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NASA NTRS2006

Convective Weather Forecast Quality Metrics for Air Traffic Management Decision-Making

Since numerical weather prediction models are unable to accurately forecast the severity and the location of the storm cells several hours into the future when compared with observation data, there has been a growing interest in probabilistic description of convective weather. The classical approach for generating uncertainty bounds consists of integrating the state equations and covariance propagation equations forward in time. This step is readily recognized as the process update step of the Kalman Filter algorithm. The second well known method, known as the Monte Carlo method, consists of generating output samples by driving the forecast algorithm with input samples selected from distributions. The statistical properties of the distributions of the output samples are then used for defining the uncertainty bounds of the output variables. This method is computationally expensive for a complex model compared to the covariance propagation method. The main advantage of the Monte Carlo method is that a complex non-linear model can be easily handled. Recently, a few different methods for probabilistic forecasting have appeared in the literature. A method for computing probability of convection in a region using forecast data is described in Ref. 5. Probability at a grid location is computed as the fraction of grid points, within a box of specified dimensions around the grid location, with forecast convection precipitation exceeding a specified threshold. The main limitation of this method is that the results are dependent on the chosen dimensions of the box. The examples presented Ref. 5 show that this process is equivalent to low-pass filtering of the forecast data with a finite support spatial filter. References 6 and 7 describe the technique for computing percentage coverage within a 92 x 92 square-kilometer box and assigning the value to the center 4 x 4 square-kilometer box. This technique is same as that described in Ref. 5. Characterizing the forecast, following the process described in Refs. 5 through 7, in terms of percentage coverage or confidence level is notionally sound compared to characterizing in terms of probabilities because the probability of the forecast being correct can only be determined using actual observations. References 5 through 7 only use the forecast data and not the observations. The method for computing the probability of detection, false alarm ratio and several forecast quality metrics (Skill Scores) using both the forecast and observation data are given in Ref. 2. This paper extends the statistical verification method in Ref. 2 to determine co-occurrence probabilities. The method consists of computing the probability that a severe weather cell (grid location) is detected in the observation data in the neighborhood of the severe weather cell in the forecast data. Probabilities of occurrence at the grid location and in its neighborhood with higher severity, and with lower severity in the observation data compared to that in the forecast data are examined. The method proposed in Refs. 5 through 7 is used for computing the probability that a certain number of cells in the neighborhood of severe weather cells in the forecast data are seen as severe weather cells in the observation data. Finally, the probability of existence of gaps in the observation data in the neighborhood of severe weather cells in forecast data is computed. Gaps are defined as openings between severe weather cells through which an aircraft can safely fly to its intended destination. The rest of the paper is organized as follows. Section II summarizes the statistical verification method described in Ref. 2. The extension of this method for computing the co-occurrence probabilities in discussed in Section HI. Numerical examples using NCWF forecast data and NCWD observation data are presented in Section III to elucidate the characteristics of the co-occurrence probabilities. This section also discusses the procedure for computing throbabilities that the severity of convection in the observation data will be higher or lower in the neighborhood of grid locations compared to that indicated at the grid locations in the forecast data. The probability of coverage of neighborhood grid cells is also described via examples in this section. Section IV discusses the gap detection algorithm and presents a numerical example to illustrate the method. The locations of the detected gaps in the observation data are used along with the locations of convective weather cells in the forecast data to determine the probability of existence of gaps in the neighborhood of these cells. Finally, the paper is concluded in Section V.

Chatterji, Gano B.↗

NASA NTRS2019

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗

NASA NTRS2013

The Ocean Colour Climate Change Initiative: III. A Round-Robin Comparison on In-Water Bio-Optical Algorithms

Satellite-derived remote-sensing reflectance (Rrs) can be used for mapping biogeochemically relevant variables, such as the chlorophyll concentration and the Inherent Optical Properties (IOPs) of the water, at global scale for use in climate-change studies. Prior to generating such products, suitable algorithms have to be selected that are appropriate for the purpose. Algorithm selection needs to account for both qualitative and quantitative requirements. In this paper we develop an objective methodology designed to rank the quantitative performance of a suite of bio-optical models. The objective classification is applied using the NASA bio-Optical Marine Algorithm Dataset (NOMAD). Using in situ Rrs as input to the models, the performance of eleven semianalytical models, as well as five empirical chlorophyll algorithms and an empirical diffuse attenuation coefficient algorithm, is ranked for spectrally-resolved IOPs, chlorophyll concentration and the diffuse attenuation coefficient at 489 nm. The sensitivity of the objective classification and the uncertainty in the ranking are tested using a Monte-Carlo approach (bootstrapping). Results indicate that the performance of the semi-analytical models varies depending on the product and wavelength of interest. For chlorophyll retrieval, empirical algorithms perform better than semi-analytical models, in general. The performance of these empirical models reflects either their immunity to scale errors or instrument noise in Rrs data, or simply that the data used for model parameterisation were not independent of NOMAD. Nonetheless, uncertainty in the classification suggests that the performance of some semi-analytical algorithms at retrieving chlorophyll is comparable with the empirical algorithms. For phytoplankton absorption at 443 nm, some semi-analytical models also perform with similar accuracy to an empirical model. We discuss the potential biases, limitations and uncertainty in the approach, as well as additional qualitative considerations for algorithm selection for climate-change studies. Our classification has the potential to be routinely implemented, such that the performance of emerging algorithms can be compared with existing algorithms as they become available. In the long-term, such an approach will further aid algorithm development for ocean-colour studies.

Phytoplankton↗

NASA NTRS2002

Studying the Warm Layer and the Hardening Factor in Cygnus X-1

As the first dynamically determined black hole X-ray binary system, Cygnus X-1 has been studied extensively. However, its broadband spectrum observed with BeppoSax is still not well understood. Besides the soft excess described by the multi-color disk model (MCD), the power-law hard component and a broad excess feature above 10 keV (a disk reflection component), there is also an additional soft component around 1 keV, whose origin is not known currently. Here we propose that the additional soft component is due to the thermal Comptonization between the soft disk photons and a warm plasma cloud just above the disk, i.e., a warm layer. We use the Monte-Carlo technique to simulate this Compton scattering process and build a table model based on our simulation results. With this table model, we study the disk structure and estimate the hardening factor to the MCD component in Cygnus X-1.

Yao, Yangsen↗

NASA NTRSDate not supplied

Uncertainty Modeling for Mars Ascent Vehicle’s Aerodatabase Development

The design of the Mars Ascent Vehicle - Mars Sample Return (MAV-MSR) trajectories requires an accurate assessment of flight performance. Typically, these trajectories are developed by flight mechanics analysis to meet complex mission requirements and then flight performance assessed through Monte Carlo simulations. Consequently, it is crucial to develop an aerodynamic aerodatabase as an input model for flight mechanics analysis to provide static and dynamic force and moment coefficients under specific flight conditions. The force and moment coefficients in the MAV aerodatabase are determined using the FUN3D computational fluid dynamics solver. Firstly, an overview of the aerodatabase is presented to demonstrate its applicability to trajectory-defined simulations. This effort is followed by an initial attempt to quantify uncertainties in the force and moment coefficients necessary for updating the current aerodatabase. The uncertainty model identifies uncertainty adders and multipliers for coefficient-based forces and moments through a direct comparison between FUN3D and wind tunnel test data from NASA Marshall Space Center's 14x14 inch Trisonic Wind Tunnel. These uncertainties aim to encompass various changes in Mach number, angle of attack, and aerodynamic roll angle.

Uncertainty analysis↗

NASA NTRSDate not supplied

Uncertainty Modeling for Mars Ascent Vehicle’s Aerodynamic Database Development

Uncertainty analysis↗

NASA NTRS2022

Effective Uncertainty Quantification for Multi-Angle Polarimetric Aerosol Remote Sensing Over Ocean

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere–ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval errors well due to issues such as local minima and the nonlinear dependence of the forward model on the retrieved parameters near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a flexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on efficient neural network forward models, is used to conduct the retrievals and uncertainty quantification on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the uncertainty evaluation technique in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantification for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP field campaign data. The uncertainty quantification methods and results can be used to evaluate the quality of data products, as well as guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission.

PACE↗

NASA NTRS2007

Comparison of Integrated Radiation Transport Models with TEPC Measurements for the Average Quality Factors in Spaceflights

The purpose of this work is to test our theoretical model for the interpretation of radiation data measured in space. During the space missions astronauts are exposed to the complex field of radiation type and kinetic energies from galactic cosmic rays (GCR), trapped protons, and sometimes solar particle events (SPEs). The tissue equivalent proportional counter (TEPC) is a simple time-dependent approach for radiation monitoring for astronauts on board the International Space Station. Another and a newer approach to Microdosimetry is the use of silicon-on-insulator (SOI) technology launched on the MidSTAR-1 mission in low Earth orbit (LEO). In the radiation protection practice, the average quality factor of a radiation field is defined as a function of linear energy transfer (LET), Q(sub ave)(LET). However, TEPC measures the average quality factor as a function of the lineal energy y, Q(sub ave)(y), defined as the average energy deposition in a volume divided by the average chord length of the volume. Lineal energy, y, deviates from LET due to energy straggling, delta-ray escape or entry, and nuclear fragments produced in the detector volume. Monte Carlo track structure simulation was employed to obtain the response of a TEPC irradiated with charged particle for an equivalent site diameter of 1 micron of wall-less counter. The calculated data of the energy absorption in the wall-less counter were compiled for various y values for several ion types at various discrete projectile energy levels. For the simulation of TEPC response from the mixed radiation environments inside a spacecraft, such as, Space Shuttle and International Space Station, the complete microdosimetric TEPC response, f( y, E, Z), were calculated with the Monte Carlo theoretical results by using the first order Lagrangian interpolation for a monovariate function at a given y value (y = 0.1 keV/micron 5000 keV/micron) at any projectile energy level (E = 0.01 MeV/u to 50,000 MeV/u) of each specific radiation type (Z = 1 to 28). Because the anomalous response has been observed at large event sizes in the experiment due to the escape of energy out of sensitive volume by delta-rays and the entry of delta-rays from the high-density wall into the low-density gas-volume cavity, Monte Carlo simulation was also made for the response of a walled-TEPC with wall thickness 2 mm and density 1 g/cm(exp 3). The radius of cavity was set to 6.35 mm and a gas density 7.874 x 10(exp -5) g/cm(exp 3). The response of the walled- and the wall-less counters were compared. The average quality factor Q(sub ave)(y) for trapped protons on STS-89 demonstrated the good agreement between the model calculations and flight TEPC data as shown. Using an integrated space radiation model (this includes the transport codes HZETRN and BRYNTRN, the quantum nuclear interaction model QMSFRG) and the resultant response distribution functions of walled-TEPC from Monte-Carlo track simulations, we compared model calculations with walled-TEPC measurements from NASA missions in LEO and made predictions for the lunar and the Mars missions. The Q(sub ave)(y) values for the trapped or the solar protons ranged from 1.9-2.5. This over-estimates the Qave(LET) values which ranged from 1.4-1.6. Both quantities increase with shield thickness due to nuclear fragmentation. The Q(sub ave)(LET) for the complete GCR spectra was found to be 3.5-4.5, while flight TEPCs measured 2.9-3.4 for Q(sub ave)(y). The GCR values are decreasing with the shield thickness. Our analysis for a proper interpretation of data supports the use of TEPCs for monitoring space radiation environment.

Kim, Myung-Hee Y.↗

NASA NTRSDate not supplied

Recommended DSMC Collision Model Parameters for Planetary Entry

Hybrid simulation frameworks combining Computational Fluid Dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) are frequently employed to efficiently perform high-fidelity simulations of environments consisting of both continuum and rarified flow. DSMC is a stochastic, particle-based method which solves the fundamental Boltzmann equation and is therefore necessary for high-Knudsen flow where continuum-based assumptions governing CFD break down. However, the DSMC methodology is generally computationally inefficient to model the continuum regime. In a CFD/DSMC hybrid approach, obtaining an accurate, high-fidelity solution hinges on the consistent treatment of transport properties and the thermo-chemical models employed within the two solvers. In principle, in regions where CFD and DSMC are both employed, the same gas mixture under the same conditions should have the same properties, regardless of simulation type. Observed differences should be due to non-equilibrium processes, rather than differences in physical models. The goal of this work is to provide a comprehensive DSMC transport database encompassing the vast majority of known gas species encountered during Earth or other planetary atmospheric entry. This goal is largely possible due to recently performed ab initio quantum chemistry calculations. Combined with other high-fidelity data, the planned database will consist of collision integral data for over 200 neutral and ionized species and over 20000 binary collisions. From these collision integrals, Nelder-Mead optimization is used to compute collision-specific Variable Soft Sphere (VSS) collision model parameters, fitted from 300 K to 20000 K. Initial comparisons of transport properties of relevant equilibrium gas mixtures show great agreement between CFD and DSMC-derived results. The completed database can be readily applied to model binary collisions of any gas mixture containing the included species over the specified temperature range, making it a valuable tool for future planetary probe modeling efforts. An example is shown below in Fig. 1. Equilibrium mixture transport properties for a 35-species mixture composed originally of 10% air and 90% pyrolysis species of a carbon-phenolic ablator material [4] are computed using both fitted VSS Parameters and the original CFD collision integral values. Deviations in computed properties between the two approaches are less than 5% for the entire temperature range.

M. R. Gosma↗

NASA NTRS1999

Modeling of Sub-Grid Heterogeneity and its Impact on GCM Global Radiation Balance

The spatial and temporal variability of high, low, and mid-level clouds is obtained from ISCCP D1 data. Monthly mean global maps of the observed cloud variability are used to re-scale GCM prognostic cloud optical depths and radiative parameters via the Monte Carlo cloud heterogeneity parameterization that utilizes the existing plane-parallel GCM radiative transfer model to compute radiative fluxes for inhomogeneous cloud distributions. The GCM radiative fluxes at TOA and the ground surface are then compared to ERBE and GEBA results. These comparisons show that including sub-grid cloud variability in the GCM radiative model improves agreement between the GCM radiative energy budget components and observations,

Lacis, Andrew↗

NASA NTRS1995

Simulated Craters on Venus

The thick atmosphere of Venus prevents all but the largest impactors from cratering the surface. The number of small craters on Venus provides an interesting, and statistically significant test of models for the disruption and deceleration of impacting bodies. Here we compare Monte Carlo simulated crater distributions to the observed crater distribution on Venus. The simulation assumes: (1) a power law mass distribution for impactors of the form N(sub cum) alpha m (exp-b) where b=0.8; (2) isotropic incidence angles; (3) velocity at the top of the atmosphere of 20 kilometers per second (more realistic velocity distributions are also considered); (4) Schmidt-Housen crater scaling, modified such that only the normal component of the impact velocity contributes to cratering, and using crater slumping as parameterized (5) and modern populations (60% carbonaceous, 40% stone, 3% iron) and fluxes of asteroids. We use our previously developed model for the disruption and deceleration of large bodies striking thick planetary atmospheres to calculate the impact velocity at the surface as a function of impactor mass, incident velocity, and incident angle. We use a drag coefficient c(sub d) =1; other parameters are as described in Chyba et al. We set a low velocity cutoff of 500 meters per second on crater-forming impacts. Venus's craters are nicely matched by the simulated craters produced by 700 million years of striking asteroids. Shown for comparison are the simulated craters produced by incident comets over the same period, where for comets we have assumed b=0.7 and a flux at 10(exp 14) g 30% that of asteroids. Systematic uncertainties in crater scaling and crater slumping may make the surface age uncertain by a factor of two.

Zahnle, Kevin↗

NASA NTRS2003

Modeling the Extended Neutral Atmosphere and Plasma Environment near Saturn

In the three years of this study we have published five papers in refereed journals. We have first examined satellite sources and their contribution to the observed neutral cloud. Based on the total calculated satellite sources and the spatial distribution of sputtered H20, we concluded that they cannot produce observed OH cloud. The E-ring contribution has been also studied in detail.In order to produce observed OH cloud we suggested that the E-ring might be the dominant source in inner Saturnian magnetosphere. We proposed a possible resupply mechanism which is needed to keep both E-ring and OH cloud in the present state: collisions between E-ring grains and remains of a disrupted satellite near Enceladus Lagrangian points. In this scenario a large amount of material, ranging from a few micrometers to hundred of meters, which is optically invisible at present, is likely to exist there. The fourth paper compares the magnetosheaths of the outer planets. A surprising result is that the hot proton component comprises about 40% of the total density, much larger than predicted by shock theory. Gas dynamic models of the boundaries show that the magnetospheres of Jupiter and Saturn are flattened at the poles. The last paper was published in GRL and is the first based of the model of neutrals developed as a main goal of this grant and which is now operational.This Monte Carlo collision code self- consistently determines the neutral distribution. from the rings and satellites until they are lost by ionization, by collisions with rings, moons, or Saturn, or by escape from Saturn. Our model is unique in that it includes the effects of plasma chemistry and both plasma-neutral and neutral neutral collisions to determine the dynamical evolution of the water group neutrals in Saturn's magnetosphere. The lifetimes of the neutrals against loss to photoionization, charge exchange, electron dissociation and electron impact dissociation are based on the model given by (Richardson et al. 1998) and vary with position in the magnetosphere. The dominant neutral dissociation channels H20->OH+H, H20-> O+H2, and OH->O+H2 are considered.

Richardson, John D.↗

NASA NTRS2005

GRAM Series of Atmospheric Models for Aeroentry and Aeroassist

The eight destinations in the Solar System with sufficient atmosphere for either aeroentry or aeroassist, including aerocapture, are: Venus, Earth, Mars, Jupiter, Saturn; Uranus. and Neptune, and Saturn's moon Titan. Engineering-level atmospheric models for four of these (Earth, Mars, Titan, and Neptune) have been developed for use in NASA's systems analysis studies of aerocapture applications in potential future missions. Work has recently commenced on development of a similar atmospheric model for Venus. This series of MSFC-sponsored models is identified as the Global Reference Atmosphere Model (GRAM) series. An important capability of all of the models in the GRAM series is their ability to simulate quasi-random perturbations for Monte Carlo analyses in developing guidance, navigation and control algorithms, and for thermal systems design. Example applications for Earth aeroentry and Mars aerocapture systems analysis studies are presented and illustrated. Current and planned updates to the Earth and Mars atmospheric models, in support of NASA's new exploration vision, are also presented.

Duvall, Aleta↗

NASA NTRS2008

Multiscale Modeling of Ablation and Pyrolysis in PICA-Like materials

During atmospheric entry of planetary probes, the thermal protection system (TIPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous fibrous TIPS materials may undergo oxidation leading to mass loss and wall recession called ablation. This work aims to improve the understanding of material/environment interactions through a study of the coupling between oxygen transport in the Knudsen regime, heterogeneous oxidation of carbon, and surface recession. A 3D Random Walk Monte Carlo simulation tool is used for this study. The fibrous architecture of a model material, consisting of high porosity random array of carbon fibers, is numerically represented on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession of the fibers is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The model is applied to Stardust mission reentry conditions and explains the unexpected behavior of the TIPS material that underwent mass loss in volume.

Lachaud, Jean↗

NASA NTRS1973

Reflection of a shock wave from a thermally accommodating wall - Molecular simulation.

Reflection of a plane shock wave from a wall has been simulated on a microscopic scale using a direct simulation Monte Carlo technique of the type developed by Bird. A monatomic gas model representing argon was used to describe the fluid medium and a simple one-parameter accommodation coefficient model was used to describe the gas-surface interaction. The influence of surface accommodation was studied parametrically by varying the accommodation coefficient from zero to one. Results are presented showing the temporal variations of flow field density, and mass, momentum, and energy fluxes to the wall during the shock wave reflection process. The energy flux was used to determine the wall temperature history. Comparisons with experiment are found to be satisfactory where data are available.

Deiwert, G. S.↗

NASA NTRS1974

Radiative transfer of visible radiation in turbid atmosphere

Methods are presented for solving radiative transfer problems; they include the doubling method and the closely related matrix method, iterative method, Chandrasekhar's method of discrete ordinates, and Monte Carlo method. To consider radiation transport through turbid atmosphere, an atmospheric model was developed characterizing aerosols by parameters. Intensity and polarization of radiation in turbid atmospheres is discussed, as well as lower atmospheric heating due to solar radiation absorption by aerosols.

Yamamoto, G.↗

NASA NTRS1978

The expected frequency of doublet craters

The problem of the expected number of doublets is investigated both by a probabilistic calculation analogous to that employed by Oberbeck and Aoyagi (1972) and by a Monte Carlo simulation procedure. On the basis of a comparison of the models and the Mars data for craters in the diameter range from 4 to 250 km it is found that at most a few percent of the craters may be nonrandomly located as doublets. It is pointed out that previous conclusions regarding a possible excess of doublets on both the moon and Mercury should also be reevaluated. Random clustering of three or more craters is not as rare as might have been expected, with at least 25% of all of the craters, for the Mars data, expected to participate in such clusters.

Woronow, A.↗

NASA NTRS1981

The stochastic evolution of asteroidal regoliths and the origin of brecciated and gas-rich meteorites

A model is constructed which views regolith evolution on asteroids as a stochastic process. Average values are shown to be poor descriptors of regolith depth. The utility of the average depth is not significantly increased by avoiding large craters or thick ejecta deposits, a procedure adopted in previous regolith studies. The statistical uncertainty associated with regolith depth severely limits the power of regolith models in predicting parent-body size for brecciated meteorites. A Monte Carlo algorithm was used to simulate the random walks and corresponding charged-particle irradiation histories of grains in regoliths. On rocky asteroids, only about 20 percent of the grains was exposed to solar cosmic ray ions. Results based on present-day conditions in the asteroid belt agree well with irradiation features observed in gas-rich meteorites. An origin during epochs of early solar system evolution is not required.

Housen, K. R.↗