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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Methodology for the Elimination of Reflection and System Vibration Effects in Particle Image Velocimetry Data Processing

A methodology to eliminate model reflection and system vibration effects from post processed particle image velocimetry data is presented. Reflection and vibration lead to loss of data, and biased velocity calculations in PIV processing. A series of algorithms were developed to alleviate these problems. Reflections emanating from the model surface caused by the laser light sheet are removed from the PIV images by subtracting an image in which only the reflections are visible from all of the images within a data acquisition set. The result is a set of PIV images where only the seeded particles are apparent. Fiduciary marks painted on the surface of the test model were used as reference points in the images. By locating the centroids of these marks it was possible to shift all of the images to a common reference frame. This image alignment procedure as well as the subtraction of model reflection are performed in a first algorithm. Once the images have been shifted, they are compared with a background image that was recorded under no flow conditions. The second and third algorithms find the coordinates of fiduciary marks in the acquisition set images and the background image and calculate the displacement between these images. The final algorithm shifts all of the images so that fiduciary mark centroids lie in the same location as the background image centroids. This methodology effectively eliminated the effects of vibration so that unbiased data could be used for PIV processing. The PIV data used for this work was generated at the NASA Langley Research Center Quiet Flow Facility. The experiment entailed flow visualization near the flap side edge region of an airfoil model. Commercial PIV software was used for data acquisition and processing. In this paper, the experiment and the PIV acquisition of the data are described. The methodology used to develop the algorithms for reflection and system vibration removal is stated, and the implementation, testing and validation of these algorithms are presented.

Bremmer, David M.↗
DOE OSTI2021

High-precision quantum algorithms for partial differential equations

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ϵ), where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ϵ)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

CyanoSCape: Freshwater Phytoplankton and Floating Aquatic Vegetation Biodiversity

In Southern Africa, the impacts of anthropogenic activities on biodiversity and ecosystem services are exacerbated by the climate crisis. Rapid land use change and the lack of emphasis on environmentally sustainable agricultural practices has hindered hydrological processes and compromised riverine and aquatic ecosystems. This poses obvious risks to natural/indigenous aquatic biodiversity and long-term ecosystem sustainability. Phytoplankton serve as the foundation of the freshwater food web with zooplankton as consumers, which feed fish, invertebrates, and so on up the food chain that comprises the biodiversity of the freshwater system that serves as habitat for biodiversity as well. The diversity of phytoplankton (microscopic organisms) includes photosynthesizing bacteria (cyanobacteria), plant-like diatoms, dinoflagellates, and green algae. Nutrient run-off from agricultural fertilizers and urban overflows, warm temperatures, abundant light availability and compromised hydrological systems provide an ideal environment for cyanobacteria to flourish. Increased prevalence of cyanobacteria, due to both natural and anthropogenic causes, can incur significant effects on the biodiversity of the overall phytoplankton assemblage. These bloom forming algae can significantly outcompete other phytoplankton classes in warmer and eutrophic waters where they are quick to dominate the freshwater system. Eutrophication and toxic cyanobacteria blooms (cyanoHABs) in the inland waters of the Greater Cape Floristic Region (GCFR) incur significant effects on the biodiversity of the overall phytoplankton assemblage and provide a favorable environment forthe overgrowth of floating aquatic vegetation (FAV), which is often invasive and associated with reduced aquatic biodiversity. The algal biodiversity of the GCFR’s freshwater systems is not well characterized. Hyperspectral optical observations are expected to facilitate the improvement of current phytoplankton functional type retrievals significantly, as the sensitivity is sufficient that the distinctive, fine spectral features of different phytoplankton groups can be detected. This will enable testing emerging algorithms and inform the development of new algorithms for use with upcoming hyperspectral satellite missions in this decade. Innovations in optical sensor sensitivity and next generation machine learning capabilities considerably enhance the potential for accurate and rapid detection of phytoplankton, namely the presence, extent, and diversity of cyanobacteria present in cyanoHABs and additionally, invasive FAV. Upcoming hyperspectral satellite missions such as NASA’s Surface Biology and Geology (SBG), Plankton, Aerosol, Cloud, ocean Ecosystem (PACE), and the European Space Agency’s Copernicus Hyperspectral Imaging Mission (CHIME) will provide imagery with unprecedented spectral and spatial resolution which will further enable the discovery of linkages between the seasonality and dynamics of HABs and FAV. The overarching goal of this project is to utilize hyperspectral data, with recently developed and next-generation algorithms, to determine the biodiversity of freshwater systems phytoplankton assemblage with emphasis on genus level distinction, as well as monitor the prevalence and diversity of FAV.

CyanoSCape↗
NASA NTRSDate not supplied

Development of Machine Learning Algorithms to Segment and Study Images of Astromaterial Samples

Introduction: Micrometer-scale chemical analyses of chondritic meteorites and mission-returned asteroid samples can reveal details of the physical and chemical processes operating in the early solar system, including processes that gave rise to planets, moons, and minor bodies. These primitive astromaterials are comprised of chondrules, calcium- and aluminum-rich inclusions (CAI), and many other silicates, oxides, metals, sulfides, and fine-grained materials. The chemical and mineralogical complexity of these samples, vast populations of different components, and heterogeneity across mm to km scales, all limit our understanding of the origin and evolution of these materials. Here, we describe recent efforts to use machine learning techniques to automate the segmentation of chemical maps of chondritic meteorites, designed to aid studies of asteroid samples returned by spacecraft. By automating the task of segmentation it will become possible to rapidly analyze and interpret the sizes, shapes, mineralogy, chemistry, and other properties of every chondrule, calcium- and aluminum-rich inclusion (CAI) and other clast within and between asteroid samples. Sample return missions significantly accelerate and heighten the need to develop such new data analysis techniques, and associated data repositories. Techniques: Neural networks require abundant training data, i.e. images which have been segmented by a human user. We have manually segmented data available from previous petrologic and chemical work at NASA Johnson Space Center and the American Museum of Natural History [1-4]. These data were derived from energy- and wavelength-dispersive X-ray spectroscopy (EDS, WDS) mapping of samples from many chondrite groups. The Deeplabv3+ [5] neural network architecture was trained on human-labeled masks and used to create machine-labeled masks. Several different algorithms were investigated, with inputs ranging from common RGB image formats through to hyperspectral datasets, with raw data comprising greyscale maps of Mg, Ca, and Al, with or without Si, Fe, Ti for both EDS and WDS data, and extending to other elements in EDS only. Each greyscale image was paired with a binary mask for each labelled particle type. Results: The trained algorithms can segment (Fig 1), classify, and measure the dimensions of thousands of particles in chemical maps of a standard 1-inch round petrographic section in seconds to minutes, rather than many hours needed by a human. Accuracy of the algorithms varied from chondrite to chondrite and across particle types. Further results and details of the algorithms will be presented at the workshop. Future directions: Machine learning has the potential to revolutionize our understanding of complex particle populations contained within primitive astromaterial, with segmentation being a critical first step. Example applications include better understanding of particle transport, nebular reservoirs, parent body accretion, and a deeper understanding of the relationships between particle populations and bulk rock elemental and isotopic compositions. In addition to benefits that machine learning can bring to individual researchers, building a community data repository of thousands to millions of particles across hundreds of samples will open up many other possibilities. For example, with a large enough dataset it will be possible to search for exceptionally closely matching particles across disparate samples. Such a capability would enable a single CAI from OSIRISREx or Hayabusa/II samples to be matched to chondritic CAIs that exhibit near-identical size, texture, and mineralogy, down to the level of similar core phenocrysts, zonation, and rim sequences. Such comparative analyses will help to disentangle precursor chemistry, chronology, gas/dust reservoirs during heating, and accretion. Such an endeavor would be impossible without machine learning and a large community data repository of astromaterial chemical/mineralogic maps.

Machine Learning↗
DOE OSTI2021

Progress on the National Solar Radiation Data Base (NSRDB): A New DNI Computation

This study introduces a new technique to compute direct normal irradiance (DNI) for improving the National Solar Radiation Data Base (NSRDB). A finite-surface integration algorithm is developed to compute solar radiation in differential solid angles and efficiently infer its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by use of the discrete ordinates radiative transfer (DISORT) model for possible solar and observing directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from approximately 200 differential solid angles. The simulated DNI is calibrated and evaluated using surface observations at the National Renewable Energy Laboratory's (NREL's) Solar Energy Research Laboratory (SRRL) and the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) facility.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2020

Developing an Active Learning algorithm for learning Bayesian classifiers under the Multiple Instance Learning scenario

In the Multiple Instance Learning scenario, the training data consists of instances grouped into bags, and each bag is labelled with whether it is positive, i.e. contains at least one positive instance. First, Active Learning, in which additional labels can be iteratively requested, has the potential to allow more accurate classifiers to be learned with less labels. Active Learning has been applied to the Multiple Instance Learning under two settings: when bag labels of unlabelled bags can be requested, and when instance labels within bags known to be positive can be requested. Second, Bayesian Active learning methods have the potential to learn accurate classifiers with few labels, because they explicitly track the classifier uncertainty and can thus address its knowledge gaps. Yet, there does not exist any Bayesian Active Learning method for the Multiple Instance Learning Scenario. In this work, we develop the first such method. We develop a Bayesian classifier for the Multiple Instance Learning scenario, show how it can be efficiently used for Bayesian Active Learning, and perform experiments assessing its performance. While its performance exceeds that when no Active Learning is used, it is sometimes better, sometimes worse than the naive baseline of uncertainty sampling, depending on the situation. This suggests future work: building more customizable Bayesian Active Learning methods for the Multiple Instance Scenario, customizable to whether bag or instance label accuracy is targeted, and the labeling budget.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Real-time adaptive aircraft scheduling

One of the most important functions of any air traffic management system is the assignment of ground-holding times to flights, i.e., the determination of whether and by how much the take-off of a particular aircraft headed for a congested part of the air traffic control (ATC) system should be postponed in order to reduce the likelihood and extent of airborne delays. An analysis is presented for the fundamental case in which flights from many destinations must be scheduled for arrival at a single congested airport; the formulation is also useful in scheduling the landing of airborne flights within the extended terminal area. A set of approaches is described for addressing a deterministic and a probabilistic version of this problem. For the deterministic case, where airport capacities are known and fixed, several models were developed with associated low-order polynomial-time algorithms. For general delay cost functions, these algorithms find an optimal solution. Under a particular natural assumption regarding the delay cost function, an extremely fast (O(n ln n)) algorithm was developed. For the probabilistic case, using an estimated probability distribution of airport capacities, a model was developed with an associated low-order polynomial-time heuristic algorithm with useful properties.

Kolitz, Stephan E.↗
DOE OSTI2024

Phase retrieval for refraction-enhanced x-ray radiography using a deep neural network

X-ray refraction-enhanced radiography (RER) or phase contrast imaging is widely used to study internal discontinuities within materials. The resulting radiograph captures both the decrease in intensity caused by material absorption along the x-ray path, as well as the phase shift, which is highly sensitive to gradients in density. A significant challenge lies in effectively analyzing the radiographs to decouple the intensity and phase information and accurately ascertain the density profile. Conventional algorithms often yield ambiguous and unrealistic results due to difficulties in including physical constraints and other relevant information. We have developed an algorithm that uses a deep neural network to address these issues and applied it to extract the detailed density profile from an experimental RER. To generalize the applicability of our algorithm, we have developed a technique that quantitatively evaluates the complexity of the phase retrieval process based on the characteristics of the sample and the configuration of the experiment. Accordingly, this evaluation aids in the selection of the neural network architecture for each specific case. Beyond RER, the model has potential applications for other diagnostics where phase retrieval analysis is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Cloud-based Testbed for Adaptive Under-Frequency Load Shedding with High DER Penetration

Increasing penetration of distributed energy resources and behind-the-meter renewables may soon disrupt the efficacy of critical protection schemes, such as under-frequency load shedding (UFLS). Improved data exchange and coordination across the transmission-distribution boundary will be required to maintain reliability of bulk electric system. Standards-based data integration platforms using agreed-upon semantic vocabularies, such as the Common Information Model, will be key to enabling adaptive protection schemes requiring synthesized data from both the bulk power system and behind-the-meter resources. This paper introduces a cloud-based open-source data integration environment and UFLS clustering algorithm being developed to enable adaptive relay coordination between transmission and distribution utilities in the state of Vermont.

Anderson, Alexander A.↗
NASA NTRS1987

Driving mechanism of unsteady separation shock motion in hypersonic interactive flow

Wall pressure fluctuations were measured under the steady separation shock waves in Mach 5 turbulent interactions induced by unswept circular cylinders on a flat plate. The wall temperature was adiabatic. A conditional sampling algorithm was developed to examine the statistics of the shock wave motion. The same algorithm was used to examine data taken in earlier studies in the Princeton University Mach 3 blowdown tunnel. In these earlier studies, hemicylindrically blunted fins of different leading-edge diameters were tested in boundary layers which developed on the tunnel floor and on a flat plate. A description of the algorithm, the reasons why it was developed and the sensitivity of the results to the threshold settings, are discussed. The results from the algorithm, together with cross correlations and power spectral density estimates suggests that the shock motion is driven by the low-frequency unsteadiness of the downstream separated, vortical flow.

Dolling, D. S.↗
NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

Ulbrich, Norbert M.↗
NASA NTRSDate not supplied

Latest Development in Radiative Transfer Models and Retrieval Algorithms Using Principal Components

The radiative transfer model (RTMs) has a wide range of applications in satellite remote sensing and atmospheric radiation applications. However, millions of line-by-line (LBL) radiative transfer calculations at fine monochromatic frequencies are needed in order to properly calculate spectral contributions of water vapor and trace gases in the atmosphere in infrared and solar spectral regions. Therefore, fast and accurate RTMs are needed to efficiently process large amount of satellite data. A Principal Component-based Radiative Transfer Model (PCRTM) was first developed in 2004 at NASA Langley Research Centre to fulfil this need. By using PC-compression, one can reduce the data dimension significantly while maintaining original information content. The PCRTM can directly compute PC-scores and their derivatives with respect to retrieved parameters. The PCRTM can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra from 0.250 µm (400000 cm-1) to 2000 µm (50 cm-1) with several orders of magnitude faster speed as compared to a LBL RTM. It is also extremely accurate compared to LBL RTM benchmarks (0.03 K RMS error in IR and 0.05% in solar). The PCRTM model has been developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, FIRST, and CLARREO-IR in thermal IR spectral region and CLARREO-Solar, CPF, TEMPO, EMIT, OMI, and SCIAMACHY in solar spectral region. The PCRTM accuracy has been demonstrated via RTM intercomparisons and with real satellite observations from AIRS, CrIS, IASI, SCHIAMACHY, and EMIT etc. In this presentation, we will describe two PCRTM-based inversion algorithms to retrieve atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties from hyperspectral sounders such as AIRS, CrIS, IASI, and NAST-I. The first one is called Single Fieldof-view Sounder Atmospheric Product (SiFSAP) algorithm. It provides L2 products with 9-times higher area spatial resolution as compared to current cloud-clearing sounder algorithms. The SiFSAP L2 and L3 products are available at NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC) for public access. The second inversion algorithm is called Climate Fingerprinting Atmospheric Product (ClimFiSP) algorithm. It is designed to produce high quality climate products (trends, anomalies, daily, and monthly profiles of temperature, water vapor, traces, clouds, and surface properties) from multiple satellite sensors such AIRS on Aqua and CrIS on multiple satellites. This product will be available at NASA GES DISC later this year. The PCRTMbased high fidelity simulators for CLARREO and CPF have been used for sensor performance trade studies, algorithm development, and inter-satellite calibrations. We have also used PCRTM generated TOA radiance spectra to train an AI-based algorithm and successfully retrieved cloud properties from EMIT solar hyperspectral imagers.

PCRTM↗
NASA NTRS1990

Framework for a space shuttle main engine health monitoring system

A framework developed for a health management system (HMS) which is directed at improving the safety of operation of the Space Shuttle Main Engine (SSME) is summarized. An emphasis was placed on near term technology through requirements to use existing SSME instrumentation and to demonstrate the HMS during SSME ground tests within five years. The HMS framework was developed through an analysis of SSME failure modes, fault detection algorithms, sensor technologies, and hardware architectures. A key feature of the HMS framework design is that a clear path from the ground test system to a flight HMS was maintained. Fault detection techniques based on time series, nonlinear regression, and clustering algorithms were developed and demonstrated on data from SSME ground test failures. The fault detection algorithms exhibited 100 percent detection of faults, had an extremely low false alarm rate, and were robust to sensor loss. These algorithms were incorporated into a hierarchical decision making strategy for overall assessment of SSME health. A preliminary design for a hardware architecture capable of supporting real time operation of the HMS functions was developed. Utilizing modular, commercial off-the-shelf components produced a reliable low cost design with the flexibility to incorporate advances in algorithm and sensor technology as they become available.

Hawman, Michael W.↗
NASA NTRS2001

A Multi-Band Analytical Algorithm for Deriving Absorption and Backscattering Coefficients from Remote-Sensing Reflectance of Optically Deep Waters

A multi-band analytical (MBA) algorithm is developed to retrieve absorption and backscattering coefficients for optically deep waters, which can be applied to data from past and current satellite sensors, as well as data from hyperspectral sensors. This MBA algorithm applies a remote-sensing reflectance model derived from the Radiative Transfer Equation, and values of absorption and backscattering coefficients are analytically calculated from values of remote-sensing reflectance. There are only limited empirical relationships involved in the algorithm, which implies that this MBA algorithm could be applied to a wide dynamic range of waters. Applying the algorithm to a simulated non-"Case 1" data set, which has no relation to the development of the algorithm, the percentage error for the total absorption coefficient at 440 nm a (sub 440) is approximately 12% for a range of 0.012 - 2.1 per meter (approximately 6% for a (sub 440) less than approximately 0.3 per meter), while a traditional band-ratio approach returns a percentage error of approximately 30%. Applying it to a field data set ranging from 0.025 to 2.0 per meter, the result for a (sub 440) is very close to that using a full spectrum optimization technique (9.6% difference). Compared to the optimization approach, the MBA algorithm cuts the computation time dramatically with only a small sacrifice in accuracy, making it suitable for processing large data sets such as satellite images. Significant improvements over empirical algorithms have also been achieved in retrieving the optical properties of optically deep waters.

Lee, Zhong-Ping↗
DOE OSTI2023

A Novel Resilience-Oriented Cellular Grid Formation Approach for Distribution Systems with Behind-the-Meter Distributed Energy Resources

This paper presents a resilience-oriented cellular grid formation approach to achieve scalable and reconfigurable community microgrid operations for distribution systems with behind-the-meter distributed energy resources. A set of interconnected solar photovoltaics, energy storage systems, and load is termed as a cell, implying a subset of the grid that can operate independently using its own resources. Cells are identified such that each cell inherently has sufficient energy resources to black start and can provide a certain level of backup power for its load under the loss of utility power supply. The proposed cell formation approach builds on a unique self-organizing map-based method (SomRes) to quantify a system's resilience. Using SomRes and a non-dominated sorting-based genetic algorithm (NSGA-II), a fast and efficient cell formation algorithm is developed to identify cells in a distribution system that are resilient against extreme events. The efficacy of the proposed approach is demonstrated on a numerical model of a real distribution feeder in Colorado, United States.

distributed energy resource↗
NASA NTRS2009

Implementation of an Adaptive Controller System from Concept to Flight Test

The National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California) is conducting ongoing flight research using adaptive controller algorithms. A highly modified McDonnell-Douglas NF-15B airplane called the F-15 Intelligent Flight Control System (IFCS) is used to test and develop these algorithms. Modifications to this airplane include adding canards and changing the flight control systems to interface a single-string research controller processor for neural network algorithms. Research goals include demonstration of revolutionary control approaches that can efficiently optimize aircraft performance in both normal and failure conditions and advancement of neural-network-based flight control technology for new aerospace system designs. This report presents an overview of the processes utilized to develop adaptive controller algorithms during a flight-test program, including a description of initial adaptive controller concepts and a discussion of modeling formulation and performance testing. Design finalization led to integration with the system interfaces, verification of the software, validation of the hardware to the requirements, design of failure detection, development of safety limiters to minimize the effect of erroneous neural network commands, and creation of flight test control room displays to maximize human situational awareness; these are also discussed.

Larson, Richard R.↗
NASA NTRS1997

A Microwave Technique for Mapping Ice Temperature in the Arctic Seasonal Sea Ice Zone

A technique for deriving ice temperature in the Arctic seasonal sea ice zone from passive microwave radiances has been developed. The algorithm operates on brightness temperatures derived from the Special Sensor Microwave/Imager (SSM/I) and uses ice concentration and type from a previously developed thin ice algorithm to estimate the surface emissivity. Comparisons of the microwave derived temperatures with estimates derived from infrared imagery of the Bering Strait yield a correlation coefficient of 0.93 and an RMS difference of 2.1 K when coastal and cloud contaminated pixels are removed. SSM/I temperatures were also compared with a time series of air temperature observations from Gambell on St. Lawrence Island and from Point Barrow, AK weather stations. These comparisons indicate that the relationship between the air temperature and the ice temperature depends on ice type.

St.Germain, Karen M.↗
NASA NTRS1994

The design and development of signal-processing algorithms for an airborne x-band Doppler weather radar

Improved measurements of precipitation will aid our understanding of the role of latent heating on global circulations. Spaceborne meteorological sensors such as the planned precipitation radar and microwave radiometers on the Tropical Rainfall Measurement Mission (TRMM) provide for the first time a comprehensive means of making these global measurements. Pre-TRMM activities include development of precipitation algorithms using existing satellite data, computer simulations, and measurements from limited aircraft campaigns. Since the TRMM radar will be the first spaceborne precipitation radar, there is limited experience with such measurements, and only recently have airborne radars become available that can attempt to address the issue of the limitations of a spaceborne radar. There are many questions regarding how much attenuation occurs in various cloud types and the effect of cloud vertical motions on the estimation of precipitation rates. The EDOP program being developed by NASA GSFC will provide data useful for testing both rain-retrieval algorithms and the importance of vertical motions on the rain measurements. The purpose of this report is to describe the design and development of real-time embedded parallel algorithms used by EDOP to extract reflectivity and Doppler products (velocity, spectrum width, and signal-to-noise ratio) as the first step in the aforementioned goals.

Nicholson, Shaun R.↗