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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 NTRS1985

Precision geodesy using the Mark-III very-long-baseline interferometer system

Very-long-baseline interferometry (VLBI) has been used to make precise measurements of the vector separation between widely separated antennas. The system for acquiring and processing VLBI data known as Mark-III is described. Tests of the system show it to have millimeter-level accuracy on short baselines; measurements of baselines longer than a few hundred kilometers suggest that accuracy is limited by the uncertainty in the calibration of tropospheric path delay to the level of a few centimeters. VLBI experiments conducted between 1976 and 1983 have demonstrated the stability of the North American plate by showing that there is no change in the distance between eastern California and Massachusetts at the level of a few millimeters per year or greater. Experiments made from 1980 to 1984 indicate that the distance from Massachusetts to Sweden is increasing by 1.7 + or - 1 cm/year where the quoted standard deviation includes the estimated effects of systematic errors.

Clark, T. A.↗
NASA NTRS2007

Global Aerosol Optical Models and Lookup Tables for the New MODIS Aerosol Retrieval over Land

Since 2000, MODIS has been deriving aerosol properties over land from MODIS observed spectral reflectance, by matching the observed reflectance with that simulated for selected aerosol optical models, aerosol loadings, wavelengths and geometrical conditions (that are contained in a lookup table or 'LUT'). Validation exercises have showed that MODIS tends to under-predict aerosol optical depth (tau) in cases of large tau (tau greater than 1.0), signaling errors in the assumed aerosol optical properties. Using the climatology of almucantur retrievals from the hundreds of global AERONET sunphotometer sites, we found that three spherical-derived models (describing fine-sized dominated aerosol), and one spheroid-derived model (describing coarse-sized dominated aerosol, presumably dust) generally described the range of observed global aerosol properties. The fine dominated models were separated mainly by their single scattering albedo (omega(sub 0)), ranging from non-absorbing aerosol (omega(sub 0) approx. 0.95) in developed urban/industrial regions, to neutrally absorbing aerosol (omega(sub 0) approx.90) in forest fire burning and developing industrial regions, to absorbing aerosol (omega(sub 0) approx. 0.85) in regions of savanna/grassland burning. We determined the dominant model type in each region and season, to create a 1 deg. x 1 deg. grid of assumed aerosol type. We used vector radiative transfer code to create a new LUT, simulating the four aerosol models, in four MODIS channels. Independent AERONET observations of spectral tau agree with the new models, indicating that the new models are suitable for use by the MODIS aerosol retrieval.

Levy, Robert C.↗
NASA NTRSDate not supplied

Spacecraft Passive Safety Assessment Using Ellipse Constraints and Relative Orbital Elements

This paper presents necessary and sufficient conditions for validating spacecraft passive safety using relative orbital elements (ROE) centered around the far-field to near-field trajectory design of a hypothetical autonomous rendezvous and docking (AR&D) mission. The specific formulation of the ROEs used in this study are of quasi-nonsingular form based on elative eccentricity/inclination vectors. Current methodologies for ensuring passive safety apply keep-out volumes (KOV) to maintain appropriate separation between the Servicer and Client. Widely used techniques to assess the integrity of the KOV involve forward propagation of the relative Cartesian state to check for a potential KOV breach. In this study, an alternative approach to the propagation-based method is proposed using ROEs due to their valuable geometric insights of spacecraft relative motion. Modeling the relative trajectory and KOV ellipsoids as ellipses into the 2-D ROE sub-space simplifies the passive safety validation to a root-finding problem within the unit disk with high computational efficiency. Other approaches to intersection detection of the KOV are also evaluated in accuracy and run-time. Furthermore, a Monte Carlo simulation was employed to compare the ROE-based and relative Cartesian approaches in terms of maneuver error.

Bruce Barbour↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Estimation of Snow Mass Information via Assimilation of C-Band Synthetic Aperture Radar Backscatter Observations Into an Advanced and Surface Model

This study assimilated Sentinel-1 C-band backscatter observations over snow-covered terrain into the Noah-Multiparameterization land surface model using support vector machine (SVM) regression and an ensemble Kalman filter to improve the modeled terrestrial snow mass estimates. The data assimilation (DA) experiment was conducted across Western Colorado from September 2016 to August 2017. As part of the DA experiments, the impact of a rule-based update was evaluated by comparing snow water equivalent (SWE) estimates via DA (with [ DAv1 ] and without [ DAv2 ] the rule-based update) against SNOTEL SWE measurements. Results confirmed that rule-based update helped minimize SVM controllability issues, and in turn, improved the accuracy of SWE estimates relative to both open loop (OL) and DAv2 . Comparison of SWE estimates from Sentinel-1 DAv1 against SNOTEL SWE revealed that 75% of stations showed improvements in bias and correlation coefficient relative to the OL. Assimilated SWE estimates also showed statistical improvements during both the snow accumulation and snow ablation periods. However, unbiased root mean square error showed a slight increase during the snow ablation period due to the large variability in the electromagnetic response of C-band backscatter over deep and/or wet snow. Improvement of the SWE estimates also resulted in improving river discharge estimates compared to in situ measurements. River discharge using Sentinel-1 DAv1 improved the Nash–Sutcliffe efficiency at all available stations. These results suggest that physically constrained SVM can serve as an efficient observation operator for snow mass DA through explicit consideration of the first-order C-band scattering mechanisms over different terrestrial snow conditions.

Jongmin Park↗
NASA NTRS2011

Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(R) (MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many cou ntries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its re al strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbo x. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using s ymbolic operations. MatLab in its interpreter programming language fo rm (command interface) is similar with well known programming languag es such as C/C++, support data structures and cell arrays to define c lasses in object oriented programming. As such, MatLab is equipped with most ofthe essential constructs of a higher programming language. M atLab is packaged with an editor and debugging functionality useful t o perform analysis of large MatLab programs and find errors. We belie ve there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and ana lysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applicati ons. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientifi c problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabu lar format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed. The presentation will emphasize creating practIcal scripts (pro grams) that extend the basic features of MatLab TOPICS mclude (1) Ma trix and vector analysis and manipulations (2) Mathematical functions (3) Symbolic calculations & functions (4) Import/export data files (5) Program lOgic and flow control (6) Writing function and passing parameters (7) Test application programs

Sen, Syamal K.↗
NASA NTRS2019

Inversion of Multiangular Polarimetric Measurements Over Open and Coastal Ocean Waters: A Joint Retrieval Algorithm for Aerosol and Water-Leaving Radiance Properties

Ocean color remote sensing is a challenging task over coastal waters due to the complex optical properties of aerosols and hydrosols. In order to conduct accurate atmospheric correction, we previously implemented a joint retrieval algorithm, hereafter referred to as the Multi-Angular Polarimetric Ocean coLor (MAPOL) algorithm, to obtain the aerosol and water-leaving signal simultaneously. The MAPOL algorithm has been validated with synthetic data generated by a vector radiative transfer model, and good retrieval performance has been demonstrated in terms of both aerosol and ocean water optical properties (Gao et al., 2018). In this work we applied the algorithm to airborne polarimetric measurements from the Research Scanning Polarimeter (RSP) over both open and coastal ocean waters acquired in two field campaigns: the Ship-Aircraft Bio-Optical Research (SABOR) in 2014 and the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES) in 2015 and 2016. Two different yet related bio-optical models are designed for ocean water properties. One model aligns with traditional open ocean water bio-optical models that parameterize the ocean optical properties in terms of the concentration of chlorophyll a. The other is a generalized bio-optical model for coastal waters that includes seven free parameters to describe the absorption and scattering by phytoplankton, colored dissolved organic matter, and nonalgal particles. The retrieval errors of both aerosol optical depth and the water-leaving radiance are evaluated. Through the comparisons with ocean color data products from both in situ measurements and the Moderate Resolution Imaging Spectroradiometer (MODIS), and the aerosol product from both the High Spectral Resolution Lidar (HSRL) and the Aerosol Robotic Network (AERONET), the MAPOL algorithm demonstrates both flexibility and accuracy in retrieving aerosol and water-leaving radiance properties under various aerosol and ocean water conditions.

Gao, Meng↗
NASA NTRSDate not supplied

Controls Algorithms, Models, and Stability Assessments of the RCS and TVC systems on Mars Ascent Vehicle

This paper presents a control systems overview of the Mars Ascent Vehicle (MAV) control design and stability analysis with two separate control methods: Thrust Vector Control (TVC) based control using main engine thrust and Reaction Control System (RCS) via thrusters. A pole-placement TVC controller is proposed to address quickly peaking thrust produced by the MAV solid propulsion engine. The controllerutilizes real-time parameter estimation to calculate control gains using an online pole-placement method. The pole-placement technique allows the controller to maintain constant stability margins throughout the flight under changing parameters and rapidly peaking thrust. A mathematical stability proof via Lyapunov inequality and Nichols method is demonstrated to support the stability of the method. In addition to the TVC control, a phase-plane based RCS control logic is applied to the vehicle for roll control during ascent and all axes during coast phases of flight. The logic implemented is an on-off type logic that applies pre-determined thrusters firings in reference to boundary parameters of pointing and rate error chosen to balance desired pointing with stability. A describing function methodology is applied to the non-linear phase plane loop response to determine linear stability across all flight phases. The controller additionally applies command alteration logic to output signals to account for RCS hardware limitations. The following paper will provide the methodology for controller implementation of the TVC and RCS, and provide a summary of results of the MAV performance applying the aforementioned control design.

Han Woong Bae↗
NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗
NASA NTRS1993

Comparison of remote sensing measurements with a two-scale polarimetric emission and scattering model for sea surfaces

Recently, it has been observed that the brightness temperatures of sea surfaces correlate with the azimuth angle of the ocean wind vector, indicating that ocean wind direction can not only be retrieved from the microwave backscatter, but also from the brightness temperature measurements. In this paper, comparison of the theoretical result calculated from a two-scale emission and scattering model with the Seasat and SSM/I model functions and aircraft measurements is presented and potential applications of microwave polarimetry are discussed. In our two-scale model, the modified reflectivities of large scale surfaces are calculated by extending the small perturbation method to the second order for small scale perturbation with anisotropic directional spectrum. It was found that the modified reflectivities derived from the second-order scattered field agree excellently well with the results obtained from a Monte Carlo simulation technique which numerically calculates the polarimetric reflectivities of one-dimensional random rough surfaces with a power-law spectrum. Without the second-order correction, the modified reflectivities of the rough surfaces are significantly over-estimated and sign errors are observed in the third and fourth Stokes parameters for thermal emissions. The surface spectrum parameters and two-scale cutoff are selected so that the calculated scattering and emission signatures agree with the reported model functions for Seasat and SSM/I. Subsequently, the polarimetric signatures of sea surfaces are illustrated to indicate the possibility of reducing the number of azimuthal looks required for spaceborne sensors in the remote sensing of ocean wind by using the polarimetric information. Furthermore, it is found that contrary to the dependence of backscattering coefficients on incidence angles, polarimetric brightness temperatures display a stronger wind direction dependence in the near nadir-looking direction than away from nadir. Finally, we discuss the potential of a single-look polarimetric radiometer for wind retrieval.

Yueh, S. H.↗
NASA NTRS1986

Geodesy by radio interferometry - Determinations of baseline vector, earth rotation, and solid earth tide parameters with the Mark I very long baseline radio interferometery system

Thirty-seven very long baseline radio interferometry experiments performed between 1972 and 1978 are analyzed and estimates of baseline vectors between six sites, five in the continental United States and one in Europe are derived. No evidence of significant changes in baseline length is found. For example, with a statistical level of confidence of approximately 85 percent, upper bounds on such changes within the United States ranged from a low of 10 mm/yr for the 850 km baseline between Westford, Massachusetts, and Green Bank, West Virginia, to a high of 90 mm/yr for the nearly 4000 km baseline between Westford and Goldstone, California. Estimates for universal time and for the x component of the position of the earth's pole are obtained. For the last 15 experiments, the only ones employing wideband receivers, the root-mean-square differences between the derived values and the corresponding ones published by the Bureau International de l'Heure are 0.0012 s and 0.018 arc sec respectively. The average value obtained for the radial Love number for the solid earth is 0.62 + or - 0.02 (estimated standard error).

Ryan, J. W.↗
NASA NTRS2011

Flight Dynamics Operations: Methods and Lessons Learned from Space Shuttle Orbit Operations

The Flight Dynamics Officer is responsible for trajectory maintenance of the Space Shuttle. This paper will cover high level operational considerations, methodology, procedures, and lessons learned involved in performing the functions of orbit and rendezvous Flight Dynamics Officer and leading the team of flight dynamics specialists during different phases of flight. The primary functions that will be address are: onboard state vector maintenance, ground ephemeris maintenance, calculation of ground and spacecraft acquisitions, collision avoidance, burn targeting for the primary mission, rendezvous, deorbit and contingencies, separation sequences, emergency deorbit preparation, mass properties coordination, payload deployment planning, coordination with the International Space Station, and coordination with worldwide trajectory customers. Each of these tasks require the Flight Dynamics Officer to have cognizance of the current trajectory state as well as the impact of future events on the trajectory plan in order to properly analyze and react to real-time changes. Additionally, considerations are made to prepare flexible alternative trajectory plans in the case timeline changes or a systems failure impact the primary plan. The evolution of the methodology, procedures, and techniques used by the Flight Dynamics Officer to perform these tasks will be discussed. Particular attention will be given to how specific Space Shuttle mission and training simulation experiences, particularly off-nominal or unexpected events such as shortened mission durations, tank failures, contingency deorbit, navigation errors, conjunctions, and unexpected payload deployments, have influenced the operational procedures and training for performing Space Shuttle flight dynamics operations over the history of the program. These lessons learned can then be extended to future vehicle trajectory operations.

Cutri-Kohart, Rebecca M.↗
NASA NTRS2007

Benefits Derived From Laser Ranging Measurements for Orbit Determination of the GPS Satellite Orbit

While navigation systems for the determination of the orbit of the Global Position System (GPS) have proven to be very effective, the current research is examining methods to lower the error in the GPS satellite ephemerides below their current level. Two GPS satellites that are currently in orbit carry retro-reflectors onboard. One notion to reduce the error in the satellite ephemerides is to utilize the retro-reflectors via laser ranging measurements taken from multiple Earth ground stations. Analysis has been performed to determine the level of reduction in the semi-major axis covariance of the GPS satellites, when laser ranging measurements are supplemented to the radiometric station keeping, which the satellites undergo. Six ground tracking systems are studied to estimate the performance of the satellite. The first system is the baseline current system approach which provides pseudo-range and integrated Doppler measurements from six ground stations. The remaining five ground tracking systems utilize all measurements from the current system and laser ranging measurements from the additional ground stations utilized within those systems. Station locations for the additional ground sites were taken from a listing of laser ranging ground stations from the International Laser Ranging Service. Results show reductions in state covariance estimates when utilizing laser ranging measurements to solve for the satellite s position component of the state vector. Results also show dependency on the number of ground stations providing laser ranging measurements, orientation of the satellite to the ground stations, and the initial covariance of the satellite's state vector.

Welch, Bryan W.↗
NASA NTRS2007

Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation

TerraSAR-X (TSX) and TanDEM-X (TDX) are two advanced synthetic aperture radar (SAR) satellites flying in formation. SAR interferometry allows a high resolution imaging of the Earth by processing SAR images obtained from two slightly different orbits. TSX operates as a repeat-pass interferometer in the first phase of its lifetime and will be supplemented after two years by TDX in order to produce digital elevation models (DEM) with unprecedented accuracy. Such a flying formation makes indeed possible a simultaneous interferometric data acquisition characterized by highly flexible baselines with range of variations between a few hundreds meters and several kilometers [1]. TSX has been successfully launched on the 15th of June, 2007. TDX is expected to be launched on the 31st of May, 2009. A safe and robust maintenance of the formation is based on the concept of relative eccentricity/inclination (e/i) vector separation whose efficiency has already been demonstrated during the Gravity Recovery and Climate Experiment (GRACE) [2]. Here, the satellite relative motion is parameterized by mean of relative orbit elements and the key idea is to align the relative eccentricity and inclination vectors to minimize the hazard of a collision. Previous studies have already shown the pertinence of this concept and have described the way of controlling the formation using an impulsive deterministic control law [3]. Despite the completely different relative orbit control requirements, the same approach can be applied to the TSX/TDX formation. The task of TDX is to maintain the close formation configuration by actively controlling its relative motion with respect to TSX, the leader of the formation. TDX must replicate the absolute orbit keeping maneuvers executed by TSX and also compensate the natural deviation of the relative e/i vectors. In fact the relative orbital elements of the formation tend to drift because of the secular non-keplerian perturbations acting on both satellites. The goal of the ground segment is thus to regularly correct this configuration by performing small orbit correction maneuvers on TDX. The ground station contacts are limited due to the geographic position of the station and the costs for contact time. Only with a polar ground station a contact visibility is possible every orbit for LEO satellites. TSX and TDX use only the Weilheim ground station (in the southern part of Germany) during routine operations. This station allows two scheduled contact per day for the nominal orbit configuration, meaning that the satellite conditions can be checked with an interval of 12 hours. While this limitation is usually not critical for single satellite operations, the visibility constraints drive the achievable orbit control accuracy for a LEO formation if a ground based approach is chosen. Along-track position uncertainties and maneuver execution errors affect the relative motion and can be compensated only after a ground station contact.

Ardaens, J. S.↗
DOE OSTI2025

Geometric Interpretation of the Cluster Location Problem Part I: Theory

We present a new framing of the seismic location problem using principles drawn from differential geometry. Our interpretation relies upon the common assumption that travel times observed across a network are continuous, differentiable functions of source location. In consequence, travel‐time functions constitute a differentiable map between the source region and a Riemannian manifold. The manifold is said to be the image of the source region embedded in a generally high‐dimension travel‐time vector space. A cluster of events in the source region has an image of discrete points on the manifold, that, except in the simplest cases, cannot be viewed directly. However, it is possible to project the image of a cluster into a tangent space of the manifold for direct visualization. The projection operator can be computed directly from the data without a velocity model, but produces a distorted rendering of the cluster geometry. With a model we can predict the distortions and correct them to estimate cluster geometry. We develop these points with the simplest possible example, one for which direct visualization of the manifold is possible, using the example as an introduction to the relevant concepts from differential geometry in a familiar setting. The tangent space, a local linearization of the manifold, plays a key role. We develop a metric to estimate the limits of linearization, that is, to determine when the curvature of the manifold invalidates the linear assumption. We also examine the interplay of model error, inadequate network geometry, and pick error. We then generalize our results from the simple case to the general case of 3D source regions observed by general networks. Although we do suggest a new “project and correct” method for location, we do not develop it into a practical algorithm. In conclusion, our intention rather is to highlight new analytical methods grounded in differential geometry.

East Pacific Ocean Islands↗
NASA NTRS2005

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.↗
DOE OSTI2025

Ancilla-entangling Floquet kicks for accelerating quantum algorithms

Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and thus places an annealing rate bottleneck for high success probability. Here, in this study, we accelerate quantum simulation using digital multiqubit gates that entangle primary system qubits with ancillary qubits. The practical benefits originate from tuning the ancillary gauge degrees of freedom to enhance the quantum algorithm's original functionality in the system registry. For simple but nontrivial short-ranged, infinite long-ranged transverse-field Ising models, and the hydrogen molecule model after qubit encoding, we show improvement in the time to solution by one hundred percent but with higher accuracy through exact state-vector numerical simulation in a digital-analog setting. The findings are further supported by time-averaged Hamiltonian theory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

A New, More Physically Based Algorithm, for Retrieving Aerosol Properties over Land from MODIS

The MOD Imaging Spectrometer (MODIS) has been successfully retrieving aerosol properties, beginning in early 2000 from Terra and from mid 2002 from Aqua. Over land, the retrieval algorithm makes use of three MODIS channels, in the blue, red and infrared wavelengths. As part of the validation exercises, retrieved spectral aerosol optical thickness (AOT) has been compared via scatterplots against spectral AOT measured by the global Aerosol Robotic NETwork (AERONET). On one hand, global and long term validation looks promising, with two-thirds (average plus and minus one standard deviation) of all points falling between published expected error bars. On the other hand, regression of these points shows a positive y-offset and a slope less than 1.0. For individual regions, such as along the U.S. East Coast, the offset and slope are even worse. Here, we introduce an overhaul of the algorithm for retrieving aerosol properties over land. Some well-known weaknesses in the current aerosol retrieval from MODIS include: a) rigid assumptions about the underlying surface reflectance, b) limited aerosol models to choose from, c) simplified (scalar) radiative transfer (RT) calculations used to simulate satellite observations, and d) assumption that aerosol is transparent in the infrared channel. The new algorithm attempts to address all four problems: a) The new algorithm will include surface type information, instead of fixed ratios of the reflectance in the visible channels to the mid-IR reflectance. b) It will include updated aerosol optical properties to reflect the growing aerosol retrieved from eight-plus years of AERONE". operation. c) The effects of polarization will be including using vector RT calculations. d) Most importantly, the new algorithm does not assume that aerosol is transparent in the infrared channel. It will be an inversion of reflectance observed in the three channels (blue, red, and infrared), rather than iterative single channel retrievals. Thus, this new formulation of the MODIS aerosol retrieval over land includes more physically based surface, aerosol and radiative transfer with fewer potentially erroneous assumptions.

Levy, Robert C.↗