SEARCH · Engineering Papers

Results for “variable geometry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58

All sources NASA NTRS DOE OSTI

NASA NTRS2004

Top-of-Atmosphere Shortwave Broadband Observed Radiance and Estimated Irradiance over Polar Regions from Clouds and the Earth's Radiant Energy System (CERES) Instruments on Terra

Empirical angular distribution models for estimating top-of-atmosphere shortwave irradiances from radiance measurements over permanent snow, fresh snow and sea ice are developed using CERES measurements on Terra. Permanent snow angular distribution models depend on cloud fraction, cloud optical thickness, and snow brightness. Fresh snow and sea ice angular distribution models depend on snow and sea ice fraction, cloud fraction, cloud optical thickness, and snow and ice brightness. These classifications lead to 10 scene types for permanent snow and 25 scene types for fresh snow and sea ice. The average radiance over clear-sky permanent snow is more isotropic with satellite viewing geometry than that over overcast permanent snow. On average, the albedo of clear-sky permanent snow varies from 0.65 to 0.68 for solar zenith angles between 60$logical and\circ$ and 80 deg, while the corresponding albedo of overcast scenes varies from 0.70 to 0.73. Clear-sky permanent snow albedos over Antarctica estimated from two independent angular distribution models are consistent to within 0.6%, on average. Despite significant variability in sea ice optical properties with season, the estimated mean relative albedo error is -1 % for very dark sea ice and 0.1% for very bright sea ice when albedos derived from different viewing angles are averaged. The estimated regional root-mean-square (RMS) relative albedo error is 5.6% and 2.6% when the sea ice angular distribution models are applied to a region that contains very dark and very bright sea ice, respectively. Similarly, the estimated relative albedo bias error for fresh snow is -0.1% for very dark snow.

Kato, S.↗

NASA NTRS2012

The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications

The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished research

CraigMcClung, R.↗

NASA NTRS2001

X-Ray and UV Orbital Phase Dependence in LMC X-3

The black-hole binary LMC X-3 is known to be variable on time scales of days to years. We investigated X-ray and ultraviolet variability in the system as a function of the 1.7 d binary orbit using a 6.4 day observation with the Rossi X-ray Timing Explorer (RXTE) in 1998 December. An abrupt 14 % flux decrease lasting nearly an entire orbit was followed by a return to previous flux levels. This behavior occurred twice at nearly the same binary phase, but is not present in consecutive orbits. When the X-ray flux is at lower intensity, a periodic amplitude modulation of 7 % is evident in data folded modulo the orbital period. The higher intensity data show weaker correlation with phase. This is the first report of X-ray variability at the orbital period of LMC X-3. Archival RXTE observations of LMC X-3 during a high flux state in 1996 December show similar phase dependence. An ultraviolet light curve obtained with the High Speed Photometer (HSP) on the Hubble Space Telescope (HST) shows a phase dependent variability consistent with that observed in the visible, ascribed to the ellipsoidal variation of the visible star. The X-ray spectrum of LMC X-3 is acceptably represented by a phenomenological disk black-body plus a power law. Changes in the spectrum of LMX X-3 during our observations are compatible with earlier observations during which variations in the 2-10 keV flux are closely correlated with the disk geometry spectral model parameter.

Dolan, Joseph F.↗

NASA NTRS1997

Etch Profile Simulation Using Level Set Methods

Etching and deposition of materials are critical steps in semiconductor processing for device manufacturing. Both etching and deposition may have isotropic and anisotropic components, due to directional sputtering and redeposition of materials, for example. Previous attempts at modeling profile evolution have used so-called "string theory" to simulate the moving solid-gas interface between the semiconductor and the plasma. One complication of this method is that extensive de-looping schemes are required at the profile corners. We will present a 2D profile evolution simulation using level set theory to model the surface. (1) By embedding the location of the interface in a field variable, the need for de-looping schemes is eliminated and profile corners are more accurately modeled. This level set profile evolution model will calculate both isotropic and anisotropic etch and deposition rates of a substrate in low pressure (10s mTorr) plasmas, considering the incident ion energy angular distribution functions and neutral fluxes. We will present etching profiles of Si substrates in Ar/Cl2 discharges for various incident ion energies and trench geometries.

Hwang, Helen H.↗

NASA NTRS2012

Tidal Control of Jet Eruptions Observed by Cassini ISS

Observations by Cassini's Imaging Science Subsystem (ISS) of Enceladus' south polar region at high phase angles has revealed jets of material venting into space. Observations by Cassini's Composite Infrared Spectrometer (CIRS) have also shown that the south polar region is anomalously warm with hotspots associated with geological features called the Tiger Stripes. The Tiger Stripes are large rifts near the south pole of Enceladus, which are typically about 130 km in length, 2 km wide, with a trough 500 m deep, and are l1anked on each side by 100m tall ridges. Preliminary triangulation of jets as viewed at different times and with different viewing geometries in Cassini ISS images taken between 2005 and 2007 have constrained the locations of eight major eruptions of material and found all of them associated with the south polar fractures unofficially the 'Tiger Stripes', and found four of them coincident with the hotspots reported in 2006 by CIRS. While published ISS observations of jet activity suggest that individual eruption sites stay active on the timescale of years, any shorter temporal variability (on timescales of an orbital period, or 1.3 Earth days, for example) is more difficult to establish because of the spotty temporal coverage and the difficulty of visually isolating one jet from the forest of many seen in a typical image. Consequently, it is not known whether individual jets are continuously active, randomly active, or if they erupt on a predictable, periodic schedule. One mechanism that may control the timing of eruptions is diurnal tidal stress, which oscillates between compression/tension as well as right and left lateral shear at any given location throughout Enceladus' orbit and may allow the cracks to open and close regularly. We examine the stresses on the Tiger Stripe regions to see how well diurnal tidal stress caused by Enceladus' orbital eccentricity may possibly correlate with and thus control the observed eruptions. We then identify possible mechanisms by which tidal stress can provide access to the surface for volatile material and implications for observed jet activity.

Hurford, T. A.↗

NASA NTRS1986

Optimally robust redundancy relations for failure detection in uncertain systems

All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables. The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties. In this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection. A procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness. This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.

Lou, X.-C.↗

NASA NTRS1991

Quasi-perpendicular/quasi-parallel divisions of earth's bow shock

Computer-drawn diagrams of the boundaries between quasi-perpendicular and quasi-parallel areas of earth's bow shock are displayed for a few selected cone angles of static interplanetary magnetic field (IMF). The effect on the boundary of variable IMF in the foreshock is also discussed and shown for one nominal case. The boundaries demand caution in applying them to the realistic, dynamic conditions of the solar wind and in interpreting the effects of small cone angles on the distributions of structures at the shock. However, the calculated, first-order boundaries are helpful in defining areas of the shock where contributions from active structures inherent in quasi-parallel geometry may be distinguishable from those derived secondarily from upstream reflected ion dynamics. The boundaries are also compatible with known behavior of daytime ULF geomagnetic waves and pulsations according to models postulating that cone angle-controlled, time-dependent ULF activity around the subsolar point of the bow shock provides the source of geomagnetic excitation.

Greenstadt, E. W.↗

NASA NTRSDate not supplied

Kalman Filtering and RTS Smoothing for Arc-Jet Sample Edge Tracking

Accurate and temporally consistent measurements of test-article recession are required to characterize material response during arc-jet ablation experiments. However, image-based boundary measurements are often affected by segmentation noise, brightness variations, and frame-to-frame variability. This work extends arcjetCV [1] with filtering methods for tracking the evolving boundaries of hemispherical and ISO-Q test articles. Two boundary-tracking approaches based on Kalman filtering [2] were implemented. The first applies a point-wise Kalman filter followed by a Rauch–Tung–Striebel smoother [3] to individual boundary-point locations. The second applies the same filtering and smoothing framework to a reduced set of geometry-dependent shape parameters. The point-wise method reduces local frame-to-frame fluctuations while preserving spatial details along the detected boundary. The shape-parameter method provides a compact and geometrically constrained estimate of the sample contour. Figure 1 illustrates the two approaches for a hemispherical test article. Both methods improve temporal consistency and support more robust estimation of surface recession from arc-jet imagery. The two filtering approaches provide complementary representations of boundary evolution and improve the reliability of image-based recession measurements during arc-jet experiments.

recession measurement↗

NASA NTRS2002

Thermal Comptonization and Disk Thermal Reprocessing in NGC3516

We present an application of the thermal Comptonization/disk reprocessing model recently proposed by Zdziarski, Lubiniski, and Smith. We show that the absence of strong optical variations in the presence of strong concurrent X-ray variations, similar to those found by Hubble Space Telescope (HST)/Rossi X-Ray Timing Explorer (RXTE) monitoring observations of NGC 3516, can be explained by changing the geometry of the Comptonizing plasma rather than the accretion disk itself. The total X-ray luminosity of the Comptonizing plasma must decrease as its spatial extent increases. In contrast, the disk inner radius must be roughly fixed in order not to produce optical/ultraviolet color variations stronger than observed. By including emission due to internal viscous dissipation in the disk, we can roughly match the optical and X-ray flux levels and variability amplitudes seen from NGC 3516 during the HST/RXTE campaign.

Chiang, James↗

NASA NTRS2005

Design Study of Wafer Seals for Future Hypersonic Vehicles

Future hypersonic vehicles require high temperature, dynamic seals in advanced hypersonic engines and on the vehicle airframe to seal the perimeters of movable panels, flaps, and doors. Current seals do not meet the demanding requirements of these applications, so NASA Glenn Research Center is developing improved designs to overcome these shortfalls. An advanced ceramic wafer seal design has shown promise in meeting these needs. Results from a design of experiments study performed on this seal revealed that several installation variables played a role in determining the amount of leakage past the seals. Lower leakage rates were achieved by using a tighter groove width around the seals, a higher seal preload, a tighter wafer height tolerance, and a looser groove length. During flow testing, a seal activating pressure acting behind the wafers combined with simulated vibrations to seat the seals more effectively against the sealing surface and produce lower leakage rates. A seal geometry study revealed comparable leakage for full-scale wafers with 0.125 and 0.25 in. thicknesses. For applications in which lower part counts are desired, fewer 0.25-in.-thick wafers may be able to be used in place of 0.125-in.-thick wafers while achieving similar performance. Tests performed on wafers with a rounded edge (0.5 in. radius) in contact with the sealing surface resulted in flow rates twice as high as those for wafers with a flat edge. Half-size wafers had leakage rates approximately three times higher than those for full-size wafers.

Dunlap, Patrick H.↗

NASA NTRS1991

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Chen, C. P.↗

NASA NTRS1990

A comparison of single-cycle versus multiple-cycle proof testing strategies

An evaluation of single-cycle and multiple-cycle proof testing (MCPT) strategies for SSME components is described. Data for initial sizes and shapes of actual SSME hardware defects are analyzed statistically. Closed-form estimates of the J-integral for surface flaws are derived with a modified reference stress method. The results of load- and displacement-controlled stable crack growth tests on thin IN-718 plates with deep surface flaws are summarized. A J-resistance curve for the surface-cracked configuration is developed and compared with data from thick compact tension specimens. The potential for further crack growth during large unload/reload cycles is discussed, highlighting conflicting data in the literature. A simple model for ductile crack growth during MCPT based on the J-resistance curve is used to study the potential effects of key variables. The projected changes in the crack size distribution during MCPT depend on the interactions between several key parameters, including the number of proof cycles, the nature of the resistance curve, the initial crack size distribution, the component boundary conditions (load vs. displacement control), and the magnitude of the applied load or displacement. The relative advantages of single-cycle and multiple-cycle proof testing appear to be specific, therefore, to individual component geometry, material, and loading.

Hudak, S. J., Jr.↗

NASA NTRS1981

Saturnian kilometric radiation - Statistical properties and beam geometry

An adequate description of the average statistical properties of Saturn's radio emissions is needed for a study of these emissions. Data regarding these properties are presented, and the implications for source location, beaming, and magnetic surface anomalies are discussed. A description is presented of the average properties of the Saturn kilometric radiation (SKR) as observed from two locations by the Voyager 1 planetary radio astronomy (PRA) instrument for a 2-month period centered on the November 12, 1980 encounter. An analysis of the occurrence pattern of SKR as a function of Saturn's rotation phase has shown that SKR occurrence is not continuous, but variable and roughly periodic. The statistical SKR properties obtained strongly constrain possible source locations. Several source locations are possible, but most intriguing is the region at high latitudes near the noon meridian.

Kaiser, M. L.↗

NASA NTRS1994

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Coirier, William John↗

NASA NTRS2014

An Efficient, Multi-Layered Crown Delineation Algorithm for Mapping Individual Tree Structure Across Multiple Ecosystems

Deriving individual tree information from discrete return, small footprint LiDAR data may improve forest above ground biomass estimates, and provide tree-level information that is important in many ecological studies. Several crown delineation algorithms have been developed to extract individual tree information from LiDAR point clouds or rasterized canopy height models (CHM), but many of these algorithms have difficulty discriminating between overlapping crowns, and also may fail to detect understory trees. Our approach uses a watershed based delineation of a CHM, which is subsequently refined using the LiDAR point cloud. Individual tree detection was validated with stem mapped field data from the Smithsonian Environmental Research Center (SERC), Maryland, and on a plot and stand level through comparisons of stem density and basal area to delineated metrics at both SERC and a study area in the Sierra Nevada, California. For individual tree detection, the algorithm correctly identified 70% of dominant trees, 58% of co-dominant trees, 35% of intermediate trees and 21% of suppressed trees at SERC. The algorithm had difficulty distinguishing between crowns of small, dense understory trees of approximately the same height. Delineated crown volume alone explained 53% and 84% of the variability in basal area at the SERC and Sierra Nevada sites, respectively. The algorithm produced crown area distributions comparable to diameter at breast height (DBH) size class distributions observed in the field in both study sites. The algorithm detected understory crowns better in the conifer-dominated Sierra Nevada site than in the closed-canopy deciduous site in Maryland. The ability for the algorithm to reproduce both accurate tree size distributions and individual crown geometries in two dissimilar and complex forests suggests great promise for applicability to a wide range of forest systems.

LiDAR↗

NASA NTRS1990

Navier-Stokes analysis of turbine blade heat transfer

Comparisons with experimental heat transfer and surface pressures were made for seven turbine vane and blade geometries using a quasi-three-dimensional thin-layer Navier-Stokes analysis. Comparisons are made for cases with both separated and unseparated flow over a range of Reynolds numbers and freestream turbulence intensities. The analysis used a modified Baldwin-Lomax turbulent eddy viscosity mode. Modifications were made to account for the effects of: (1) freestream turbulence on both transition and leading edge heat transfer; (2) strong favorable pressure gradients on relaminarization; and (3) variable turbulent Prandtl number heat transfer. In addition, the effect of heat transfer on the near wall model of Deissler is compared with the Van Driest model.

Boyle, R. J.↗

NASA NTRS1990

Navier-Stokes analysis of turbine blade heat transfer

Boyle, R. J.↗

NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC):: Radiative Transfer Basis and Look-up Tables - 1

This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Lyapustin, Alexei↗