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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Investigation of the notch sensitivity of tailorable long fiber discontinuous prepreg composite laminates

Tailorable discontinuous fiber composite laminates provide relative formability beyond that of continuous fiber laminates, while achieving improved mechanical performance over comparable stochastic systems. Here, in this work, the notch sensitivity of engineered prepreg platelet molded composite (PPMC) laminates is investigated using the open-hole tension (OHT) test and compared to available data for stochastic PPMCs and continuous fiber laminates made with the same material. The press-formed thermoplastic composites (AS4/PEKK) were molded with a quasi-isotropic stacking sequence. The discontinuous PPMC laminate was found to be notch insensitive with OHT strengths ranging from 145.4 MPa (CV $=$ 7%) for d/w $=$ 0.5 to 229.3 MPa (CV $=$ 9%) for d/w $=$ 0.25. The highly ordered meso-structure of the engineered PPMC laminate yields comparatively excellent mechanical properties for relatively thin laminates in contrast to stochastic systems. Both net- and gross-section failures were observed for d/w $=$ 0.25, which suggests that the engineered PPMC laminates studied here maintain a degree of inherent, internal stress concentrations that compete with those caused by geometric features such as a circular hole. Computational simulations of the OHT tests with explicitly represented platelets were found to be in good agreement with experimental measurements. The progressive failure analysis was used to conduct a numerical investigation of the stacking sequence and platelet meso-morphology.

36 MATERIALS SCIENCE↗
NASA NTRS1998

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Lakota, Barbara Anne↗
NASA NTRS1981

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Noor, A. K.↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗
DOE OSTI2022

Physically rigorous reduced-order flow models of fractured subsurface environments without explosive computational cost

Fractured media models comprise discontinuities of multiple lengths (e.g. fracture lengths and apertures, wellbore area) that fall into the relatively insignificant length scales spanning millimeter-scale fractures to centimeter-scale wellbores in comparison to the extensions of the field of interest, and challenge the conventional discretization methods imposing highly-fine meshing and formidably large numerical cost. By utilizing the recent developments in the finite element analysis of electromagnetics that allow to represent material properties on a hierarchical geometry, this project develops computational capabilities to model fluid flow, heat conduction, transport and induced polarization in large-scale geologic environments that possess geometrically-complex fractures and man-made infrastructures without explosive computational cost. The computational efficiency and robustness of this multi-physics modeling tool are demonstrated by considering various highly-realistic complex geologic environments that are common in many energy and national security related engineering problems.

42 ENGINEERING↗
NASA NTRS1990

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing

An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described.

Bailey, R. T.↗
NASA NTRS1990

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method

An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.

Shih, T. I.-P.↗
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↗
NASA NTRS2002

Damping of Quasi-stationary Waves Between Two Miscible Liquids

Two viscous miscible liquids with an initially sharp interface oriented vertically inside a cavity become unstable against oscillatory external forcing due to Kelvin-Helmholtz instability. The instability causes growth of quasi-stationary (q-s) waves at the interface between the two liquids. We examine computationally the dynamics of a four-mode q-s wave, for a fixed energy input, when one of the components of the external forcing is suddenly ceased. The external forcing consists of a steady and oscillatory component as realizable in a microgravity environment. Results show that when there is a jump discontinuity in the oscillatory excitation that produced the four-mode q-s wave, the interface does not return to its equilibrium position, the structure of the q-s wave remains imbedded between the two fluids over a long time scale. The damping characteristics of the q-s wave from the time history of the velocity field show overdamped and critically damped response; there is no underdamped oscillation as the flow field approaches steady state. Viscous effects serve as a dissipative mechanism to effectively damp the system. The stability of the four-mode q-s wave is dependent on both a geometric length scale as well as the level of background steady acceleration.

Duval, Walter M. B.↗
NASA NTRS2002

Navigation Algorithms for the SeaWiFS Mission

The navigation algorithms for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) were designed to meet the requirement of 1-pixel accuracy-a standard deviation (sigma) of 2. The objective has been to extract the best possible accuracy from the spacecraft telemetry and avoid the need for costly manual renavigation or geometric rectification. The requirement is addressed by postprocessing of both the Global Positioning System (GPS) receiver and Attitude Control System (ACS) data in the spacecraft telemetry stream. The navigation algorithms described are separated into four areas: orbit processing, attitude sensor processing, attitude determination, and final navigation processing. There has been substantial modification during the mission of the attitude determination and attitude sensor processing algorithms. For the former, the basic approach was completely changed during the first year of the mission, from a single-frame deterministic method to a Kalman smoother. This was done for several reasons: a) to improve the overall accuracy of the attitude determination, particularly near the sub-solar point; b) to reduce discontinuities; c) to support the single-ACS-string spacecraft operation that was started after the first mission year, which causes gaps in attitude sensor coverage; and d) to handle data quality problems (which became evident after launch) in the direct-broadcast data. The changes to the attitude sensor processing algorithms primarily involved the development of a model for the Earth horizon height, also needed for single-string operation; the incorporation of improved sensor calibration data; and improved data quality checking and smoothing to handle the data quality issues. The attitude sensor alignments have also been revised multiple times, generally in conjunction with the other changes. The orbit and final navigation processing algorithms have remained largely unchanged during the mission, aside from refinements to data quality checking. Although further improvements are certainly possible, future evolution of the algorithms is expected to be limited to refinements of the methods presented here, and no substantial changes are anticipated.

Hooker, Stanford B.↗
NASA NTRS2002

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗
NASA NTRS1975

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

Results for cylindrical configurations using the STAGS computer program were presented. Discontinuities were imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements. The cutout problem has been shown to be highly nonlinear for smooth surface shells, but it was found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following: (1) comparison between smeared and discrete stiffener theory for linear solutions, (2) numerical finite difference convergence as directed toward buckling determination, (3) collapse load results with the various skin stiffeners. A linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces was included. Comparisons were made between a variety of geometric positions considering cutout frame and thickened skin additions.

Palazotto, A. N.↗
NASA NTRS2014

Electron Beam Freeform Fabrication of Titanium Alloy Gradient Structures

Historically, the structural optimization of aerospace components has been done through geometric methods. A monolithic material is chosen based on the best compromise between the competing design limiting criteria. Then the structure is geometrically optimized to give the best overall performance using the single material chosen. Functionally graded materials offer the potential to further improve structural efficiency by allowing the material composition and/or microstructural features to spatially vary within a single structure. Thus, local properties could be tailored to the local design limiting criteria. Additive manufacturing techniques enable the fabrication of such graded materials and structures. This paper presents the results of a graded material study using two titanium alloys processed using electron beam freeform fabrication, an additive manufacturing process. The results show that the two alloys uniformly mix at various ratios and the resultant static tensile properties of the mixed alloys behave according to rule-of-mixtures. Additionally, the crack growth behavior across an abrupt change from one alloy to the other shows no discontinuity and the crack smoothly transitions from one crack growth regime into another.

Brice, Craig A.↗
NASA NTRS2012

Stability Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13.5. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis. The transition behavior during this re-entry segment of HIFiRE-1 flight shares some common features with the predicted transition front along the elliptic cone shaped HIFiRE-5 flight article, which was designed to provide hypersonic transition data for a fully 3D geometric configuration. To compare and contrast the crossflow dominated transition over the HIFiRE-1 and HIFiRE-5 configurations, this paper also analyzes boundary layer instabilities over a subscale model of the HIFiRE-5 flight configuration that was tested in the Mach 6 quiet tunnel facility at Purdue University.

Li, Fei↗
NASA NTRS1994

High-frequency techniques for RCS prediction of plate geometries and a physical optics/equivalent currents model for the RCS of trihedral corner reflectors, parts 1 and 2

Formulations for scattering from the coated plate and the coated dihedral corner reflector are included. A coated plate model based upon the Uniform Theory of Diffraction (UTD) for impedance wedges was presented in the last report. In order to resolve inaccuracies and discontinuities in the predicted patterns using the UTD-based model, an improved model that uses more accurate diffraction coefficients is presented. A Physical Optics (PO) model for the coated dihedral corner reflector is presented as an intermediary step in developing a high-frequency model for this structure. The PO model is based upon the reflection coefficients for a metal-backed lossy material. Preliminary PO results for the dihedral corner reflector suggest that, in addition to being much faster computationally, this model may be more accurate than existing moment method (MM) models. An improved Physical Optics (PO)/Equivalent Currents model for modeling the Radar Cross Section (RCS) of both square and triangular, perfectly conducting, trihedral corner reflectors is presented. The new model uses the PO approximation at each reflection for the first- and second-order reflection terms. For the third-order reflection terms, a Geometrical Optics (GO) approximation is used for the first reflection; and PO approximations are used for the remaining reflections. The previously reported model used GO for all reflections except the terminating reflection. Using PO for most of the reflections results in a computationally slower model because many integrations must be performed numerically, but the advantage is that the predicted RCS using the new model is much more accurate. Comparisons between the two PO models, Finite-Difference Time-Domain (FDTD) and experimental data are presented for validation of the new model.

Balanis, Constantine A.↗
NASA NTRS1992

SAR backscatter from coniferous forest gaps

A study is in progress comparing Airborne Synthetic Aperture Radar (AIRSAR) backscatter from coniferous forest plots containing gaps to backscatter from adjacent gap-free plots. Issues discussed are how do gaps in the range of 400 to 1600 sq m (approximately 4-14 pixels at intermediate incidence angles) affect forest backscatter statistics and what incidence angles, wavelengths, and polarizations are most sensitive to forest gaps. In order to visualize the slant-range imaging of forest and gaps, a simple conceptual model is used. This strictly qualitative model has led us to hypothesize that forest radar returns at short wavelengths (eg., C-band) and large incidence angles (e.g., 50 deg) should be most affected by the presence of gaps, whereas returns at long wavelengths and small angles should be least affected. Preliminary analysis of 1989 AIRSAR data from forest near Mt. Shasta supports the hypothesis. Current forest backscatter models such as MIMICS and Santa Barbara Discontinuous Canopy Backscatter Model have in several cases correctly predicted backscatter from forest stands based on inputs of measured or estimated forest parameters. These models do not, however, predict within-stand SAR scene texture, or 'intrinsic scene variability' as Ulaby et al. has referred to it. For instance, the Santa Barbara model, which may be the most spatially coupled of the existing models, is not truly spatial. Tree locations within a simulated pixel are distributed according to a Poisson process, as they are in many natural forests, but tree size is unrelated to location, which is not the case in nature. Furthermore, since pixels of a simulated stand are generated independently in the Santa Barbara model, spatial processes larger than one pixel are not modeled. Using a different approach, Oliver modeled scene texture based on an hypothetical forest geometry. His simulated scenes do not agree well with SAR data, perhaps due to the simple geometric model used. Insofar as texture is the expression of biological forest processes, such as succession and disease, and physical ones, such as fire and wind-throw, it contains useful information about the forest, and has value in image interpretation and classification. Forest gaps are undoubtedly important contributors to scene variance. By studying the localized effects of gaps on forest backscatter, guided by our qualitative model, we hope to understand more clearly the manner in which spatial heterogeneities in forests produce variations in backscatter, which collectively give rise to scene texture.

Day, John L.↗
NASA NTRS1989

Physically-based parameterization of spatially variable soil and vegetation using satellite multispectral data

A stochastic-geometric landsurface reflectance model is formulated and tested for the parameterization of spatially variable vegetation and soil at subpixel scales using satellite multispectral images without ground truth. Landscapes are conceptualized as 3-D Lambertian reflecting surfaces consisting of plant canopies, represented by solid geometric figures, superposed on a flat soil background. A computer simulation program is developed to investigate image characteristics at various spatial aggregations representative of satellite observational scales, or pixels. The evolution of the shape and structure of the red-infrared space, or scattergram, of typical semivegetated scenes is investigated by sequentially introducing model variables into the simulation. The analytical moments of the total pixel reflectance, including the mean, variance, spatial covariance, and cross-spectral covariance, are derived in terms of the moments of the individual fractional cover and reflectance components. The moments are applied to the solution of the inverse problem: The estimation of subpixel landscape properties on a pixel-by-pixel basis, given only one multispectral image and limited assumptions on the structure of the landscape. The landsurface reflectance model and inversion technique are tested using actual aerial radiometric data collected over regularly spaced pecan trees, and using both aerial and LANDSAT Thematic Mapper data obtained over discontinuous, randomly spaced conifer canopies in a natural forested watershed. Different amounts of solar backscattered diffuse radiation are assumed and the sensitivity of the estimated landsurface parameters to those amounts is examined.

Jasinski, Michael F.↗
NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗