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NASA NTRS2017

Path Profiles of Cn2 Derived from Radiometer Temperature Measurements and Geometrical Ray Tracing

Atmospheric turbulence has significant impairments on the operation of Free-Space Optical (FSO) communication systems, in particular temporal and spatial intensity fluctuations at the receiving aperture resulting in power surges and fades, changes in angle of arrival, spatial coherence degradation, etc. The refractive index structure parameter Cn2 is a statistical measure of the strength of turbulence in the atmosphere and is highly dependent upon vertical height. Therefore to understand atmospheric turbulence effects on vertical FSO communication links such as space-to-ground links, it is necessary to specify Cn2 profiles along the atmospheric propagation path. To avoid the limitations on the applicability of classical approaches, propagation simulation through geometrical ray tracing is applied. This is achieved by considering the atmosphere along the optical propagation path as a spatial distribution of spherical bubbles with varying relative refractive index deviations representing turbulent eddies. The relative deviations of the refractive index are statistically determined from altitude-dependent and time-varying temperature fluctuations, as measured by a microwave profiling radiometer. For each representative atmosphere ray paths are analyzed using geometrical optics, which is particularly advantageous in situations of strong turbulence where there is severe wavefront distortion and discontinuity. The refractive index structure parameter is then determined as a function of height and time.

Atmospheric turbulence↗

NASA NTRS2009

Mineralogy of the Almahata Sitta Ureilite

Mineralogy & Petrography: Almahata Sitta, deriving from the asteroid 2008 TC3, is a coarse-grained- to porous, fine-grained, fragmental breccia with subrounded mineral fragments and olivine aggregates embedded in a cataclastic matrix of ureilitic material. Mineral fragments include polycrystalline olivine, low-calcium, pigeonite, and augite. Abundant carbonaceous aggregates containing graphite, microdiamonds and aliphatics. Kamacite, Cr-rich troilite, silica and schreibersite are abundant. The compositional range of the silicates is characteristic of the ureilites as a group, but unusually broad for an individual ureilite. The dense lithology is typical for ureilites, but the porous lithology is anomalous. In the porous lithology pore walls are largely coated by crystals of olivine. Classification: Almahata Sitta is an anomalous, polymict eucrite. Anomalous features include large compositional range of silicates, high abundance and large size of pores, crystalline pore wall linings, and fine-grained texture. Tomography reveals that the pores define thin, discontinuous "sheets" connected in three dimensions, suggesting that they outline grains that have been incompletely welded together. The crystals lining the pore walls are probably vapor phase deposits. Therefore Almahata Sitta may represent an agglomeration of coarse- to fine-grained, incompletely reduced pellets formed during impact, and subsequently welded together at high temperature.

Zolensky, Michael E.↗

NASA NTRS2004

Over-Luminous Elliptical Galaxies

We have completed a first draft of a paper on the galaxy group ESO3060170, the hottest known fossil group. We have submitted a first draft of the paper but the final completion is delayed due to several issues mentioned by the referee that we wish to revisit and discuss in more detail. The XMM data was combined with Chandra data which allowed a rich set of projects. The paper discusses the north-south elongation which is similar to that of the central dominant galaxy as well as the galaxy distribution. We detect an X-ray 'finger' or small tail emanating from the central galaxy to the north, suggesting motion of the galaxy within the elongated gravitational potential. The overall agreement between XMM and Chandra data are excellent (although the XMM data extend to larger radii). Both data sets show a cool core centered on the dominant galaxy. Surprisingly, - the temperature maps and detailed spectra indicate that the finger of gas is NOT cool, but has the same temperature as the ambient gas. We extracted surface brightness profiles, deprojected gas density profiles, cooling time profiles, and entropy profiles. There is a sharp discontinuity in gas temperature where the surface brightness profile starts to rise rapidly at 10 kpc. This produces a decrease in the cooling time and the gas entropy within 10 kpc. The central cooling time (within 10 kpc) is less than 109 years and falls to almost half that value in the inner 5 kpc. Despite the very short cooling time, we find no evidence (even with the excellent statistics from XMM-Newton) for multi-phased gas, i.e., a cooling flow. We find two 'edges' associated with the gas distribution (common in peaked X-ray groups and galaxies). On large scales, the temperature profile is flat and disagrees with the profile predicted by Loken et al. (2003) from detailed numerical simulations. We studied the galaxy distribution within one virial radius. The galaxy concentration associated with the group is detectable only within 0.3 of the virial radius (450 kpc) given the available depth of the optical galaxy catalogs at present. We have derived total mass and gas mass distributions (from the X-ray data) and find the gas fraction approaches a constant 8% (for H0 = 70).

Mushotsky, Richard↗

NASA NTRS2004

Over-Luminous Elliptical Galaxies

We have completed a first draft of a paper on the galaxy group ES03060170, the hottest known fossil group. We have submitted a first draft of the paper but the final completion is delayed due to several issues mentioned by the referee that we wish to revisit and discuss in more detail. The XMM data was combined with Chandra data which allowed a rich set of projects. The paper discusses the north-south elongation which is similar to that of the central dominant galaxy as well as the galaxy distribution. We detect an X-ray "finger" or small tail emanating from the central galaxy to the north, suggesting motion of the galaxy within the elongated gravitational potential. The overall agreement between XMM and Chandra data are excellent (although the XMM data extend to larger radii). Both data sets show a cool core centered on the dominant galaxy. Surprisingly, the temperature maps and detailed spectra indicate that the finger of gas is NOT cool, but has the same temperature as the ambient gas. We extracted surface brightness profiles, deprojected gas density profiles, cooling time profiles, and entropy profiles. There is a sharp discontinuity in gas temperature where the surface brightness profile starts to rise rapidly at 10 kpc. This produces a decrease in the cooling time and the gas entropy within 10 kpc. The central cooling time (within 10 kpc) is less than l0(exp 9) years and falls to almost half that value in the inner 5 kpc. Despite the very short cooling time, we find no evidence (even with the excellent statistics from XMM-Newton) for multi-phased gas, i.e., a cooling flow. We find two "edges" associated with the gas distribution (common in peaked X-ray groups and galaxies). On large scales, the temperature profile is flat and disagrees with the profile predicted by Loken et al. (2003) from detailed numerical simulations. We studied the galaxy distribution within one virial radius. The galaxy concentration associated with the group is detectable only within 0.3 of the virial radius (450 kpc) given the available depth of the optical galaxy catalogs at present. We have derived total mass and gas mass distributions (from the X- ray data) and find the gas fraction approaches a constant 8% (for Ho = 70).

Mushotzky, Richard↗

NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗

NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗

NASA NTRS1975

Fixed-range optimum trajectories for short-haul aircraft

An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum.

Erzberger, H.↗

NASA NTRS2002

Controls on Variations of Surface Energy, Water, and Carbon Budgets within Large-Scale Amazon Basin

A key research focus of the LBA Research Program is understanding the space-time variations in interlinked surface energy, water, and carbon budgets, the controls on these variations, and the implications of these controls on the carbon sequestering capacity of the large scale forest-pasture system that dominates the Amaz6nia landscape. Quantification of these variations and controls are investigated by a combination of in situ measurements, remotely sensed measurements from space, and a realistically forced hydrometeorological model coupled to a carbon assimilation model, capable of simulating details within the surface energy and water budgets along with the principle processes of photosynthesis and respiration. Herein we describe the results of an investigation concerning the space-time controls of carbon sources and sinks distributed over the large scale Amazon basin. The results are derived from a carbon-water-energy budget retrieval system for the large scale Amazon basin, which uses a coupled carbon assimilation-hydrometeorological model as an integrating system, forced by both in situ meteorological measurements and remotely sensed radiation and precipitation fluxes obtained from a combination of GOES, SSM/I, TOMS, and TRh4M satellite measurements. Results include validation of (a) retrieved surface radiation and precipitation fluxes based on 30-min averaged surface measurements taken at Ji-Parani in Rondania and Manaus in Amazonas, and (b) modeled sensible, latent, and C02 fluxes based on tower measurements taken at Reserva Jaru, Manaus and Fazenda Nossa Senhora. The space-time controls on carbon sequestration are partitioned into sets of factors classified by: (1) above canopy meteorology, (2) incoming surface radiation, (3) precipitation interception, and (4) indigenous stomatal processes varied over the different land covers of pristine rainforest, partially, and fully logged rainforests, and pasture lands. These are the principle meteorological, thermodynamical, hydrological, and biophysical control paths which perturb net carbon fluxes and sequestration, produce time-space switching of carbon sources and sinks, undergo modulation through atmospheric boundary layer feedbacks, and respond to any discontinuous intervention on the landscape itself such as produced by human intervention in converting rainforest to pasture or conducting selective/clearcut logging operations. The results demonstrate how relative carbon sequestration capacity of the Amazonian ecosystem responds to these controls, and how interpretation of space-time heterogeneities in carbon sequestration depends on a fairly exact quantification of the interacting non-linear properties of photosynthesis in response to incoming solar flux, air-canopy temperatures, and leaf water interception -- and soil respiration in response to upper layer soil temperature and water content. The results also show how the interpretation of the control processes is highly sensitive to the scales at which the surface fluxes are analyzed.

Smith, Eric A.↗

NASA NTRS2002

Space-Time Controls on Carbon Sequestration Over Large-Scale Amazon Basin

A major research focus of the LBA Ecology Program is an assessment of the carbon budget and the carbon sequestering capacity of the large scale forest-pasture system that dominates the Amazonia landscape, and its time-space heterogeneity manifest in carbon fluxes across the large scale Amazon basin ecosystem. Quantification of these processes requires a combination of in situ measurements, remotely sensed measurements from space, and a realistically forced hydrometeorological model coupled to a carbon assimilation model, capable of simulating details within the surface energy and water budgets along with the principle modes of photosynthesis and respiration. Here we describe the results of an investigation concerning the space-time controls of carbon sources and sinks distributed over the large scale Amazon basin. The results are derived from a carbon-water-energy budget retrieval system for the large scale Amazon basin, which uses a coupled carbon assimilation-hydrometeorological model as an integrating system, forced by both in situ meteorological measurements and remotely sensed radiation fluxes and precipitation retrieval retrieved from a combination of GOES, SSM/I, TOMS, and TRMM satellite measurements. Brief discussion concerning validation of (a) retrieved surface radiation fluxes and precipitation based on 30-min averaged surface measurements taken at Ji-Parana in Rondonia and Manaus in Amazonas, and (b) modeled carbon fluxes based on tower CO2 flux measurements taken at Reserva Jaru, Manaus and Fazenda Nossa Senhora. The space-time controls on carbon sequestration are partitioned into sets of factors classified by: (1) above canopy meteorology, (2) incoming surface radiation, (3) precipitation interception, and (4) indigenous stomatal processes varied over the different land covers of pristine rainforest, partially, and fully logged rainforests, and pasture lands. These are the principle meteorological, thermodynamical, hydrological, and biophysical control paths which perturb net carbon fluxes and sequestration, produce time-space switching of carbon sources and sinks, undergo modulation through atmospheric boundary layer feedbacks, and respond to any discontinuous intervention on the landscape itself such as produced by human intervention in converting rainforest to pasture or conducting selective/clearcut logging operations.

Smith, Eric A.↗

NASA NTRS1997

A Unified Directional Spectrum for Long and Short Wind-Driven Waves

Review of several recent ocean surface wave models finds that while comprehensive in many regards, these spectral models do not satisfy certain additional, but fundamental, criteria. We propose that these criteria include the ability to properly describe diverse fetch conditions and to provide agreement with in situ observations of Cox and Munk [1954] and Jiihne and Riemer [1990] and Hara et al. [1994] data in the high-wavenumber regime. Moreover, we find numerous analytically undesirable aspects such as discontinuities across wavenumber limits, nonphysical tuning or adjustment parameters, and noncentrosymmetric directional spreading functions. This paper describes a two-dimensional wavenumber spectrum valid over all wavenumbers and analytically amenable to usage in electromagnetic models. The two regime model is formulated based on the Joint North Sea Wave Project (JONSWAP) in the long-wave regime and on the work of Phillips [1985] and Kitaigorodskii [1973] at the high wavenumbers. The omnidirectional and wind-dependent spectrum is constructed to agree with past and recent observations including the criteria mentioned above. The key feature of this model is the similarity of description for the high- and low-wavenumber regimes; both forms are posed to stress that the air-sea interaction process of friction between wind and waves (i.e., generalized wave age, u/c) is occurring at all wavelengths simultaneously. This wave age parameterization is the unifying feature of the spectrum. The spectrum's directional spreading function is symmetric about the wind direction and has both wavenumber and wind speed dependence. A ratio method is described that enables comparison of this spreading function with previous noncentrosymmetric forms. Radar data are purposefully excluded from this spectral development. Finally, a test of the spectrum is made by deriving roughness length using the boundary layer model of Kitaigorodskii. Our inference of drag coefficient versus wind speed and wave age shows encouraging agreement with Humidity Exchange Over the Sea (HEXOS) campaign results.

Elfouhaily, T.↗

NASA NTRS2011

Finding Every Root of a Broad Class of Real, Continuous Functions in a Given Interval

One of the most pervasive needs within the Deep Space Network (DSN) Metric Prediction Generator (MPG) view period event generation is that of finding solutions to given occurrence conditions. While the general form of an equation expresses equivalence between its left-hand and right-hand expressions, the traditional treatment of the subject subtracts the two sides, leaving an expression of the form Integral of(x) = 0. Values of the independent variable x satisfying this condition are roots, or solutions. Generally speaking, there may be no solutions, a unique solution, multiple solutions, or a continuum of solutions to a given equation. In particular, all view period events are modeled as zero crossings of various metrics; for example, the time at which the elevation of a spacecraft reaches its maximum value, as viewed from a Deep Space Station (DSS), is found by locating that point at which the derivative of the elevation function becomes zero. Moreover, each event type may have several occurrences within a given time interval of interest. For example, a spacecraft in a low Moon orbit will experience several possible occultations per day, each of which must be located in time. The MPG is charged with finding all specified event occurrences that take place within a given time interval (or pass ), without any special clues from operators as to when they may occur, for the entire spectrum of missions undertaken by the DSN. For each event type, the event metric function is a known form that can be computed for any instant within the interval. A method has been created for a mathematical root finder to be capable of finding all roots of an arbitrary continuous function, within a given interval, to be subject to very lenient, parameterized assumptions. One assumption is that adjacent roots are separated at least by a given amount, xGuard. Any point whose function value is less than ef in magnitude is considered to be a root, and the function values at distances xGuard away from a root are larger than ef, unless there is another root located in this vicinity. A root is considered found if, during iteration, two root candidates differ by less than a pre-specified ex, and the optimum cubic polynomial matching the function at the end and at two interval points (that is within a relative error fraction L at its midpoint) is reliable in indicating whether the function has extrema within the interval. The robustness of this method depends solely on choosing these four parameters that control the search. The roots of discontinuous functions were also found, but at degraded performance.

Tausworthe, Robert C.↗

NASA NTRS2010

Satellite Gravimetry Applied to Drought Monitoring

Near-surface wetness conditions change rapidly with the weather, which limits their usefulness as drought indicators. Deeper stores of water, including root-zone soil wetness and groundwater, portend longer-term weather trends and climate variations, thus they are well suited for quantifying droughts. However, the existing in situ networks for monitoring these variables suffer from significant discontinuities (short records and spatial undersampling), as well as the inherent human and mechanical errors associated with the soil moisture and groundwater observation. Remote sensing is a promising alternative, but standard remote sensors, which measure various wavelengths of light emitted or reflected from Earth's surface and atmosphere, can only directly detect wetness conditions within the first few centimeters of the land s surface. Such sensors include the Advanced Microwave Scanning Radiometer - Earth Observing System (AMSR-E) C-band passive microwave measurement system on the National Aeronautic and Space Administration's (NASA) Aqua satellite, and the combined active and passive L-band microwave system currently under development for NASA's planned Soil Moisture Active Passive (SMAP) satellite mission. These instruments are sensitive to water as deep as the top 2 cm and 5 cm of the soil column, respectively, with the specific depth depending on vegetation cover. Thermal infrared (TIR) imaging has been used to infer water stored in the full root zone, with limitations: auxiliary information including soil grain size is required, the TIR temperature versus soil water content curve becomes flat as wetness increases, and dense vegetation and cloud cover impede measurement. Numerical models of land surface hydrology are another potential solution, but the quality of output from such models is limited by errors in the input data and tradeoffs between model realism and computational efficiency. This chapter is divided into eight sections, the next of which describes the theory behind satellite gravimetry. Following that is a summary of the GRACE mission and how hydrological information is gleaned from its gravity products. The fourth section provides examples of hydrological science enabled by GRACE. The fifth and sixth sections list the challenging aspects of GRACE derived hydrology data and how they are being overcome, including the use of data assimilation. The seventh section describes recent progress in applying GRACE for drought monitoring, including the development of new soil moisture and drought indicator products, and that is followed by a discussion of future prospects in satellite gravimetry based drought monitoring.

Rodell, Matthew↗

NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗