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NASA NTRS2023

Split-Step Simulations to Assess the Effects of Atmospheric Boundary Layer Turbulence on the Dose Variability of N-Waves and Shaped Booms

The effects of atmospheric boundary layer turbulence on the loudness variability of a sonic boom N-wave and shaped boom are examined with split-step simulations. The shaped boom is representative of a design iteration of the NASA X-59 aircraft. Inhomogeneous atmospheric boundary layer turbulence is generated in the computational domain by a Fourier synthesis method. The N-wave and shaped boom are propagated through turbulent fields representing eight different convection levels measured at the NASA Kennedy Space Center and the NASA Armstrong Flight Research Center. Probability density functions of the formation of caustic regions along the propagation direction are computed from the N-wave results, and a parameter to collapse the caustic PDFs that accounts for both fluctuation intensities and length scales is proposed. Statistical results concerning loudness metric variability are presented, and the standard deviations of several metrics are shown to collapse across different convection levels of turbulence for small nondimensional propagation distances. The loudness metric distributions are observed to be well approximated by a normal distribution for a given range of propagation distances, and become increasingly skewed as distance increases. A model function for the dose variability is proposed, and the function parameters are found to be related to the convection level of the turbulence. The model for the dose variability distribution is compared to simulation data that were not used to find the regression parameters of the model. At several nondimensional propagation distances, agreement is observed between the model and the simulation data. These results indicate that the model may be suitable for providing quick estimates of noise dose variability in the primary carpet region across a wide range of atmospheric boundary layer conditions.

Sonic boom↗

NASA NTRSDate not supplied

The Impact of Pixel Size on the Characterization of Deep Convective Clouds for Calibration

The NASA CERES project provides the scientific community the observed TOA SW and LW fluxes for climate monitoring and climate model validation. CERES utilizes hourly geostationary imager derived broadband fluxes, which rely on the channel radiances and associated cloud retrievals, to estimate the broadband fluxes between CERES observations. This requires stable imager visible channel calibration, which the CERES project verifies by utilizing deep convective clouds (DCC) as an invariant Earth target. GSICS, which is an international collaboration, is also evaluating the DCC invariant target calibration methodology to provide consistent calibration coefficients across geostationary imagers anchored to the Aqua-MODIS calibration reference. Tropical DCC are the brightest, coldest, most Lambertian, top of the atmosphere Earth targets. The DCC invariant target calibration methodology relies on a large ensemble of tropical DCC-identified pixel-level reflectances, which are histogrammed to find the mode reflectance of the probability density function (PDF). The imager stability is monitored by tracking the monthly DCC PDF mode reflectance over time. Radiometric scaling is accomplished by ratioing the GEO and VIIRS DCC mode reflectance values. The PDF shape and mode dependency on sensor pixel resolution, which varies among sensors, is unknown. This study will characterize the impact of pixel resolution on the DCC PDFs by aggregating Landsat 30-m pixel reflectances into various coarser pixel resolutions ranging from 100-m to 4-km, and comparing the corresponding PDF statistics. This analysis will assist in improving the uncertainty in a DCC-based intercalibration between instruments with different pixel resolutions.

Conor Haney↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

Global Precipitation Measuremen↗

NASA NTRSDate not supplied

The Impact of Pixel Size on the Characterization of Deep Convective Clouds for Calibration

The NASA CERES project provides the scientific community the observed TOA SW and LW fluxes for climate monitoring and climate model validation. CERES utilizes hourly geostationary imager derived broadband fluxes, which rely on the channel radiances and associated cloud retrievals, are used to estimate the broadband fluxes between CERES observations. This requires stable and consistent cross-platform imager visible channel calibration. The CERES project utilizes deep convective clouds (DCC) as an invariant Earth target to both monitor the stability of sensors and for radiometric scaling. GSICS, an international collaboration, is also evaluating and implementing the DCC invariant target calibration methodology to provide consistent calibration coefficients across geostationary imagers anchored to the AquaMODIS or the NOAA-20 VIIRS calibration reference. Tropical DCC are the brightest, coldest, most Lambertian, top of the atmosphere Earth targets. The DCC invariant target calibration methodology relies on a large ensemble of tropical D CC-identified pixel-level reflectances, which are aggregated as probability density functions (PDF). By assuming the monthly PDF shape is otherwise consistent in time excepting shifts in reflectance caused by changes in the sensor calibration, the imager stability is monitored. Radiometric scaling is accomplished by ratioing the sensor pair DCC PDF reflectance values. The success of the DCC methodology relies on consistent PDF distributions. The goal of this study is to determine the impact of pixel resolution on the DCC reflectance distribution. Single SNPP-VIIRS 750-m and Landsat 8 OLI 30-m granules are aggregated to degrade the pixel resolution from the native level. The DCC pixels are identified using a BT threshold. Most of the brightest DCC pixels are also the coldest, although there are exceptions. It was found that increasing the BT threshold exponentially increased the number of darker pixels. The pixel resolution did not seem to impact the DCC reflectance PDF distribution for pixel resolutions less than 3 km, which suggests that imagers of varying pixel resolutions may be radiometrically scaled to each other using DCC targets.

DCC↗

NASA NTRSDate not supplied

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗

NASA NTRSDate not supplied

Consistent Pixel Resolution Characterization of Deep Convective Clouds for Calibration

The NASA CERES project provides global TOA shortwave and longwave fluxes for climate monitoring and validation that spans over 20 years. CERES utilizes broadband fluxes derived from geostationary (GEO) imagers to estimate broadband fluxes between the CERES observations. In order for these fluxes to be viable, the GEO imager calibration must be stable over time. One such calibration method used by CERES is to evaluate ensemble sets of deep convective clouds (DCC) as invariant targets (IT) over time. DCC targets can also provide radiometric scaling between sensors. An international collaboration through GSICS is also evaluating the DCC-IT calibration methodology to provide consistent calibration coefficients across geostationary sensors. Tropical DCC are the coldest, brightest, and most Lambertian TOA Earth targets identified using a window channel brightness temperature threshold. The DCC-IT technique involves a large ensemble of TOA pixel-level reflectances, which are binned into probability density functions (PDF). The PDF structure dependency on sensor pixel resolution, which can vary greatly among sensors, is not well known. This study will identify the impact of pixel resolution on the DCC PDFs by aggregating VIIRS and Landsat OLI/TIRS pixel resolutions into various coarser pixel resolutions and comparing the shape and statistics of the resulting PDFs. This study should assist in mitigating the pixel resolution dependency in the DCC-IT approach for providing scaling factors between sensors.

Conor Haney↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

The joint U.S.-Japan Global Precipitation Measurement (GPM) mission is approaching a decade of operations, and continues to pursue research, dataset production, and outreach related to precipitation. Key activities over the last year were the release of an improved “Version 07” of all GPM precipitation and latent heating products, boosting the orbit of the GPM Core Observatory (GPM CO) to 435 km, and improving quality control on precipitation retrievals from the GPM constellation of passive microwave satellites. This presentation summarizes key improvements to the GPM products and provides some examples of the changes between Versions 06 and 07 in algorithm performance. One important operational change that affected Version 07 is that the scanning strategy for the Ka-band radar channel changed in May 2018; all products that depend on Ka were revised to accommodate this change. For example, in Version 07 the Goddard Profiling (GPROF) algorithm has implemented improvements in regions where orographic enhancement and suppression take place and where the surface is snowy/icy, and again covers radiometers reaching back to 1987. The Combined Radar Radiometer Algorithm (CORRA) now incorporates modified drop-size distribution constraints that substantially reduce bias. Revisions to the Convective-Stratiform Heating (CSH) algorithm employ new radiative transfer retrievals as well as accounting for terrain in the vertical coordinates. Each algorithm was adjusted to ensure continuity for each product across the boundary in 2014 between the predecessor Tropical Rainfall Measuring Mission (TRMM) and the GPM CO. The U.S. Science Team’s Integrated Multi-satellitE Retrievals for GPM (IMERG) was upgraded to account for distortions in the probability density function of regional precipitation rates due to weighted averaging in the Kalman filter used for “morphing” the passive microwave data. Maintaining the GPM CO orbital altitude in the the current very active solar cycle has been forcing the use of more fuel than planned and consequently shortening the forecasted life of the mission from the early 2030's to the late 2020's. It was considered vital to regain some of this lifetime to ensure overlap with the upcoming Atmosphere Observing System mission to provide crosscalibration of instruments. To accomplish this, the orbital altitude was raised from 400 to 435 km on 7-8 November 2023. Thereafter, the primary GPM CO algorithms had to be revised to account for the change in observing parameters. By meeting time this action should be complete. Recently, a screening algorithm based on auto-encoding was developed that uncovered 162 orbits (out of the many thousands of orbits across all years and all satellites) of passive microwave retrievals that had highly anomalous values. Removing these defective retrievals has improved the integrity of both the GPROF and IMERG records. However, the nature of the IMERG processing interacted sufficiently badly with the now-discovered anomalous orbits that it was necessary to completely reprocess the IMERG Final Run record, now labeled Version 07B. The presentation also considers major issues that require continued attention, including the use of machine learning algorithms and the operational challenge of swarms of “small”, perhaps short-lived satellites.

GPM↗

NASA NTRSDate not supplied

Seasonal, Spectral, and Regional Characterization of Deep Convective Clouds Top-of-Atmosphere Bidirectional Reflectance for Improved Satellite Intercalibration

The NASA CERES project provides the scientific community with regional broadband fluxes designed for long-term climate monitoring. The CERES climate quality dataset requires that the CERES instrument, as well as the MODIS and VIIRS imager records to be radiometrically stable over time. Deep Convective Clouds (DCCs) are spectrally uniform, near-Lambertian natural diffusers offering high signal-to-noise ratio and stable radiometric response in the VIS-NIR spectrum. For shortwave infrared (SWIR) wavelengths greater than 1.2µm, the DCC response is significantly influenced by cloud particle size and atmospheric absorption. Previous studies improved the characterization of the SWIR band DCC radiance, by using channel specific monthly empirical BRDFs as well as using the probability density function mean statistic to track the SWIR band stability. Also, that the DCC radiance is greater over land than over ocean and that the TWP DCC radiance has the lowest tropical DCC radiance. This study confirms and improves upon the previous studies. The study stratified the tropics regionally into land and ocean domains and applied their respective ocean-only and land-only empirical monthly BRDFs and normalized the land DCC BRDF corrected radiances with their ocean counterpart. This approach provided the most stable DCC response. The DCC BRDF corrected radiance monthly standard error was 0.24%, 0.62%, 0.59%, and 0.43% for the 1.24µm, 1.37µm, 1.61µm, and 2.25µm SWIR bands, which reduced the standard error 20%, 13%, 24%, and 26%, respectively when compared with the all-surface approach. The same approach was attempted over the Tropical Western Pacific and found not to be an improvement over the tropical domain. Further stratification of the tropical domain will need to balance sufficient sampling while accounting for regional DCC radiance differences.

Prathana Khakurel↗

NASA NTRSDate not supplied

Deep Convective Cloud Calibration Sensitivity Studies in Support of Radiometrically Scaling GEO Imagers With VIIRS

The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS or VIIRS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Tropical deep convective clouds (DCC) are bright, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident ray-matched radiance pairs to radiometrically scale sensors to a common calibration reference. The DCC invariant target (DCC-IT) methodology collectively analyzes all tropical DCC identified pixel radiances by way of probability density function (PDF) distributions. Perfectly inter-calibrated sensor pairs should reveal nearly identical PDF distributions given the same DCC identification criterion. The PDF median, mean, mode, and inflection point statistics were tested as a function of DCC identification criterion using SNPP-VIIRS and Himawari-8 AHI 0.65μm channel radiances during January 2019. It was found that the PDF inflection point provided inter-calibration factors within 0.25% that were nearly independent of DCC identification criterion. The PDF median provided inter-calibration factors within 0.25% for the coldest BT and most stringent homogeneity factors. The PDF mean and mode statistics were inadequate under any DCC conditions. It is critical for the DCC pixel radiances to be anisotropically corrected. The DCC-IT methodology will also be tested for other visible and SWIR bands.

DCC↗

NASA NTRS1989

Probability density and exceedance rate functions of locally Gaussian turbulence

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Mark, W. D.↗

NASA NTRS1991

Scalar dissipation and mixing in turbulent reacting flows

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 64-cubed Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence-dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions were compared to predictions of D/D models that make use of parameters evaluated from the nonreacting or inert system.

Leonard, Andy D.↗

NASA NTRS1985

Birds and insects as radar targets - A review

A review of radar cross-section measurements of birds and insects is presented. A brief discussion of some possible theoretical models is also given and comparisons made with the measurements. The comparisons suggest that most targets are, at present, better modeled by a prolate spheroid having a length-to-width ratio between 3 and 10 than by the often used equivalent weight water sphere. In addition, many targets observed with linear horizontal polarization have maximum cross sections much better estimated by a resonant half-wave dipole than by a water sphere. Also considered are birds and insects in the aggregate as a local radar 'clutter' source. Order-of-magnitude estimates are given for many reasonable target number densities. These estimates are then used to predict X-band volume reflectivities. Other topics that are of interest to the radar engineer are discussed, including the doppler bandwidth due to the internal motions of a single bird, the radar cross-section probability densities of single birds and insects, the variability of the functional form of the probability density functions, and the Fourier spectra of single birds and insects.

Vaughn, C. R.↗

NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗

NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗

NASA NTRS1967

Second-order statistics of alternated stepwise processes.

Generalization of binary processes, discussing time domain and frequency domain analysis

STATISTICAL ANALYSIS↗

NASA NTRS1992

Discrete-time entropy formulation of optimal and adaptive control problems

The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

Tsai, Yweting A.↗

NASA NTRS2011

Entanglement in Quantum-Classical Hybrid

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

Zak, Michail↗

NASA NTRS1966

Signal fading characteristics, Echo II

Signal fading characteristics of Echo II SATELLITE - fade duration, and fade period probability distribution and density functions at various cross section levels

COMMUNICATION SYSTEM↗