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NASA NTRS2020

An Introduction to the NASA GMAO Coupled Atmosphere-Ocean System - GEOS-S2S Version 3

Recently NASA's Global Modeling and Assimilation Office (GMAO) has developed a new Subseasonal to Seasonal Prediction system Version 3 (GEOS-S2S-3). This upgrade replaces the GEOS-S2S-2 which is NASA's current contribution to the North American Multi-Model Experiment seasonal prediction project (Kirtman et al., 2014). The main improvements for our S2S-3 system include 1) a higher resolution MOM5 (Griffies et al., 2005) ocean model (now 0.25o x 0.25o x 50 layers), 2) an improved atmospheric/ocean interface layer (Akella and Suarez, 2018), and 3) assimilation of a long-track satellite salinity into the ocean model (Hackert et al, 2019). Atmospheric forcing is provided by the NASA MERRA-2 reanalysis (Gelaro et al., 2017). Initialization for the ocean relies on the GMAO ocean reanalysis system which assimilates all available in situ temperature and salinity, satellite sea surface salinity, and sea level using the Local Ensemble Transform Kalman Filter (LETKF) implementation of (Penny et al., 2013) on a 5 day assimilation cycle with 20 fixed ensemble members.In this presentation, we will authenticate our new S2S-3 ocean reanalysis using standard GODAE validation metrics. For example, we will compare gridded fields of mean and standard deviation of the ocean reanalysis versus observed fields. We will show correlation/RMS of model versus observations and temperature and salinity mean profiles for the various basins and latitude bands. Basin-scale volume transports, such as the Atlantic Meridional Overturning Circulation and the Indonesian Throughflow will be validated. Equatorial ocean waves will be compared by decomposing sea level into Kelvin and Rossby components. For each of these metrics, we plan to validate the results and then compare our new S2S-3 against the current production version, S2S-2. Finally, we will compare 9-month seasonal forecasts initialized from these two systems for the tropical Pacific NINO3.4 region over the period 1981-present.

Molod, Andrea↗

NASA NTRS1999

High-Resolution Mapping of Lunar Crustal Magnetic Fields: Correlations with Albedo Markings of the Reiner Gamma Class

During the last eight months of the Lunar Prospector mission (December 1999-July 1999), the spacecraft was placed in a relatively low-altitude (15-30-km perapsis), near-polar orbit that allowed high-resolution mapping of crustal magnetic fields. We report here initial studies of the correlation of locally strong magnetic anomalies with unusual, swirl-like albedo markings of the Reiner Gamma class. Based on this correlation, which is known from earlier studies of Apollo subsatellite magnetometer data, it has been proposed that the swirls represent regions whose higher albedos have been preserved via deflection of the solar-wind ion bombardment by strong crustal fields. This model in turn depends on the hypothesis that solar-wind implanted H is at least one component of the process that optically matures exposed silicate surfaces in the inner solar system . Specifically, it is hypothesized that implanted H acts as an effective reducing agent to enhance the rate of production of nanophase metallic Fe particles from preexisting silicates during micrometeoroid impacts. According to the model, the curvilinear shapes of these albedo markings are caused, at least in part, by the geometry of ion deflections in a magnetic field. The improved resolution and coverage of the Prospector data allow more detailed mapping of the fields, especially on the lunar farside. This permits a more quantitative test of whether all albedo markings of this class are associated with strong local magnetic fields.Only if the latter condition is met can the solar-wind deflection hypothesis he valid. The basic procedure for mapping crustal magnetic fields using Lunar Prospector magnetometer data follows that developed for analysis of Apollo subsatellite magnetometer data. The specific mapping steps are (1) selection of mission time intervals suitable for mapping crustal fields; these are limited essentially either to times when the Moon is in a lobe of the geomagnetic tail or to times when the Moon is in the solar wind but the spacecraft is in the lunar wake; the data are transformed to a radial, east, and north coordinate system with measurements given as a function of spacecraft latitude, longitude, and altitude; (2) visual editing of individual orbit segments selected for minimal external field disturbances; (3) minimization of remaining low-frequency external fields for individual orbit data segments by quadratic detrending; and (4) two-dimensional filtering of individual orbit segments to produce a vector field map along the slightly curved surface defined by the spacecraft altitude; maps of the three field components (radial, east, and north), the field magnitude, and the spacecraft altitude are constructed. For data obtained at low to middle latitudes, the horizontal resolution of the field maps is limited by the orbit-track separation (about 30 km at the equator). Maps of the field magnitude have been constructed within limited selenographic regions based mainly on data acquired in March, April, and May of 1999. This was a time period when the orbit plane was nearly aligned with the Sun-Moon line so that field mapping was possible at times when the Moon was in the solar wind as well as when the Moon was in the geomagnetic tail. Most of the coverage is across the lunar farside. However, a shows an example of a field map produced from solar-wind wake data for a region including Reiner Gamm on western Oceanus Procellarum (location: 58.5W, 7.5N). The contour interval is 3 nT and the mean spacecraft altitude is 18 km to within the accuracy allowed by the resolution of the map (30 km or about 1 deg.); strong magnetic anomalies correlate closely with swirl locations. Individual orbit profiles (whose resolution along the orbit track is comparable to the spacecraft altitude of 18 km) also demonstrate a good correlation of field magnitude with surface albedo. In order to investigate the correlation of magnetic fields with the location of swirl features, we have reexamined available lunar imagery (Lunar Orbiter, Apollo, and Clementine) to identify and map swirl locations within regions where swirls have previously been mapped. In these images, swirls were distinguished from other high-albedo features such as crater rays by their curvilinear shapes and increased visibility in forward-scattered light. Digital maps of swirls identified by all available imagery were then superposed on maps of the field magnitude at the spacecraft altitude. Based upon analysis of these composite magnetic/geologic maps, we draw the preliminary conclusion that swirl features are associated with magnetic anomalies revealed by Lunar Prospector. Detailed maps of these swirl features are currently being constructed for the magnetically strong regions antipodal to the Imbrium, Serenitatis, and Crisium Basins. Additional information contained in the original,

Hood, L. L.↗

NASA NTRS1990

Application of CFD to sonic boom near and mid flow-field prediction

A 3-D parabolized Navier-Stokes (PNS) code was used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.

Cheung, Samson H.↗

NASA NTRS2015

Atmospheric Research 2014 Technical Highlights

Atmospheric research in the Earth Sciences Division (610) consists of research and technology development programs dedicated to advancing knowledge and understanding of the atmosphere and its interaction with the climate of Earth. The Division's goals are to improve understanding of the dynamics and physical properties of precipitation, clouds, and aerosols; atmospheric chemistry, including the role of natural and anthropogenic trace species on the ozone balance in the stratosphere and the troposphere; and radiative properties of Earth's atmosphere and the influence of solar variability on the Earth's climate. Major research activities are carried out in the Mesoscale Atmospheric Processes Laboratory, the Climate and Radiation Laboratory, the Atmospheric Chemistry and Dynamics Laboratory, and the Wallops Field Support Office. The overall scope of the research covers an end-to-end process, starting with the identification of scientific problems, leading to observation requirements for remote-sensing platforms, technology and retrieval algorithm development; followed by flight projects and satellite missions; and eventually, resulting in data processing, analyses of measurements, and dissemination from flight projects and missions. Instrument scientists conceive, design, develop, and implement ultraviolet, infrared, optical, radar, laser, and lidar technology to remotely sense the atmosphere. Members of the various Laboratories conduct field measurements for satellite sensor calibration and data validation, and carry out numerous modeling activities. These modeling activities include climate model simulations, modeling the chemistry and transport of trace species on regional-to-global scales, cloud resolving models, and developing the next-generation Earth system models. Satellite missions, field campaigns, peer-reviewed publications, and successful proposals are essential at every stage of the research process to meeting our goals and maintaining leadership of the Earth Sciences Division in atmospheric science research. Figure 1.1 shows the 20-year record of peer-reviewed publications and proposals among the various Laboratories. This data shows that the scientific work being conducted in the Laboratories is competitive with the work being done elsewhere in universities and other government agencies. The office of Deputy Director for Atmospheric Research will strive to maintain this record by rigorously monitoring and promoting quality while emphasizing coordination and integration among atmospheric disciplines. Also, an appropriate balance will be maintained between the scientists' responsibility for large collaborative projects and missions and their need to carry out active science research as a principal investigator. This balance allows members of the Laboratories to improve their scientific credentials, and develop leadership potentials. Interdisciplinary research is carried out in collaboration with other laboratories and research groups within the Earth Sciences Division, across the Sciences and Exploration Directorate, and with partners in universities and other government agencies. Members of the Laboratories interact with the general public to support a wide range of interests in the atmospheric sciences. Among other activities, the Laboratories raise the public's awareness of atmospheric science by presenting public lectures and demonstrations, by making scientific data available to wide audiences, by teaching, and by mentoring students and teachers. The Atmosphere Laboratories make substantial efforts to attract and recruit new scientists to the various areas of atmospheric research. We strongly encourage the establishment of partnerships with Federal and state agencies that have operational responsibilities to promote the societal application of our science products. This report describes our role in NASA's mission, provides highlights of our research scope and activities, and summarizes our scientists' major accomplishments during calendar year 2014. The composition of the organization is shown in Figure 1.2 for each code. This report is published in a printed version with an electronic version on our atmospheres Web site, http://atmospheres.gsfc.nasa.gov/.

Technical↗

NASA NTRS2017

Atmospheric Research 2016 Technical Highlights

Atmospheric↗

DOE OSTI2022

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak à configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets—giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models—GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP—both in terms of profile shape and absolute magnitude—while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Diii-D Research Advancing The Physics Basis For Optimizing The Tokamak Approach To Fusion Energy

DIII-D physics research addresses critical challenges for operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter-Ip steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs. ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high-Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. With this physics understanding and suite of actuators, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q=10 in ITER at 9 MA was coupled to a detached divertor, and a near Super H-mode optimized-pedestal scenario with co-Ip beam injection, was coupled to a radiative divertor. The Hybrid core scenario was achieved directly, without the need for internal flux pumping, using off-axis current drive actuators, and a controller to avoid mode locking and disruptions in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.

Fenstermacher, M.↗

DOE OSTI2026

Schiff Moment of 129 Xe and 199 Hg [Slides]

Using Chicoma in 2025, we advanced DFT-based calculations needed to connect fundamental T violating interactions to measurable Schiff moments in heavy nuclei. We implemented DFT for polarized odd nuclear systems, a first step toward treating the time-reversal-breaking mean fields required for Schiff moment calculations. As a validation test, we computed polarizabilities using a perturbation with the dipole operator (see figure to the right) for the odd systems shown in Table 1; while no odd-system effect is expected for polarizabilities, this capability is essential for Schiff moments. Initial mean-field solutions for 129 Xe Schiff moment calculations were also generated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

DIII-D research advancing the physics basis for optimizing the tokamak approach to fusion energy

DIII-D physics research addresses critical challenges for the operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter-I p steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high-Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. For the non-nuclear phase of ITER, two actuators are identified to lower the L–H threshold power in hydrogen plasmas. With this physics understanding and suite of capabilities, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q = 10 in ITER at ~8 MA was coupled to a detached divertor, and a near super H-mode optimized-pedestal scenario with co-I p beam injection was coupled to a radiative divertor. The hybrid core scenario was achieved directly, without the need for anomalous current diffusion, using off-axis current drive actuators. Also, a controller to assess proximity to stability limits and regulate β N in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally, innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1996

Theoretical Basis for Finite Difference Extrapolation of Sonic Boom Signatures

Calculation of sonic boom signatures for aircraft has traditionally followed the methods of Whitham' and Walkden. The wave disturbance generated by the vehicle is obtained by area rule linearized supersonic flow methods, which yield a locally axisymmetric asymptotic solution. This solution is acoustic in nature, i.e., first order in disturbance quantities, and corresponds to ray acoustics. Cumulative nonlinear distortion of the signature is incorporated by using this solution to adjust propagation speed to first order, thus yielding a solution second order in disturbance quantities. The effects of atmospheric gradients are treated by Blokhintzov's method of geometrical acoustics. Both nonlinear signature evolution and ray tracing are applied as if the pressure field very close to the vehicle were actually that given by the source term (the 'F-function') of the asymptotic linearized flow solution. The viewpoint is thus that the flow solution exists at a small radius near the vehicle, and may be treated as an input to an extrapolation procedure consisting of ray tracing and nonlinear aging. The F-function is often regarded as a representation of a near-field pressure signature, and it is common for computational implementations to treat it interchangeably with the pressure signature. There is a 'matching radius' between the source function and the subsequent propagation extrapolation. This viewpoint has been supported by wind tunnel tests of simple models, and very typically yields correct results for actual flight vehicles. The assumption that the F-function and near-field signature are interchangeable is generally not correct. The flowfield of a vehicle which is not axisymmetric contains crossflow components which are very significant at small radii and less so at larger distances. From an acoustical viewpoint, the crossflow is equivalent to source diffraction portions of the wave field. Use of the F-function as a near field signature effectively assumes that the diminution of the crossflow/diffraction component may be applied all at once at the matching radius noted above. This approximation, though not rigorously validated, is responsible for the usual correct far-field results. On the other hand, if an actual near-field signature (either from wind tunnel or CFD data) is used at a starting point rather than one based on th effective source distribution, the predicted far-field signature is generally wrong.

Plotkin, Kenneth J.↗

NASA NTRS2016

Modeling a Miniaturized Scanning Electron Microscope Focusing Column - Lessons Learned in Electron Optics Simulation

This presentation discusses work done to assess the design of a focusing column in a miniaturized Scanning Electron Microscope (SEM) developed at the NASA Marshall Space Flight Center (MSFC) for use in-situ on the Moon-in particular for mineralogical analysis. The MSFC beam column design uses purely electrostatic fields for focusing, because of the severe constraints on mass and electrical power consumption imposed by the goals of lunar exploration and of spaceflight in general. The resolution of an SEM ultimately depends on the size of the focused spot of the scanning beam probe, for which the stated goal here is a diameter of 10 nanometers. Optical aberrations are the main challenge to this performance goal, because they blur the ideal geometrical optical image of the electron source, effectively widening the ideal spot size of the beam probe. In the present work the optical aberrations of the mini SEM focusing column were assessed using direct tracing of non-paraxial rays, as opposed to mathematical estimates of aberrations based on paraxial ray-traces. The geometrical ray-tracing employed here is completely analogous to ray-tracing as conventionally understood in the realm of photon optics, with the major difference being that in electron optics the lens is simply a smoothly varying electric field in vacuum, formed by precisely machined electrodes. Ray-tracing in this context, therefore, relies upon a model of the electrostatic field inside the focusing column to provide the mathematical description of the "lens" being traced. This work relied fundamentally on the boundary element method (BEM) for this electric field model. In carrying out this research the authors discovered that higher accuracy in the field model was essential if aberrations were to be reliably assessed using direct ray-tracing. This led to some work in testing alternative techniques for modeling the electrostatic field. Ultimately, the necessary accuracy was attained using a BEM/Fourier series hybrid approach. The presentation will give background remarks about the MSFC mini Lunar SEM concept and electron optics modeling, followed by a description of the alternate field modeling techniques that were tried, along with their incorporation into a ray-trace simulation. Next, the validation of this simulation against commercially available software will be discussed using an example lens as a test case. Then, the efficacy of aberration assessment using direct ray-tracing will be demonstrated, using this same validation case. The discussion will include practical error checks of the field solution. Finally, the ray-trace assessment of the MSFC mini Lunar SEM concept will be shown and discussed. The authors believe this presentation will be of general interest to practitioners of modeling and simulation, as well as those with a general optics background. Because electron optics and photon optics share many basic concepts (e.g., lenses, images, aberrations, etc.), the appeal of this presentation need not be restricted to just those interested in charged particle optics.

Modeling Miniaturizing Scanning↗

DOE OSTI2021

Stochastic Inflation at NNLO

Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Wide-blocky veins explained by dependency of crystal growth rate on fracture surface type: Insights from phase-field modeling

Vein microstructures contain a wealth of information on coupled chemical and mechanical processes of fracturing, fluid transport, and crystal growth. Numerical simulations have been used for exploring the factors controlling the development of vein microstructures; however, they have not been quantitatively validated against natural veins. Here we combined phase-field modeling with microtextural analysis of previously unexplained wide-blocky calcite veins in natural limestone and of the fresh fracture surface in this limestone. Results show that the wide-blocky vein textures can only be reproduced if ~10%–20% of crystals grow faster than the rest. This fraction corresponds to the amount of transgranularly broken grains that were observed on the experimental fracture surfaces, which are dominantly intergranular. We hypothesize that transgranular fractures allow faster growth of vein minerals due to the lack of clay coatings and other nucleation discontinuities that are common along intergranular cracks. Our simulation results show remarkable similarity to the natural veins and reproduce the nonlinear relationship between vein crystal width and vein aperture. This allows accurate simulations of crystal growth processes and related permeability evolution in fractured rocks.

Geology↗

NASA NTRS1991

Radiative widths and splitting of cyclotron lines in superstrong magnetic fields

The radiative line widths of the Landau levels in a superstrong magnetic field are calculated and simple analytic expressions and fits are given for these which are valid over a wide range of the principal quantum number and the magnetic field strength. If QED corrections are not taken into account, all levels but the first are doubly degenerate, corresponding to the two possible spin projections. However, the interaction with the QED vacuum removes this degeneracy, leading to an energy splitting of each level which exceeds the radiative linewidth for low Landau levels if the magnetic field is not too large (B is less than approximately 10 exp 13 G). Estimations are presented of the splitting in various limits as a function of field strength and Landau number. The possibility of observing this splitting in accreting X-ray pulsars and in gamma-ray bursters is discussed.

Pavlov, G. G.↗

DOE OSTI2026

Variational neural network approach to QFT in the field basis

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.

Klein-Gordon model↗

NASA NTRS1994

On current sheet approximations in models of eruptive flares

We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.

Bungey, T. N.↗

NASA NTRS2009

MODIS Tree Cover Validation for the Circumpolar Taiga-Tundra Transition Zone

A validation of the 2005 500m MODIS vegetation continuous fields (VCF) tree cover product in the circumpolar taiga-tundra ecotone was performed using high resolution Quickbird imagery. Assessing the VCF's performance near the northern limits of the boreal forest can help quantify the accuracy of the product within this vegetation transition area. The circumpolar region was divided into longitudinal zones and validation sites were selected in areas of varying tree cover where Quickbird imagery is available in Google Earth. Each site was linked to the corresponding VCF pixel and overlaid with a regular dot grid within the VCF pixel's boundary to estimate percent tree crown cover in the area. Percent tree crown cover was estimated using Quickbird imagery for 396 sites throughout the circumpolar region and related to the VCF's estimates of canopy cover for 2000-2005. Regression results of VCF inter-annual comparisons (2000-2005) and VCF-Quickbird image-interpreted estimates indicate that: (1) Pixel-level, inter-annual comparisons of VCF estimates of percent canopy cover were linearly related (mean R(sup 2) = 0.77) and exhibited an average root mean square error (RMSE) of 10.1 % and an average root mean square difference (RMSD) of 7.3%. (2) A comparison of image-interpreted percent tree crown cover estimates based on dot counts on Quickbird color images by two different interpreters were more variable (R(sup 2) = 0.73, RMSE = 14.8%, RMSD = 18.7%) than VCF inter-annual comparisons. (3) Across the circumpolar boreal region, 2005 VCF-Quickbird comparisons were linearly related, with an R(sup 2) = 0.57, a RMSE = 13.4% and a RMSD = 21.3%, with a tendency to over-estimate areas of low percent tree cover and anomalous VCF results in Scandinavia. The relationship of the VCF estimates and ground reference indicate to potential users that the VCF's tree cover values for individual pixels, particularly those below 20% tree cover, may not be precise enough to monitor 500m pixel-level tree cover in the taiga-tundra transition zone.

Montesano, P. M.↗

NASA NTRS1985

Two-photon collisional redistribution of radiation

Collisional redistribution in the presence of two weakly exciting laser fields is studied, including the effects due to degeneracy of the radiator states. A general expression for the total redistributed intensity is derived valid for arbitrary detunings and polarizations of the exciting laser fields. In particular, this expression contains all single-collision and sequential-collision contributions, which are equally important under certain circumstances. The similarities and differences between the redistributed intensity as calculated in this paper and the collisionally aided radiative excitation cross sections studied by Yeh and Berman (1979) and Light and Szoke (1978) are pointed out.

Alber, G.↗