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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Assessing the Behavior of Typically Lithophile Elements Under Highly Reducing Conditions Relevant to the Planet Mercury

With the data returned from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (lvtESSENGER) mission, there are now numerous constraints on the physical and chemical properties of Mercury, including its surface composition. The high S and low FeO contents observed from MESSENGER suggest a low oxygen fugacity of the present materials on the planet's surface. Most of our understanding of elemental partitioning behavior comes from observations made on terrestrial rocks, but Mercury's oxygen fugacity is far outside the conditions of those samples, estimated at approximately 3-7 log units below the Iron-Wustite (lW) oxygen buffer, several orders of magnitude more reducing than other terrestrial bodies we have data from. With limited oxygen available, lithophile elements may instead exhibit chalcophile, halophile, or siderophile behaviors. Furthermore, very few natural samples of rocks that formed under reducing conditions (e.g., enstatite chondrites, achondrites, aubrites) are available in our collections for examination of this change in geochemical affinity. Our goal is to determine the elemental partitioning behavior of typically lithophile elements at lower oxygen fugacity as a function of temperature and pressure. Experiments were conducted at I GPa in a 13 mm QUICKpress piston cylinder and at 4 GPa in an 880-ton multi-anvil press, at temperatures up to 1850 C. The composition of starting materials for the experiments were designed so the final run products contained metal, silicate melt, and sulfide melt phases. Oxygen fugacity was controlled in the experiments by adding silicon metal to the samples, in order to utilize the Si-Si02 buffer, which is approx. 5 log units more reducing than the IW buffer at our temperatures of interest. The target silicate melt composition was diopside (CaMgSi206) because measured surface compositions indicate partial melting of a pyroxene-rich mantle. The results of our experiments will aid in our understanding of the fate of elements during the differentiation and thermal evolution of Mercury and other highly reducing planetary bodies.

Rowland, Rick, II↗
NASA NTRS1994

What we have learned about Mars from SNC meteorites

The SNC meteorites are thought to be igneous martian rocks, based on their young crystallization ages and a close match between the composition of gases implanted in them during shock and the atmosphere of Mars. A related meteorite, ALH84001, may be older and thus may represent ancient martian crust. These petrologically diverse basalts and ultramafic rocks are mostly cumulates, but their parent magmas share geochemical and radiogenic isotopic characteristics that suggest they may have formed by remelting the same mantle source region at different times. Information and inferences about martian geology drawn from these samples include the following: Planetary differentiation occured early at approximately 4.5 GA, probably concurrently with accretion. The martian mantle contains different abundances of moderately volatile and siderophile elements and is more Fe-rich than that of the Earth, which has implications for its mineralogy, density, and origin. The estimated core composition has a S abundance near the threshold value for inner core solidification. The former presence of a core dynamo may be suggested by remanent magnetization in Shergottite-Nakhlite-Chassignite (SNC) meteorites, although these rocks may have been magnetized during shock. The mineralogy of martian surface units, inferred from reflectance spectra, matches that of basaltic shergottites, but SNC lithologies thought to have crystallized in the subsurface are not presently recognized. The rheological properties of martian magmas are more accurately derived form these metorites than from observations of martian flow morphology, although the sampled range of magma compositions islimited. Estimates of planetary water abundance and the amount of outgassed water based on these meteorites are contridictory but overlap estimates based on geological observations and atmospheric measurements. Stable isotope measurements indicate that the martian hydrosphere experienced only limited exchange with the lithosphere, but it is in isotopic equilibrium with the atmosphere and has been since 1.3 Ga. The isotopically heavy atmosphere/hydrosphere composition deduced from these rocks reflects a loss process more severe than current atmospheric evolution models, and the occurence of carbonates in SNC meteorites suggest that they, rather than scapolite or hydrous carbonates, are the major crustal sink for CO2. Weathering products in SNC meteorites support the idea of limited alteration of the lithosphere by small volumes of saline, CO2-bearing water. Atmospheric composition and evolution are further constrained by noble gases in these meteorites, although Xe and Kr isotopes suggest different origins for the atmosphere. Planetary ejection of these rocks has promoted an advance in the understanding of impact physics, which has been accomplished by a model involving spallation during large cratering events. Ejection of all the SNC meteorites (except ALH84001) in one or two events may provide a plausible solution to most constraints imposed by chronology, geochemistry, and cosmic ray exposure, although problems remain with this scenario; ALH84001 may represent older martian crust sampled during a separate impact.

Mcsween, Harry Y., Jr.↗
NASA NTRS2015

Construction of Polarimetric Radar-Based Reference Rain Maps for the Iowa Flood Studies Campaign

The Global Precipitation Measurement (GPM) Mission Iowa Flood Studies (IFloodS) campaign was conducted in central and northeastern Iowa during the months of April-June, 2013. Specific science objectives for IFloodS included quantification of uncertainties in satellite and ground-based estimates of precipitation, 4-D characterization of precipitation physical processes and associated parameters (e.g., size distributions, water contents, types, structure etc.), assessment of the impact of precipitation estimation uncertainty and physical processes on hydrologic predictive skill, and refinement of field observations and data analysis approaches as they pertain to future GPM integrated hydrologic validation and related field studies. In addition to field campaign archival of raw and processed satellite data (including precipitation products), key ground-based platforms such as the NASA NPOL S-band and D3R Ka/Ku-band dual-polarimetric radars, University of Iowa X-band dual-polarimetric radars, a large network of paired rain gauge platforms, and a large network of 2D Video and Parsivel disdrometers were deployed. In something of a canonical approach, the radar (NPOL in particular), gauge and disdrometer observational assets were deployed to create a consistent high-quality distributed (time and space sampling) radar-based ground "reference" rainfall dataset, with known uncertainties, that could be used for assessing the satellite-based precipitation products at a range of space/time scales. Subsequently, the impact of uncertainties in the satellite products could be evaluated relative to the ground-benchmark in coupled weather, land-surface and distributed hydrologic modeling frameworks as related to flood prediction. Relative to establishing the ground-based "benchmark", numerous avenues were pursued in the making and verification of IFloodS "reference" dual-polarimetric radar-based rain maps, and this study documents the process and results as they pertain specifically to efforts using the NPOL radar dataset. The initial portions of the "process" involved dual-polarimetric quality control procedures which employed standard phase and correlation-based approaches to removal of clutter and non-meteorological echo. Calculation of a scale-adaptive KDP was accomplished using the method of Wang and Chandrasekar (2009; J. Atmos. Oceanic Tech.). A dual-polarimetric blockage algorithm based on Lang et al. (2009; J. Atmos. Oceanic Tech.) was then implemented to correct radar reflectivity and differential reflectivity at low elevation angles. Next, hydrometeor identification algorithms were run to identify liquid and ice hydrometeors. After the quality control and data preparation steps were completed several different dual-polarimetric rain estimation algorithms were employed to estimate rainfall rates using rainfall scans collected approximately every two to three minutes throughout the campaign. These algorithms included a polarimetrically-tuned Z-R algorithm that adjusts for drop oscillations (via Bringi et al., 2004, J. Atmos. Oceanic Tech.), and several different hybrid polarimetric variable approaches, including one that made use of parameters tuned to IFloodS 2D Video Disdrometer measurements. Finally, a hybrid scan algorithm was designed to merge the rain rate estimates from multiple low level elevation angle scans (where blockages could not be appropriately corrected) in order to create individual low-level rain maps. Individual rain maps at each time step were subsequently accumulated over multiple time scales for comparison to gauge network data. The comparison results and overall error character depended strongly on rain event type, polarimetric estimator applied, and range from the radar. We will present the outcome of these comparisons and their impact on constructing composited "reference" rainfall maps at select time and space scales.

Radar↗
NASA NTRS2000

Lidar Technology at the Goddard Laser and Electro-Optics Branch

The Laser and Electro-Optics Branch at Goddard Space flight Center was established about three years ago to provide a focused center of engineering support and technology development in these disciplines with an emphasis on spaced based instruments for Earth and Space Science. The Branch has approximately 15 engineers and technicians with backgrounds in physics, optics, and electrical engineering. Members of the Branch are currently supporting a number of space based lidar efforts as well as several technology efforts aimed at enabling future missions. The largest effort within the Branch is support of the Ice, Cloud, and land Elevation Satellite (ICESAT) carrying the Geoscience Laser Altimeter System (GLAS) instrument. The ICESAT/GLAS primary science objectives are: 1) To determine the mass balance of the polar ice sheets and their contributions to global sea level change; and 2) To obtain essential data for prediction of future changes in ice volume and sea-level. The secondary science objectives are: 1) To measure cloud heights and the vertical structure of clouds and aerosols in the atmosphere; 2) To map the topography of land surfaces; and 3) To measure roughness, reflectivity, vegetation heights, snow-cover, and sea-ice surface characteristics. Our efforts have concentrated on the GLAS receiver component development, the Laser Reference Sensor for the Stellar Reference System, the GLAS fiber optics subsystems, and the prelaunch calibration facilities. We will report on our efforts in the development of the space qualified interference filter [Allan], etalon filter, photon counting detectors, etalor/laser tracking system, and instrument fiber optics, as well as specification and selection of the star tracker and development of the calibration test bed. We are also engaged in development work on lidar sounders for chemical species. We are developing new lidar technology to enable a new class of miniature lidar instruments that are compatible with small Discovery-class orbiters now in the NASA planetary program. The purpose of the lidar is to continuously profile the water vapor and dust in the Mars atmosphere from orbit in order to quantify its dynamics, their relationship in the diurnal cycles, and to infer water vapor exchange with the Mars surface. To remotely measure the water-vapor height profiles, we will use the differential absorption lidar (DIAL) technique. We are also developing a laser sensor for measuring the total column content of CO2 in the atmosphere of the earth. CO2 is the principal greenhouse gas and has increased by roughly 80 ppm in the last century and a half. We will report our efforts in the development of the laser transmitter and photon counting detector components for a Mars Orbiting DIAL system and for the CO2 sounder.

Heaps, William S.↗
NASA NTRS2011

Robust IR Remote Sensing Technique of the Total Column of Trace Gases Including Carbon Dioxide and Methane

Progress on the development of a differential radiometer based upon the Fabry-Perot interferometer (FPI) for methane (CH4) and carbon dioxide (C02) detection in the atmosphere is presented. Methane measurements are becoming increasingly important as a component of NASA's programs to understand the global carbon cycle and quantifY the threat of global warming. Methane is the third most important greenhouse gas in the Earth's radiation budget (after water vapor and carbon dioxide) and the second most important anthropogenic contributor to global warming. The importance of global warming and air quality to society caused the National Research Council to recommend that NASA develop the following missions [1]: ASCENDS (Active Sensing of C02 Emissions over Nights, Days, and Seasons), GEOCAPE (Geostationary Coastal and Air Pollution Events), and GACM (Global Atmosphere Composition Mission). Though methane measurements are not specifically called out in these missions, ongoing environmental changes have raised the importance of understanding the methane budget. In the decadal survey is stated that "to close the carbon budget, we would also address methane, but the required technology is not obvious at this time. If appropriate and cost-effective methane technology becomes available, we strongly recommend adding a methane capability". In its 2007 report the International Panel on Climate Change identified methane as a key uncertainty in our understanding saying that the causes of recent changes in the growth rate of atmospheric CH4 are not well understood. What we do know is that methane arises from a number of natural sources including wet lands and the oceans plus man made sources from agriculture, as well as coal and petroleum production and distribution. It has recently been pointed out that large amount of methane are frozen in the permafrost of Canada and Siberia. There is a fear that melting of this permafrost driven by global warming may release large amounts of methane very suddenly further exacerbating climate change [2]. Last year our group began a joint effort with Johns Hopkins Applied Physics Laboratory to investigate the possibility of developing a small unmanned aerial vehicle (UAV) equipped to measure greenhouse gases-particularly methane. Although we are targeting our system for smaller UAV's the instrument will be directly applicable to missions involving larger NASA UAV's such as Global Hawk or even on missions utilizing manned aircraft. Because of its small size, inherent ruggedness and simplicity some version of our proposed instrument may find a role as a satellite instrument for NASA or NOAA.

Georgieva, E. M.↗
NASA NTRSDate not supplied

Machine Learning based Aircraft Performance Model Estimation for Trajectory Prediction

The accurate prediction of aircraft trajectory by ground-based decision support tools is a critical component of air traffic management in the US National Airspace System (NAS). Accurate predictions of where the aircraft will be in the future or when they will arrive at specific locations (e.g., fixes) is a key enabler for sequencing and efficient arrival management of flights. Traditional physics based aircraft trajectory prediction relies on a simplified point-mass total energy model whose parameters are referred to as Aircraft Performance Model (APM) parameters. Even though the performance coefficients and weight of an aircraft are a vital part of the aircraft performance model’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to decision-support tools. Current approaches freeze some coefficients to default base of aircraft data (BADA) values and optimize others. However, the APM parameters are highly coupled by the flight dynamics and prioritizing one parameter over others leads to bias and skewed predictions. To alleviate this problem, we provide a combined optimization framework to predict all the critical (thrust, drag and weight) APM parameters. This paper is focused on training Machine Learning (ML) models that map historical flights to optimized APM parameters that provide the best fit (in terms of prediction error). Our dataset obtained from NASA’s Sherlock data warehouse is comprised of thousands of historical flights and includes weather and track data collected from 2019. Using different subsets of relevant features (e.g., aircraft type), we trained several ML models to estimate the aircraft’s take off weight, drag polar coefficients (both parasitic and lift induced), and thrust settings (multiplier applied to the maximum engine thrust). The chosen flights are from three of the most common aircraft types (B738, B737, and A320) arriving at four airports (LAX, DEN, MSP, and DFW). Our ML approach is comprised of two different solutions: 1- using a subset of features that are known prior to the flight departure and do not change during flight (such as engine type, current temperature at departure & destination airports, aircraft type) and 2 - using a subset of temporal features of the flight trajectory (such as cruise altitude, Mach, airspeed, and rate of climb) in addition to the pre-departure features from the first solution. The labels or target variables are the APM parameters that were obtained by an optimized ordinary differential equations (ODE) fitting process (applied to individual flights). The ODE-fitting is very time intensive and is therefore performed offline. Thus, training an ML model to learn the relationship between the flight features and ODE-generated labels enables faster estimation of the APM parameters and is therefore amenable to real-time prediction. Various ML models including linear regression, random forest, XGBoost, and neural network were trained, and the results are compared. After model validation and hyperparameter-tuning, we observed that the Random Forest model outperformed the other three models by the overall mean square error (MSE) of 2% for the first solution and 1.5% for the second solution. Finally, the ML-derived parameters are compared against default BADA APM parameters using NASA’s Autonomy Development toolkit (ADK) simulation software. The simulation results for one of each aircraft type is shown and discussed.

Aida Sharif Rohani↗
NASA NTRS2019

Simulated Weightlessness Alters Cardiomyocyte Structure and Transcriptional Regulation of Mediators Related to Immunity and Cardiovascular Disease

Spaceflight and the ensuing fluid shifts, together with an overall reduction in physical activity, lead to acute and latent effects on the cardiovascular system. This current study makes use of the rodent hindlimb unloading (HU) model to determine how factors such as sex, age, and duration of exposure impact cardiac responses to weightlessness. We hypothesize that extended exposure to simulated weightlessness and the ensuing recovery alters cardiac structure and expression of select genes, including those involved in redox signaling which together, negatively impact long-term cardiac tissue health. To begin to test this hypothesis, male and female rats underwent HU at various durations up to 90 days, with a subset reambulated after 90 days of HU. Physiological stress or contractility changes lead to alterations in ventricular cardiomyocyte size and ventricular wall thickness to adapt to greater functional demand and mitigate mechanical stress to ventricular tissue; under certain conditions, these changes also may mark progression to cardiac failure. Hence, left ventricular cardiomyocyte size (cardiomyocyte cross sectional area, CSA) was quantified to determine if HU leads to structural adaptation responses in cardiac tissue and if age and sex had any impact on this outcome. Cardiomyocyte CSA of older males (9 months) were altered by HU in a time-dependent manner, where HU led to decreases in CSA at 14 days and increases at 90 days. In contrast, younger males (3 months) did not show any changes at day 14 of HU. CSA of females (3 months) was increased in response to short-term HU (14 days) suggesting sex-dependence of structural changes. In older HU males, cardiomyocyte CSA was comparable to controls after 90 days of re-ambulation. Levels of the DNA oxidative damage marker, 8-hydroxydeoxyguanosine (8-OHdG) were greater in left ventricular tissue of females that underwent HU compared to sex-matched controls, while there were no such differences in older or younger males. To gain insight into the signals that drive cardiac adaptations to HU, global transcriptomic analysis (RNAseq) was performed on left ventricular tissue of older males that underwent 14 days of HU. Short-term simulated weightlessness led to differential expression of genes involved in immune and pro-inflammatory signaling. A subset of these genes play a role in autoimmune and cardiovascular disease and are targets of current drugs used to treat bradycardia, hypertension, atherosclerosis and rheumatoid arthritis, amongst others. Oxidative damage/redox signaling pathways were not enriched at the timepoint tested in older males. Since young females displayed greater oxidative damage to DNA, activation of oxidative stress responses at earlier or later time points cannot be ruled out. In summary, simulated weightlessness in adult rats caused changes in cardiomyocyte structure in a sex and age-dependent manner, and the transcriptional regulation of key mediators of immunity and cardiovascular disease, meriting further study to define cardiac risks for interplanetary travel of human crew. Our findings also confirm the value of the rat HU model for cardiac health and countermeasure research.

Tahimic, Candice↗
NASA NTRS2017

Toward Understanding Tip Leakage Flows in Small Compressor Cores Including Stator Leakage Flow

The focus of this work was to provide additional data to supplement the work reported in NASA/CR-2015-218868 (Berdanier and Key, 2015b). The aim of that project was to characterize the fundamental flow physics and the overall performance effects due to increased rotor tip clearance heights in axial compressors. Data have been collected in the three-stage axial research compressor at Purdue University with a specific focus on analyzing the multistage effects resulting from the tip leakage flow. Three separate rotor tip clearances were studied with nominal tip clearance gaps of 1.5 percent, 3.0 percent, and 4.0 percent based on a constant annulus height. Overall compressor performance was previously investigated at four corrected speedlines (100 percent, 90 percent, 80 percent, and 68 percent) for each of the three tip clearance configurations. This study extends the previously published results to include detailed steady and time-resolved pressure data at two loading conditions, nominal loading (NL) and high loading (HL), on the 100 percent corrected speedline for the intermediate clearance level (3.0 percent). Steady detailed radial traverses of total pressure at the exit of each stator row are supported by flow visualization techniques to identify regions of flow recirculation and separation. Furthermore, detailed radial traverses of time-resolved total pressures at the exit of each rotor row have been measured with a fast-response pressure probe. These data were combined with existing three-component velocity measurements to identify a novel technique for calculating blockage in a multistage compressor. Time-resolved static pressure measurements have been collected over the rotor tips for all rotors with each of the three tip clearance configurations for up to five loading conditions along the 100 percent corrected speedline using fast-response piezoresistive pressure sensors. These time-resolved static pressure measurements reveal new knowledge about the trajectory of the tip leakage flow through the rotor passage. Further, these data extend previous measurements identifying a modulation of the tip leakage flow due to upstream stator wake propagation. Finally, a novel instrumentation technique has been implemented to measure pressures in the shrouded stator cavities. These data provide boundary conditions relating to the flow across the shrouded stator knife seal teeth. Moreover, the utilization of fast-response pressure sensors provides a new look at the time-resolved pressure field, leading to instantaneous differential pressures across the seal teeth. Ultimately, the data collected for this project represent a unique data set which contributes to build a better understanding of the tip leakage flow field and its associated loss mechanisms. These data will facilitate future engine design goals leading to small blade heights in the rear stages of high pressure compressors and aid in the development of new blade designs which are desensitized to the performance penalties attributed to rotor tip leakage flows.

Berdanier, Reid A.↗
NASA NTRS2010

Experimental Study of Abiotic Organic Synthesis at High Temperature and Pressure Conditions: Carbon Isotope and Mineral Surface Characterizations

Abiotic organic synthesis processes have been proposed as potential mechanisms for methane generation in subseafloor hydrothermal systems on Earth, and on other planets. To better understand the detailed reaction pathways and carbon isotope fractionations in this process under a wide range of physical and chemical conditions, hydrothermal experiments at high temperature (750 C) and pressure (0.55 GPa) were performed using piston cylinder apparatus. Formic acid was used as the source of CO2 and H2, and magnetite was the mineral catalyst. The chemical and carbon isotopic compositions of dissolved organic products were determined by GC-C-MS-IRMS, while organic intermediaries on the mineral catalyst were characterized by Pyrolysis-GC-MS. Among experimental products, dissolved CO2 was the dominant carbon species with a relative abundance of 88 mol%. Dissolved CH4 and C2H6 were also identified with a mole ratio of CH4 over C2H6 of 15:1. No dissolved CO was detected in the experiment, which might be attributable to the loss of H2 through the Au capsule used in the experiments at high temperature and pressure conditions and corresponding conversion of CO to CO2 by the water-gas shift reaction. Carbon isotope results showed that the 13C values of CH4 and C2H6 were -50.3% and -39.3% (V-PDB), respectively. CO2 derived from decarboxylation of formic acid had a (sigma)C-13 value of -19.2%, which was 3.2% heavier than its source, formic acid. The (sigma)C-13 difference between CO2 and CH4 was 31.1%, which was higher than the value of 9.4% calculated from theoretical isotopic equilibrium predictions at experimental conditions, suggesting the presence of a kinetic isotope effect. This number was also higher than the values (4.6 to 27.1%) observed in similar experiments previously performed at 400 C and 50 MPa with longer reaction times. CH4 is 11.0% less enriched in C-13 than C2H6. Alcohols were observed as carbon compounds on magnetite surfaces by Pyrolysis-GC-MS, which confirms the hypothesis regarding the reaction pathways of hydrothermal abiotic organic synthesis proposed by Fu et al. (2007, 2008). In this proposed pathway, hydroxymethylene (-CHOH) groups serve as organic intermediaries on mineral surfaces while dissolved H2 serves as a chain terminator/breaker to generate short chain hydrocarbons and oxygenated compounds. This pathway is different from the carbide polymerization theory of Fischer- Tropsch-type (FTT) synthesis in a gas phase. The observed increase of (sigma)C-13 values of C1 and C2 alkanes with carbon number in our hydrothermal experiments can be readily interpreted by hydroxymethylene pathway, and might be used to differentiate between hydroxymethylene and carbide polymerization pathways. Carbon isotope analysis of alcohols on mineral catalyst surfaces is under way to provide further constraints on formation of organic compounds by FTT in hydrothermal systems.

Fu, Qi↗
NASA NTRS2006

The Use of Dynamic Visual Acuity as a Functional Test of Gaze Stabilization Following Space Flight

After prolonged exposure to a given gravitational environment the transition to another is accompanied by adaptations in the sensorimotor subsystems, including the vestibular system. Variation in the adaptation time course of these subsystems, and the functional redundancies that exist between them make it difficult to accurately assess the functional capacity and physical limitations of astro/cosmonauts using tests on individual subsystems. While isolated tests of subsystem performance may be the only means to address where interventions are required, direct measures of performance may be more suitable for assessing the operational consequences of incomplete adaptation to changes in the gravitational environment. A test of dynamic visual acuity (DVA) is currently being used in the JSC Neurosciences Laboratory as part of a series of measures to assess the efficacy of a countermeasure to mitigate postflight locomotor dysfunction. In the current protocol, subjects visual acuity is determined using Landolt ring optotypes presented sequentially on a computer display. Visual acuity assessments are made both while standing and while walking at 1.8 m/s on a motorized treadmill. The use of a psychophysical threshold detection algorithm reduces the required number of optotype presentations and the results can be presented immediately after the test. The difference between the walking and standing acuity measures provides a metric of the change in the subject s ability to maintain gaze fixation on the visual target while walking. This functional consequence is observable regardless of the underlying subsystem most responsible for the change. Data from 15 cosmo/astronauts have been collected following long-duration (approx. 6 months) stays in space using a visual target viewing distance of 4.0 meters. An investigation of the group mean shows a change in DVA soon after the flight that asymptotes back to baseline approximately one week following their return to earth. The performance of some subjects nicely parallels the stereotypical recovery curve observed in the group mean data. Others show dramatic changes in DVA from one test day to another. These changes may be indicative of a re-adaptation process that is not characterized by a steady improvement with the passage of time, but is instead a dynamic search for appropriate coordinative strategy to achieve the desired gaze stabilization goal. Ground-based data have been collected in our lab using DVA with one of the goals being to improve the DVA test itself. In one of these studies, the DVA test was repeated using a visual target viewing distance of 0.5 meters. While walking, the relative contributions of the otoliths and semi-circular canals that are required to stabilize gaze are affected by visual target viewing distance. It may be possible to exploit this using the current treadmill DVA test to differentially assess changes in these vestibular subsystems. The postflight DVA evaluations currently used have been augmented to include the near target version of the test. Preliminary results from these assessments, as well as the results from the ground-based tests will also be reported. DVA provides a direct measure of a subject's ability to see clearly in the presence of self-motion. The use of the current tests for providing a functionally relevant metric is evident. However, it is possible to expand the scope of DVA testing to include scenarios other than walking. A facility for measuring DVA in the presence of passive movements is being created. Using a mechanized platform to provide the perturbation, it should be possible to simulate aircraft and automobile vibration profiles. Used in conjunction with the far and near visual displays this facility should be able to assess a subject s ability to clearly see distant objects as well as those that appear on the dashboard or instrument control panel during functionally relevant situations.

Peters, B. T.↗
NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗
NASA NTRS1999

The Distribution of Titanium in Lunar Soils on the Basis of Sensor and In Situ Data Fusion

A variety of remote-sensing measurements have been used to map the distribution of elements on the Moon as a means of providing constraints on the processes from which its crust and major terranes originated. Discussed here is Ti, which is incorporated into refractory minerals such as ilmenite during the latter stages of differentiation, and is thus a most useful element for understanding mare basalt petrogenesis. One of the earliest Ti maps showed Ti variations in nearside maria on the basis of groundbased spectral reflectance measurements. A map of Ti derived from gamma-ray measurements on Apollo 15 and 16 was produced at about the same time, and was improved upon considerably by Davis and coworkers, who effectively removed sources of spurious variation from Fe and Al or REE (e.g., Th) interference, and calibrated Ti on the bases of landing-site soil averages. In recent years, spectral reflectance measurements from Clementine have been used by Lucey and coworkers to produce global Ti distribution maps as well. As we indicated previously, the Lucey and Davis maps agree to first order. Meanwhile, we are using the concept of sensor data fusion to combine measurements from the AGR (Apollo gamma-ray) and CSR (Clementine Spectral Reflectance) techniques with ground truth from lunar soils to utilize the differences between the two maps to understand the distribution of Ti within lunar soil components, as we have done with Fe. This technique should be verified and applied on Lunar Prospector gamma-ray measurements of Ti, as the calibrated data become available within the next couple of years. Lunar Ti is found principally in the mineral ilmenite, and is associated with certain components of lunar soil: crystalline Ilmenite mineral fragments and high Ti-bearing glass. All data indicate that Ti is associated with maria and mafic minerals. In AGR and CSR datasets, Ti is highest on the nearside and in the maria, particularly in southern Serenitatis/northern Tranquillitatis and northwestern Procellarum. Unlike CSR-derived values, AGR Ti values show modest increase (up to 0.7%) on the northern farside. Both techniques show a primarily unimodal distribution with a shoulder in the high Ti direction and a primary mode at approximately 0.2% (0.15% for CSR and 0.25% for AGR data), but the AGR Ti data have more structure in the shoulder, including an apparent minor mode at 1.2% Ti, representing non-highland areas. Recalibrating the two datasets on the basis of matching the peaks and range on the histograms would not account for this additional structure in the AGR data. Low Ti areas, which occur predominantly on the farside, are not represented well in the lunar sample collection, although several meteorites thought to be of lunar highland origin show Ti abundances averaging about 0.2%. (Error bars on AGR Ti values are about 0.5%.) Gamma-ray measurements reflect intrinsic Ti surface composition, regardless of the physical or chemical state of Ti. Lucey and coworkers have attempted to produce an equivalent bulk Ti map by normalizing the spectral feature at 415 nm to remove the effects of physical variations from soil to soil. The normalization is based on laboratory measurements of available samples, primarily nearside maria, and is undoubtedly optimized for the proportions in which Ti- components are found in these soils. In particular, mare soils tend to have a much higher proportion of opaque mineral grains, which appears to be well correlated with Ti abundance. The relationship between Ti abundance and proportion of Ti-bearing glass (weighted for Ti abundance) is not as direct. Also shows the relationship between landing site soil average, AGR, and CSR Ti abundances (with CSR filtered to match resolution and field of view of AGR data). AGR Ti values show the best agreement with Ti soil averages, CSR Ti values being somewhat higher in high-Ti soils, and lower in low-Ti soils. These results would tend to support the argument that the technique for deriving Ti from the CSR measurements is optimized for one of the primary Ti-bearing components, most likely opaque mineral grains, and is thus over-compensating and reporting higher Ti values in mare areas, and underreporting Ti in highland areas with much lower proportions of opaque mineral grains. More information is contained in original.

Clark, P. E.↗
NASA NTRS2000

Differential baroreflex control of heart rate in sedentary and aerobically fit individuals

PURPOSE: We compared arterial, aortic, and carotid-cardiac baroreflex sensitivity in eight average fit (maximal oxygen uptake, VO2max = 42.2+/-1.9 mL x kg(-1) x min(-1)) and eight high fit (VO2max = 61.9+/-2.2 mL x kg(-1) x min(-1)) healthy young adults. METHODS: Arterial and aortic (ABR) baroreflex functions were assessed utilizing hypo- and hyper-tensive challenges induced by graded bolus injections of sodium nitroprusside (SN) and phenylephrine (PE), respectively. Carotid baroreflex (CBR) sensitivity was determined using ramped 5-s pulses of both pressure and suction delivered to the carotid sinus via a neck chamber collar, independent of drug administration. RESULTS: During vasoactive drug injection, mean arterial pressure (MAP) was similarly altered in average fit (AF) and high fit (HF) groups. However, the heart rate (HR) response range of the arterial baroreflex was significantly attenuated (P < 0.05) in HF (31+/-4 beats x min(-1)) compared with AF individuals (46+/-4 beats x min(-1)). When sustained neck suction and pressure were applied to counteract altered carotid sinus pressure during SN and PE administration, isolating the ABR response, the response range remained diminished (P < 0.05) in the HF population (24+/-3 beats x min(-1)) compared with the AF group (41+/-4 beats x min(-1)). During CBR perturbation, the HF (14+/-1 beats-min(-1)) and AF (16+/-1 beats-min(-1)) response ranges were similar. The arterial baroreflex response range was significantly less than the simple sum of the CBR and ABR (HF, 38+/-3 beats x min(-1) and AF, 57+/-4 beats x min(-1)) in both fitness groups. CONCLUSIONS: These data confirm that reductions in arterial-cardiac reflex sensitivity are mediated by diminished ABR function. More importantly, these data suggest that the integrative relationship between the ABR and CBR contributing to arterial baroreflex control of HR is inhibitory in nature and not altered by exercise training.

NASA Discipline Cardiopulmonary↗
NASA NTRS2003

Touch and gravitropic set-point angle interact to modulate gravitropic growth in roots

Plant roots must sense and respond to a variety of environmental stimuli as they grow through the soil. Touch and gravity represent two of the mechanical signals that roots must integrate to elicit the appropriate root growth patterns and root system architecture. Obstacles such as rocks will impede the general downwardly directed gravitropic growth of the root system and so these soil features must be sensed and this information processed for an appropriate alteration in gravitropic growth to allow the root to avoid the obstruction. We show that primary and lateral roots of Arabidopsis do appear to sense and respond to mechanical barriers placed in their path of growth in a qualitatively similar fashion. Both types of roots exhibited a differential growth response upon contacting the obstacle that directed the main axis of elongation parallel to the barrier. This growth habit was maintained until the obstacle was circumvented, at which point normal gravitropic growth was resumed. Thus, the gravitational set-point angle of the primary and lateral roots prior to encountering the barrier were 95 degrees and 136 degrees respectively and after growing off the end of the obstacle identical set-point angles were reinstated. However, whilst tracking across the barrier, quantitative differences in response were observed between these two classes of roots. The root tip of the primary root maintained an angle of 136 degrees to the horizontal as it traversed the barrier whereas the lateral roots adopted an angle of 154 degrees. Thus, this root tip angle appeared dependent on the gravitropic set-point angle of the root type with the difference in tracking angle quantitatively reflecting differences in initial set-point angle. Concave and convex barriers were also used to analyze the response of the root to tracking along a continuously varying surface. The roots maintained the a fairly fixed angle to gravity on the curved surface implying a constant resetting of this tip angle/tracking response as the curve of the surface changed. We propose that the interaction of touch and gravity sensing/response systems combine to strictly control the tropic growth of the root. Such signal integration is likely a critical part of growth control in the stimulus-rich environment of the soil. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Discipline Plant Biology↗
NASA NTRS1997

Impact Cratering Calculations

Understanding the physical processes of impact cratering on planetary surfaces and atmospheres as well as collisions of finite-size self-gravitating objects is vitally important to planetary science. The observation has often been made that craters are the most ubiquitous landform on the solid planets and the satellites. The density of craters is used to date surfaces on planets and satellites. For large ringed basin craters (e.g. Chicxulub), the issue of identification of exactly what 'diameter' transient crater is associated with this structure is exemplified by the arguments of Sharpton et al. (1993) versus those of Hildebrand et al. (1995). The size of a transient crater, such as the K/T extinction crater at Yucatan, Mexico, which is thought to be the source of SO,-induced sulfuric acid aerosol that globally acidified surface waters as the result of massive vaporization of CASO, in the target rock, is addressed by our present project. The impact process excavates samples of planetary interiors. The degree to which this occurs (e.g. how deeply does excavation occur for a given crater diameter) has been of interest, both with regard to exposing mantle rocks in crater floors, as well as launching samples into space which become part of the terrestrial meteorite collection (e.g. lunar meteorites, SNC's from Mars). Only in the case of the Earth can we test calculations in the laboratory and field. Previous calculations predict, independent of diameter, that the depth of excavation, normalized by crater diameter, is d(sub ex)/D = 0.085 (O'Keefe and Ahrens, 1993). For Comet Shoemaker-Levy 9 (SL9) fragments impacting Jupiter, predicted excavation depths of different gas-rich layers in the atmosphere, were much larger. The trajectory and fate of highly shocked material from a large impact on the Earth, such as the K/T bolide is of interest. Melosh et al. (1990) proposed that the condensed material from the impact upon reentering the Earth's atmosphere induced. radiative heating, and producing global firestorms. The observed reentry splash of the SL-9 impact-induced plumes that reimpact Jupiter (Boslough et al., 1994) supported Melosh's K/T model. The fate of early primitive planetary atmospheres during the latter stages of planetary accretion, resulting from impactors in the 100 to 103 km diameter require modeling, e.g. Newman et al. (1997). Ahrens (1990; 1993) and Chen and Ahrens (1997) found that upon delivery of most of the impact energy to the solid planet, very large ground motions arise, which couple sufficient kinetic energy to the atmosphere to cause substantial atmospheric escape. The trade-off of this model with that of Cameron (1997) who suggests that atmospheric blow-off occurs as a result of the massive impact-induced heating of the atmosphere and Pepin (1997) who uses this heating event to model differential hydrodynamic loss of lighter atmospheric gases, requires further research.

Ahrens, Thomas J.↗
NASA NTRS2013

Are Soft Short Tests Good Indicators of Internal Li-ion Cell Defects?

The self discharge test at full state of charge, may not be a good one to detect subtle defects since the li-ion chemistry has the highest self discharge at full state of charge. One should characterize self discharge versus storage time for each cell manufacturer/design to differentiate between normal self discharge and that due to a subtle manufacturing defect. The various soft short test methods indicate that if this test is carried out at full discharge (0% SOC) with all capacity removed (by lowering the current load in a stepwise manner to the same end of discharge voltage), then the cells need to be placed in storage for more than 72 hours to get a good analysis on the presence of subtle defects since it takes more than 72 hours to achieve voltage stabilization. If the cells are to be charged up even to a small percentage (ex. 1%), 72 hours are sufficient to determine issues. However, the pass/fail criteria should be based on a valid OCV decline. Less than 10 mV voltage decline is not a good method to detect subtle defects. As mentioned in the first bullet, self discharge is a competing reaction when a charge is introduced and hence a characterization of the self discharge versus storage time is required to fully correlate voltage decline to a failure due to a subtle defect. Soft short test method cannot be relied on for defect detection because cells with and without voltage decline seemed to have similar defects and characteristics. Screening methods such as internal resistance and capacity as well as a 3-sigma range for OCV, mass and dimensions should be used to screen out outliers. A very critical aspect in the understanding of subtle defects is to carry out destructive analysis of cells from every lot to confirm the quality of production and screen all cells and batteries in a stringent manner to have a high quality set of flight cells. Self Discharge Test: Fully charged cells shall be placed in Open circuit stand for 72 hours (OCV measurement twice a day); continue for total of 14 days with 1 reading per day 2. Soft Short Test 1: Fully charge; cells discharged to manufacturer's end of disch. Voltage (EODV) cutoff at C/5 rate; stand for 30 minutes; discharge with C/500 to the same EODV. stand for another 30 minutes; discharge the cells again using C/1000 current to the same EODV. OCV measurements twice a day for 72 hours and then for total of 14 days (data collection same as in 1.) 3. Soft Short Test 2: Fully charge; cells discharged to the manuf. EODV with a C/13 constant current; provide a 10 hour rest, discharge again to the same EODV with a current of C/250, provide a 10 hour rest, discharge again using a C/250 rate, provide a 24 hour rest, charge using C/250 to 3.15 V (for ~12 hours). OCV measurements twice a day for at 72 hours. (data collection same as in 1.) 4. Soft Short Test 3: Fully charge; cells shall be discharged using C/10 current to manuf. EODV. Allow the cell to remain at Open circuit for 10 seconds. Discharge the cell at C/20 rate to the same EODV, hold open circuit for 24 hours. Discharge the cells at C/200 rate to the same end of voltage cutoff and hold open circuit for 24 hours. Discharge the cells one more time at C/200 rate to the same EODV and hold open circuit for 36 hours. Charge at C/200 rate to 3.15 V and hold for 3 days. Record OCV during the open circuit stand periods every 12 hours and at the beginning and end of the 3 day hold (include the 12 hour OCV recording during this time also). Capacity Cycling: Cells with declining voltages - one cell from each manufacturer chosen for cycling Destructive Physical Analysis (DPA): Cells with and without decline chosen from each lot for DPA.

Jeevarajan, J.↗
NASA NTRS2018

Towards an Enhanced Droplet Activation Scheme for Multi-Moment Bulk Microphysics Schemes

Initial droplet spectra produced upon activation impact the ensuing chain of microphysical processes andtherefore play a crucial role in cloud evolution. This work re-examines dependencies of newly formed clouddroplet size distribution (CDSD) characteristics on environmental and aerosol properties via parcel model simulationsthat serve as the basis for a multi-moment bulk microphysics droplet activation scheme suitable for acloud-resolving model (CRM). It is found that applying a fixed size threshold to define activated droplets versusemploying physical considerations can lead to erroneous activation and overly broad CDSDs for high aerosolconcentration and weak updraft conditions. Aerosol distributions characterized by larger median sizes and/orincreased solubility can result in greater activated droplet numbers, whereas impacts of these parameters onCDSD spectral width depend on both aerosol number concentration and updraft velocity. An expansion of theactivation scheme to include CDSD spectral width is proposed to aid efforts to extend high-order momentprediction to cloud droplet categories in CRMs as well as better represent variability in the activation process onthe cloud scale.simulations to investigate the regime dependence of the relative dispersion(d)1 of newly activated CDSDs, where d is the ratio of dropletradius standard deviation (σ) to the mean radius (r ). C16 demonstratedthat increasing Na resulted in increasing (decreasing) d values via reducedcondensational narrowing (spectral broadening) rates within theAL (UL) regime, with d values peaking in the TR regime. Their findingssuggest a similar regime dependence for d as R09 noted for Nc and helpexplain reportedly conflicting relationships between Na and CDSDspectral characteristics (cf. Hudson and Noble, 2014; Liu et al., 2014),although the applicability of these results within bulk microphysicalschemes was not addressed.Simulating aerosol-cloud interactions with CRMs employing bulkmicrophysics requires that the scheme minimally predict two CDSDparameters, namely mass and number concentrations, and represent thedroplet activation process. Various activation schemes aim to determineNc from aerosol and environmental properties and include analyticalexpressions (e.g., Abdul-Razzak et al., 1998; Morrison et al., 2005) aswell as lookup tables (LUTs) based on detailed parcel model calculations(e.g., Saleeby and Cotton, 2004, hereafter SC04; Segal and Khain,2006; Thompson and Eidhammer, 2014). Expressions to diagnose CDSDspectral width from Nc (Grabowski, 1998; Liu et al., 2006; Morrison andGrabowski, 2007) or cloud water content (Geoffroy et al., 2010) havealso been developed, although more robust methods to obtain CDSDspectral width upon activation are presently lacking. This latter point isrelevant for triple-moment (3 M) bulk microphysics that aim to predictdistribution spectral width alongside number and mass concentrations(e.g., Loftus et al., 2014; Milbrandt and Yau, 2005).The current work extends the findings of C16 to the current LUTbasedaerosol activation scheme used in the Regional AtmosphericModeling System (RAMS) (Cotton et al., 2003; SC04; Saleeby and vanden Heever, 2013, hereafter SvdH13) and additionally examinesaerosol size and solubility impacts on newly activated CDSD properties.Because early cloud development processes such as condensationalgrowth, evaporation, and droplet self-collection depend on and impactCDSD spectral width (Hudson and Yum, 1997; Seifert and Beheng 2001;Lu and Seinfeld, 2006; Igel and van den Heever, 2017), an expansion ofthe activation LUTs to include CDSD spectral width is proposed as apreliminary step for extending 3M prediction to CDSDs in CRMs forimproved simulations of aerosol-cloud interactions.2. MethodologyThe current RAMS two-moment microphysics module determinesthe fractional number of aerosol particles that activate to cloud dropletsfrom five-dimensional LUTs based on model predicted air temperature(T), w, Na, and the geometric median radius (rg) and soluble fraction (ε)of the aerosol size distribution (SvdH13). These LUTs are created offlineusing a one-dimensional Lagrangian adiabatic parcel model (Feingoldand Heymsfield, 1992; Heymsfield and Sabin, 1989; SC04) to simulateexplicit droplet activation and initial CDSD growth for a range of ambientatmospheric conditions [T, w] and binned lognormal aerosol sizedistributions given by= ⎡⎣ ⎢− ⎤⎦ ⎥N r Nr π σr rσ( )2 lnexp[ln( / )]2(ln )aggg22 (1)where r is the dry aerosol particle bin radius and σg is the geometricstandard deviation of the distribution. As the parcel model simulationsfocus on the activation process, other processes such as coalescence,sedimentation, and mixing are not considered. Details of the parcelmodel can be found in SC04 and SvdH13, and only a brief description isprovided here. At the onset of parcel model calculations, the initiallydry aerosol particles in all bins first deliquesce and reach theirequilibrium diameters in a sub-saturated environment based on theKöhler equation for solution droplets. The parcel is then lifted at a fixedupward velocity w, and particle growth by vapor diffusion, along withconcurrent changes in the ambient environment, are iteratively computedusing the Variable-coefficient Ordinary Differential Equation(VODE) solver (Brown et al., 1989). The time resolution of these calculationsis determined within the VODE solver, and the frequency atwhich the solver is called is controlled by a longer model time stepbased on fixed upward parcel displacement increments (Δz) at thespecified w (Δt=Δz/w). Model calculations proceed until the parcelreaches a height 50m beyond the level of maximum saturation ratio(Smax) or total parcel displacement exceeds 2 km. Upon model termination,Smax and the fractional number of aerosols (factv) resulting innewly formed cloud droplets, defined as particles having diameters of atleast 2 μm, are cataloged in the LUTs according to the specified T, w, Na,rg, and ε parameter values.A critical point regarding the creation of these LUTs is the use of afixed minimum diameter (Dmin) to define cloud droplets in the parcelmodel, which can produce erroneous CDSD characteristics, particularlywithin the UL regime. For aerosol distributions with large rg valuesunder low SS conditions, for example, deliquesced aerosols within thelarge tail of the distribution can exceed 2 μm in diameter yet remainunactivated as ‘haze’ particles (Levin and Cotton, 2009; McFigganset al., 2006). For this study, aerosol particles activate to cloud dropletsbased on the critical diameter Dcrit as a function of parcel supersaturationratio (Sr) as in R09:D = σ MS RTρ83 ln( ) critsol wr w (2)where σsol is the surface tension of a solution droplet, Mw and ρw are themolar mass and density of liquid water, respectively, and R is theuniversal gas constant. Additionally, at relatively large w values withinthe AL regime, Nc stabilizes shortly after reaching supersaturation.However, parcel ascent and condensational growth continue beyondthe level of Smax, potentially causing additional narrowing of the CDSD.In the current work, model calculations terminate upon reaching Smaxas changes in Nc are negligible with continued ascent (Peng et al., 2007;R09).Parcel model simulations are performed to examine the sensitivitiesof CDSD characteristics to w, Na, rg, and ε, with the ranges for theseparameters listed in Table 1. Aerosols are assumed to be a mix of solubleand insoluble material of equal density, specified by ε, where fullysoluble aerosols correspond to ammonium sulfate with hygroscopicityparameter κ=0.61 (Petters and Kreidenweis, 2007). FollowingSvdH13, aerosol geometric standard deviation is fixed at σg=1.8, andaerosol distributions (Eq. 1) are partitioned into 100 logarithmicallyspacedbins spanning a size range specific to each rg value. For all simulations,Δz=1 m, and initial values of relative humidity, air temperatureand pressure are set to RH=0.99, T=10 °C and p=900 hPa,respectively.

Loftus, Adrian M.↗