set of observational data, covering the object size range from 10 mm to 10 m, into the ORDEM2000 debris database, utilizing a maximum likelihood estimator to convert observations into debris population probability distribution functions. These functions then form the basis of debris populations. We developed a finite element model to process the debris populations to form the debris environment. A more capable input and output structure and a user-friendly graphical user interface are also implemented in the model. ORDEM2000 has been subjected to a significant verification and validation effort. This document describes ORDEM2000, which supersedes the previous model, ORDEM96. The availability of new sensor and in situ data, as well as new analytical techniques, has enabled the construction of this new model. Section 1 describes the general requirements and scope of an engineering model. Data analyses and the theoretical formulation of the model are described in Sections 2 and 3. Section 4 describes the verification and validation effort and the sensitivity and uncertainty analyses. Finally, Section 5 describes the graphical user interface, software installation, and test cases for the user.
Three recent Arctic winters have been unusually warm or cold compared to the 1979-2001 mean, resulting in either a warm, disturbed vortex or a cold, quiet vortex. Interannual differences n ozone transport in the lower stratospheric Arctic vortex are investigated using data from the Polar Ozone and Aerosol Measurement (POAM) III satellite instrument obtained between May 1998 and April 2001. Time series of probability distribution functions (PDFs) of the FOAM data are used to identify seasonal and interannual variations in the transport processes controlling polar ozone. A major warming occurred in December, 1998, that caused the middle stratospheric vortex to be displaced from the pole for nearly a month and dissipate. Ozone transport is inferred from the PDFs and supported by potential vorticity (PV) analyses. The vortex reformed in January, 1999, filled with high O3 air from lower latitudes, which then cooled and descended. As a result, by the end of winter 1999, ozone at 500K in the vortex was 0.5-1.0 ppm higher than in the cold winter of 2000. The winter of 2000-1 had frequent wave disturbances, beginning with a fairly large event in November. However, at the end of this wave activity, the high PV core of the vortex was still intact, and by February, 03 in the vortex looked the same as in 2000. This study demonstrates that interannual variability in the 03-PV relationship can be caused by transport, independent of 03 loss by polar stratospheric clouds (PSCs). Ozone in the vortex in a very disturbed winter does not necessarily represent'pre-PSC' O3 levels in other years.
Global precipitation is monitored from a variety of platforms including space-borne, ground- and ocean-based platforms. Intercomparisons of these observations are crucial to validating the measurements and providing confidence for each measurement technique. Probability distribution functions of rain rates are used to compare satellite and ground-based radar observations. A preferred adjustment technique for improving rain rate distribution estimates is identified using measurements from ground-based radar and radar and rain gauges within the coverage area of the radar. The underwater measurement of rainfall shows similarities to radar measurements, but with intermediate spatial resolution and high temporal resolution. Reconciling these different measurement techniques provides understanding and confidence for all of the methods.
When performing chemical data assimilation the observational, representativeness, and theoretical uncertainties have very different characteristics. In this study we have accurately characterized the representativeness uncertainty by studying the probability distribution function (PDF) of the observations. The average deviation has been used as a measure of the width of the PDF and of the variability (representativeness uncertainty) for the grid cell. It turns out that for long-lived tracers such as N2O and CH4 the representativeness uncertainty is markedly different from the observational uncertainty and clearly delineates mixing barriers such as the polar vortex edge, the tropical pipe and the tropopause.
The "physics of complexity" in space plasmas is the central theme of this exposition. It is demonstrated that the sporadic and localized interactions of magnetic coherent structures arising from the plasma resonances can be the source for the coexistence of nonpropagating spatiotemporal fluctuations and propagating modes. Non-Gaussian probability distribution functions of the intermittent fluctuations from direct numerical simulations are obtained and discussed. Power spectra and local intermittency measures using the wavelet analyses are presented to display the spottiness of the small-scale turbulent fluctuations and the non-uniformity of coarse-grained dissipation that can lead to magnetic topological reconfigurations. The technique of the dynamic renormalization group is applied to the study of the scaling properties of such type of multiscale fluctuations. Charged particle interactions with both the propagating and nonpropagating portions of the intermittent turbulence are also described.
Two full months (July 2003 and January 2004) of MODIS Atmosphere Level-3 data from the Terra and Aqua satellites are analyzed in order to characterize the horizontal variability of cloud optical thickness and water path at global scales. Various options to derive cloud variability parameters are discussed. The climatology of cloud inhomogeneity is built by first calculating daily parameter values at spatial scales of l degree x 1 degree, and then at zonal and global scales, followed by averaging over monthly time scales. Geographical, diurnal, and seasonal changes of inhomogeneity parameters are examined separately for the two cloud phases, and separately over land and ocean. We find that cloud inhomogeneity is weaker in summer than in winter, weaker over land than ocean for liquid clouds, weaker for local morning than local afternoon, about the same for liquid and ice clouds on a global scale, but with wider probability distribution functions (PDFs) and larger latitudinal variations for ice, and relatively insensitive to whether water path or optical thickness products are used. Typical mean values at hemispheric and global scales of the inhomogeneity parameter nu (roughly the mean over the standard deviation of water path or optical thickness), range from approximately 2.5 to 3, while for the inhomogeneity parameter chi (the ratio of the logarithmic to linear mean) from approximately 0.7 to 0.8. Values of chi for zonal averages can occasionally fall below 0.6 and for individual gridpoints below 0.5. Our results demonstrate that MODIS is capable of revealing significant fluctuations in cloud horizontal inhomogenity and stress the need to model their global radiative effect in future studies.