Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized linear model”

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.

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

At least 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Small-Scale Drop-Size Variability: Empirical Models for Drop-Size-Dependent Clustering in Clouds

By analyzing aircraft measurements of individual drop sizes in clouds, it has been shown in a companion paper that the probability of finding a drop of radius r at a linear scale l decreases as l(sup D(r)), where 0 less than or equals D(r) less than or equals 1. This paper shows striking examples of the spatial distribution of large cloud drops using models that simulate the observed power laws. In contrast to currently used models that assume homogeneity and a Poisson distribution of cloud drops, these models illustrate strong drop clustering, especially with larger drops. The degree of clustering is determined by the observed exponents D(r). The strong clustering of large drops arises naturally from the observed power-law statistics. This clustering has vital consequences for rain physics, including how fast rain can form. For radiative transfer theory, clustering of large drops enhances their impact on the cloud optical path. The clustering phenomenon also helps explain why remotely sensed cloud drop size is generally larger than that measured in situ.

Marshak, Alexander↗
NASA NTRS1976

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Kamp, L. W.↗
NASA NTRS1987

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗
NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗
NASA NTRS1993

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Voorhies, Coerte V.↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRSDate not supplied

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗
NASA NTRS1976

An improved method for the prediction of completely three-dimensional aerodynamic load distributions of configurations with leading edge vortex separation

The application of a higher-order subsonic potential flow panel method to the solution of three-dimensional flow about wing and wing-body combinations with leading-edge vortex separation is presented. The governing equations are the linear flow differential equation and nonlinear boundary conditions which require that the flow be parallel to the wing and body surfaces and that the free vortex sheet, springing from the leading and trailing edges, be aligned with the local flow and support no pressure jump. The vortex core is modeled as a simple line vortex which receives vorticity from the free sheet through a connecting sheet. The Kutta condition is imposed on all appropriate edges of the wing. This set of nonlinear equations is solved by an iterative procedure. The Goethert rule accounts for compressibility. The method has been programmed for the CDC 6600. Delta wings, gothic wings, arrow wings, cambered wings, and wing with body have been analyzed. Initial studies involving variations of panel density, vortex sheet sizing, Jacobian update, and initial geometry demonstrate that the present method generally exhibits good convergence characteristics.

Rubbert, p. E.↗
NASA NTRS1995

Interface Instabilities in the Interstellar Medium

In the present communication, we reexamine two limiting cases of star-forming mechanisms involving self-gravity, thermodynamics, and velocity fields, that we believe must be ubiquitous in the ISM -- the generally oblique collision of supersonic gas streams or turbulent eddies. The general case of oblique collisions has not yet been examined. However, two limiting cases have been studied in detail: (1) The head-on collision of two identical gas streams that form dense, cool accretion shocks that become unstable and may form Jeans mass clouds, which subsequently undergo collapse. (2) Linearly unstable tangential velocity discontinuities, which result in Kelvin-Helmholtz (K-H) instabilities and related phenomena. The compressible K-H instabilities exhibit rich and unexpected behaviors. Moreover a new thermal-dynamic (T-D) mode was discovered that arises from the coupling of the perturbed thermal behavior and the unperturbed flow. The T-D mode has the curious characteristic that it may be strongly unstable to interface modes when the global modes in either medium are absolutely thermally stable. In the present communication additional models of case 1 are described and discussed, and self-gravity is added in the linear theory of tangential discontinuities, case 2. We prove that self-gravity fundamentally changes the behavior of interfacial modes -- density discontinuities (or steps) are inherently unstable on roughly the free-fall timescale of the denser medium to perturbations of all wavelengths.

Hunter, J. H., Jr.↗
NASA NTRS1994

An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids

An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over a RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3 element and 4 element airfoil configurations. For the calculations, two one equation turbulence models are utilized. For the NACA 0012 airfoil, a pressure distribution and force data are compared with other computational results as well as with experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3 element configuration. For the 4 element case, comparisons of surface pressure distributions with experiment are made. In general, the agreement between the computations and the experiment is good.

Anerson, W. Kyle↗
NASA NTRS2005

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

Fink, P. W.↗
NASA NTRS1983

Aerothermal modeling, phase 1. Volume 1: Model assessment

Phase 1 was conducted as part of the overall NASA Hot Section Technology (HOST) Program. The purpose of this effort was to determine the predictive accuracy of and the deficiencies within the various analytical modules comprising the overall combustor aerothermal model used at General Electric, as well as to formulate recommendations for improvement where needed. This effort involved the assembly of a benchmark quality data base from selected available literature, and from General Electric engine and combustor component test data. This data base was supplemented with additional definitive data obtained from an experimental test program conducted as part of the Phase 1 effort. Using selections from this data base, assessment studies were conducted to evaluate the various modules. Assessment of the internal flow module was conducted using 2-D parabolic and ellipitic, as well as 3-D elliptic internal flow calculations of definitive test data selected from the assembled data base. The 2-D assessment provided methodical examination of the mathematical techniques and the physical submodules, while the 3-D assessment focused on usefulness as a design tool. Calculations of combustor linear metal temperatures, pressure loss performance, and airflow distribution were performed using aerothermal modules which were in general use for many years at General Electric. The results of these assessment provided for the identification of deficiencies within the modules. The deficiencies were addressed in some detail providing a foundation on which to formulate a prioritized list of recommendations for improvement.

Kenworthy, M. J.↗
NASA NTRS1999

Ultrasonic Nondestructive Characterization of Adhesive Bonds

Adhesives and adhesive joints are widely used in various industrial applications to reduce weight and costs, and to increase reliability. For example, advances in aerospace technology have been made possible, in part, through the use of lightweight materials and weight-saving structural designs. Joints, in particular, have been and continue to be areas in which weight can be trimmed from an airframe through the use of novel attachment techniques. In order to save weight over traditional riveted designs, to avoid the introduction of stress concentrations associated with rivet holes, and to take full advantage of advanced composite materials, engineers and designers have been specifying an ever-increasing number of adhesively bonded joints for use on airframes. Nondestructive characterization for quality control and remaining life prediction has been a key enabling technology for the effective use of adhesive joints. Conventional linear ultrasonic techniques generally can only detect flaws (delamination, cracks, voids, etc) in the joint assembly. However, more important to structural reliability is the bond strength. Although strength, in principle, cannot be measured nondestructively, a slight change in material nonlinearity may indicate the onset of failure. Furthermore, microstructural variations due to aging or under-curing may also cause changes in the third order elastic constants, which are related to the ultrasonic nonlinear parameter of the polymer adhesive. It is therefore reasonable to anticipate a correlation between changes in the ultrasonic nonlinear acoustic parameter and the remaining bond strength. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasonic wave passes through a nonlinear material. It seems that such nonlinearity can be effectively used to characterize bond strength. Several theories have been developed to model this nonlinear effect. Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented. Recently, a comparison between the experimental and simulated results based on a similar theoretical model was presented. A through-transmission setup for water immersion mode-converted shear waves was used to analyze the ultrasonic nonlinear parameter of an adhesive bond. In addition, ultrasonic guided waves have been used to analyze adhesive or diffusion bonded joints. In this paper, the ultrasonic nonlinear parameter is used to characterize the curing state of a polymer/aluminum adhesive joint. Ultrasonic through-transmission tests were conducted on samples cured under various conditions. The magnitude of the second order harmonic was measured and the corresponding ultrasonic nonlinear parameter was evaluated. A fairly good correlation between the curing condition and the nonlinear parameter is observed. The results show that the nonlinear parameter might be used as a good indicator of the cure state for adhesive joints.

Qu, Jianmin↗
NASA NTRS2004

Investigation of Three-Dimensional Stress Fields and Slip Systems for FCC Single Crystal Superalloy Notched Specimens

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e. plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g. cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing, become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a FCC single crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of 3D stress fields and evolution of slip sector boundaries near notches in FCC single crystal tension test specimens, and demonstrate that a 3D linear elastic finite element model that includes the effect of material anisotropy is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near FCC single crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single crystal notches.

Arakere, Nagaraj K.↗
NASA NTRS2015

Simulation of VSPT Experimental Cascade Under High and Low Free-Stream Turbulence Conditions

Variable-Speed Power Turbines (VSPT) for rotorcraft applications operate at low Reynolds number and over a wide range in incidence associated with shaft speed change. A comprehensive linear cascade data set obtained includes the effects of Reynolds number, free-stream turbulence and incidence is available and this paper concerns itself with the presentation and numerical simulation of conditions resulting in a selected set of those data. As such, post-dictions of blade pressure loading, total-pressure loss and exit flow angles under conditions of high and low turbulence intensity for a single Reynolds number are presented. Analyses are performed with the three-equation turbulence models of Walters- Leylek and Walters and Cokljat. Transition, loading, total-pressure loss and exit angle variations are presented and comparisons are made with experimental data as available. It is concluded that at the low freestream turbulence conditions the Walters-Cokljat model is better suited to predictions while for high freestream conditions the two models generate similar predications that are generally satisfactory.

turbulence modeling↗
NASA NTRS1979

Convective instability when the temperature gradient and rotation vector are oblique to gravity. I - Fluids without diffusion

A linear stability analysis of fluid layers under uniform rotation (generally oblique to gravity) which possess both vertical and horizontal temperature gradients is made by considering ideal fluids without diffusion within a Boussinesq approximation. This simplified configuration is used to assess the preferred convective modes as a function of latitude on a planet like Jupiter. The tilted rotation vector introduces a preference for roll-like disturbances with north-south orientations, while the horizontal temperature gradient produces a thermal wind shear which favors convective rolls oriented parallel to the flow in an east-west direction. It is found that the horizontal temperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with an increasing rotation rate and a decreasing latitude. The parameter values for Jupiter are estimated with the use of a simple radiative convective model, indicating a preference for axisymmetric rolls at nearly all latitudes if the convection zone depth is greater than about 200 km below the one atmosphere pressure level and convective roll characteristics which contribute to an equatorial acceleration.

Hathaway, D. H.↗
NASA NTRS1986

Expected performance of m-solution backtracking

This paper derives upper bounds on the expected number of search tree nodes visited during an m-solution backtracking search, a search which terminates after some preselected number m problem solutions are found. The search behavior is assumed to have a general probabilistic structure. The results are stated in terms of node expansion and contraction. A visited search tree node is said to be expanding if the mean number of its children visited by the search exceeds 1 and is contracting otherwise. It is shown that if every node expands, or if every node contracts, then the number of search tree nodes visited by a search has an upper bound which is linear in the depth of the tree, in the mean number of children a node has, and in the number of solutions sought. Also derived are bounds linear in the depth of the tree in some situations where an upper portion of the tree contracts (expands), while the lower portion expands (contracts). While previous analyses of 1-solution backtracking have concluded that the expected performance is always linear in the tree depth, the model allows superlinear expected performance.

Nicol, D. M.↗
NASA NTRS1994

Global shortwave energy budget at the earth's surface from ERBE observations

A method is proposed to compute the net solar (shortwave) irradiance at the earth's surface from Earth Radiation Budget Experiment (ERBE) data in the S4 format. The S4 data are monthly averaged broadband planetary albedo collected at selected times during the day. Net surface shortwave irradiance is obtained from the shortwave irradiance incident at the top of the atmosphere (known) by subtracting both the shortwave energy flux reflected by the earth-atmosphere system (measured) and the energy flux absorbed by the atmosphere (modeled). Precalculated atmospheric- and surface-dependent functions that characterize scattering and absorption in the atmosphere are used, which makes the method easily applicable and computationally efficient. Four surface types are distinguished, namely, ocean, vegetation, desert, and snow/ice. Over the tropical Pacific Ocean, the estimates based on ERBE data compare well with those obtained from International Satellite Cloud Climatology Project (ISCCP) B3 data. For the 9 months analyzed the linear correlation coefficient and the standard difference between the two datasets are 0.95 and 14 W/sq m (about 6% of the average shortwave irradiance), respectively, and the bias is 15 W/sq m (higher ERBE values). The bias, a strong function of ISCCP satellite viewing zenith angle, is mostly in the ISCCP-based estimates. Over snow/ice, vegetation, and desert no comparison is made with other satellite-based estimates, but theoretical calculations using the discrete ordinate method suggest that over highly reflective surfaces (snow/ice, desert) the model, which accounts crudely for multiple reflection between the surface and clouds, may substantially overestimate the absorbed solar energy flux at the surface, especially when clouds are optically thick. The monthly surface shortwave irradiance fields produced for 1986 exhibit the main features characteristic of the earth's climate. As found in other studies, our values are generally higher than Esbensen and Kushnir's by as much as 80 W/sq m in the tropical oceans. A cloud parameter, defined as the difference between clear-sky and actual irradiances normalized to top-of-atmosphere clear-sky irradiance, is also examined. This parameter, minimally affected by sun zenith angle, is higher in the midlatitude regions of storm tracks than in the intertropical convergence zone (ITCZ), suggesting that, on average, the higher cloud coverage in midlatitudes is more effective at reducing surface shortwave irradiance than opaque, convective, yet sparser clouds in the ITCZ. Surface albedo estimates are realistic, generally not exceeding 0.06 in the ocean, as high as 0.9 in polar regions, and reaching 0.5 in the Sahara and Arabian deserts.

Breon, Francois-Marie↗