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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.

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NASA NTRS1987

Systems simulations supporting NASA telerobotics

Two simulation and analysis environments have been developed to support telerobotics research at the Langley Research Center. One is a high-fidelity, nonreal-time, interactive model called ROBSIM, which combines user-generated models of workspace environment, robots, and loads into a working system and simulates the interaction among the system components. Models include user-specified actuator, sensor, and control parameters, as well as kinematic and dynamic characteristics. Kinematic, dynamic, and response analyses can be selected, with system configuration, task trajectories, and arm states displayed using computer graphics. The second environment is a real-time, manned Telerobotic Systems Simulation (TRSS) which uses the facilities of the Intelligent Systems Research Laboratory (ISRL). It utilizes a hierarchical structure of functionally distributed computers communicating over both parallel and high-speed serial data paths to enable studies of advanced telerobotic systems. Multiple processes perform motion planning, operator communications, forward and inverse kinematics, control/sensor fusion, and I/O processing while communicating via common memory. This paper describes both ROBSIM and TRSS, including their capability, status, and future plans. Also described is the architecture of ISRL and recent telerobotic system studies in ISRL.

Harrison, F. Wallace, Jr.↗
NASA NTRS1987

Systems simulations supporting NASA telerobotics

Two simulation and analysis environments have been developed to support telerobotics research at the Langley Research Center. One is a high-fidelity, nonreal-time, interactive model called ROBSIM, which combines user-generated models of workspace environment, robots, and loads into a working system and simulates the interaction among the system components. Models include user-specified actuator, sensor, and control parameters, as well as kinematic and dynamic characteristics. Kinematic, dynamic, and response analyses can be selected, with system configuration, task trajectories, and arm states displayed using computer graphics. The second environment is a real-time, manned Telerobotic Systems Simulation (TRSS) which uses the facilities of the Intelligent Systems Research Laboratory (ISRL). It utilizes a hierarchical structure of functionally distributed computers communicating over both parallel and high-speed serial data paths to enable studies of advanced telerobotic systems. Multiple processes perform motion planning, operator communications, forward and inverse kinematics, control/sensor fusion, and I/O processing while communicating via common memory. Both ROBSIM and TRSS, including their capability, status, and future plans are discussed. Also described is the architecture of ISRL and recent telerobotic system studies in ISRL.

Harrison, F. W., Jr.↗
NASA NTRS2015

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is configured for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight-test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center Fullscale Advanced Systems Testbed (FAST), a modified F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois), over a range of scenarios designed to stress the SLS's Adaptive Augmenting Control (AAC) algorithm.

airborne simulation↗
NASA NTRS2014

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity-turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is optimized for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using NASA Dryden Flight Research Center's Full-scale Advanced Systems Testbed (FAST), a modified F/A-18 airplane, over a range of scenarios designed to stress the SLS's adaptive augmenting control (AAC) algorithm.

Gilligan, Eric T.↗
NASA NTRS1989

Nonlinear and distributed parameter models of the mini-mast truss

Large spacecraft such as Space Station Freedom employ large trusses in their construction. The structural dynamics of such trusses often exhibit nonlinear behavior and little damping which can impact significantly the performance of control systems. The Mini-MAST truss was constructed to research such structural dynamics and control systems. The Mini-MAST truss is an object of study for the guest investigator program as part of NASA's controls-structures interaction program. The Mini-MAST truss is deployable and about 65 ft long. Although the bending characteristics of the Mini-MAST truss are essentially linear, the angular deflection under torsional loading has exhibited significant hysteresis and nonlinear stiffness. It is the purpose to develop nonlinear and distributed parameter models of the truss and to compare the model dynamics with actual measurements. Distributed parameter models have the advantage of requiring fewer model parameters. A tangent function is used to describe the nonlinear stiffness in torsion, partly because of the convenience of its easily expressed inverse. Hysteretic slip elements are introduced and extended to a continuum to account for the observed hysteresis in torsion. The contribution of slipping to the structural damping is analyzed and found to be strongly dependent on the applied loads. Because of the many factors which affect the damping and stiffness in a truss, it is risky to assume linearity.

Taylor, Lawrence W., Jr.↗
NASA NTRS2009

G(sup 4)FET Implementations of Some Logic Circuits

Some logic circuits have been built and demonstrated to work substantially as intended, all as part of a continuing effort to exploit the high degrees of design flexibility and functionality of the electronic devices known as G(sup 4)FETs and described below. These logic circuits are intended to serve as prototypes of more complex advanced programmable-logicdevice-type integrated circuits, including field-programmable gate arrays (FPGAs). In comparison with prior FPGAs, these advanced FPGAs could be much more efficient because the functionality of G(sup 4)FETs is such that fewer discrete components are needed to perform a given logic function in G(sup 4)FET circuitry than are needed perform the same logic function in conventional transistor-based circuitry. The underlying concept of using G(sup 4)FETs as building blocks of programmable logic circuitry was also described, from a different perspective, in G(sup 4)FETs as Universal and Programmable Logic Gates (NPO-41698), NASA Tech Briefs, Vol. 31, No. 7 (July 2007), page 44. A G(sup 4)FET can be characterized as an accumulation-mode silicon-on-insulator (SOI) metal oxide/semiconductor field-effect transistor (MOSFET) featuring two junction field-effect transistor (JFET) gates. The structure of a G(sup 4)FET (see Figure 1) is the same as that of a p-channel inversion-mode SOI MOSFET with two body contacts on each side of the channel. The top gate (G1), the substrate emulating a back gate (G2), and the junction gates (JG1 and JG2) can be biased independently of each other and, hence, each can be used to independently control some aspects of the conduction characteristics of the transistor. The independence of the actions of the four gates is what affords the enhanced functionality and design flexibility of G(sup 4)FETs. The present G(sup 4)FET logic circuits include an adjustable-threshold inverter, a real-time-reconfigurable logic gate, and a dynamic random-access memory (DRAM) cell (see Figure 2). The configuration of the adjustable-threshold inverter is similar to that of an ordinary complementary metal oxide semiconductor (CMOS) inverter except that an NMOSFET (a MOSFET having an n-doped channel and a p-doped Si substrate) is replaced by an n-channel G(sup 4)FET

Mojarradi, Mohammad↗
NASA NTRS1993

Trajectory optimization for the National aerospace plane

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Lu, Ping↗
NASA NTRS1993

Theoretical constraints in the design of multivariable control systems

The theoretical constraints inherent in the design of multivariable control systems were defined and investigated. These constraints are manifested by the system transmission zeros that limit or bound the areas in which closed loop poles and individual transfer function zeros may be placed. These constraints were investigated primarily in the context of system decoupling or non-interaction. It was proven that decoupling requires the placement of closed loop poles at the system transmission zeros. Therefore, the system transmission zeros must be minimum phase to guarantee a stable decoupled system. Once decoupling has been accomplished, the remaining part of the system exhibits transmission zeros at infinity, so nearly complete design freedom is possible in terms of placing both poles and zeros of individual closed loop transfer functions. A general, dynamic inversion model following system architecture was developed that encompasses both the implicit and explicit configuration. Robustness properties are developed along with other attributes of this type of system. Finally, a direct design is developed for the longitudinal-vertical degrees of freedom of aircraft motion to show how a direct lift flap can be used to improve the pitch-heave maneuvering coordination for enhanced flying qualities.

Rynaski, E. G.↗
NASA NTRS1997

Revised Simulation Model of the Control System, Displays, and Propulsion System for a ASTOVL Lift Fan Aircraft

This report describes revisions to a simulation model that was developed for use in piloted evaluations of takeoff, transition, hover, and landing characteristics of an advanced short takeoff and vertical landing lift fan fighter aircraft. These revisions have been made to the flight/propulsion control system, head-up display, and propulsion system to reflect recent flight and simulation experience with short takeoff and vertical landing operations. They include nonlinear inverse control laws in all axes (eliminating earlier versions with state rate feedback), throttle scaling laws for flightpath and thrust command, control selector commands apportioned based on relative effectiveness of the individual controls, lateral guidance algorithms that provide more flexibility for terminal area operations, and a simpler representation of the propulsion system. The model includes modes tailored to the phases of the aircraft's operation, with several response types which are coupled to the aircraft's aerodynamic and propulsion system effectors through a control selector tailored to the propulsion system. Head-up display modes for approach and hover are integrated with the corresponding control modes. Propulsion system components modeled include a remote lift fan and a lift-cruise engine. Their static performance and dynamic responses are represented by the model. A separate report describes the subsonic, power-off aerodynamics and jet induced aerodynamics in hover and forward flight, including ground effects.

Franklin, James A.↗
NASA NTRS2022

Impact of Meteorological Factors on the Mesoscale Morphology of Cloud Streets during a Cold-Air Outbreak over the Western North Atlantic

Postfrontal clouds (PFC) are ubiquitous in the marine boundary layer, and their morphology is essential to estimating the radiation budget in weather and climate models. Here we examine the roles of sea surface temperature (SST) and meteorological factors in controlling the mesoscale morphology and evolution of shallow clouds associated with a cold-air outbreak that occurred on 1 March 2020 during phase I of the Aerosol Cloud Meteorology Interactions over the Western Atlantic Experiment (ACTIVATE). Our results show that the simulated PFC structure and ambient conditions by the Weather Research and Forecasting (WRF) Model are generally consistent with observations from GOES-16 and dropsonde measurements. We also examine the thermodynamical and dynamical influences in the cloud mesoscale morphology using WRF sensitivity experiments driven by two meteorological forcing datasets with different domain-mean SST and spatial gradients, which lead to dissimilar values of hydrometeor water path and cloud core fraction. The SST from ERA5 leads to weaker stability and higher inversion height than the SST from FNL does. In addition, the use of large-scale meteorological forcings from ERA5 yields a distinctive time evolution of wind direction shear in the inner domain, which favors the formation and persistence of longer cloud rolls. Both factors contribute to a change in the time evolution of domain-mean water path and cloud core fraction of cloud streets. Our study takes advantage of the simulation driven by the differences between two large-scale forcing datasets to illustrate the importance of SST and wind direction shear in the cloud street morphology in a realistic scenario

Jingyi Chen↗
NASA NTRS1998

Reveal, A General Reverse Engineering Algorithm for Inference of Genetic Network Architectures

Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/output patterns of its variables? We investigated this possibility using binary models of genetic networks. Trajectories, or state transition tables of Boolean nets, resemble time series of gene expression. By systematically analyzing the mutual information between input states and output states, one is able to infer the sets of input elements controlling each element or gene in the network. This process is unequivocal and exact for complete state transition tables. We implemented this REVerse Engineering ALgorithm (REVEAL) in a C program, and found the problem to be tractable within the conditions tested so far. For n = 50 (elements) and k = 3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10(exp 15)) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean networks, the algorithm is generalizable to include multi-state models, essentially allowing direct application to realistic biological data sets. The ability to adequately solve the inverse problem may enable in-depth analysis of complex dynamic systems in biology and other fields.

Liang, Shoudan↗
NASA NTRS1988

Analysis of a closed-kinematic chain robot manipulator

Presented are the research results from the research grant entitled: Active Control of Robot Manipulators, sponsored by the Goddard Space Flight Center (NASA) under grant number NAG-780. This report considers a class of robot manipulators based on the closed-kinematic chain mechanism (CKCM). This type of robot manipulators mainly consists of two platforms, one is stationary and the other moving, and they are coupled together through a number of in-parallel actuators. Using spatial geometry and homogeneous transformation, a closed-form solution is derived for the inverse kinematic problem of the six-degree-of-freedom manipulator, built to study robotic assembly in space. Iterative Newton Raphson method is employed to solve the forward kinematic problem. Finally, the equations of motion of the above manipulators are obtained by employing the Lagrangian method. Study of the manipulator dynamics is performed using computer simulation whose results show that the robot actuating forces are strongly dependent on the mass and centroid locations of the robot links.

Nguyen, Charles C.↗
NASA NTRS1989

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

Bayo, Eduardo↗
NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗
NASA NTRS1990

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

The optimization of trajectories for coplaner, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Miele, A.↗
NASA NTRS2008

Interactive Inverse Design Optimization of Fuselage Shape for Low-Boom Supersonic Concepts

This paper introduces a tool called BOSS (Boom Optimization using Smoothest Shape modifications). BOSS utilizes interactive inverse design optimization to develop a fuselage shape that yields a low-boom aircraft configuration. A fundamental reason for developing BOSS is the need to generate feasible low-boom conceptual designs that are appropriate for further refinement using computational fluid dynamics (CFD) based preliminary design methods. BOSS was not developed to provide a numerical solution to the inverse design problem. Instead, BOSS was intended to help designers find the right configuration among an infinite number of possible configurations that are equally good using any numerical figure of merit. BOSS uses the smoothest shape modification strategy for modifying the fuselage radius distribution at 100 or more longitudinal locations to find a smooth fuselage shape that reduces the discrepancies between the design and target equivalent area distributions over any specified range of effective distance. For any given supersonic concept (with wing, fuselage, nacelles, tails, and/or canards), a designer can examine the differences between the design and target equivalent areas, decide which part of the design equivalent area curve needs to be modified, choose a desirable rate for the reduction of the discrepancies over the specified range, and select a parameter for smoothness control of the fuselage shape. BOSS will then generate a fuselage shape based on the designer's inputs in a matter of seconds. Using BOSS, within a few hours, a designer can either generate a realistic fuselage shape that yields a supersonic configuration with a low-boom ground signature or quickly eliminate any configuration that cannot achieve low-boom characteristics with fuselage shaping alone. A conceptual design case study is documented to demonstrate how BOSS can be used to develop a low-boom supersonic concept from a low-drag supersonic concept. The paper also contains a study on how perturbations in the equivalent area distribution affect the ground signature shape and how new target area distributions for low-boom signatures can be constructed using superposition of equivalent area distributions derived from the Seebass-George-Darden (SGD) theory.

Li, Wu↗
NASA NTRS1990

A cloudiness transition in a marine boundary layer

Boundary layer cloudiness plays several important roles in the energy budget of the earth. Low level stratocumulus are highly reflective clouds which reduce the net incoming shortwave radiation at the earth's surface. Climatically, the transition to a small area fraction of scattered cumulus clouds occurs as the air flows over warmer water. Although these clouds reflect less sunlight, they still play an important role in the boundary layer equilibrium by transporting water vapor upwards, and enhancing the surface evaporation. The First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment (FIRE) included a marine stratocumulus experiment off the southern California coast from June 29 to July 19, 1987. The objectives of this experiment were to study the controls on fractional cloudiness, and to assess the role of cloud-top entrainment instability (CTEI) and mesoscale structure in determining cloud type. The focus is one research day, July 7, 1987, when coordinated aircraft missions were flown by four research aircraft, centered on a LANDSAT scene at 1830 UTC. The remarkable feature of this LANDSAT scene is the transition from a clear sky in the west through broken cumulus to solid stratocumulus in the east. The dynamic and thermodynamic structure of this transition in cloudiness is analyzed using data from the NCAR Electra. By averaging the aircraft data, the internal structure of the different cloud regimes is documented, and it is shown that the transition between broken cumulus and stratocumulus is associated with a change in structure with respect to the CTEI condition. However, this results not from sea surface temperature changes, but mostly from a transition in the air above the inversion, and the breakup appears to be at a structure on the unstable side of the wet virtual adiabat.

Betts, Alan K.↗
NASA NTRS2012

New Approaches to Quantifying Transport Model Error in Atmospheric CO2 Simulations

In recent years, much progress has been made in observing CO2 distributions from space. However, the use of these observations to infer source/sink distributions in inversion studies continues to be complicated by difficulty in quantifying atmospheric transport model errors. We will present results from several different experiments designed to quantify different aspects of transport error using the Goddard Earth Observing System, Version 5 (GEOS-5) Atmospheric General Circulation Model (AGCM). In the first set of experiments, an ensemble of simulations is constructed using perturbations to parameters in the model s moist physics and turbulence parameterizations that control sub-grid scale transport of trace gases. Analysis of the ensemble spread and scales of temporal and spatial variability among the simulations allows insight into how parameterized, small-scale transport processes influence simulated CO2 distributions. In the second set of experiments, atmospheric tracers representing model error are constructed using observation minus analysis statistics from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA). The goal of these simulations is to understand how errors in large scale dynamics are distributed, and how they propagate in space and time, affecting trace gas distributions. These simulations will also be compared to results from NASA's Carbon Monitoring System Flux Pilot Project that quantified the impact of uncertainty in satellite constrained CO2 flux estimates on atmospheric mixing ratios to assess the major factors governing uncertainty in global and regional trace gas distributions.

Ott, L.↗