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NASA NTRS2004

Objective Lightning Forecasting at Kennedy Space Center/Cape Canaveral Air Force Station using Cloud-to-Ground Lightning Surveillance System Data

The 45th Weather Squadron (45 WS) forecasters at Cape Canaveral Air Force Station (CCAFS) in Florida include a probability of thunderstorm occurrence in their daily morning briefings. This information is used by personnel involved in determining the possibility of violating Launch Commit Criteria, evaluating Flight Rules for the Space Shuttle, and daily planning for ground operation activities on Kennedy Space Center (KSC)/CCAFS. Much of the current lightning probability forecast is based on a subjective analysis of model and observational data. The forecasters requested that a lightning probability forecast tool based on statistical analysis of historical warm-season (May - September) data be developed in order to increase the objectivity of the daily thunderstorm probability forecast. The tool is a set of statistical lightning forecast equations that provide a lightning occurrence probability for the day by 1100 UTC (0700 EDT) during the warm season. This study used 15 years (1989-2003) of warm season data to develop the objective forecast equations. The local CCAFS 1000 UTC sounding was used to calculate stability parameters for equation predictors. The Cloud-to-Ground Lightning Surveillance System (CGLSS) data were used to determine lightning occurrence for each day. The CGLSS data have been found to be more reliable indicators of lightning in the area than surface observations through local informal analyses. This work was based on the results from two earlier research projects. Everitt (1999) used surface observations and rawinsonde data to develop logistic regression equations that forecast the daily thunderstorm probability at CCAFS. The Everitt (1999) equations showed an improvement in skill over the Neumann-Pfeffer thunderstorm index (Neumann 1971), which uses multiple linear regression, and also persistence and climatology forecasts. Lericos et al. (2002) developed lightning distributions over the Florida peninsula based on specific flow regimes. The flow regimes were inferred from the average wind direction in the 1000-700 mb layer at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), Florida, and the lightning data were from the National Lightning Detection Network. The results suggested that the daily flow regime may be an important predictor of lightning occurrence on KSC/CCAFS.

Lambert, Winifred↗
NASA NTRS2022

A Survey of Mathematical Structures for Lunar Networks

To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay tolerant networking↗
NASA NTRS2016

Global Carbon Budget 2016

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere the global carbon budget is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics, and model estimates and their interpretation by a broad scientific community. We discuss changes compared to previous estimates and consistency within and among components, alongside methodology and data limitations. CO2 emissions from fossil fuels and industry (EFF) are based on energy statistics and cement production data, respectively, while emissions from land-use change (ELUC), mainly deforestation, are based on combined evidence from land-cover change data, fire activity associated with deforestation, and models. The global atmospheric CO2 concentration is measured directly and its rate of growth (GATM) is computed from the annual changes in concentration. The mean ocean CO2 sink (SOCEAN) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in SOCEAN is evaluated with data products based on surveys of ocean CO2 measurements. The global residual terrestrial CO2 sink (SLAND) is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models. We compare the mean land and ocean fluxes and their variability to estimates from three atmospheric inverse methods for three broad latitude bands. All uncertainties are reported as +/- 1(sigma), reflecting the current capacity to characterize the annual estimates of each component of the global carbon budget. For the last decade available (2006-2015), EFF was 9.3+/-0.5 GtC/yr, ELUC 1.0+/-0.5 GtC/yr,GATM 4.5+/-0.1 GtC/yr, SOCEAN 2.6+/-0.5 GtC/yr, and SLAND 3.1+/-0.9 GtC/yr. For year 2015 alone, the growth in EFF was approximately zero and emissions remained at 9.9+/-0.5 GtC/yr, showing a slowdown in growth of these emissions compared to the average growth of 1.8/yr that took place during 2006-2015.Also, for 2015, ELUC was 1.3+/-0.5 GtC/yr, GATM was 6.3+/-0.2 GtC/yr, SOCEAN was 3.0+/-0.5 GtC/yr, and SLAND was 1.9+/-0.9 GtC/yr. GATM was higher in 2015 compared to the past decade (2006-2015), reflecting a smaller SLAND for that year. The global atmospheric CO2 concentration reached 399.4+/-0.1 ppm averaged over 2015. For 2016, preliminary data indicate the continuation of low growth in EFF with +0.2% (range of -1.0 to +1.8% ) based on national emissions projections for China and USA, and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. In spite of the low growth of EFF in 2016, the growth rate in atmospheric CO2 concentration is expected to be relatively high because of the persistence of the smaller residual terrestrial sink (SLAND) in response to El Nino conditions of 2015-2016. From this projection of EFF and assumed constant ELUC for 2016, cumulative emissions of CO2 will reach 565+/-55 GtC (2075+/-205 GtCO2) for 1870-2016, about 75% from EFF and 25% from ELUC. This living data update documents changes in the methods and data sets used in this new carbon budget compared with previous publications of this data set.

Quéré, Corinne Le↗
NASA NTRS2001

Combining Information on Multiple Detection Techniques to Estimate the Effect of Patent Foramen Ovale on Susceptibility to Decompression Illness

The assembly and the maintenance of the International Space Station is expected to require hundreds of extravehicular excursions (EVA's) in the next 10 years. During an EVA, in order to allow movement and bending of limbs, spacesuit pressures are reduced to about 4.3 psi. as compared with about 14.7 psi. for normal atmospheric pressure at sea level. However, the exposure of astronauts to reduced pressures in spacesuits, is conducive to fonnation and growth of gas bubbles within venous blood or tissues, which could cause decompression illness (DCI), a pathology best known to occur among deep-sea divers when they return to the surface. To reduce the risk of DCI, astronauts adjust to the reduced pressure in stages for a prolonged time known as a "pre-breathe" period prior to their extravehicular activity. Despite the use of pre-breathe protocols, an increased risk of DCI can arise for about 25% of humans who have a small hole, known as a patent foramen ovale (PFO), between two chambers of the heart. The atrial septum's fossa oval is, an embryological remnant of a flap between the septae primum and secundum allows fetal right atrial blood to pass into the left atrium, and usually closes after birth (Hagen, et al,. 1984). If fusion does not occur, a valve-like opening, the foramen ovale persists between the two atria. It has been suggested that astronauts with PFO's might be at greater risk of stroke or other serious neurological DCI because bubbles from a venous site may traverse a PFO, travel to the aorta and then enter the cerebral circulatory system causing a stroke (Figure 1). Astronauts are not now screened for PFO's, however consideration is being given to doing so. Here, we study three main methods abbreviated here as "ITE", "TCD" and "TEE", for detecting PFO's in living subjects. All involve the introduction of bubbles into a vein, immediately after which a sensory probe attempts to detect the bubbles in systemic circulation. Presence of the injected bubbles in the systemic circulation is indicative of a PFO. More detailed descriptions are given after the explanation of PFO's under Figure I. Even if a true PFO affects the risk of DCI, there remains a question of how effective screening would be if the detection method has errors of omission and/or commission. Of the three methods studied here, TEE is the "gold standard", matching autopsy results with near-perfect sensitivity and specificity (Schneider, et al. , 1996). However TEE is also the most difficult method to implement, requiring an internal esophagal probe, and is therefore not widely used. Currently, the easiest to use and most common PFO detection method is TTE, which uses an external chest probe. This method has a specificity of near 100%, but suffers from a low sensitivity rate (about 30%). More recently, TCD has been developed, which uses ultrasound probes to detect the presence of bubbles in cerebral arteries. Studies indicate that TCD is quite effective, having a sensitivity of about 91% and a specificity of about 93% (Droste, et al., 1999) when applied correctly, however implementation is difficult and requires considerable training.

Feiveson, Alan H.↗
NASA NTRS2021

Long-term Pulse Period Evolution of the Ultra-luminous X-ray Pulsar NGC 7793 P13

Ultra-luminous X-ray pulsars (ULXPs) provide a unique opportunity to study persistent super-Eddington accretion. Here we present the results of a long-term monitoring campaign of ULXP NGC 7793 P13, focusing on the pulse period evolution and the determination of the orbital ephemeris. Over our four year monitoring campaign with Swift, XMM-Newton, and NuSTAR, we measure a continuous spin-up with an average value of ̇P≈−3.8×10−11s s−1. We find that the strength of the spin-up is independent of the observed X-ray flux, indicating that despite a drop in observed flux in 2019, accretion onto the source has continued at largely similar rates. The source entered an apparent off-state in early 2020, which might have resulted in a change of the accretion geometry as no pulsations were found in observations in July/August 2020.We use the long-term monitoring to update the orbital ephemeris, as well as the periodicities seen in both the observed optical/UV and X-ray fluxes. We find that the optical/UV period is very stable over the years, with PUV=63.75+0.17−0.12d. The best-fit orbital period determined from our X-ray timing results is 64.86±0.19 d, almost a day longer than previously implied, and the X-ray flux period is65.21±0.15 d, slightly shorter than measured previously. The physical origin of these different flux periods is currently unknown. We study the hardness ratio of the XMM-Newton and NuSTAR data between 2013–2020 to search for indications of spectral changes. We find that the hardness ratios at high energies are very stable and not directly correlated with the observed flux. At lower energies we observe a small hardening with increased flux, which might indicate increased obscuration through outflows at higher luminosities. Comparing the changes in flux with the observed pulsed fraction, we find that the pulsed fraction is significantly higher at low fluxes. This seems to imply that the accretion geometry already changed before the source entered the deep off-state. We discuss possible scenarios to explain this behavior, which is likely driven by a precessing accretion disk.

Neutron stars↗
NASA NTRS2009

Return to Flying Duties Following Centrifuge or Vibration Exposures

Introduction: In an effort to determine the human performance limits for vibration in spacecraft being developed by NASA, astronauts were evaluated during a simulated launch profile in a centrifuge/vibration environment and separate vibration-only simulation. Current USAF and Army standards for return to flight following centrifuge exposures require 12-24 hours to pass before a crewmember may return to flying duties. There are no standards on vibration exposures and return to flying duties. Based on direct observation and provocative neurological testing of the astronauts, a new standard for return to flying duties following centrifuge and/or vibration exposures was established. Methods: 13 astronaut participants were exposed to simulated launch profiles in a + 3.5 Gx bias centrifuge/vibration environment and separately on a vibration table at the NASA-Ames Research Center. Each subject had complete neurological evaluations pre- and post-exposure for the centrifuge/vibration runs with the NASA neurological function rating scale (NFRS). Subjects who participated in the vibration-only exposures had video oculography performed with provocative maneuvers in addition to the NFRS. NFRS evaluations occurred immediately following each exposure and at 1 hour post-run. Astronauts who remained symptomatic at 1 hour had repeat NFRS performed at 1 hour intervals until the crewmember was asymptomatic. Results: Astronauts in the centrifuge/vibration study averaged a 3-5 point increase in NFRS scores immediately following exposure but returned to baseline 3 hours post-run. Subjects exposed to the vibration-only simulation had a 1-3 point increase following exposure and returned to baseline within 1-2 hours. Pre- and post- vibration exposure video oculography did not reveal any persistent ocular findings with provocative testing 1 hour post-exposure. Discussion: Based on direct observations and objective measurement of neurological function in astronauts following simulated launch profiles, asymptomatic individuals are allowed to return to flying duties within 3 hours following centrifuge/vibration and 2 hours after vibration-only exposures.

Scheuring, Richard A.↗
NASA NTRS2004

Winds, Water Budgets and Stable Isotopes in Tropical Cyclones using TRMM and QUICKSCAT

Water vapor is the most abundant greenhouse gas in the atmosphere. Changes in its concentration and distribution are controlled by the hydrologic cycle. Because of its capacity to absorb and emit long wave radiation, release latent heat during condensation in storms and reflect short wave radiation when clouds form it has a major impact on Global climate change. The stable isotope ratios of water are H20 H2l6O and H0 H2l6O. These ratios change whenever water undergoes a phase change. They also change in both rain and water vapor whenever an air parcel is exposed to rain. In addition the relative changes in the two ratios differ as a &nction of the relative humidity. In short, the stable isotope ratios in water vapor in the atmosphere contain an integrated history of the processes affecting the concentration and distribution of water vapor in the atmosphere. Therefore the measurement and interpretation of changes in these stable isotope ratios are a powerful tool matched by no other method in tracing the transport history of water in the atmosphere. Our initial studies under this grant focused on the changes of the stable isotope ratios of precipitation and water vapor in tropical cyclones. The changes in time and space were found to be very large and to trace the transport of water in the storms reflecting changes in basic structural features. Because the stable isotope ratios of rains from tropical cyclones are so low flooding associated with land falling tropical cyclones introduces a negative isotopic spike into the coastal surface waters. In addition the stable isotope ratios of water vapor in the vicinity of tropical cyclones is anomalously low. This suggests that carbonate shelled organisms such as ostracoda living in coastal waters have the potential to record the isotopic spike and thereby provide a long term record of tropical storm activity in sediment cores containing fossil shells. Likewise, tree rings in coastal environments offer a similar potential. We have analyzed the oxygen isotopic composition of ostrcoda shells formed in the floodwaters of Tropical Storm Allison (2001) and discovered the negative isotopic 1 16 spike. Because we had learned that storm activity has a major impact on the stable isotope ratios of water vapor in the tropics and sub-tropics we decided to analyze the isotopic compositions of water vapor in different locations in the tropics. We did this in Puerto Escondido, Mexico in July 1998, near Kwajalein Island in the Pacific in 1999 as part of a TRMM summer field program and in 2001 in Key West, Florida as part of the CAMEX 4 summer field program. Our isotopic studies along with our earlier tropical cyclone studies showed that the low isotopic ratios in water vapor induced by exposure to rains the storms persisted for 48 hours often far away from the original storm site. We also noted that positive isotopic spikes were introduced into atmospheric water vapor if winds were high and extensive sea spray was present. These findings have a significant impact on the interpretation of the stable isotope studies of tropical ice cores found in the high mountain regions of the tropics. The assumption made in interpreting the ice core record is that the source water vapor evaporated from the sea surface is in near isotopic equilibrium with the seawater and undergoes a decrease during its transport that reflects the change in temperature from the sea surface to the site of the ice core. Because an additional isotopic depletion occurs at the sea surface source area that depends on the intensity, duration and size of the tropical rain system the isotopic variations found in the ice cores must take into account changes in past storm activity in the tropics. These systems must be an important source of water vapor to the ice cores because they charge the troposphere with water vapor to a far greater vertical height than evaporation in quiescent regions. Finally, an interest in increased heat transfer in thnterior of tropical cyclones resulting from greater amounts of sea spray is a topic of considerable interest to the research community. Increases in sea spray may be related to rapid changes in the intensity of hurricanes, a feature of hurricanes that currently is very poorly forecast. Project CBLAST of the Hurricane Research Division of NOAA is an active program that uses P3 research aircraft to evaluate this problem. An instrument has been designed and built at the University of Houston that will be placed on the P3 research aircraft during the 2004 hurricane season. It continuously measures the salt content of rain in hurricanes. Changes in the salt content of the rains should reflect the abundance of sea spray at the sea surface. In this way maps of sea spray intensity in hurricanes may be forthcoming. This should help computer modelers who simulate hurricanes to better understand the potential of changes in sea spray to change the intensity of hurricanes. The cost of designing, building and installing this instrument was borne largely by funding from this NASA grant. A list of presentations at national meetings and publications that were as the result of funding from this NASA grant are found in the report.

Lawrence, James R.↗
NASA NTRS1999

"Dust Devils": Gardening Agents on the Surface of Mars, and Hidden Hazards to Human Exploration?

Dust devils are familiar sites in the and regions of the world: they can produce quite spectacular displays of dust lofting when the vortices scavenge very loose dust from a dry lake bed or from recently disturbed agricultural fields. If one were to arrive at the center of an arid region, take one photograph, or even a series of photographs over a period of several days, then return the images for laboratory analysis, it would be most likely concluded that the region was inactive from an aeolian perspective. No images of general dust movement were obtained, nor were any dust devils "caught on camera" owing to their ephemeral and unpredictable appearance, and the fact that there was deceptively little residue of their actions. If, however, a camera were to take a 360 degree continuous recording over a period of a year, and the film were then to be shown at high speed over a period a several minutes, the impression might be that of a region ravaged by air vorticity and dust movement. Extrapolate this over geological time, and it is possible to visualize dust devils as prime aeolian agents, rather than insignificant vagaries of nature, On Mars, the thin atmosphere permits the surface of the planet to be heated but it does not itself retain heat with the capacity of the earth's atmosphere. This gives rise to greater thermal instability near the surface of Mars as "warm" air pockets diapiritically inject themselves into higher atmospheric layers. Resulting boundary-layer vorticity on Mars might therefore be expected to produce dust devils in abundance, if only seasonally. The spectacular images of dust devils obtained by Pathfinder within its brief functional period on the planet testify to the probability of highly frequent surface vorticity in light of the above reasoning about observational probability. Notably, the Pathfinder devils appeared to be at least a kilometer in height. There are several consequences for the geology of Mars, and for human exploration, if dust devils are to be expected in reasonable abundance. First, from a geological perspective, the vortices will act as "gardening" agents for the top few centimeters of entrainable material. Over time (hundreds of millions, or billions of years being available), they will cover the surface with scouring paths, and the grain sizes that can be lofted by a vortex probably extends over the whole sand to dust range. The depositional paths are, of course, much larger, so that vortex-induced deposition is more widespread than vortex-induced erosion, and will without doubt, affect the whole region in which the dust devils occur (this might explain why rocks at the Viking site seemed oddly capped with dust in a region apparently subject to general aeolian scouring). On Mars, the lift forces in dust devils might be less than on earth owing to the much thinner atmosphere, but this may be counterbalanced by lower gravity and greater vortex velocities. Certainly, when active, other aeolian phenomena on Mars --sand motion and dust storms, seem no less energetic and no less capable of lofting sediments than equivalent terrestrial aeolian phenomena. Every several years, within the current climatic regime, the surface of Mars is subject to light dust fall from global dust storms. Over time, this should develop a very uniform surface layer, with commensurate uniformity in grain size, mineralogy, albedo, color, and general spectroscopic properties. Dust devils will disturb this situation by continually mixing the surface dust with underlying layers, perhaps composed of silt and sand. This size mixing will also involve compositional mixing. After some years, the thin layer of dust that may be difficult to entrain alone, becomes progressively mixed with coarser materials that could reduce the general aeolian threshold of the soil. Certainly the continual disturbance by vorticity will prevent surface stabilization that may bind or indurate grains (caused by slow cementation or ice welding at grain boundaries). If dust devils continually loft dust to kilometer heights, and the dust is sprayed into many cubic kilometers of atmosphere each time, could the devils produce a continual background of atmospheric dust that might be mistaken for the fallout of a distant large-scale dust storm? From a human exploration perspective, dust devils are unlikely to pose any, life- threatening situation for an astronaut unfortunate enough to encounter a momentary swirling cloud of loose soil. However, it is noted that pervasive dust is probably one of the greatest long-term hazards for a human encampment. The fineness and penetration capabilities of the dust, its electrostatic adhesive properties, and its complete ubiquity, render the material a persistent nuisance at best, but at worst, over a period of many months it is possible that space suits, machinery, habitat interiors, air filters, and so forth, could become jeopardized. Owing to dust penetration, the space suits used in the Apollo landings were rendered unusable after a few EVA activities. There will be a definite attempt to situate a human colony on Mars in an area that is far removed from the regions of the planet known for being the centers of major dust storms. At the heart of these storm systems, the dust lofting mechanics are unknown, but they are energetic and perhaps potentially life-threatening for an astronaut. Locating a colony in a region that appears from space to be meteorologically benign may lead to colony placement in a region prone to dust devils, but dust devils are not (or have not been) detectable from orbital observations: the region surveyed for placement will appear like the apparently inactive and area referred to earlier. The region may be spared from highly energetic weather systems, but it may not be necessarily immune from continual dust disturbance. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS2012

The Effects of Solar Variability on Earth's Climate: A Workshop Report

Solar irradiance, the flux of the Sun s output directed toward Earth, is Earth s main energy source.1 The Sun itself varies on several timescales over billions of years its luminosity increases as it evolves on the main sequence toward becoming a red giant; about every 11 years its sunspot activity cycles; and within just minutes flares can erupt and release massive amounts of energy. Most of the fluctuations from tens to thousands of years are associated with changes in the solar magnetic field. The focus of the National Research Council's September 2011 workshop on solar variability and Earth's climate, and of this summary report, is mainly magnetically driven variability and its possible connection with Earth's climate variations in the past 10,000 years. Even small variations in the amount or distribution of energy received at Earth can have a major influence on Earth's climate when they persist for decades. However, no satellite measurements have indicated that solar output and variability have contributed in a significant way to the increase in global mean temperature in the last 50 years. Locally, however, correlations between solar activity and variations in average weather may stand out beyond the global trend; such has been argued to be the case for the El Nino-Southern Oscillation, even in the present day. A key area of inquiry deals with establishing a unified record of the solar output and solar-modified particles that extends from the present to the prescientific past. The workshop focused attention on the need for a better understanding of the links between indices of solar activity such as cosmogenic isotopes and solar irradiance. A number of presentations focused on the timescale of the solar cycle and of the satellite record, and on the problem of extending this record back in time. Highlights included a report of progress on pyroheliometer calibration, leading to greater confidence in the time history and future stability of total solar irradiance (TSI), and surprising results on changes in spectral irradiance over the last solar cycle, which elicited spirited discussion. New perspectives on connections between features of the quiet and active areas of the photosphere and variations in TSI were also presented, emphasizing the importance of developing better understanding in order to extrapolate back in time using activity indices. Workshop participants reviews highlighted difficulties as well as causes for optimism in current understanding of the cosmogenic isotope record and the use of observed variability in Sun-like stars in reconstructing variations in TSI occurring on lower frequencies than the sunspot cycle. The workshop succeeded in bringing together informed, focused presentations on major drivers of the Sun-climate connection. The importance of the solar cycle as a unique quasi-periodic probe of climate responses on a timescale between the seasonal and Milankovitch cycles was recognized in several presentations. The signal need only be detectable, not dominant, for it to play this role of a useful probe. Some workshop participants also found encouraging progress in the top-down perspective, according to which solar variability affects surface climate by first perturbing the stratosphere, which then forces the troposphere and surface. This work is now informing and being informed by research on tropospheric responses to the Antarctic ozone hole and volcanic aerosols. In contrast to the top-down perspective is the bottom-up view that the interaction of solar energy with the ocean and surface leads to changes in dynamics and temperature. During the discussion of how dynamical air-sea coupling in the tropical Pacific and solar variability interact from a bottom-up perspective, several participants remarked on the wealth of open research questions in the dynamics of the climatic response to TSI and spectral variability. The discussion of the paleoclimate record emphasized that the link between solar varbility and Earth s climate is multifaceted and that some components are understood better than others. According to two presenters on paleoclimate, there is a need to study the idiosyncrasies of each key proxy record. Yet they also emphasized that there may be an emerging pattern of paleoclimate change coincident with periods of solar activity and inactivity, but only on long timescales of multiple decades to millennia. Several speakers discussed the effects of particle events and cosmic-ray variability. These are all areas of exciting fundamental research; however, they have not yet led to conclusive evidence for significant related climate effects. The key problem of attribution of climate variability on the timescales of the Little Ice Age and the Maunder Minimum were directly addressed in several presentations. Several workshop participants remarked that the combination of solar, paleoclimatic, and climate modeling research has the potential to dramatically improve the credibility of these attribution studies.

Source record↗
NASA NTRS2003

Jet Noise Modeling for Coannular Nozzles Including the Effects of Chevrons

Development of good predictive models for jet noise has always been plagued by the difficulty in obtaining good quality data over a wide range of conditions in different facilities.We consider such issues very carefully in selecting data to be used in developing our model. Flight effects are of critical importance, and none of the means of determining them are without significant problems. Free-jet flight simulation facilities are very useful, and can provide meaningful data so long as they can be analytically transformed to the flight frame of reference. In this report we show that different methodologies used by NASA and industry to perform this transformation produce very different results, especially in the rear quadrant; this compels us to rely largely on static data to develop our model, but we show reasonable agreement with simulated flight data when these transformation issues are considered. A persistent problem in obtaining good quality data is noise generated in the experimental facility upstream of the test nozzle: valves, elbows, obstructions, and especially the combustor can contribute significant noise, and much of this noise is of a broadband nature, easily confused with jet noise. Muffling of these sources is costly in terms of size as well as expense, and it is particularly difficult in flight simulation facilities, where compactness of hardware is very important, as discussed by Viswanathan (Ref. 13). We feel that the effects of jet density on jet mixing noise may have been somewhat obscured by these problems, leading to the variable density exponent used in most jet noise prediction procedures including our own. We investigate this issue, applying Occam s razor, (e.g., Ref. 14), in a search for the simplest physically meaningful model that adequately describes the observed phenomena. In a similar vein, we see no reason to reject the Lighthill approach; it provides a very solid basis upon which to build a predictive procedure, as we believe we demonstrate in this report. Another feature of our approach is that the analyses are all conducted with lossless spectra, rather than Standard Day spectra, as is often done in industry. We feel that it is important to isolate the effects of as many physical processes as practical. Atmospheric attenuation can then be included using the relations developed for NASA by Shields and Bass (Ref. 15), which are available in both FOOTPR and ANOPP. The current approach to coannular jet noise prediction used in FOOTPR is reported in Reference 16, which updates the earlier conventional-velocity-profile (CVP, Ref. 17) and inverted-velocity-profile (IVP, Ref. 18) models.

Stone, James R.↗
NASA NTRSDate not supplied

Mars 2020's First Sample: The Fractured Rough Rock Unit on the Floor of Jezero Crater

A central goal of the Mars 2020 mission is to select and cache samples for future return to Earth. The first samples targeted for collection are from the crater-retaining, Crater Floor Fractured Rough (CF-Fr) unit of Stack et al., 2020.The CF-Fr unit is a topographically low unit in the current Jezero setting, likely overlain by morphologically discrete units, including possible Jezero delta deposits and eolian features. CF-Fr is an aerially extensive unit with lobate margins. Two distinct morphologies are observed: a locally-exposed lower expression, with flat relatively horizontal light-toned surfaces and polygonal fracturing, and an upper expression consisting of up to ~5vertical meters of massive, sometimes boulder-producing, material. The locally-exposed lower expression appears to represent a local ground level in which the upper material has been removed. Near the Octavia E. Butler landing site, the lower morphology is exposed as polygonally-fractured, light-toned bedrock that appears to grade continuously into higher-standing massive outcrops, often with no clearly exposed contact. Further south, a darker upper expression of the CF-Fr unit is more distinct and the unit exhibits some horizontal layering. The Perseverance rover will initially sample the flat-lying expression of this unit. Hypotheses for the origin of CF-Fr include fluvial, aeolian, or lacustrine sediment likely derived from the Jezero watershed, and/or pyroclastic material resulting from regional volcanism. Geochronology of the returned sample could be used to help constrain the timing of geological events in Jezero. It may also help constrain stratigraphic relationships with crater-retaining units outside of Jezero within the Nili Planum, which could be used to calibrate the cratering chronology of Mars. Paleomagnetic analyses of an oriented sample could establish the history of the martian dynamo and whether it persisted into the Hesperian. Finally, if present, secondary phases within the primary deposit would help constrain diagenetic conditions and inform post-depositional aqueous and potentially habitable environmental conditions.

Justin I Simon↗
NASA NTRS1997

Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal, and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineers perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(sub x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for 'graceful' rather than catastrophic failure. When loaded in the fiber direction these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; map a simplistic future strength envelope of the material; develop a statistically based reliability computer algorithm; verify the reliability model and computer algorithm-, and model stator vanes for rig tests. Thus establishing design protocols that enable the engineer to analyze and predict the mechanical behavior of ceramic composites and intermetallics would mitigate the prototype (trial and error) approach currently used by the engineering community. The primary objective of the research effort supported by this short term grant is the continued creation of enabling technologies for the macro-analysis of components fabricated from ceramic composites and intermetallic material systems. The creation of enabling technologies aids in shortening the product development cycle of components fabricated from the new high technology materials.

Duffy, Stephen F.↗
NASA NTRS1997

Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineer's perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for "graceful" rather than catastrophic failure. When loaded in the fiber direction, these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; map a simplistic failure strength envelope of the material; develop a statistically based reliability computer algorithm, verify the reliability model and computer algorithm, and model stator vanes for rig tests. Thus establishing design protocols that enable the engineer to analyze and predict the mechanical behavior of ceramic composites and intermetallics would mitigate the prototype (trial and error) approach currently used by the engineering community. The primary objective of the research effort supported by this short term grant is the continued creation of enabling technologies for the macroanalysis of components fabricated from ceramic composites and intermetallic material systems. The creation of enabling technologies aids in shortening the product development cycle of components fabricated from the new high technology materials.

Duffy, Stephen F.↗
NASA NTRS2007

Science Archives in the 21st Century: A NASA LAMBDA Report

Lambda is a thematic data center that focuses on serving the cosmic microwave background (CMB) research community. LAMBDA is an active archive for NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) mission data sets. In addition, LAMBDA provides analysis software, on-line tools, relevant ancillary data and important web links. LAMBDA also tries to preserve the most important ground-based and suborbital CMB data sets. CMB data is unlike other astrophysical data, consisting of intrinsically diffuse surface brightness photometry with a signal contrast of the order 1 part in 100,000 relative to the uniform background. Because of the extremely faint signal levels, the signal-to-noise ratio is relatively low and detailed instrument-specific knowledge of the data is essential. While the number of data sets being produced is not especially large, those data sets are becoming large and complex. That tendency will increase when the many polarization experiments currently being deployed begin producing data. The LAMBDA experience supports many aspects of the NASA data archive model developed informally over the last ten years-that small focused data centers are often more effective than larger more ambitious collections, for example; that data centers are usually best run by active scientists; that it can be particularly advantageous if those scientists are leaders in the use of the archived data sets; etc. LAMBDA has done some things so well that they might provide lessons for other archives. A lot of effort has been devoted to developing a simple and consistent interface to data sets, for example; and serving all the documentation required via simple 'more' pages and longer explanatory supplements. Many of the problems faced by LAMBDA will also not surprise anyone trying to manage other space science data. These range from persuading mission scientists to provide their data as quickly as possible, to dealing with a high volume of nuisance (spam) messages. Because so many data center problems and solutions are common across individual data centers and disciplines it would be very valuable to establish some new systems of communication - such as informal email lists for administrators and developers. But resources are very limited, so new timeconsuming and inefficient mechanisms - like too-frequent and too-structured meetingsshould be avoided. Although there are great advantages to being small, agile and independent, there are also some areas where science data centers within and without NASA could be better coordinated - for the assignment of persistent identifiers; to encourage the early adoption of useful standards and technologies; etc. Some super-structure to facilitate such coordination might be beneficial as long as it doesn't begin to control the other work of the archives, and become a "methodology police". In this respect the CCSDS "Reference Model for an Open Archive Information System" is a little worrying. It may be that the closer a data center gets to following such a detailed prescription, the less effective it will become. It is much better to have an informal coordination process than a bureaucratic straight-jacket.

Butterworth, P.↗
NASA NTRS2015

Evidence Report: Risk of Cardiovascular Disease and Other Degenerative Tissue Effects from Radiation Exposure

Occupational radiation exposure from the space environment may result in non-cancer or non-CNS degenerative tissue diseases, such as cardiovascular disease, cataracts, and respiratory or digestive diseases. However, the magnitude of influence and mechanisms of action of radiation leading to these diseases are not well characterized. Radiation and synergistic effects of radiation cause DNA damage, persistent oxidative stress, chronic inflammation, and accelerated tissue aging and degeneration, which may lead to acute or chronic disease of susceptible organ tissues. In particular, cardiovascular pathologies such as atherosclerosis are of major concern following gamma-ray exposure. This provides evidence for possible degenerative tissue effects following exposures to ionizing radiation in the form of the GCR or SPEs expected during long-duration spaceflight. However, the existence of low dose thresholds and dose-rate and radiation quality effects, as well as mechanisms and major risk pathways, are not well-characterized. Degenerative disease risks are difficult to assess because multiple factors, including radiation, are believed to play a role in the etiology of the diseases. As additional evidence is pointing to lower, space-relevant thresholds for these degenerative effects, particularly for cardiovascular disease, additional research with cell and animal studies is required to quantify the magnitude of this risk, understand mechanisms, and determine if additional protection strategies are required.The NASA PEL (Permissive Exposure Limit)s for cataract and cardiovascular risks are based on existing human epidemiology data. Although animal and clinical astronaut data show a significant increase in cataracts following exposure and a reassessment of atomic bomb (A-bomb) data suggests an increase in cardiovascular disease from radiation exposure, additional research is required to fully understand and quantify these adverse outcomes at lower doses (less than 0.5 gray (SI unit for ionizing radiation dosage, i.e. one joule of radiation energy per one kilogram of matter)) to facilitate risk prediction. This risk has considerable uncertainty associated with it, and no acceptable model for projecting degenerative tissue risk is currently available. In particular, risk factors such as obesity, alcohol, and tobacco use can act as confounding factors that contribute to the large uncertainties. The PELs could be violated under certain scenarios, including following a large SPE (solar proton event) or long-term GCR (galactic cosmic ray) exposure. Specifically, for a Mars mission, the accumulated dose is sufficiently high that epidemiology data and preliminary risk estimates suggest a significant risk for cardiovascular disease. Ongoing research in this area is intended to provide the evidence base for accurate risk quantification to determine criticality for extended duration missions. Data specific to the space radiation environment must be compiled to quantify the magnitude of this risk to decrease the uncertainty in current PELs and to determine if additional protection strategies are required. New research results could lead to estimates of cumulative radiation risk from CNS and degenerative tissue diseases that, when combined with the cancer risk, may have major negative impacts on mission design, costs, schedule, and crew selection. The current report amends an earlier report (Human Research Program Requirements Document, HRP-47052, Rev. C, dated Jan 2009) in order to provide an update of evidence since 2009.

Patel, Zarana↗
NASA NTRS2016

Unmanned Aerial Systems Traffic Management (UTM): Safely Enabling UAS Operations in Low-Altitude Airspace

Currently, there is no established infrastructure to enable and safely manage the widespread use of low-altitude airspace and UAS flight operations. Given this, and understanding that the FAA faces a mandate to modernize the present air traffic management system through computer automation and significantly reduce the number of air traffic controllers by FY 2020, the FAA maintains that a comprehensive, yet fully automated UAS traffic management (UTM) system for low-altitude airspace is needed. The concept of UTM is to begin by leveraging concepts from the system of roads, lanes, stop signs, rules and lights that govern vehicles on the ground today. Building on its legacy of work in air traffic management (ATM), NASA is working with industry to develop prototype technologies for a UAS Traffic Management (UTM) system that would evolve airspace integration procedures for enabling safe, efficient low-altitude flight operations that autonomously manage UAS operating in an approved low-altitude airspace environment. UTM is a cloud-based system that will autonomously manage all traffic at low altitudes to include UASs being operated beyond visual line of sight of an operator. UTM would thus enable safe and efficient flight operations by providing fully integrated traffic management services such as airspace design, corridors, dynamic geofencing, severe weather and wind avoidance, congestion management, terrain avoidance, route planning re-routing, separation management, sequencing spacing, and contingency management. UTM removes the need for human operators to continuously monitor aircraft operating in approved areas. NASA envisions concepts for two types of UTM systems. The first would be a small portable system, which could be moved between geographical areas in support of operations such as precision agriculture and public safety. The second would be a Persistent system, which would support low-altitude operations in an approved area by providing continuous automated coverage. Both would require persistent communication, navigation, and surveillance (CNS) coverage to track, ensure, and monitor conformance. UTM is creating an airspace management tool that allows the ATM system to accommodate the number of UAS that will operate in the low altitude airspace. The analogy is just because we have a car, whether its autonomous or someone is driving, does not diminish the need for a road or road signs or rules of the road.

traffic management↗
NASA NTRSDate not supplied

VERNE: Revealing the Mysteries and Histories of Venus

Introduction: The three Venus missions that were recently selected for upcoming flight (VERITAS, DAVINCI+, and EnVision) will be incredibly valuable to our understanding of Venus’ history, geology, and atmosphere. However, even once completed, key gaps in our knowledge of Venus, and more generally the formation and active processes on rocky, Earth-like planets, will still persist. Remaining questions include 1) how global intrinsic magnetic fields might be maintained on rocky worlds, and how they could then go extinct, and 2) what role atmospheric sulfur chemistry plays in climates of Earth-like planets, which is an increasingly timely subject as Earth’s own atmospheric sulfur content is climbing due to human activity. These questions require in-situ observations from Venus’ cloud deck, at the altitudes at which the UV absorber exists. The Venus Environment Research and Novel Exploration (VERNE) mission will address these questions with an aerial platform that will drift around the equatorial region of the planet for 9 days. VERNE will collect data to determine the identity of the mysterious UV absorber, while also taking magnetic field measurements over the tesserae, the regions on Venus that are most likely to retain remanent crustal magnetization, in order to understand the potential role of a past intrinsically-generated global magnetic field on Venus. Mission Objectives: The two major science objectives that drive the VERNE mission are: 1) Determine the identity of the Venusian unknown ultraviolet absorber(s). First observed approximately a century ago [1], the composition of Venus’ ultraviolet (UV) absorber is one of the oldest mysteries in Venus atmospheric chemistry [2,3]. While several candidate UV absorbers (mostly sulfur species) have been proposed, no consensus has been reached on its composition and its specific interactions with the atmosphere. Determining the identity of the UV absorber will aid climate models by showing how and where incident solar energy is absorbed by the atmosphere and make progress towards understanding the chemical and energetic processes taking place above Venus’ upper cloud deck [4]. 2) Determine if Venus retains evidence of a past, internally-generated magnetic field. While Venus does not currently have an intrinsically-generated magnetic field, evidence for the existence of a past field on Venus and a timeline of its decay will fill in a more holistic picture of the evolution of Venus’ geological record and atmosphere. As the oldest geologic units on the surface, Venus’ tesserae may still have remanent crustal magnetization signatures within the rocky composition [5]. In any case, the signatures detected will provide insight into Venus’ past geological and core dynamo activity. Mission Summary: VERNE includes a 3-part flight system made up of 1) an entry system with a HEEET (Heatshield for Extreme Entry Environment Technology) aeroshell, 2) an orbiter for data relay, and 3) an in-situ balloon and gondola. After entry into Venus’ atmosphere, the balloon will be deployed within the upper cloud deck, at an altitude of 62 km, over a tesserae region. The in-situ data collection will last for the duration of 2 full circumnavigations of the planet, which will take ~9 days. Instrumentation Suite: The four instruments that comprise VERNE’s instrument payload will enable the identification of the unknown UV absorber and the detection of remanent crustal magnetization if it exists in the tesserae. The proposed instrument suite cycle during mission operations is shown in Fig. 1. The four instruments are described below: 1) Adams (ion neutral mass spectrometer) has a range of 18-257 AMU and will detect and distinguish the mixing ratios of O₂, H₂O, H₂SO₄, S, S₂, S₃, S₄, S₅, S₆, S₇, S₈, SO, SO₂, OSSO, SO₃, Cl₂, FeCl₃ and other trace sulfur and organic species. The spatial (longitudinal) and temporal (day/night) variations will be observed throughout 2 circumnavigations with a sample cadence of 12 minutes. 2) Shelley (nephelometer) will determine the size distribution of the aerosols (0.4 to 36 um) in the atmosphere. With a size resolution of <0.7 um, it can determine which mode of H2SO4 is present and characterize the large (>30 um) organic particles previously detected by the Venera and Galileo missions [6,7]. 3) Herbert (UV imager) will measure UV radiance at 283 nm (the wavelength of SO2 absorption) and 365 nm (the unknown part of the absorber). UV images will be taken concurrently with the INMS and nephelometer to correlate UV absorption with abundances of the UV absorber species. 4) Vonnegut (magnetometer) has a range of >600 nT and a precision and accuracy of 1 nT. If magnetized by a past field, the crust may have retained a magnetization of up to 3 A/m2 [5]. With a noise floor of 10 nT, the magnetometer will be able to detect RCM from an altitude of 62 km, even if the thickness of the magnetized crust is just 1 km (Fig. 2). Mission Concept Design: VERNE will be launched with a mass of 3300 kg in an intermediate-high performance class vehicle with a 4-m fairing. The 475-day mission includes 466 days for the cruise, coasting, and orbit initialization phases before entry, descent, and balloon deployment. During the 9-day science phase, the aerial platform will make 2 circumnavigations of the planet at an altitude of 62 km. The INMS and the nephelometer will acquire data for 2 hours during the daytime and nighttime during each circumnavigation, while the UV imager will be on for the duration of the daytime, and the magnetometer will be operational throughout the entirety of the science phase. Data will be stored and processed with the JPL-designed Sphinx command and data handling system. Data will be sent from the balloon to the orbiter using an S-band relay link, stored on the orbiter, and then forwarded to Earth where it will be received by the DSN. Conclusion: VERNE will fill key gaps in our understanding of the history and ongoing processes related to the geology and atmosphere of Venus and rocky worlds in general. Even with adequate flight system contingencies and expected costs below the $900M New Frontiers cost cap, VERNE is not without its risks and challenges. Further trade spaces to explore include 1) using solely battery power vs. including solar panels to increase the mission duration and 2) investigating the use of lightweight materials and 3D-printed structures to reduce the gondola mass, among others. Acknowledgments: We would like to thank the JPL Planetary Science Summer School, especially our mentors Troy Hudson, Karl Mitchell, and Leslie Lowes, as well as our Team-X study lead Al Nash and the members of Team-X. We’d additionally like to thank our review panel for asking insightful questions and providing valuable feedback. References: [1] Ross, F. E. (1928) Astrophysical J., 68, 57-92. [2] Rossow, W. B. et al. (1980) J. Geophysical Research, 85, 8107-8128. [3] Pinto, J. P. et al. (2021) Nature Communications, 12, 175. [4] Titov, D. V. et al. (2007) Cosmic Research, 21, 401. [5] O’Rourke, J. et al. (2019) Geophysical Research Lett., 46, 5768–5777. [6] Limaye, S. S. et al. (2018) Astrobiology, 18(9), 1181-1198. [7] Grinspoon, D. H. et al. (2013) Planetary and Space Sci., 41(7), 515-542. [8] Parker, R. L. (2003) J. Geophysical Research, 108, 5006. *The cost information contained in this document is of a budgetary and planning nature and is intended for informational purposes only. It does not constitute a commitment on the part of JPL and/or Caltech.

H Alpert↗
NASA NTRS1994

Stability of the Martian atmosphere: Is heterogeneous catalysis essential?

A comprehensive homogeneous gas phase photochemical model is developed to study the problem of stability of the Martian atmosphere. The one-dimensional model extends from the ground up to 220 km, passing through the homopause at 125 km. The model thus couples the lower (neutral) atmosphere to the ionosphere above which provides significant downward flux of carbon monoxide and oxygen atoms. It is concluded on the basic of currently accepted values for globally and seasonally averaged water vapor abundance, dust opacity and the middle atmospheric eddy mixing coefficient, as well as the relevant laboratory data (particularly the temperature dependence of CO2 absorption cross section and the rate constant for CO+OH reaction), that the rate of re-formation of carbon dioxide exceeds its photolytic destruction rate by about 40%. Furthermore, it is found that this result is virtually independent of the choice of eddy mixing coefficient, unless its value in the middle atmosphere exceeds 10(exp 8) sq cm/sec or is far smaller than 10(exp 5)sq cm/sec, or the dust opacity, unless it exceeds unity, or the water vapor mixing ratio at the surface, unless it is far smaller (less than or = 1 ppm) or far greater (greater than or = 500 ppm) than the average value (approximately 150 ppm). Since none of these extremes represent globally and seasonally averaged conditions on Mars, we propose that the present model requires existence of a mechanism to throttle down the recycling rate of carbon dioxide on Mars. Therefore, it is suggested that a heterogeneous process which provides a sink to the species that participate in the recycling of CO2, i.e., H2O, H2O2, OH, CO or O, in particular, may be necessary to bring about the balance between the CO2 recycling rate and its photolytic destruction rate. Aerosols of dust or ice (pure or doped water or carbon dioxide ice present in the atmosphere of Mars) can provide the appropriate adsorption sites for the above heterogeneous process. Despite our conclusion that some heterogeneous process may be needed, it is important to recognize that one-dimensional models can only provide first-order results which, most likely, represent globally and seasonally averaged conditions. However, it is only after actual temporal, latitudinal and longitudinal variations of relevant atmospheric parameters are included in the model that one can determine fuly whether the problem of atmospheric stabiltiy still continues to persist and whether some heterogeneous process is required to correct it.

Atreya, Sushil K.↗