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NASA NTRS2017

The Global Precipitation Measurement (GPM) Mission for Science and Society

Precipitation is a key source of freshwater; therefore, observing global patterns of precipitation and its intensity is important for science, society, and understanding our planet in a changing climate. In 2014, the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA) launched the Global Precipitation Measurement (GPM) Core Observatory (CO) spacecraft. The GPM CO carries the most advanced precipitation sensors currently in space including a dual-frequency precipitation radar provided by JAXA for measuring the three-dimensional structures of precipitation and a well-calibrated, multifrequency passive microwave radiometer that provides wide-swath precipitation data. The GPM CO was designed to measure rain rates from 0.2 to 110.0 mm h1 and to detect moderate to intense snow events. The GPM CO serves as a reference for unifying the data from a constellation of partner satellites to provide next-generation, merged precipitation estimates globally and with high spatial and temporal resolutions. Through improved measurements of rain and snow, precipitation data from GPM provides new information such as details on precipitation structure and intensity; observations of hurricanes and typhoons as they transition from the tropics to the midlatitudes; data to advance near-real-time hazard assessment for floods, landslides, and droughts; inputs to improve weather and climate models; and insights into agricultural productivity, famine, and public health. Since launch, GPM teams have calibrated satellite instruments, refined precipitation retrieval algorithms, expanded science investigations, and processed and disseminated precipitation data for a range of applications. The current status of GPM, its ongoing science, and its future plans are presented.

Gail Skofronick-Jackson↗
NASA NTRS2022

Detecting the Greatest Changes in Global Satellite-Based Precipitation Observations

In recent years, the analysis of abrupt and non-abrupt changes in precipitation has received much attention due to the importance of climate change-related issues (e.g., extreme climate events). In this study, we used a novel segmentation algorithm, DBEST (Detecting Breakpoints and Estimating Segments in Trend), to analyze the greatest changes in precipitation using a monthly pixel-based satellite precipitation dataset (TRMM 3B43) at three different scales: (i) global, (ii) continental, and (iii) climate zone, during the 1998–2019 period. We found significant breakpoints, 14.1%, both in the form of abrupt and non-abrupt changes, in the global scale precipitation at the 0.05 significance level. Most of the abrupt changes were observed near the Equator in the Pacific Ocean and Asian continent, relative to the rest of the globe. Most detected breakpoints occurred during the 1998–1999 and 2009–2011 periods on the global scale. The average precipitation change for the detected breakpoint was ±100 mm, with some regions reaching ±3000 mm. For instance, most portions of northern Africa and Asia experienced major changes of approximately +100 mm. In contrast, most of the South Pacific and South Atlantic Ocean experienced changes of −100 mm during the studied period. Our findings indicated that the larger areas of Africa (23.9%), Asia (22.9%), and Australia (15.4%) experienced significant precipitation breakpoints compared to North America (11.6%), South America (9.3%), Europe (8.3%), and Oceania (9.6%). Furthermore, we found that the majority of detected significant breakpoints occurred in the arid (31.6%) and polar (24.1%) climate zones, while the least significant breakpoints were found for snow-covered (11.5%), equatorial (7.5%), and warm temperate (7.7%) climate zones. Positive breakpoints’ temporal coverage in the arid (54.0%) and equatorial (51.9%) climates were more than those in other climates zones. Here, the findings indicated that large areas of Africa and Asia experienced significant changes in precipitation (−250 to +250 mm). Compared to the average state (trend during a specific period), the greatest changes in precipitation were more abrupt and unpredictable, which might impose a severe threat to the ecology, environment, and natural resources.

Breakpoint↗
NASA NTRS2023

Retrieval of Normalized Gamma Size Distribution Parameters Using Precipitation Imaging Package (Pip) Snowfall Observations During Ice-Pop 2018

Parameters of the normalized gamma particle size distribution (PSD) have been retrieved from the Precipitation Image Package (PIP) snowfall observations collected during the International Collaborative Experiment - PyeongChang Olympics and Paralympic (ICE-POP 2018). Two of the gamma PSD parameters, the mass weighted particle diameter (Dmass) and the normalized intercept parameter NW, have median values of 1.15-1.31 mm and 2.84-3.04 log(mm-1 m-3), respectively. This range arises from the choice of the relationship between the maximum versus equivalent diameter, Dmx-Deq, and the relationship between the Reynolds and Best numbers, Re-X. Normalization of snow water equivalent rate (SWER) and ice water content (W) by NW reduces the range in NW resulting in well fitted power law relationship, between SWER/NW and Dmass and between W/NW and Dmass. The bulk descriptors of snowfall are calculated from PIP observations and from the gamma PSD with values of the shape parameter (μ) ranging from -2 to 10. NASA’s Global Precipitation Measurement (GPM) mission, which adopted the normalized gamma PSD, assumes μ = 2 and μ = 3 in its two separate algorithms. The mean fractional bias (MFB) of the snowfall parameters changes with μ, where the functional dependence on μ depends on the specific snowfall parameter of interest. The MFB of the total concentration was underestimated by 0.23-0.34 when μ = 2 and by 0.29-0.40 when μ = 3, while the MFB of SWER had a much narrower range (-0.03 to 0.04) for the same μ values.

Snowfall↗
NASA NTRS2010

Shallow and Deep Latent Heating Modes Over Tropical Oceans Observed with TRMM PR Spectral Latent Heating Data

The global hydrological cycle is central to the Earth's climate system, with rainfall and the physics of its formation acting as the key links in the cycle. Two-thirds of global rainfall occurs in the Tropics. Associated with this rainfall is a vast amount of heat, which is known as latent heat. It arises mainly due to the phase change of water vapor condensing into liquid droplets; three-fourths of the total heat energy available to the Earth's atmosphere comes from tropical rainfall. In addition, fresh water provided by tropical rainfall and its variability exerts a large impact upon the structure and motions of the upper ocean layer. Three-dimensional distributions of latent heating estimated from Tropical Rainfall Measuring Mission Precipitation Radar (TRMM PR)utilizing the Spectral Latent Heating (SLH) algorithm are analyzed. Mass-weighted and vertically integrated latent heating averaged over the tropical oceans is estimated as approx.72.6 J/s (approx.2.51 mm/day), and that over tropical land is approx.73.7 J/s (approx.2.55 mm/day), for 30degN-30degS. It is shown that non-drizzle precipitation over tropical and subtropical oceans consists of two dominant modes of rainfall systems, deep systems and congestus. A rough estimate of shallow mode contribution against the total heating is about 46.7 % for the average tropical oceans, which is substantially larger than 23.7 % over tropical land. While cumulus congestus heating linearly correlates with the SST, deep mode is dynamically bounded by large-scale subsidence. It is notable that substantial amount of rain, as large as 2.38 mm day-1 in average, is brought from congestus clouds under the large-scale subsiding circulation. It is also notable that even in the region with SST warmer than 28 oC, large-scale subsidence effectively suppresses the deep convection, remaining the heating by congestus clouds. Our results support that the entrainment of mid-to-lower-tropospheric dry air, which accompanies the large-scale subsidence is the major factor suppressing the deep convection. Therefore, representation of the realistic entrainment is very important for proper reproduction of precipitation distribution and resultant large-scale circulation.

Takayabu, Yukari N.↗
NASA NTRS2011

A New Inversion Routine to Produce Vertical Electron-Density Profiles from Ionospheric Topside-Sounder Data

Two software applications have been produced specifically for the analysis of some million digital topside ionograms produced by a recent analog-to-digital conversion effort of selected analog telemetry tapes from the Alouette-2, ISIS-1 and ISIS-2 satellites. One, TOPIST (TOPside Ionogram Scalar with True-height algorithm) from the University of Massachusetts Lowell, is designed for the automatic identification of the topside-ionogram ionospheric-reflection traces and their inversion into vertical electron-density profiles Ne(h). TOPIST also has the capability of manual intervention. The other application, from the Goddard Space Flight Center based on the FORTRAN code of John E. Jackson from the 1960s, is designed as an IDL-based interactive program for the scaling of selected digital topside-sounder ionograms. The Jackson code has also been modified, with some effort, so as to run on modern computers. This modification was motivated by the need to scale selected ionograms from the millions of Alouette/ISIS topside-sounder ionograms that only exist on 35-mm film. During this modification, it became evident that it would be more efficient to design a new code, based on the capabilities of present-day computers, than to continue to modify the old code. Such a new code has been produced and here we will describe its capabilities and compare Ne(h) profiles produced from it with those produced by the Jackson code. The concept of the new code is to assume an initial Ne(h) and derive a final Ne(h) through an iteration process that makes the resulting apparent-height profile fir the scaled values within a certain error range. The new code can be used on the X-, O-, and Z-mode traces. It does not assume any predefined profile shape between two contiguous points, like the exponential rule used in Jackson s program. Instead, Monotone Piecewise Cubic Interpolation is applied in the global profile to keep the monotone nature of the profile, which also ensures better smoothness in the final profile than in Jackson s program. The new code uses the complete refractive index expression for a cold collisionless plasma and can accommodate the IGRF, T96, and other geomagnetic field models.

Wang, Yongli↗
NASA NTRS1998

Giant Molecular Clouds and High-Mass Star Formation in the Milky Way

We are conducting an extensive investigation of high-mass (OB) star formation within the dense cores of giant molecular clouds (GMCS) throughout the first Galactic quadrant of the Milky Way using enhanced resolution Infrared Astronomical Satellite (IRAS) images in combination with high-resolution ground-based observations in millimeter wave molecular transitions and radio continuum. As part of this investigation several resolution enhancement algorithms are applied to the IRAS data, including the HIgh RESolution (HIRES) algorithm developed at the IRAS Processing and Analysis Center (IPAC), as well as others ("pixon" image reconstruction). In addition, as part of a related study, we have completed a large survey of the CO emission in the first Galactic quadrant using the 15-element array detector (QUARRY) with the Five College Radio Astronomy Observatory (FCRAO) 14 m antenna, which provides sampling at an angular resolution of 50", comparable to that attained in the reprocessed IRAS data. Both of these data sets are compared with a sample of ultra-compact (UC) H II regions taken from a high-resolution multi-wavelength (6 and 20 cm) radio survey of the Galactic plane using the NRAO Very Large Array (VLA). Selected regions are observed in 1.3 mm continuum, which has proven to be particularly sensitive to the dust column density. Extensive observations of molecular clouds at high resolution in CO, CS and HCN are combined with the reprocessed IRAS high-resolution images to give a more complete picture of the physical conditions and kinematics of high-mass star forming GMCS. Our goals are to study in detail the morphology, structure, and rate of high-mass star formation within GMCs throughout the Galactic disk from the inner edge of the molecular ring to the outer Galaxy.

Source record↗
NASA NTRS2014

Automated Optical Meteor Fluxes and Preliminary Results of Major Showers

NASA's Meteoroid Environment Office (MEO) recently established a two‐station system to calculate daily automated meteor fluxes in the millimeter‐size‐range for both single‐station and double‐station meteors. The cameras each consist of a 17 mm focal length Schneider lens (f/0.95) on a Watec 902H2 Ultimate CCD video camera, producing a 21.7x15.5 degree field of view. This configuration sees meteors down to a magnitude of +6. This paper outlines the concepts of the system, the hardware and software, and results of 3,000+ orbits from the first 18 months of operations. Video from the cameras are run through ASGARD (All Sky and Guided Automatic Real‐time Detection), which performs the meteor detection/photometry, and invokes MILIG and MORB (Borovicka 1990) codes to determine the trajectory, speed, and orbit of the meteor. A subroutine in ASGARD allows for approximate shower identification in single‐station detections. The ASGARD output is used in routines to calculate the flux. Before a flux can be calculated, a weather algorithm indicates if sky conditions are clear enough to calculate fluxes, at which point a limiting magnitude algorithm is employed. The limiting stellar magnitude is found using astrometry.net (Lang et al. 2012) to identify stars and translated to the corresponding shower and sporadic limiting meteor magnitude. It is found every 10 minutes and is able to react to quickly changing sky conditions. The extensive testing of these results on the Geminids and Eta Aquariids is shown. The flux involves dividing the number of meteors by the collecting area of the system, over the time interval for which that collecting area is valid. The flux algorithm employed here differs from others currently in use in that it does not make the gross oversimplication of choosing a single height to calculate the collection area of the system. In the MEO system, the volume is broken up into a set of height intervals, with the collecting areas determined by the position of the active shower or sporadic source radiant. The flux per height interval is calculated and summed to obtain the total meteor flux. Both single station and double station fluxes are currently found daily. Geminid fluxes on the peak night in 2012 (12‐14‐2012) were 0.058 meteors/km2/hr as found with double‐station meteors and 0.057 meteors/ km2/hr as found with single‐station meteors, to a limiting magnitude of +6.5. Both of those numbers are in agreement with the well‐calibrated fluxes from the Canadian Meteor Orbit Radar. Along with flux algorithms and initial flux results, presented will be results from the first 18 months of operation, covering 3,000+ meteoroid orbits.

Blaauw, R.↗
NASA NTRS2006

Percentage Contributions from Atmospheric and Surface Features to Computed Brightness Temperatures

Over the past few years, there has become an increasing interest in the use of millimeter-wave (mm-wave) and sub-millimeter-wave (submm-wave) radiometer observations to investigate the properties of ice particles in clouds. Passive radiometric channels respond to both the integrated particle mass throughout the volume and field of view, and to the amount, location, and size distribution of the frozen (and liquid) particles with the sensitivity varying for different frequencies and hydrometeor types. One methodology used since the 1960's to discern the relationship between the physical state observed and the brightness temperature (TB) is through the temperature weighting function profile. In this research, the temperature weighting function concept is exploited to analyze the sensitivity of various characteristics of the cloud profile, such as relative humidity, ice water path, liquid water path, and surface emissivity. In our numerical analysis, we compute the contribution (in Kelvin) from each of these cloud and surface characteristics, so that the sum of these various parts equals the computed TB. Furthermore, the percentage contribution from each of these characteristics is assessed. There is some intermingling/contamination of the contributions from various components due to the integrated nature of passive observations and the absorption and scattering between the vertical layers, but all in all the knowledge gained is useful. This investigation probes the sensitivity over several cloud classifications, such as cirrus, blizzards, light snow, anvil clouds, and heavy rain. The focus is on mm-wave and submm-wave frequencies, however discussions of the effects of cloud variations to frequencies as low as 10 GHz and up to 874 GHz will also be presented. The results show that nearly 60% of the TB value at 89 GHz comes from the earth's surface for even the heaviest blizzard snow rates. On the other hand, a significant percentage of the TB value comes from the snow in the cloud for 166, and 183 plus or minus 7 GHz for the heavy and medium snow rates. For submm-wave channels, there is no contribution from the surface because these channels cannot probe through clouds, nor normal water vapor amounts in clear air regions. This work is extremely valuable in physically-based retrieval algorithm development research.

Gail Skofronick-Jackson↗
NASA NTRS2002

Measurements of Turbulence Attenuation by a Dilute Dispersion of Solid Particles in Homogeneous Isotropic Turbulence

This research addresses turbulent gas flows laden with fine solid particles at sufficiently large mass loading that strong two-way coupling occurs. By two-way coupling we mean that the particle motion is governed largely by the flow, while the particles affect the gas-phase mean flow and the turbulence properties. Our main interest is in understanding how the particles affect the turbulence. Computational techniques have been developed which can accurately predict flows carrying particles that are much smaller than the smallest scales of turbulence. Also, advanced computational techniques and burgeoning computer resources make it feasible to fully resolve very large particles moving through turbulent flows. However, flows with particle diameters of the same order as the Kolmogorov scale of the turbulence are notoriously difficult to predict. Some simple flows show strong turbulence attenuation with reductions in the turbulent kinetic energy by up to a factor of five. On the other hand, some seemingly similar flows show almost no modification. No model has been proposed that allows prediction of when the strong attenuation will occur. Unfortunately, many technological and natural two-phase flows fall into this regime, so there is a strong need for new physical understanding and modeling capability. Our objective is to study the simplest possible turbulent particle-laden flow, namely homogeneous, isotropic turbulence with a uniform dispersion of monodisperse particles. We chose such a simple flow for two reasons. First, the simplicity allows us to probe the interaction in more detail and offers analytical simplicity in interpreting the results. Secondly, this flow can be addressed by numerical simulation, and many research groups are already working on calculating the flow. Our detailed data can help guide some of these efforts. By using microgravity, we can further simplify the flow to the case of no mean velocity for either the turbulence or the particles. In fact the addition of gravity as a variable parameter may help us to better understand the physics of turbulence attenuation. The experiments are conducted in a turbulence chamber capable of producing stationary or decaying isotropic turbulence with nearly zero mean flow and Taylor microscale Reynolds numbers up to nearly 500. The chamber is a 410 mm cubic box with the corners cut off to make it approximately spherical. Synthetic jet turbulence generators are mounted in each of the eight corners of the box. Each generator consists of a loudspeaker forcing a plenum and producing a pulsed jet through a 20 mm diameter orifice. These synthetic jets are directed into ejector tubes pointing towards the chamber center. The ejector tubes increase the jet mass flow and decrease the velocity. The jets then pass through a turbulence grid. Each of the eight loudspeakers is forced with a random phase and frequency. The resulting turbulence is highly Isotropic and matches typical behavior of grid turbulence. Measurements of both phases are acquired using particle image velocimetry (PIV). The gas is seeded with approximately 1 micron diameter seeding particles while the solid phase is typically 150 micron diameter spherical glass particles. A double-pulsed YAG laser and a Kodak ES-1.0 10-bit PIV camera provide the PIV images. Custom software is used to separate the images into individual images containing either gas-phase tracers or large particles. Modern high-resolution PIV algorithms are then used to calculate the velocity field. A large set of image pairs are acquired for each case, then the results are averaged both spatially and over the ensemble of acquired images. The entire apparatus is mounted in two racks which are carried aboard NASA's KC-135 Flying Microgravity Laboratory. The rack containing the turbulence chamber, the laser head, and the camera floats freely in the airplane cabin (constrained by competent NASA personnel) to minimize g-jitter.

Eaton, John↗
NASA NTRS2018

Orion Optical Navigation Progress Toward Exploration Mission 1

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is past its Critical Design Review, and is progressing through test and certification for human rating. The filter architecture uses a square-root-free UDU covariance factorization. Linear Covariance Analysis (LinCov) was used to analyze the measurement models and the measurement error models on a representative EM-1 trajectory. The Orion EM-1 flight camera was calibrated at the Johnson Space Center (JSC) electro-optics lab. To permanently stake the focal length of the camera a 500 mm focal length refractive collimator was used. Two Engineering Design Unit (EDU) cameras and an EDU star tracker were used for a live-sky test in Denver. In-space imagery with high-fidelity truth metadata is rare so these live-sky tests provide one of the closest real-world analogs to operational use. A hardware-in-the-loop test rig was developed in the Johnson Space Center Electro-Optics Lab to exercise the OpNav system prior to integrated testing on the Orion vehicle. The software is verified with synthetic images. Several hundred off-nominal images are also used to analyze robustness and fault detection in the software. These include effects such as stray light, excess radiation damage, and specular reflections, and are used to help verify the tuning parameters chosen for the algorithms such as earth atmosphere bias, minimum pixel intensity, and star detection thresholds.

Holt, Greg N.↗
NASA NTRS2014

Characteristics of the 2012 Geminids

The parent of the Geminids, 3200 Phaethon, is a unique body in that it is classified as an asteroid, however is responsible for one of the most prolific meteor showers of the year and has shown comet-like behavior in its past (Jewitt and Li 2010). The Geminid meteor shower is also anomalous as its rates have been increasing since it was first detected. Understanding the composition and properties of meteoroids that belong to this meteor shower is an important area of study and of interest to both theoreticians and experimentalists. Using the light curve and decelerations of ten double-station Geminids as seen in the Meteoroid Environment Office's widefield meteor cameras, densities were able to be approximated using a model of meteoroid ablation by Campbell-Brown et al (2013) which employs thermal disruption to model the release of grains during ablation. Bulk densities of Geminids give unique insight into the composition of Phaethon that would only be derived by going to the asteroid itself. The bulk densities of these ten Geminids were found to be between 2.6 and 3.0 g/cm(3), supporting results from Babadzhanov (2009) and Borovicka et al (2010) which prove Phaethon has a much lower porosity than most other meteor shower parents. NASA's Meteoroid Environment Office established these two wide-field meteor cameras to observe meteors in the milligram-mass-range. Each camera consists of a 17 mm focal length Schneider lens (f/0.95) on a Watec 902U2 Ultimate CCD video camera, producing a 21.7x15.5 degree field-of-view. This configuration sees meteors down to a magnitude of +6. Data from these cameras are currently being used to calculate daily automated meteor fluxes. On the first night of operation, December 13-14, 2012, 18 double-station and 53 unique single-station Geminids were detected. The Geminid flux results from this system will be presented as well as ZHR's over the peak of the Geminids. The average flux density over the night was 0.058, 0.052, and 0.062 meteors/km(2)/hour down to a limiting magnitude of +6.5, for the double-station results and each single-station's results. This equates to ZHR's of 113, 102, and 122 respectively. Included in the flux algorithm is a process to find the collecting area per height and a method to find the limiting meteor magnitude per 10 minute time period.

Blaauw, R.↗
NASA NTRS1991

A very high speed lossless compression/decompression chip set

A chip is described that will perform lossless compression and decompression using the Rice Algorithm. The chip set is designed to compress and decompress source data in real time for many applications. The encoder is designed to code at 20 M samples/second at MIL specifications. That corresponds to 280 Mbits/second at maximum quantization or approximately 500 Mbits/second under nominal conditions. The decoder is designed to decode at 10 M samples/second at industrial specifications. A wide range of quantization levels is allowed (4...14 bits) and both nearest neighbor prediction and external prediction are supported. When the pre and post processors are bypassed, the chip set performs high speed entropy coding and decoding. This frees the chip set from being tied to one modeling technique or specific application. Both the encoder and decoder are being fabricated in a 1.0 micron CMOS process that has been tested to survive 1 megarad of total radiation dosage. The CMOS chips are small, only 5 mm on a side, and both are estimated to consume less than 1/4 of a Watt of power while operating at maximum frequency.

Venbrux, Jack↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS2006

Phase Calibration of Microphones by Measurement in the Free-field

Over the past several years, significant effort has been expended at NASA Langley developing new Micro-Electro-Mechanical System (MEMS)-based microphone directional array instrumentation for high-frequency aeroacoustic measurements in wind tunnels. This new type of array construction solves two challenges which have limited the widespread use of large channel-count arrays, namely by providing a lower cost-per-channel and a simpler method for mounting microphones in wind tunnels and in field-deployable arrays. The current generation of array instrumentation is capable of extracting accurate noise source location and directivity on a variety of airframe components using sophisticated data reduction algorithms [1-2]. Commercially-available MEMS microphones are condenser-type devices and have some desirable characteristics when compared with conventional condenser-type microphones. The most important advantages of MEMS microphones are their size, price, and power consumption. However, the commercially-available units suffer from certain important shortcomings. Based on experiments with array prototypes, it was found that both the bandwidth and the sound pressure limit of the microphones should be increased significantly to improve the performance and flexibility of the microphone array [3]. It was also desired to modify the packaging to eliminate unwanted Helmholtz resonance s exhibited by the commercial devices. Thus, new requirements were defined as follows: Frequency response: 100 Hz to 100 KHz (+/-3dB) Upper sound pressure limit: Design 1: 130 dB SPL (THD less than 5%) Design 2: 150-160 dB SPL (THD less than 5%) Packaging: 3.73 x 6.13 x 1.3 mm can with laser-etched lid. In collaboration with Novusonic Acoustic Innovation, NASA modified a Knowles SiSonic MEMS design to meet these new requirements. Coupled with the design of the enhanced MEMS microphones was the development of a new calibration method for simultaneously obtaining the sensitivity and phase response of the devices over their entire broadband frequency range. Traditionally, electrostatic actuators (EA) have been used to characterize air-condenser microphones; however, MEMS microphones are not adaptable to the EA method due to their construction and very small diaphragm size [4]. Hence a substitution based, free-field method was developed to calibrate these microphones at frequencies up to 80 kHz. The technique relied on the use of a random, ultrasonic broadband centrifugal sound source located in a small anechoic chamber. The free-field sensitivity (voltage per unit sound pressure) was obtained using the procedure outlined in reference 4. Phase calibrations of the MEMS microphones were derived from cross spectral phase comparisons between the reference and test substitution microphones and an adjacent and invariant grazing-incidence 1/8-inch standard microphone. The free-field calibration procedure along with representative sensitivity and phase responses for the new high-frequency MEMS microphones are presented here.

Shams, Qamar A.↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS2017

Integrating Growth Stage Deficit Irrigation into a Process Based Crop Model

Current rates of agricultural water use are unsustainable in many regions, creating an urgent need to identify improved irrigation strategies for water limited areas. Crop models can be used to quantify plant water requirements, predict the impact of water shortages on yield, and calculate water productivity (WP) to link water availability and crop yields for economic analyses. Many simulations of crop growth and development, especially in regional and global assessments, rely on automatic irrigation algorithms to estimate irrigation dates and amounts. However, these algorithms are not well suited for water limited regions because they have simplistic irrigation rules, such as a single soil-moisture based threshold, and assume unlimited water. To address this constraint, a new modeling framework to simulate agricultural production in water limited areas was developed. The framework consists of a new automatic irrigation algorithm for the simulation of growth stage based deficit irrigation under limited seasonal water availability; and optimization of growth stage specific parameters. The new automatic irrigation algorithm was used to simulate maize and soybean in Gainesville, Florida, and first used to evaluate the sensitivity of maize and soybean simulations to irrigation at different growth stages and then to test the hypothesis that water productivity calculated using simplistic irrigation rules underestimates WP. In the first experiment, the effect of irrigating at specific growth stages on yield and irrigation water use efficiency (IWUE) in maize and soybean was evaluated. In the reproductive stages, IWUE tended to be higher than in the vegetative stages (e.g. IWUE was 18% higher than the well watered treatment when irrigating only during R3 in soybean), and when rainfall events were less frequent. In the second experiment, water productivity (WP) was significantly greater with optimized irrigation schedules compared to non-optimized irrigation schedules in water restricted scenarios. For example, the mean WP across 38 years of maize production was 1.1 kg/cu m for non-optimized irrigation schedules with 50 mm of seasonal available water and 2.1 kg/cu m optimized ion schedules, a 91% improvement in WP with optimized irrigation schedules. The framework described in this work could be used to estimate WP for regional to global assessments, as well as derive location specific irrigation guidance.

crop model↗
NASA NTRS2021

Daily Rainfall Estimate by Emissivity Temporal Variation from 10 Satellites

Rainfall retrieval algorithms for passive microwave radiometers often exploit the brightness temperature depression due to ice scattering at high-frequency channels (≥85 GHz) over land. This study presents an alternate method to estimate the daily rainfall amount using the emissivity temporal variation (i.e., Δe) under rain-free conditions at low-frequency channels (19, 24, and 37 GHz). Emissivity is derived from 10 passive microwave radiometers, including the Global Precipitation Measurement (GPM) Microwave Imager (GMI), the Advanced Microwave Scanning Radiometer 2 (AMSR2), three Special Sensor Microwave Imager/Sounders (SSMIS), the Advanced Technology Microwave Sounder (ATMS), and four Advanced Microwave Sounding Units-A (AMSU-A). Four different satellite combination schemes are used to derive the Δe for daily rainfall estimates. They are all 10 satellites, 5 imagers, 6 satellites with very different equator crossing times, and GMI only. Results show that Δe from all 10 satellites has the best performance with a correlation of 0.60 and RMSE of 6.52 mm, compared with the Integrated Multisatellite Retrievals for GPM (IMERG) Final run product. The 6-satellites scheme has comparable performance with the all-10-satellites scheme. The 5-imagers scheme performs noticeably worse with a correlation of 0.49 and RMSE of 7.28 mm, while the GMI-only scheme performs the worst with a correlation of 0.25 and RMSE of 11.36 mm. The inferior performance from the 5-imagers and GMI-only schemes can be explained by the much longer revisit time, which cannot accurately capture the emissivity temporal variation.

Yalei You↗
NASA NTRS2017

Imaging Systems for Size Measurements of Debrisat Fragments

The overall objective of the DebriSat project is to provide data to update existing standard spacecraft breakup models. One of the key sets of parameters used in these models is the physical dimensions of the fragments (i.e., length, average-cross sectional area, and volume). For the DebriSat project, only fragments with at least one dimension greater than 2 mm are collected and processed. Additionally, a significant portion of the fragments recovered from the impact test are needle-like and/or flat plate-like fragments where their heights are almost negligible in comparison to their other dimensions. As a result, two fragment size categories were defined: 2D objects and 3D objects. While measurement systems are commercially available, factors such as measurement rates, system adaptability, size characterization limitations and equipment costs presented significant challenges to the project and a decision was made to develop our own size characterization systems. The size characterization systems consist of two automated image systems, one referred to as the 3D imaging system and the other as the 2D imaging system. Which imaging system to use depends on the classification of the fragment being measured. Both imaging systems utilize point-and-shoot cameras for object image acquisition and create representative point clouds of the fragments. The 3D imaging system utilizes a space-carving algorithm to generate a 3D point cloud, while the 2D imaging system utilizes an edge detection algorithm to generate a 2D point cloud. From the point clouds, the three largest orthogonal dimensions are determined using a convex hull algorithm. For 3D objects, in addition to the three largest orthogonal dimensions, the volume is computed via an alpha-shape algorithm applied to the point clouds. The average cross-sectional area is also computed for 3D objects. Both imaging systems have automated size measurements (image acquisition and image processing) driven by the need to quickly and accurately measure tens of thousands of debris fragments. Moreover, the automated size measurement reduces potential fragment damage/mishandling and ability for accuracy and repeatability. As the fragment characterization progressed, it became evident that the imaging systems had to be revised. For example, an additional view was added to the 2D imaging system to capture the height of the 2D object. This paper presents the DebriSat project's imaging systems and calculation techniques in detail; from design and development to maturation. The experiences and challenges are also shared.

Shiotani, B.↗