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NASA NTRS1977

Two phase sampling for wheat acreage estimation

A two-phase Landsat-based sample allocation and wheat proportion estimation method was developed. The technique employs manual, Landsat full frame-based wheat or cultivated land proportion estimates from a large number of segments comprising a first sample phase to optimally allocate a small phase-two sample of computer or manually processed segments. Proportion estimates from each phase are then linked by regression or probability proportional to estimated size estimators to provide wheat proportion estimates and standard errors by reporting unit. Application to the Kansas Southwest CRD (Crop Reporting District) for 1974 produced a wheat acreage estimate for that CRD within 2.42% of the USDA SRS-based estimate using a lower CRD inventory budget than for a simulated reference LACIE (Large Area Crop Inventory Experiment) system.

Thomas, R. W.↗

NASA NTRS1996

Algorithms for Automatic Alignment of Arrays

Aggregate data objects (such as arrays) are distributed across the processor memories when compiling a data-parallel language for a distributed-memory machine. The mapping determines the amount of communication needed to bring operands of parallel operations into alignment with each other. A common approach is to break the mapping into two stages: an alignment that maps all the objects to an abstract template, followed by a distribution that maps the template to the processors. This paper describes algorithms for solving the various facets of the alignment problem: axis and stride alignment, static and mobile offset alignment, and replication labeling. We show that optimal axis and stride alignment is NP-complete for general program graphs, and give a heuristic method that can explore the space of possible solutions in a number of ways. We show that some of these strategies can give better solutions than a simple greedy approach proposed earlier. We also show how local graph contractions can reduce the size of the problem significantly without changing the best solution. This allows more complex and effective heuristics to be used. We show how to model the static offset alignment problem using linear programming, and we show that loop-dependent mobile offset alignment is sometimes necessary for optimum performance. We describe an algorithm with for determining mobile alignments for objects within do loops. We also identify situations in which replicated alignment is either required by the program itself or can be used to improve performance. We describe an algorithm based on network flow that replicates objects so as to minimize the total amount of broadcast communication in replication.

Chatterjee, Siddhartha↗

NASA NTRSDate not supplied

Magnetohydrodynamics (MHD) Aerocapture System for Enabling Faster-Larger Planetary Science & Human Exploration Missions

Since our completing the NIAC Phase I NIAC on this Advanced Aerocapture System, NASA Langley Research Center has funded or supported a number of studies and code enhancements through its Center Innovation Fund (CIF) and NASA’s NSTGRO and Internship Programs to mature the analysis capabilities and quantify the merits of the MHD Aerocapture System technology. These efforts have resulted in a plug and play analysis capability for assessing MHD aerocapture system performance for arrival at many planetary bodies of interest. Our efforts have especially focused on the potential mass savings for improving the capacity for science observations at Neptune and Triton. A re-cent Forbes article published “‘Orbital mechanics is probably going to decide for us whether we go to Uranus or Neptune because we need to flyby Jupiter,’ said Kunio Sayanagi at Hampton University, Virginia, who also worked on the Neptune Odyssey proposal…. Exactly when a mission can be sent to Uranus, or Neptune, depends on the relative position of Jupiter, which can help give a spacecraft a gravitational slingshot. That drastically shortens the cruise phase.” [1] Since shortening the cruise phase is important for these science missions, any mass savings enabled by the MHD Aerocapture System could be reallocated to increasing Thermal Protection System mass to allow faster arrival speeds and/or for onboarding additional payloads such as science instruments, batteries, or propellant for conducting more science for longer durations in the desired orbits. The analysis steps and codes for conducting trades and sizing vehicles for aerocapture are as follows: Step 1 is to conduct aeroheating analysis using LAURA of the selected entry vehicle shape to identify locations on the forebody where ionization and flow velocity are sufficient for producing Lo-rentz forces. LAURA is a multiblock structured grid finite-volume CFD solver developed at the NASA Langley Research Center. [2] LAURA has been used for aerothermal analysis support of the entry, de-scent and landing (EDL) phase of interplanetary missions over the last three decades [3-7]. Step 2 is to port the LAURA results into CFDWARP to calcu-late electrical and thermal conductivities of ionized flow for sizing MHD patch system and calculating Lorentz forces needed for controls analysis. CFDWARP is a CFD code that uses advanced nu-merical methods that enable the simulation of the full coupling between the aerodynamics, the magne-tohydrodynamics, and the non-neutral plasma sheaths. CFDWARP has the unique capability to simulate efficiently the non-neutral sheaths (near the electrodes) in coupled form with the quasi-neutral bulk MHD flow [8-11]. Step 3 is to link re-sults from LAURA and CFDWARP into POST2 for calculating entry trajectories and comparing MHD control results with other aerodynamic control strategies. The Program to Optimize Simulated Tra-jectories II (POST2) is a generalized point mass, discrete parameter targeting and optimization pro-gram. POST2 provides the capability to target and optimize point mass trajectories for multiple pow-ered or un-powered vehicles near an arbitrary rotat-ing, oblate planet [12]. Step 4: TPS sizing was per-formed using the Fully Implicit Ablation and Ther-mal-response code (FIAT) tool which computes the transient one-dimensional thermal response and surface thermochemistry of a multilayer stackup of thermal protection, bonding, and structural materi-als subject to aeroheating on one surface [13]. The sizing and margining methodology used was based on the approach documented by Mahzari and Milos [14] for the dual-layered heatshield for extreme entry environment technology (DL-HEEET) TPS concept. TPS analysis utilizes trajectory information from POST2. Using this step-wise plug and play MHD Aerocapture performance assessment process, our analysis targets a Neptune aerocapture trajectory that will place the spacecraft in an observation orbit for Triton. [15]. Magnetohydrodynamic (MHD) control of a 4.5-meter diameter MSL-style capsule resulted in TPS mass savings of nearly 2000 kg when using an MHD system mass of under 200 kg. The flight path for a vehicle using the MHD control strategy has a much lower heat rate and heat load compared to the conventional aerodynamic aerocapture strategies known as bank angle con-trolled (BAC) and direct force controlled (DFC). Both BAC and DFC have heat rates significantly greater than 1500 W/cm2 typically used as an upper limit for PICA. Thus, DL-HEEET TPS concept was required for the BAC and DFC control strategies. However, considering the more benign environ-ments for the MHD case, additional TPS concepts with improved mass efficiency were also assessed. PICA was considered for the MHD controlled strat-egy since the maximum heat rate was well within the limits (<1500 W/cm2) of PICA. TPS sizing re-sulted in a significant mass reduction. The PICA layer for this sizing case was about 7.8 cm. As a point of reference, the Mars 2020 mission, which used this same PICA concept, had a PICA thickness of 3.18 cm [16]. The trajectories used for the TPS sizing originat-ed from the POST2 simulations. The current, I, to an electromagnet configuration can be manipulated to allow for active control of the vehicle. Manipula-tion of the current, I, changes the magnetic field, B, which affects the Lorentz force and therefore the MHD drag force on the vehicle. Our analysis in-cluded both open-loop and close-loop control. Closed-loop control will enable improved overall performance when taking into account mission level uncertainties, such as interplanetary delivery errors and atmospheric modeling uncertainties. The open-loop and closed-loop MHD control cases do not dip as deep into the atmosphere as the aerodynamic cases. Three types of aerodynamic-only approach-es are investigated: bank angle modulation (BAM), director force control (DFC), and Drag Modulated. BAM and DFC make use of vehicle aerodynamic angles to steer the vehicle. Thus, changing the aer-odynamic forces acting on the vehicle for control, aerodynamic drag modulated case requires a vary-ing drag area to modulate the drag force. The MHD drag modulated case modulates MHD generated drag force that adds to the aerodynamic drag. This higher atmospheric activation of drag forces by the MHD patch results in significantly less heat flux on the vehicle. The MHD technology will enable shorter cruise times and deceleration of larger payloads for increasing the capacity for science at the Ice Giants or for returning astronauts to Earth from cislunar space or from Mars. The purpose of this presentation is to provide more details about this work and to highlight plans for further research and development including a flight demonstration.

R. W. Moses↗

NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗

NASA NTRS1993

Application of dual-fuel propulsion to a single stage AMLS vehicle

As part of NASA's Advanced Manned Launch System (AMLS) study to determine a follow-on, or complement, to the Space Shuttle, a reusable single-stage-to-orbit concept utilizing dual-fuel rocket propulsion has been examined. Several dual-fuel propulsion concepts were investigated. These include: a separate engine concept combining Russian RD-170 kerosene-fueled engines with SSME-derivative engines; the kerosene and hydrogen-fueled Russian RD-701 engine concept; and a dual-fuel, dual-expander engine concept. Analysis to determine vehicle weight and size characteristics was performed using conceptual level design techniques. A response surface methodology for multidisciplinary design was utilized to optimize the dual-fuel vehicle concepts with respect to several important propulsion system and vehicle design parameters in order to achieve minimum empty weight. Comparisons were then made with a hydrogen-fueled reference, single-stage vehicle. The tools and methods employed in the analysis process are also summarized.

Lepsch, Roger A., Jr.↗

NASA NTRSDate not supplied

Propulsive trajectory optimization to minimize surface contamination

MOTIVATION: We present an optimization technique for propulsive vehicles that autonomously minimizes contamination during surface approach and landing. In addition to short-range hoppers, the optimization technique is also fully applicable to traditional orbit-to-surface landers. This study addresses scenarios where surface alterations from propulsion events are counterproductive or hazardous to the mission objectives. This is of immediate interest for landers (whether human or robotic), that may rely on pristine soils collected in the immediate vicinity of landing sites to accomplish science investigations, mining, or ISRU surface operations. Such missions are averse to various surface-plume interactions such as thermal scoring, physical agitation, and contamination. The capability can be applied with minimal impact to the baseline mission concept. METHODS: Optimization algorithms have been developed to calculate descent trajectories and maneuvers, thrust magnitude, and attitude for various mission cases. These parameters are determined as an optimal solution when minimizing either fuel consumption, contamination deposited at the landing site, or some weighted combination of both. Among constraints imposed on the solution, we examined pitch rate, vertical takeoff and vertical landing (VTVL) requirements, size of the contamination zone, and minimum ground clearance during flight. This tool provides unique, non-intuitive solutions and can be a valuable resource for mission planners. RESULTS: A variety of agile trajectory solutions were obtained, each yielding different reductions in landing site contamination and corresponding to only modest increases in fuel consumption. Several optimal trajectories were obtained by varying the contamination weight in the fitness function. As expected, when the contamination weight is zero, the trajectory appears close to parabolic since the optimization scheme only attempts to minimize for fuel utilization, yielding essentially, the expected ballistic trajectory. Notably for contamination weights greater than zero, trajectory inflections are observed in the descent phase, which manifests as hovering or additional, mini “pseudo hops” before the final touchdown. A trajectory inflection is characterized by arresting the majority of the spacecraft vertical velocity component at a coordinate outside of the landing target, and without violating ground clearance constraints. FUTURE WORK: Our optimization technique is ready for laboratory or field demonstrations to validate the sophisticated maneuvering solutions obtained for fuel optimization and surface preservation. An appropriate testbed would validate the optimal guidance algorithms, the navigation system, and sensor suite by emulating vehicle flight in closed loop robotic tests. Critically, these algorithms could then be ported to flight software for implementation.

surface contamination↗

NASA NTRSDate not supplied

A UNIQUE APPROACH TO ACHIEVING SIZE-CONSTRAINED QUASI-HALO ORBITS FOR THE ROMAN SPACE TELESCOPE

The Nancy Grace Roman Space Telescope (RST) is an infrared space observatory planned for launch in the mid-2020’s. The launch window design for RST is subject to a wide variety of simultaneous requirements that require careful consideration and control of mission orbits and the trajectories used to achieve them. This work describes an innovative methodology that blends classical methods with modern manifold approaches and numerical optimization to flexibly determine optimal transfers to desriable mission orbits for any day of the year.Solutions found with this highly automated strategy are gaurunteed to meet requirements by construction. Results show that RST can launch for 80% of the year using maneuvers that are well within the fuel budget, significantly reducing cost and risk to the mission

Lauren Schlenker↗

NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗

NASA NTRS1991

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗

NASA NTRS1992

Phasing of a space based segmented submillimeter wavelength telescope using focal plane measurements

As part of a technology development program for realizing a space based submillimeter telescope, two different approaches to the absolute phasing of a segmented primary mirror using focal plane measurements have been implemented for feasibility. The method of optimization by simulated annealing evaluates the image quality of a point spread function after all the telescope segments have been randomly moved. It accepts each iteration which improves the image quality, as well as a random number of iterations which do not, thus keeping the Strehl in the initialization procedure from falling into local maxima. Methods for determining the annealing schedule, and the step size for random segment movements are presented and discussed. Using phase diversity and a model for the telescope imaging system, a nonlinear least squares algorithm has also been implemented which parameterizes each of the segment actuator movements. Using multiple out of focus images, the segment actuator positions are estimated using an iterative procedure. Nonlinear least squares, although computationally intensive, offers a large savings in the actuator movements over simulated annealing and pairwise phasing methods for large numbers of segments. These algorithms have been integrated into a general simulation program which models the behavior of the telescope under anticipated space conditions.

Levine, B. M.↗

NASA NTRS2001

Methodology Development for Assessment of Spaceport Technology Returns and Risks

As part of Kennedy Space Center's (KSC's) challenge to open the space frontier, new spaceport technologies must be developed, matured and successfully transitioned to operational systems. R&D investment decisions can be considered from multiple perspectives. Near mid and far term technology horizons must be understood. Because a multitude of technology investment opportunities are available, we must identify choices that promise the greatest likelihood of significant lifecycle At the same time, the costs and risks of any choice must be well understood and balanced against its potential returns The problem is not one of simply rank- ordering projects in terms of their desirability. KSC wants to determine a portfolio of projects that simultaneously satisfies multiple goals, such as getting the biggest bang for the buck, supporting projects that may be too risky for private funding, staying within annual budget cycles without foregoing the requirements of a long term technology vision, and ensuring the development of a diversity of technologies that, support the variety of operational functions involved in space transportation. This work aims to assist in the development of in methods and techniques that support strategic technology investment decisions and ease the process of determining an optimal portfolio of spaceport R&D investments. Available literature on risks and returns to R&D is reviewed and most useful pieces are brought to the attention of the Spaceport Technology Development Office (STDO). KSC's current project management procedures are reviewed. It is found that the "one size fits all" nature of KSC's existing procedures and project selection criteria is not conducive to prudent decision-making. Directions for improving KSC's - procedures and criteria are outlined. With help of a contractor, STDO is currently developing a tool, named Change Management Analysis Tool (CMAT)/ Portfolio Analysis Tool (PAT), to assist KSC's R&D portfolio determination. A critical review of CMAT/PAT is undertaken. Directions for the improvement of this tool are provided. STDO and KSC intend to follow up on many, if not all, of the recommendations provided.

Joglekar, Prafulla↗

NASA NTRSDate not supplied

Packing and flow particle simulations

Granular material is present across natural and industrial processes on Earth and other planets. Granular particles show up in space exploration (lunar regolith), avalanches (boulders), food (coffee), construction (concrete powder) and manufacturing (additive manufacturing powder, battery slurries). Important phenomena emerge from large collections of granular particles. The size scales of the particles in granular material, 10 μm diameter or larger, makes particle-based simulations a tractable computational method. This seminar will present the packing and flow of granular matter using particle-based discrete element modeling simulations. Particles modeled with rotational friction only require as few as 2.6 contacts for mechanical stability, as opposed to 6 contacts for frictionless particles. Optimal parameters for in-space manufacturing particulate material are identified. Specifically, the maximum density and contacts occurs for a large-to-small particle volume ratio of 0.265. Stress and contact fabric fluctuations of flowing dry granular matter have power-law scaling with strain rate, and a kink. The pressure-dependent slope change kink could identify the transition between slower, quasistatic and faster, inertial flows.

granular↗

NASA NTRSDate not supplied

Packing and flow particle simulations

granular↗

NASA NTRS1994

A manufacturing database of advanced materials used in spacecraft structures

Cost savings opportunities over the life cycle of a product are highest in the early exploratory phase when different design alternatives are evaluated not only for their performance characteristics but also their methods of fabrication which really control the ultimate manufacturing costs of the product. In the past, Design-To-Cost methodologies for spacecraft design concentrated on the sizing and weight issues more than anything else at the early so-called 'Vehicle Level' (Ref: DOD/NASA Advanced Composites Design Guide). Given the impact of manufacturing cost, the objective of this study is to identify the principal cost drivers for each materials technology and propose a quantitative approach to incorporating these cost drivers into the family of optimization tools used by the Vehicle Analysis Branch of NASA LaRC to assess various conceptual vehicle designs. The advanced materials being considered include aluminum-lithium alloys, thermoplastic graphite-polyether etherketone composites, graphite-bismaleimide composites, graphite- polyimide composites, and carbon-carbon composites. Two conventional materials are added to the study to serve as baseline materials against which the other materials are compared. These two conventional materials are aircraft aluminum alloys series 2000 and series 7000, and graphite-epoxy composites T-300/934. The following information is available in the database. For each material type, the mechanical, physical, thermal, and environmental properties are first listed. Next the principal manufacturing processes are described. Whenever possible, guidelines for optimum processing conditions for specific applications are provided. Finally, six categories of cost drivers are discussed. They include, design features affecting processing, tooling, materials, fabrication, joining/assembly, and quality assurance issues. It should be emphasized that this database is not an exhaustive database. Its primary use is to make the vehicle designer aware of some of the most important aspects of manufacturing associated with his/her choice of the structural materials. The other objective of this study is to propose a quantitative method to determine a Manufacturing Complexity Factor (MCF) for each material being contemplated. This MCF is derived on the basis of the six cost drivers mentioned above plus a Technology Readiness Factor which is very closely related to the Technology Readiness Level (TRL) as defined in the Access To Space final report. Short of any manufacturing information, our MCF is equivalent to the inverse of TRL. As more manufacturing information is available, our MCF is a better representation (than TRL) of the fabrication processes involved. The most likely application for MCF is in cost modeling for trade studies. On-going work is being pursued to expand the potential applications of MCF.

Bao, Han P.↗

NASA NTRS2005

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Desai, Prasun N.↗

NASA NTRS1980

Discrete-continuous variable structural synthesis using dual methods

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Schmit, L. A.↗

NASA NTRS1990

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics.

Wrenn, Gregory A.↗

NASA NTRS1994

Evaluating the design of an earth radiation budget instrument with system simulations. Part 2: Minimization of instantaneous sampling errors for CERES-I

Much of the new record of broadband earth radiation budget satellite measurements to be obtained during the late 1990s and early twenty-first century will come from the dual-radiometer Clouds and Earth's Radiant Energy System Instrument (CERES-I) flown aboard sun-synchronous polar orbiters. Simulation studies conducted in this work for an early afternoon satellite orbit indicate that spatial root-mean-square (rms) sampling errors of instantaneous CERES-I shortwave flux estimates will range from about 8.5 to 14.0 W/m on a 2.5 deg latitude and longitude grid resolution. Rms errors in longwave flux estimates are only about 20% as large and range from 1.5 to 3.5 W/sq m. These results are based on an optimal cross-track scanner design that includes 50% footprint overlap to eliminate gaps in the top-of-the-atmosphere coverage, and a 'smallest' footprint size to increase the ratio in the number of observations lying within to the number of observations lying on grid area boundaries. Total instantaneous measurement error also depends on the variability of anisotropic reflectance and emission patterns and on retrieval methods used to generate target area fluxes. Three retrieval procedures from both CERES-I scanners (cross-track and rotating azimuth plane) are used. (1) The baseline Earth Radiaton Budget Experiment (ERBE) procedure, which assumes that errors due to the use of mean angular dependence models (ADMs) in the radiance-to-flux inversion process nearly cancel when averaged over grid areas. (2) To estimate N, instantaneous ADMs are estimated from the multiangular, collocated observations of the two scanners. These observed models replace the mean models in computation of satellite flux estimates. (3) The scene flux approach, conducts separate target-area retrievals for each ERBE scene category and combines their results using area weighting by scene type. The ERBE retrieval performs best when the simulated radiance field departs from the ERBE mean models by less than 10%. For larger perturbations, both the scene flux and collocation methods produce less error than the ERBE retrieval. The scene flux technique is preferable, however, because it involves fewer restrictive assumptions.

Stowe, Larry↗