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At least 19 records

A nonsmooth nonconvex optimization algorithm for two-stage optimization problems

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.

97 MATHEMATICS AND COMPUTING↗

Assessment of Precision in Temperatures from the Microwave Sounding Units

Monitoring the earth system has traditionally focused on measurements at the earth's surface because this is where we live and perform our most obvious life sustaining functions. In just the past few decades, however, efforts have been initiated to assess the character of the atmosphere above the surface. Regular upper-air measurements by balloon ascents in scattered locations began in the 1940's and observations from satellites generally began in 1979. The upper air is important in the climate context because changes in these higher levels may offer more discernible relationships to such phenomena as global warming due to the enhanced greenhouse effect than seen at other levels. The probability that climate-change trends in the mid-troposphere (5-8 km) will be more clearly evident against the background of natural variability than at, for example, the surface. Indeed, results from coupled ocean-atmosphere models indicate that in terms of a global mean quantity the troposphere will actually warm at a rate greater than that of the surface temperature. At higher elevations, above 12 km, the IPCC (Intergovernmental Panel on Climate Change) 1990 indicates there is a high degree of certainty that a greenhouse-gas induced decrease in stratospheric temperatures will occur. The measure of change in these upper atmospheric layers, in combination with quantities observed at the surface, provide an ensemble of information to give the most robust opportunity for climate change detection.

Christy, John R.↗

Impacts, processes and projections of the quasi-biennial oscillation

In the tropical stratosphere, deep layers of eastward and westward winds encircle the globe and descend regularly from the upper stratosphere to the tropical tropopause. With a complete cycle typically lasting almost 2.5 years, this quasi-biennial oscillation (QBO) is arguably the most predictable mode of atmospheric variability that is not linked to the changing seasons. Here, the QBO affects climate phenomena outside the tropical stratosphere, including ozone transport, the North Atlantic Oscillation and the Madden–Julian Oscillation, and its high predictability could enable better forecasts of these phenomena if models can accurately represent the coupling processes. Climate and forecasting models are increasingly able to simulate stratospheric oscillations resembling the QBO, but exhibit common systematic errors such as weak amplitude in the lowermost tropical stratosphere. Uncertainties about the waves that force the oscillation, particularly the momentum fluxes from small-scale gravity waves excited by deep convection, make its simulation challenging. Improved representation of the processes governing the QBO is expected to lead to better forecasts of the oscillation and its impacts, increased understanding of unusual events such as the two QBO disruptions observed since 2016, and more reliable future projections of QBO behaviour under climate change.

54 ENVIRONMENTAL SCIENCES↗

Objectively Identifying Transverse Cirrus Bands in Tropical Cyclones using a Convolutional Neural Network

Transverse cirrus bands (TCBs) are bands of upper-level clouds regularly seen in mesoscale and synoptic-scale weather systems. In tropical cyclones, their appearance has been subjectively linked to intensification and the diurnal cycle. However, these hypothesized relationships have not been rigorously tested due to the subjective nature of TCBs in satellite images. A machine learning technique that successfully identifies TCBs objectively in imagery from the GOES-16 Advanced Baseline Imager (ABI) has been developed to solve this problem. The technique uses a U-Net convolutional neural network (CNN) that assigns a probability to each pixel in an image based on the likelihood of the pixel being associated with a TCB. Using the U-Net CNN, a database of TCBs from 2019 to 2022 was developed for the Atlantic tropical cyclone basin by defining an appropriate probability threshold that defines the difference between TCB and non-TCB pixels. This threshold is where the Jaccard score, calculated using manually identified TCBs and model identified TCBs, is maximized. Statistics for TCB occurrence will also be presented, including the relationships between TCBs and storm relative motion, shear relative direction, cardinal direction, tropical cyclone intensity, tropical cyclone intensification rates, and time of day.

John Mark Mayhall↗

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k ℓ (s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f ℓ (s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Experiment M411: Two color earth limb photography

Some simple calculations were made regarding the scattered light phenomenon of a sunlit earth limb. It was assumed that the light was to be scattered by an atmosphere irradiated by a zenith sun. Calculations were made with several different scattering coefficients assignable to various wavelengths of the extended visual region. The dependence of the excess blue-limb elevation was less obviously determined by the scattering angle than was suspected. It is reasonable to surmise that the variation of the values of excess blue-limb elevation originated principally from the red-limb variance, because the form of the blue-limb profiles (at least in their upper part) was more regular than was that of the red-limb profiles.

Petersen, M.↗

Objectively Identifying Transverse Cirrus Bands in Tropical Cyclones using a Convolutional Neural Network

Transverse cirrus bands (TCBs) are bands of upper-level clouds that are regularly seen in mesoscale and synoptic-scale weather systems. In tropical cyclones, their appearance has been subjectively linked to intensification and the diurnal cycle, but these hypothesized relationships have not been rigorously tested due to the difficulty of objectively identifying TCBs in satellite images. This presentation describes a machine learning technique that successfully identifies TCBs in imagery from the GOES-16 Advanced Baseline Imager. The technique uses a convolutional neural network (CNN) that assigns a probability of each pixel in the image being associated with a TCB. Using the CNN, a database of TCBs from 2018 to 2022 was developed for the Atlantic basin. Statistics using this database will be presented, including the relationship between TCBs and deep-layer vertical wind shear, intensity change, and the TC diurnal cycle.

John Mark Mayhall↗

Intra-seasonal Oscillations (ISO) of Zonal-Mean Meridional Winds and Temperatures as Measured by UARS

Based on an empirical analysis of measurements with the High Resolution Doppler Imager (HRDI) on the UARS spacecraft in the upper mesosphere (95 km), persistent and regular intra-seasonal oscillations (ISO) with periods of about 2 to 4 months have recently been reported in the zonal-mean meridional winds. Similar oscillations have also been discussed independently in a modeling study, and they were attributed to wave-mean-flow interactions. The observed and modeled meridional wind ISOs were largely confined to low latitudes. We report here an analysis of concurrent temperature measurements on UARS, which produces oscillations similar to those seen in the meridional winds. Although the temperature oscillations are observed at lower altitudes (55 km), their phase variations with latitude are qualitatively consistent with the inferred properties seen in the meridional winds and thus provide independent evidence for the existence of ISOs in the mesosphere.

Huang, Frank T.↗

Upper semicontinuous global attractors for viscous flow

A particular form of regularization of the Navier-Stokes equations is studied. It is shown that as the regularization parameter goes to zero, the global attractor for the regularized system converges to the global attractor for the conventional Navier-Stokes system.

Ou, Yuh-Roung↗

Exploring the veiled planet

An overview of data obtained from various experiments which characterize geological features and atmospheric properties of Venus is presented. Data from the two Pioneer sounder probes (one located at Venus's equator and the other near the north pole) exhibit a reversal in the equator-to-pole temperature patterns at 60 km altitude which suggests that two circulation cells exist within the atmospheric region. However, the atmospheric temperature and pressure beneath the clouds are found to be nearly identical everywhere on Venus and both temperature and pressure conditions at the surface are lower than first expected. The identification of sulphur dioxide clouds which appear to coincide with Venus's characteristic global patterns of C- and Y-shaped dark markings support the hypothesis of a regular pattern of planet spanning breaks in the upper cloud layer. Explanations of a Venus sulphur cycle and of observed magnetic field structures are suggested

Source record↗

Efficient diagnosis of multiprocessor systems under probabilistic models

The problem of fault diagnosis in multiprocessor systems is considered under a probabilistic fault model. The focus is on minimizing the number of tests that must be conducted in order to correctly diagnose the state of every processor in the system with high probability. A diagnosis algorithm that can correctly diagnose the state of every processor with probability approaching one in a class of systems performing slightly greater than a linear number of tests is presented. A nearly matching lower bound on the number of tests required to achieve correct diagnosis in arbitrary systems is also proven. Lower and upper bounds on the number of tests required for regular systems are also presented. A class of regular systems which includes hypercubes is shown to be correctly diagnosable with high probability. In all cases, the number of tests required under this probabilistic model is shown to be significantly less than under a bounded-size fault set model. Because the number of tests that must be conducted is a measure of the diagnosis overhead, these results represent a dramatic improvement in the performance of system-level diagnosis techniques.

Blough, Douglas M.↗

Twenty-two-year cycle of the upper limiting rigidity of Daly waves

The method of calculating energy losses along regular particle trajectories is applied to obtain the predicted cosmic ray anisotropies from 200 to 500 GV. The tilt angle of the interplanetary neutral sheet varies to simulate a 22-year cycle magnetic cycle. The calculated values of solar diurnal and semidiurnal, and sidereal diurnal intensity waves are compared with observations.

Erdos, G.↗

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗

Regularized Chapman-Enskog expansion for scalar conservation laws

Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

Schochet, Steven↗

Measurements of the methane relaxation times for application to the infrared emission models of the upper atmospheres of outer planets and Titan

The 7.8 micrometer emission from the nu(sub 4) band of methane (CH4) is a regularly observed feature in the stratosphere of all the giant planets and Titan. On Jupiter, enhancements in this emission are associated with the infrared hot spots in the auroral zone. Attempts to model this phenomenon in particular, and to understand the role of methane in general, have been hampered in part by a lack of adequate laboratory measurements of the collisional relaxation times for the nu(sub 3) and nu(sub 4) levels over the appropriate temperature range. To provide this needed data, a series of laboratory experiments were initiated. In the experimental arrangement the nu(sub3) band of methane is pumped at 3.3 micrometers using a pulsed infrared source (Nd:YAG/dye laser system equipped with a wave-length extender). The radiative lifetime of the nu(sub 3) level (approximately 37 ms) is much shorter than the nu(sub 4) lifetime (approximately 390 ms); however, a rapid V-V energy transfer rate ensures that the nu(sub 4) level is substantially populated. The photoacoustic technique is used to acquire relaxation rate information. The experiments are performed using a low-temperature, low-pressure cell. Experimental apparatus and technique are described. In addition some of the experimental difficulties associated with making these measurements are discussed and some preliminary results are presented.

Halthore, Rangasayi N.↗

The Remarkable 2003--2004 Winter and Other Recent Warm Winters in the Arctic Stratosphere Since the Late 1990s

The 2003-2004 Arctic winter was remarkable in the approximately 50-year record of meteorological analyses. A major warming beginning in early January 2004 led to nearly 2 months of vortex disruption with high-latitude easterlies in the middle to lower stratosphere. The upper stratospheric vortex broke up in late December, but began to recover by early January, and in February and March was the strongest since regular observations began in 1979. The lower stratospheric vortex broke up in late January. Comparison with 2 previous years, 1984-1985 and 1986-1987, with prolonged midwinter warming periods shows unique characteristics of the 2003-2004 warming period: The length of the vortex disruption, the strong and rapid recovery in the upper stratosphere, and the slow progression of the warming from upper to lower stratosphere. January 2004 zonal mean winds in the middle and lower stratosphere were over 2 standard deviations below average. Examination of past variability shows that the recent frequency of major stratospheric warmings (7 in the past 6 years) is unprecedented. Lower stratospheric temperatures were unusually high during 6 of the past 7 years, with 5 having much lower than usual potential for polar stratospheric cloud (PSC) formation and ozone loss (nearly none in 1998-1999, 2001-2002, and 2003-2004, and very little in 1997-1998 and 2000-2001). Middle and upper stratospheric temperatures, however, were unusually low during and after February. The pattern of 5 of the last 7 years with very low PSC potential would be expected to occur randomly once every 850 years. This cluster of warm winters, immediately following a period of unusually cold winters, may have important implications for possible changes in interannual variability and for determination and attribution of trends in stratospheric temperatures and ozone.

ozone↗

The Remarkable 2003-2004 Winter and Other Recent Warm Winters in the Arctic Stratosphere Since the Late 1990s

The 2003-2004 Arctic winter was remarkable in the 40-year record of meteorological analyses. A major warming beginning in early January 2004 led to nearly two months of vortex disruption with high-latitude easterlies in the middle to lower stratosphere. The upper stratospheric vortex broke up in late December, but began to recover by early January, and in February and March was the strongest since regular observations began in 1979. The lower stratospheric vortex broke up in late January. Comparison with two previous years, 1984-1985 and 1986-1987, with prolonged mid-winter warming periods shows unique characteristics of the 2003-2004 warming period: The length of the vortex disruption, the strong and rapid recovery in the upper stratosphere, and the slow progression of the warming from upper to lower stratosphere. January 2004 zonal mean winds in the middle and lower stratosphere were over two standard deviations below average. Examination of past variability shows that the recent frequency of major stratospheric warmings (seven in the past six years) is unprecedented. Lower stratospheric temperatures were unusually high during six of the past seven years, with five having much lower than usual potential for PSC formation and ozone loss (nearly none in 1998-1999, 2001-2002 and 2003-2004, and very little in 1997-1998 and 2000-2001). Middle and upper stratospheric temperatures, however, were unusually low during and after February. The pattern of five of the last seven years with very low PSC potential would be expected to occur randomly once every approximately 850 years. This cluster of warm winters, immediately following a period of unusually cold winters, may have important implications for possible changes in interannual variability and for determination and attribution of trends in stratospheric temperatures and ozone.

Manney, Gloria L.↗

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗