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NASA NTRS2019

Approach for Propagating Radiometric Data Uncertainties Through NASA Ocean Color Algorithms

Spectroradiometric satellite observations of the ocean are commonly referred to as “ocean color” remote sensing. NASA has continuously collected, processed, and distributed ocean color datasets since the launch of the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) in 1997. While numerous ocean color algorithms have been developed in the past two decades that derive geophysical data products from sensor-observed radiometry, few papers have clearly demonstrated how to estimate measurement uncertainty in derived data products. As the uptake of ocean color data products continues to grow with the launch of new and advanced sensors, it is critical that pixel-by-pixel data product uncertainties are estimated during routine data processing. Knowledge of uncertainties can be used when studying long-term climate records, or to assist in the development and performance appraisal of bio-optical algorithms. In this method paper we provide a comprehensive overview of how to formulate first-order first-moment (FOFM) calculus for propagating radiometric uncertainties through a selection of bio-optical models. We demonstrate FOFM uncertainty formulations for the following NASA ocean color data products: chlorophyll-a pigment concentration (Chl), the diffuse attenuation coefficient at 490 nm (K(sub d,490)), particulate organic carbon (POC), normalized fluorescent line height (nflh), and inherent optical properties (IOPs). Using a quality-controlled in situ hyperspectral remote sensing reflectance (R(sub rs,i)) dataset, we show how computationally inexpensive, yet algebraically complex, FOFM calculations may be evaluated for correctness using the more computationally expensive Monte Carlo approach. We compare bio-optical product uncertainties derived using our test R(sub rs) dataset assuming spectrally-flat, uncorrelated relative uncertainties of 1, 5, and 10%. We also consider spectrally dependent, uncorrelated relative uncertainties in R(sub rs). The importance of considering spectral covariances in R(sub rs), where practicable, in the FOFM methodology is highlighted with an example SeaWiFS image. We also present a brief case study of two POC algorithms to illustrate how FOFM formulations may be used to construct measurement uncertainty budgets for ecologically-relevant data products. Such knowledge, even if rudimentary, may provide useful information to end-users when selecting data products or when developing their own algorithms.

Bio-optics↗
NASA NTRS1994

Diffusion model for lightning radiative transfer

A one-speed Boltzmann transport theory, with diffusion approximations, is applied to study the radiative transfer properties of lightning in optically thick thunderclouds. Near-infrared (lambda = 0.7774 micrometers) photons associated with a prominent oxygen emission triplet in the lightning spectrum are considered. Transient and spatially complex lightning radiation sources are placed inside a rectangular parallelepiped thundercloud geometry and the effects of multiple scattering are studied. The cloud is assumed to be composed of a homogeneous collection of identical spherical water droplets, each droplet a nearly conservative, anisotropic scatterer. Conceptually, we treat the thundercloud like a nuclear reactor, with photons replaced by neutrons, and utilize standard one-speed neutron diffusion techniques common in nuclear reactor analyses. Valid analytic results for the intensity distribution (expanded in spherical harmonics) are obtained for regions sufficiently far from sources. Model estimates of the arrival-time delay and pulse width broadening of lightning signals radiated from within the cloud are determined and the results are in good agreement with both experimental data and previous Monte Carlo estimates. Additional model studies of this kind will be used to study the general information content of cloud top lightning radiation signatures.

Koshak, William J.↗
NASA NTRS1999

Cloud Thickness from Diffusion of Lidar Pulses in Clouds

Measurements of the distribution of reflected light from a laser beam incident on an aqueous suspension of particles or "cloud" with known thickness and particle size distribution are reported. The distribution is referred to as the "cloud radiative Green's function", G. In the diffusion domain, G is sensitive to cloud thickness, allowing that important quantity to be retrieved. The goal of the laboratory simulation is to provide preliminary estimates of sensitivity of G to cloud thickness,for use in the optimal design of an offbeam Lidar instrument for remote sensing of cloud thickness (THOR, Thickness from Offbeam Returns). These clouds of polystyrene microspheres suspended in water are analogous to real clouds of water droplets suspended in air. The microsphere size distribution is roughly lognormal, from 0.5 microns to 25 microns, similar to real clouds. Density of suspended spheres is adjusted so mean-free-path of visible photons is about 10 cm, approximately 1000 times smaller than in real clouds. The light source is a ND:YAG laser at 530 nm. Detectors are flux and photon-counting Photomultiplier Tube (PMTS), with a glass probe for precise positioning. A Labview 5 VI controls positioning, and data acquisition, via an NI Motion Control board connected to a stepper motor driving an Edmund linear slider, and a 16-channel 16-bit NI-DAQ board. The stepper motor is accurate to 10 microns, and step size is selectable from the VI software. Far from the incident beam, the rate of exponential increase as the direction of the incident beam is approached scales as expected from diffusion theory, linearly with the cloud thickness, and inversely as the square root of the reduced optical thickness, and is independent of particle size. Near the beam the signal begins to increase faster than exponential, due to single and low-order scattering near the backward direction, and here the distribution depends on particle size. Results are being used to verify 3D Monte Carlo radiative transfer simulations, used to estimate signal-to-noise ratios for remotely sensed off beam returns, for both homogeneous and inhomogeneous clouds. Signal-to-noise estimates show that unfiltered observations are straight forward at night, while narrow band pass filters are being studied for day.

Cahalan, Robert F.↗
NASA NTRS1974

Model of an anisotropy solar proton event

The anisotropy of the particle distribution and its variation with time at 1 AU early in a solar cosmic-ray event can provide information on the pitch-angle scattering of the particles in the interplanetary medium. One proton event (7.6-55 MeV) is described in which the anisotropy remained large well into the decay of the omnidirectional intensity. A Monte Carlo technique which gives the pitch-angle distribution is employed to investigate two models put forward to explain the sustained anisotropy. It is shown that the observed event is consistent with a model in which the injection of particles at the sun reaches a peak 1.5 hours after flare maximum before decaying with an e-folding time of 7 hours. The uniform diffusion coefficient in this model corresponds to a classical mean free path of 1.6 AU.

Palmer, I. D.↗
NASA NTRS1992

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models

Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

Hsu, Andrew T.↗
NASA NTRS2004

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The PI (Cranmer) and Co-I (A. van Ballegooijen) made substantial progress toward the goal of producing a unified model of the basic physical processes responsible for solar wind acceleration. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a 1D model of plasma heating and acceleration. The accomplishments in Year 2 are divided into these two categories: 1a. Focused Study of Kinetic Magnetohydrodynamic (MHD) Turbulence. lb. Focused Study of Non - WKB Alfven Wave Rejection. and 2. The Unified Model Code. We have continued the development of the computational model of a time-study open flux tube in the extended corona. The proton-electron Monte Carlo model is being tested, and collisionless wave-particle interactions are being included. In order to better understand how to easily incorporate various kinds of wave-particle processes into the code, the PI performed a detailed study of the so-called "Ito Calculus", i.e., the mathematical theory of how to update the positions of particles in a probabilistic manner when their motions are governed by diffusion in velocity space.

Cranmer, Steven R.↗
NASA NTRS2005

Prediction of the Aerothermodynamic Environment of the Huygens Probe

An investigation of the aerothermodynamic environment of the Huygens entry probe has been conducted. A Monte Carlo simulation of the trajectory of the probe during entry into Titan's atmosphere was performed to identify a worst-case heating rate trajectory. Flowfield and radiation transport computations were performed at points along this trajectory to obtain convective and radiative heat-transfer distributions on the probe's heat shield. This investigation identified important physical and numerical factors, including atmospheric CH4 concentration, transition to turbulence, numerical diffusion modeling, and radiation modeling, which strongly influenced the aerothermodynamic environment.

Hollis, Brian R.↗
NASA NTRS1990

DSMC calculations for the double ellipse

The direct simulation Monte Carlo (DSMC) method involves the simultaneous computation of the trajectories of thousands of simulated molecules in simulated physical space. Rarefied flow about the double ellipse for test case 6.4.1 has been calculated with the DSMC method of Bird. The gas is assumed to be nonreacting nitrogen flowing at a 30 degree incidence with respect to the body axis, and for the surface boundary conditions, the wall is assumed to be diffuse with full thermal accommodation and at a constant wall temperature of 620 K. A parametric study is presented that considers the effect of variations of computational domain, gas model, cell size, and freestream density on surface quantities.

Moss, James N.↗
NASA NTRS1992

Theoretical studies of the outer envelopes of young stellar objects

With the Monte Carlo code developed by Whitney and Hartmann, a series of models was computed of scattering in disks around young stellar objects. The code calculates scattering by dust, including polarization, in arbitrary geometries. By computing model images, it was found that disk, by themselves, around young stellar objects would be very difficult to detect with present day imaging techniques. In comparing these images to observations of young stellar objects which show diffuse structure, little resemblance was found. A flared disk system will only give high polarization when viewed edge-on, and the position angle is always oriented perpendicular to the disk plane. This suggests that an envelope, perhaps the remnant infalling envelope, must be present to scatter more stellar light than a disk can, and obscure the star at many inclinations. A grid was computed of models of scattering in a disk+envelope system. Evidence is presented that the wind of the pre-main sequence object FU Orionis arises from the surface of the luminous prostellar accretion disk. A disk wind model calculated assuming radiative equilibrium explains the differential behavior of the observed asymmetrical absorption line profiles. The model predicts that strong lines should be asymmetric and blueshifted, while weak lines should be symmetric and doubled peaked due to disk rotation, in agreement with observations.

Hartmann, Lee↗
NASA NTRS1994

The effect of wave-particle interactions on the polar winds O(+)

The escape of the polar wind plasma is an important element in the ionosphere-magnetosphere coupling. Both theory and observations indicate that the wave-particle interactions (WPI) play a significant role in the dynamics of ion outflow along open geomagnetic field lines. A Monte Carlo simulation was developed in order to include the effect of the WPI in addition to the factors that are traditionally included in the 'classical' polar wind (i.e. gravity, electrostatic field, and divergence of geomagnetic field lines). The ion distribution function (f(sub j)), as well as the profiles of its moments (density, drift velocity, temperature, etc.) were found for different levels of WPI, that is, for different values of the normalized diffusion rate in the velocity space (D(tilde) (sub j perpendicular). Although the model included O(=), H(+) and eletrons, we presented only the results related to the O(+) ion. We found that (1) both the density and drift velocity of O(+) increased with the WPI strength, and consequently, the O(+) escape flux was enhanced by a factor of up to 10(exp 5), (2) The O(+) ions could be energized up to a few electron volts; (3) for moderate and high levels of WPI D(tilde) (sub perpendicular) (O(+) greater than (tilde) 1, the distribution function f(O(+)) displayed very pronounced conic features at altitudes around 3 R(sub e). Finally, the interplay between the downward body force, the upward mirror force, and the perpendicular heating resulted in the formation of the 'pressure cooker' effect. This phenomena explained some interesting features of our solution, such as, the peak in the O(=) temperature, and the formation of 'ears' and conics for f(O(+)) around 2.5 R(sub e).

Barakat, A. R.↗
NASA NTRS1998

Direct Acceleration of Pickup Ions at The Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

We have modeled the injection and acceleration of pickup ions at the solar wind termination shock and investigated the parameters needed to produce the observed Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo technique was employed, which in effect solves the Boltzmann equation and is not restricted to near-isotropic particle distribution functions. This technique models the injection of thermal and pickup ions, the acceleration of these ions, and the determination of the shock structure under the influence of the accelerated ions. The essential effects of injection are treated in a mostly self-consistent manner, including effects from shock obliquity, cross- field diffusion, and pitch-angle scattering. Using recent determinations of pickup ion densities, we are able to match the absolute flux of hydrogen in the ACRs by assuming that pickup ion scattering mean free paths, at the termination shock, are much less than an AU and that modestly strong cross-field diffusion occurs. Simultaneously, we match the flux ratios He(+)/H(+) or O(+)/H(+) to within a factor approx. 5. If the conditions of strong scattering apply, no pre-termination-shock injection phase is required and the injection and acceleration of pickup ions at the termination shock is totally analogous to the injection and acceleration of ions at highly oblique interplanetary shocks recently observed by the Ulysses spacecraft. The fact that ACR fluxes can be modeled with standard shock assumptions suggests that the much-discussed "injection problem" for highly oblique shocks stems from incomplete (either mathematical or computer) modeling of these shocks rather than from any actual difficulty shocks may have in injecting and accelerating thermal or quasi-thermal particles.

Ellison, Donald C.↗
NASA NTRS1991

Gamma ray constraints on the Galactic supernova rate

We perform Monte Carlo simulations of the expected gamma ray signatures of Galactic supernovae of all types to estimate the significance of the lack of a gamma ray signal due to supernovae occurring during the last millenium. Using recent estimates of the nuclear yields, we determine mean Galactic supernova rates consistent with the historic supernova record and the gamma ray limits. Another objective of these calculations of Galactic supernova histories is their application to surveys of diffuse Galactic gamma ray line emission.

Hartmann, D.↗
NASA NTRS1998

EUPDF: Eulerian Monte Carlo Probability Density Function Solver for Applications With Parallel Computing, Unstructured Grids, and Sprays

The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic-diffusion flames and spray flames. The EUPDF source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, M. S.↗
NASA NTRS2020

A Second Look at 12 Candidate Dual AGNs Using BAYMAX

We present an analysis of 12 optically selected dual active galactic nucleus (AGN) candidates at z < 0.34. Each candidate was originally identified via double-peaked [O III] λ5007 emission lines and received follow-up Chandra and Hubble Space Telescope (HST) observations. Because the X-ray data are low-count (<100 counts) with small separations (<1''), a robust analysis is necessary for classifying each source. Pairing long-slit [O III] observations with existing Chandra observations, we re-analyze the X-ray observations with Bayesian AnalYsis of AGNs in X-rays to determine whether the X-ray emission from each system is more likely a single or dual point source. We find that 4 of the 12 sources are likely dual X-ray point-source systems. We examine each point source's spectra via a Monte Carlo method that probabilistically identifies the likely origin of each photon. When doing so, we find that (i) the secondary X-ray point sources in two of the systems have L(X)< 10(exp 40) erg/s, such that we cannot rule out a non-AGN origin, (ii) one source has a secondary with L(X)> 10(exp 40) erg/s but a spectrum that is too soft to definitively preclude being X-ray emitting diffuse gas that was photoionized by the primary AGN, and (iii) one system (SDSS J1126+2944) is a dual AGN. Additionally, using complementary HST observations, we analyze a subsample of systems that are visually identified as merging. Our results suggest that dual AGNs may preferentially reside in mergers with small separations, consistent with both simulations and observations.

Adi Foord↗
NASA NTRS2010

Monte Carlo Modeling of Sodium in Mercury's Exosphere During the First Two MESSENGER Flybys

We present a Monte Carlo model of the distribution of neutral sodium in Mercury's exosphere and tail using data from the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft during the first two flybys of the planet in January and September 2008. We show that the dominant source mechanism for ejecting sodium from the surface is photon-stimulated desorption (PSD) and that the desorption rate is limited by the diffusion rate of sodium from the interior of grains in the regolith to the topmost few monolayers where PSD is effective. In the absence of ion precipitation, we find that the sodium source rate is limited to approximately 10(exp 6) - 10(exp 7) per square centimeter per second, depending on the sticking efficiency of exospheric sodium that returns to the surface. The diffusion rate must be at least a factor of 5 higher in regions of ion precipitation to explain the MASCS observations during the second MESSENGER f1yby. We estimate that impact vaporization of micrometeoroids may provide up to 15% of the total sodium source rate in the regions observed. Although sputtering by precipitating ions was found not to be a significant source of sodium during the MESSENGER flybys, ion precipitation is responsible for increasing the source rate at high latitudes through ion-enhanced diffusion.

Burger, Matthew H.↗
NASA NTRS1992

Gamma ray constraints on the galactic supernova rate

Monte Carlo simulations of the expected gamma-ray signatures of galactic supernovae of all types are performed in order to estimate the significance of the lack of a gamma-ray signal due to supernovae occurring during the last millenium. Using recent estimates of nuclear yields, we determine galactic supernova rates consistent with the historic supernova record and the gamma-ray limits. Another objective of these calculations of galactic supernova histories is their application to surveys of diffuse galactic gamma-ray line emission.

Hartmann, D.↗
NASA NTRS1985

Determination of rarefied-flow aerodynamics of the Shuttle orbiter from flight measurements on STS-6 and STS-7

This report presents the flight data results from the High Resolution Accelerometer Package (HiRAP) experimment on the sixth and seventh Shuttle missions (i.e. STS-6 and STS-7). The data have been reduced to produce aerodynamic force coefficients, principally L/D in the rarefied flow regime. Also, a technique is used to extract approximate body-axis aerodynamic coefficients from the flight data. Comparisons of the rarefied transition flow aerodynamic behavior between the two sets of flight data indicate differences, primarily in the free-molecule flow coefficients; i.e. STS-7 shows a free-molecule flow behavior which correlates with diffuse surface reflection conditions, while STS-6 does not. The data have also been used to estimate the density profiles in the atmosphere. The atmospheric density is generated from 60 to 160 km from each flight. The density profiles produced have a primary wave structure and differences are observed between the two sets of flight data. A new rarefied transitional flow aerodynamic bridging formula has been generated from the flight data. Comparisons with the flight bridging formula and existing Monte Carlo and wind-tunnel data are made.

Blanchard, R. C.↗
NASA NTRS1976

Wind enhanced planetary escape: Collisional modifications

The problem of thermal escape is considered in which both the effects of thermospheric winds at the exobase and collisions below the exobase are included in a Monte Carlo calculation. The collisions are included by means of a collisional relaxation layer of a background gas which models the transition region between the exosphere and the thermosphere. The wind effects are considered in the limiting cases of vertical and horizontal flows. Two species are considered: terrestrial hydrogen and terrestrial helium. In the cases of terrestrial hydrogen the escape fluxes were found to be strongly filtered or throttled by collisions at high exospheric temperatures. The model is applied to molecular hydrogen diffusing through a methane relaxation layer under conditions possible on Titan. The results are similar to the case of terrestrial hydrogen with wind enhanced escape being strongly suppressed by collisions. It is concluded that wind enhanced escape is not an important process on Titan.

Curtis, S. A.↗