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DOE OSTI2024

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

3D fault architecture controls the dynamism of earthquake swarms

The vibrant evolutionary patterns made by earthquake swarms are incompatible with standard, effectively two-dimensional (2D) models for general fault architecture. Here we leverage advances in earthquake monitoring with a deep-learning algorithm to image a fault zone hosting a 4-year-long swarm in southern California. We infer that fluids are naturally injected into the fault zone from below and diffuse through strike-parallel channels while triggering earthquakes. A permeability barrier initially limits up-dip swarm migration but ultimately is circumvented. This enables fluid migration within a shallower section of the fault with fundamentally different mechanical properties. Our observations provide high-resolution constraints on the processes by which swarms initiate, grow, and arrest. These findings illustrate how swarm evolution is strongly controlled by 3D variations in fault architecture.

58 GEOSCIENCES↗

DOE OSTI2020

Study of the Mu2e sensitivity to the $\mu^-\rightarrow e^+$ conversion process

The Mu2e experiment at Fermilab (Batavia, IL) will search for the coherent neutrinoless conversion of a muon into an electron in the electric field of an aluminum atom. The conversion process results in a monochromatic electron with energy slightly below the muon rest mass ($E_e= 104.97$ MeV). The experiment goal is to improve the previous measurement by four orders of magnitude and reach a single event sensitivity of $3 \times 10^{-17} $ on the conversion rate with respect to the muon capture rate. \\ The experiment will deliver a very intense pulsed negative muon beam to an aluminum target to achieve a total number of $10^{18}$ stopped muons in three years of running. Production and transport of the muons are accomplished with a sophisticated magnetic system comprised of a Production, a Transport and a Detector solenoid, with the last one hosting a Straw-tube Tracker and a Crystal Calorimeter. The entire detector region is surrounded by a Cosmic Ray Veto system. Mu2e is und er construction at the Muon Campus of Fermilab. \\ The INFN italian group is responsible for the design and construction of the crystal calorimeter, which plays a crucial role in the Mu2e measurement, providing particle identification capabilities fundamental for the rejection of the different background sources that can mimic a conversion electron. The calorimeter information allows also to improve the tracking performances it provides a fast standalone trigger for the experiment.\\ After a long R\&D phase, the final drawings see a calorimeter comprised of 1348 pure CsI crystals arranged in two annular disks. Each crystal is readout by two custom UV-extended Silicon Photomultipliers (SiPMs). Performances of the selected components were verified with an electron beam test, carried out in 2017 at the Beam Test Facility (BTF) at the National Laboratories of Frascati, on a large size prototype of 51 crystals and 102 SiPMs, confirming excellent energy ($\sigma_{E}/E = \mathcal{O }(10\%)$) and timing ($\sigma_{T} <500$ ps) resolutions in a! greement with the Mu2e specifications.\\ In the first chapters of this thesis, I describe my involvement in the calorimeter activities, with particular emphasis on the data analysis of the prototype energy response and resolution, that I was personally leading. Moreover, a description of the tuning of the simulation and the careful data-MC comparison is also reported.\\ An auxiliary measurement that can be performed with Mu2e is the search for a Lepton Number Violation (LNV) process where the negatively charged muon converts, without neutrinos, into a positron, $\mu ^{-} +N(A,Z) \rightarrow $ e$^+ +N(A,Z-2)$. At the moment of writing, Neutrinoless Double Beta Decay (0$\nu \beta \beta$) has set the most stringent limit on the LNV processes (T$^{0\nu \beta \beta}_{1/2} > 1.1 \times 10^{26} $ yr at 90$\%$ CL) with the GERDA experiment. In 0$\nu \beta \beta$ a pair of free electrons is created in the transformation from a nucleus $(A, Z)$ into its daughter $(A, Z + 2)$, namely: $(A,Z)\rightarrow (A, Z+2) =2 e^-$. Similar transitions could proceed through the emission of a pair of positrons, double electron capture (EC), or EC and single emission of a positron, with the nucleus changing from $(A, Z)$ to $(A, Z - 2)$. All these variations are equally interesting when discussing of new Physics, since they all manifest a non-conservation of the number of leptons.\\ Moreover, recent studies show that, because of flavor effect, off-diagonal processes, such as the $\mu^- -e^+$ conversion, can have their rate enhanced with respect to processes occurring in the $e-e$ sector.\\ Mu2e will search for $\mu^- + Al(27,13) \rightarrow e^+ +Na(27,11)$, only considering ground state transition, producing a conversion positron with energy $E_{e^+}= 92.32 $ MeV.\\ This thesis is focused on this search. In particular, I developed an algorithm to account for the radiative corrections to be applied to the conversion positrons that resulted in a few percent reduction in s ignal acceptance.\\ One of the most prominent background to ! this sear! ch is the Radiative Muon Capture (RMC) $ \mu+ N(Z,A)\rightarrow \gamma + \nu_{\mu} + N(Z-1,A)$. The produced photon can convert, virtually or in the detector materials (in the following referred as internal or external conversion respectively) in an electron-positron pair, producing positrons with energies approaching the expected conversion energy. Experimental results from previous experiments indicate the RMC endpoint ($\kmax$) to be of $\sim$ 90 MeV. A precise modeling of this background is relevant due to the proximity of the photon spectrum endpoint to the positron conversion energy. The calorimeter group is obviously interested to reconstruct the RMC distribution having also the opportunity to improve the current knowledge of the process. \\ A toy MC has been developed to evaluate the number of $e^+$ from external RMC background in the signal window. Knowing this value and ev...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Performance Demonstration of an Occupancy Sensor-enabled Integrated Solution for Commercial Buildings

Traditionally, a single-loop fixed-gain controller is applied to supply fan (SF) and cooling coil (CC) valve controls while a fixed-damper position control is applied to outdoor air (OA) damper control at air handling units (AHUs) in commercial buildings. With the increasing application of occupancy sensors, the information generated by occupancy sensors is applied to not only reduce the electricity loads from lighting and controllable plug loads, but also reset OA intake and minimum supply airflow setpoints. Meanwhile, these intermittent operation actions greatly elevate the dynamics of AHU systems, which may introduce unstable SF and CC valve operations and inaccurate OA flow control at AHUs and consequently degrade maximum energy efficiency gains. With virtual fan and valve flow meter technologies, two advanced controls, including cascade control and gain scheduling control, can be implemented on both the SF and CC valve, and an advanced control using a virtual OA flow meter can be implemented on OA damper integrated with occupancy sensors. The goal of this project is to demonstrate the savings, cost, and performance of an integrated solution that integrates the three advanced HVAC controls with occupancy sensors to allow accurate and stable AHU operations in real buildings. The project objectives are to: 1) develop and validate an advance SF control algorithm; 2) develop and validate an advanced CC valve control algorithm; 3) validate an algorithm to implement a virtual OA flow meter; and 4) demonstrate the savings, cost, and performance of the integrated solution in real buildings. The technical approaches are to: 1) select a test system at the University of Oklahoma; 2) develop and implement the algorithms of advanced SF and CC valve controls and validate the performance; 3) develop and implement the advanced OA control using a virtual OA flow meter and validate the performance; 4) demonstrate the savings, cost, and performance of the proposed integrated solution with and without three advanced HVAC controls; and 5) disseminate the project results through publications and presentations. For the SF control, both the gain scheduling and cascade controls can improve the fan energy performance by reducing the fan power during the transient period and the fan control performance at lower speeds by reducing fan speed variation. Moreover, the gain scheduling control provides a simple and low-cost solution and is recommended. The fan power savings can reach 30% in a transient period. For the CC valve control, the gain scheduling control can considerably reduce the supply air temperature oscillation range and frequency under both higher and lower load conditions and the control valve response is much more stable. As a result, the gain scheduling control is recommended. The projected pump energy consumption can be reduced by 68.5%. With the developed virtual OA flow meter, the OA can be accurately controlled at its setpoint, which is determined based on the actual number of occupants in the building provided by occupancy sensors. The RMSE of the proposed OA control is 15.9 L/s. The energy data shows that the fan power and CC cooling energy were significantly reduced. On the other hand, the energy savings majorly results from the occupancy sensors and the energy savings by the advanced HVAC controls is minimal because that the controllers in the test AHU were tuned with very slow response. An annual technical savings potential is estimated as 0.5 quads in the commercial sector.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2001

Integral Twist Actuation of Helicopter Rotor Blades for Vibration Reduction

Active integral twist control for vibration reduction of helicopter rotors during forward flight is investigated. The twist deformation is obtained using embedded anisotropic piezocomposite actuators. An analytical framework is developed to examine integrally-twisted blades and their aeroelastic response during different flight conditions: frequency domain analysis for hover, and time domain analysis for forward flight. Both stem from the same three-dimensional electroelastic beam formulation with geometrical-exactness, and axe coupled with a finite-state dynamic inflow aerodynamics model. A prototype Active Twist Rotor blade was designed with this framework using Active Fiber Composites as the actuator. The ATR prototype blade was successfully tested under non-rotating conditions. Hover testing was conducted to evaluate structural integrity and dynamic response. In both conditions, a very good correlation was obtained against the analysis. Finally, a four-bladed ATR system is built and tested to demonstrate its concept in forward flight. This experiment was conducted at NASA Langley T~ansonic Dynamics Tunnel and represents the first-of-a-kind Mach-scaled fully-active-twist rotor system to undergo forward flight test. In parallel, the impact upon the fixed- and rotating-system loads is estimated by the analysis. While discrepancies are found in the amplitude of the loads under actuation, the predicted trend of load variation with respect to its control phase correlates well. It was also shown, both experimentally and numerically, that the ATR blade design has the potential for hub vibratory load reduction of up to 90% using individual blade control actuation. Using the numerical framework, system identification is performed to estimate the harmonic transfer functions. The linear time-periodic system can be represented by a linear time-invariant system under the three modes of blade actuation: collective, longitudinal cyclic, and lateral cyclic. A vibration minimizing controller is designed based on this result, which implements classical disturbance rejection algorithm with some modifications. The controller is simulated numerically, and more than 90% of the 4P hub vibratory load is eliminated. By accomplishing the experimental and analytical steps described in this thesis, the present concept is found to be a viable candidate for future generation low-vibration helicopters. Also, the analytical framework is shown to be very appropriate for exploring active blade designs, aeroelastic behavior prediction, and as simulation tool for closed-loop controllers.

Shin, SangJoon↗

NASA NTRS2002

Version 2 Goddard Satellite-Based Surface Turbulent Fluxes (GSSTF2)

Information on the turbulent fluxes of momentum, moisture, and heat at the air-sea interface is essential in improving model simulations of climate variations and in climate studies. We have derived a 13.5-year (July 1987-December 2000) dataset of daily surface turbulent fluxes over global oceans from the Special Sensor Mcrowave/Imager (SSM/I) radiance measurements. This dataset, version 2 Goddard Satellite-based Surface Turbulent Fluxes (GSSTF2), has a spatial resolution of 1 degree x 1 degree latitude-longitude and a temporal resolution of 1 day. Turbulent fluxes are derived from the SSM/I surface winds and surface air humidity, as well as the 2-m air and sea surface temperatures (SST) of the NCEP/NCAR reanalysis, using a bulk aerodynamic algorithm based on the surface layer similarity theory.

Chou, Shu-Hsien↗

NASA NTRS2009

Aqua MODIS Thermal Emissive Band On-Orbit Calibration, Characterization, and Performance

The NASA's Earth Observing System Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) has continued to operate with satisfactory performance since its launch in May 2002, exceeding its nominal six-year design lifetime. Its continuous Earth observations have been used to generate many science data products for studies of the Earth's, system. MODIS has 36 spectral bands; 20 reflective solar bands and 16 thermal emissive bands (TEBs). All TEB observations are made at 1-km nadir spatial resolution with spectral wavelengths from 3.7 to 14.4 pm. Primary applications of MODIS TEB 'include surface, cloud, and atmospheric temperatures, water vapor, and cloud top altitude. MODIS TEB on-orbit calibration uses a quadratic algorithm with its calibration coefficients derived using an onboard blackbody (BB). This paper will present Aqua MODIS TEB on-orbit calibration, characterization, and performance over its six-year mission. Examples of instrument thermal behavior, BB temperature stability, detector short-term stability, and changes in long-term response (or system gain) will be presented. Comparisons will also be made with Terra MODIS, launched in December 1999. On-orbit results show that Aqua MODIS and its focal plane temperatures have behaved normally. BB temperature has remained extremely stable with typical scan -to-scan variations of less than +/-0.15 mK. Most TEB detectors continue to exceed their specified signal-to-noise ratio requirements, exhibiting excellent short-term stability and calibration accuracy. Excluding a few noisy detectors, either identified prelaunch or occurring postlaunch, on-orbit changes in TEB responses have been less than 0.5% on an annual basis. By comparison; the overall Aqua TEB performance has been better than that of Terra MODIS,

Xiong, Xiaoxiong↗

NASA NTRS1986

Development of an algorithm to model an aircraft equipped with a generic CDTI display

A model of human pilot performance of a tracking task using a generic Cockpit Display of Traffic Information (CDTI) display is developed from experimental data. The tracking task is to use CDTI in tracking a leading aircraft at a nominal separation of three nautical miles over a prescribed trajectory in space. The analysis of the data resulting from a factorial design of experiments reveals that the tracking task performance depends on the pilot and his experience at performing the task. Performance was not strongly affected by the type of control system used (velocity vector control wheel steering versus 3D automatic flight path guidance and control). The model that is developed and verified results in state trajectories whose difference from the experimental state trajectories is small compared to the variation due to the pilot and experience factors.

Driscoll, W. C.↗

DOE OSTI2020

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2007

A Sequential Shifting Algorithm for Variable Rotor Speed Control

A proof of concept of a continuously variable rotor speed control methodology for rotorcraft is described. Variable rotor speed is desirable for several reasons including improved maneuverability, agility, and noise reduction. However, it has been difficult to implement because turboshaft engines are designed to operate within a narrow speed band, and a reliable drive train that can provide continuous power over a wide speed range does not exist. The new methodology proposed here is a sequential shifting control for twin-engine rotorcraft that coordinates the disengagement and engagement of the two turboshaft engines in such a way that the rotor speed may vary over a wide range, but the engines remain within their prescribed speed bands and provide continuous torque to the rotor; two multi-speed gearboxes facilitate the wide rotor speed variation. The shifting process begins when one engine slows down and disengages from the transmission by way of a standard freewheeling clutch mechanism; the other engine continues to apply torque to the rotor. Once one engine disengages, its gear shifts, the multi-speed gearbox output shaft speed resynchronizes and it re-engages. This process is then repeated with the other engine. By tailoring the sequential shifting, the rotor may perform large, rapid speed changes smoothly, as demonstrated in several examples. The emphasis of this effort is on the coordination and control aspects for proof of concept. The engines, rotor, and transmission are all simplified linear models, integrated to capture the basic dynamics of the problem.

Litt, Jonathan S.↗

DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Encoding the complete electric field of an ultraviolet ultrashort laser pulse in a near-infrared nonlinear-optical signal

We introduce a variation on the cross-correlation frequency-resolved optical gating (XFROG) technique that uses a near-infrared (NIR) nonlinear-optical signal to characterize pulses in the ultraviolet (UV). Using a transient-grating XFROG beam geometry, we create a grating using two copies of the unknown UV pulse and diffract a NIR reference pulse from it. We show that, by varying the delay between the UV pulses creating the grating, the UV pulse intensity-and-phase information can be encoded into a NIR signal. We also implemented a modified generalized-projections phase-retrieval algorithm for retrieving the UV pulses from these spectrograms. We performed proof-of-principle measurements of chirped pulses and double pulses, all at 400 nm. This approach should be extendable deeper into the UV and potentially even into the extreme UV or x-ray range.

47 OTHER INSTRUMENTATION↗

NASA NTRS2001

Traveling-Wave Tube Amplifier Model to Predict High-Order Modulation Intersymbol Interference

Demands for increased data rates in satellite communications necessitate higher order modulation schemes, larger system bandwidth, and minimum distortion of the modulated signal as it is passed through the traveling wave tube amplifier (TWTA). One type of distortion that the TWTA contributes to is intersymbol interference (ISI), and this becomes particularly disruptive with wide-band, complex modulation schemes. It is suspected that in addition to the dispersion of the TWT, frequency dependent reflections due to mismatches within the TWT are a significant contributor to ISI. To experimentally investigate the effect of these mismatches within the physical TWT on ISI would be prohibitively expensive, as it would require manufacturing numerous amplifiers in addition to the acquisition of the required digital hardware. In an attempt to develop a more accurate model to correlate IS1 with the TWTA and the operational signal, a fully three-dimensional (3D), time-dependent, TWT interaction model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm). The model includes a user defined slow-wave circuit with a spatially tapered region of loss to implement a sever, and spatially varied geometry (such as helical pitch) to implement a phase velocity taper. The model also includes user defined input/output coupling and an electron beam contained by solenoidal, electrostatic, or periodic permanent magnet (PPM) focusing allowing standard or novel TWTs to be investigated. This model comprehensively takes into account the effects of frequency dependent nonlinear distortions (MAM and AMPM); gain ripple due to frequency dependent reflections at the input/output coupling, severs, and mismatches from dynamic pitch variations; drive induced oscillations; harmonic generation; intermodulation products; and backward waves.

Kory, Carol L.↗

DOE OSTI2025

Learning nuclear cross sections across the chart of nuclides with graph neural networks

We explore the use of deep learning techniques to learn how nuclear cross sections change as we add or remove protons and neutrons. As a proof of principle, we focus on the neutron-induced reactions in the fast energy regime. Our approach follows a two-stage learning framework. First, we apply representation learning to encode cross section data into a latent space using either variational autoencoders (VAEs) or implicit neural representations (INRs). Then, we train graph neural networks (GNNs) on the resulting embeddings to predict missing values across the nuclear chart by leveraging the topological structure of neighboring isotopes. We demonstrate accurate cross section predictions within a 9 × 9 block of missing nuclei. We also find that the optimal GNN training strategy depends on the type of latent representation used, with VAE embeddings performing best under end-to-end optimization in the original space, while INR embeddings achieve better results when the GNN is trained only in the latent space. Furthermore, using clustering algorithms, we map groups of latent vectors into regions of the nuclear chart and show that VAEs and INRs can discover some of the neutron magic numbers. These findings suggest that deep-learning models based on the representation encoding of cross sections combined with graph neural networks hold significant potential in augmenting nuclear theory models, e.g., by providing reliable estimates of covariances of cross sections, including cross-material covariances.

Machine learning↗

NASA NTRS1990

On three dimensional object recognition and pose-determination: An abstraction based approach

A method of computing reliable Gaussian and mean curvature sign-map descriptors from the polynomial approximation of surfaces was demonstrated. Such descriptors which are invariant under perspective variation are suitable for hypothesis generation. A means for determining the pose of constructed geometric forms whose algebraic surface descriptors are nonlinear in terms of their orienting parameters was developed. This was done by means of linear functions which are capable of approximating nonlinear forms and determining their parameters. It was shown that biquadratic surfaces are suitable companion linear forms for cylindrical approximation and parameter estimation. The estimates provided the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data. A hypothesis-based split-merge algorithm for extraction and pose determination of cylinders and planes which merge smoothly into other surfaces was developed. It was shown that all split-merge algorithms are hypothesis-based. A finite-state algorithm for the extraction of the boundaries of run-length regions was developed. The computation takes advantage of the run list topology and boundary direction constraints implicit in the run-length encoding.

Quek, Kok How Francis↗

NASA NTRS1991

Multi-resolution analysis for ENO schemes

Given an function, u(x), which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. This multi-resolution analysis was applied to essentially non-oscillatory (ENO) schemes in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. An efficient algorithm for implementing this program in the 1-D case is presented; this algorithm can be extended to the multi-dimensional case with Cartesian grids.

Harten, Ami↗

NASA NTRS2014

Improvement of Aerosol Optical Depth Retrieval over Hong Kong from a Geostationary Meteorological Satellite Using Critical Reflectance with Background Optical Depth Correction

Despite continuous efforts to retrieve aerosol optical depth (AOD) using a conventional 5-channelmeteorological imager in geostationary orbit, the accuracy in urban areas has been poorer than other areas primarily due to complex urban surface properties and mixed aerosol types from different emission sources. The two largest error sources in aerosol retrieval have been aerosol type selection and surface reflectance. In selecting the aerosol type from a single visible channel, the season-dependent aerosol optical properties were adopted from longterm measurements of Aerosol Robotic Network (AERONET) sun-photometers. With the aerosol optical properties obtained fromthe AERONET inversion data, look-up tableswere calculated by using a radiative transfer code: the Second Simulation of the Satellite Signal in the Solar Spectrum (6S). Surface reflectance was estimated using the clear sky composite method, awidely used technique for geostationary retrievals. Over East Asia, the AOD retrieved from the Meteorological Imager showed good agreement, although the values were affected by cloud contamination errors. However, the conventional retrieval of the AOD over Hong Kong was largely underestimated due to the lack of information on the aerosol type and surface properties. To detect spatial and temporal variation of aerosol type over the area, the critical reflectance method, a technique to retrieve single scattering albedo (SSA), was applied. Additionally, the background aerosol effect was corrected to improve the accuracy of the surface reflectance over Hong Kong. The AOD retrieved froma modified algorithmwas compared to the collocated data measured by AERONET in Hong Kong. The comparison showed that the new aerosol type selection using the critical reflectance and the corrected surface reflectance significantly improved the accuracy of AODs in Hong Kong areas,with a correlation coefficient increase from0.65 to 0.76 and a regression line change from τMI [basic algorithm] = 0.41τAERONET + 0.16 to τMI [new algorithm] = 0.70τAERONET + 0.01.

aerosols↗

NASA NTRS2001

Extending unbiased stereology of brain ultrastructure to three-dimensional volumes

OBJECTIVE: Analysis of brain ultrastructure is needed to reveal how neurons communicate with one another via synapses and how disease processes alter this communication. In the past, such analyses have usually been based on single or paired sections obtained by electron microscopy. Reconstruction from multiple serial sections provides a much needed, richer representation of the three-dimensional organization of the brain. This paper introduces a new reconstruction system and new methods for analyzing in three dimensions the location and ultrastructure of neuronal components, such as synapses, which are distributed non-randomly throughout the brain. DESIGN AND MEASUREMENTS: Volumes are reconstructed by defining transformations that align the entire area of adjacent sections. Whole-field alignment requires rotation, translation, skew, scaling, and second-order nonlinear deformations. Such transformations are implemented by a linear combination of bivariate polynomials. Computer software for generating transformations based on user input is described. Stereological techniques for assessing structural distributions in reconstructed volumes are the unbiased bricking, disector, unbiased ratio, and per-length counting techniques. A new general method, the fractional counter, is also described. This unbiased technique relies on the counting of fractions of objects contained in a test volume. A volume of brain tissue from stratum radiatum of hippocampal area CA1 is reconstructed and analyzed for synaptic density to demonstrate and compare the techniques. RESULTS AND CONCLUSIONS: Reconstruction makes practicable volume-oriented analysis of ultrastructure using such techniques as the unbiased bricking and fractional counter methods. These analysis methods are less sensitive to the section-to-section variations in counts and section thickness, factors that contribute to the inaccuracy of other stereological methods. In addition, volume reconstruction facilitates visualization and modeling of structures and analysis of three-dimensional relationships such as synaptic connectivity.

NASA Discipline Neuroscience↗