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Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

Everitt, C. W. F.↗

Modeling Increased Complexity and the Reliance on Automation: FLightdeck Automation Problems (FLAP) Model

This paper highlights the development of a model that is focused on the safety issue of increasing complexity and reliance on automation systems in transport category aircraft. Recent statistics show an increase in mishaps related to manual handling and automation errors due to pilot complacency and over-reliance on automation, loss of situational awareness, automation system failures and/or pilot deficiencies. Consequently, the aircraft can enter a state outside the flight envelope and/or air traffic safety margins which potentially can lead to loss-of-control (LOC), controlled-flight-into-terrain (CFIT), or runway excursion/confusion accidents, etc. The goal of this modeling effort is to provide NASA's Aviation Safety Program (AvSP) with a platform capable of assessing the impacts of AvSP technologies and products towards reducing the relative risk of automation related accidents and incidents. In order to do so, a generic framework, capable of mapping both latent and active causal factors leading to automation errors, is developed. Next, the framework is converted into a Bayesian Belief Network model and populated with data gathered from Subject Matter Experts (SMEs). With the insertion of technologies and products, the model provides individual and collective risk reduction acquired by technologies and methodologies developed within AvSP.

Ancel, Ersin↗

Correlated Changes in Retinal Thickness and Visuomotor Function in Asymptomatic Plaquenil Toxicity Patients

We have previously shown that a 5-minute eye-movement test can capture a number of largely independent “oculometric” parameters of human visual/visuomotor function (Liston & Stone, 2014). This test has been successfully used to characterize mild neural impairment due to traumatic brain injury, sleep and circadian disruption, and alcohol consumption (Liston et al., 2017; Stone et al, 2019; Tyson et al, 2021). Here, we extend this approach to study patients at risk of progressive posterior-segment illness to see how oculometrics relate to standard clinical ophthalmological measures. Five female patients (<20:40 BCVA, 34-60 years old) undergoing hydroxychloroquine treatment (2-7mg/kg/day for 10-23 years for rheumatologic illness) have participated thus far. Under monocular viewing conditions in randomized order, they tracked a moving spot undergoing radial step-ramp motion in one of 90 randomized directions, at one of 5 randomized speeds, starting at random times (for details, see Stone et al, 2019). We computed nine independent oculometrics (latency, initial acceleration, steady-state gain, proportion smooth, saccadic rate, saccadic amplitude, direction noise, speed responsiveness, and speed noise). Spectral-domain optical coherence tomography (Zeiss, Dublin, CA) was used to measure the average thickness of the nine Early Treatment Diabetic Retinopathy Study macular sectors from the internal limiting membrane to the retinal pigmented epithelium. We used Pearson’s correlation between retinal thickness and our oculometrics with t-statistics to test separate one-sided hypotheses across 10 retinae. Our preliminary analysis found significant changes in several different aspects of visuomotor performance. Most notably, latency increased, initial acceleration decreased, and steady-state pursuit gain decreased as retinal thickness decreased (r2 = 0.364, 0.579, and 0.692; one-tailed P = 0.032, 0.005, and 0.001, respectively). Speed responsiveness appeared to decrease, but this effect was marginal for our current sample (r2 = 0.253, P = 0.069). Lastly, direction discrimination and saccadic behavior appeared unchanged. We conclude that oculometrics may provide sensitive measures of changes in retinal thickness. More importantly, oculometrics have the potential to detect impairment before it becomes evident with standard clinical imaging tools, while also providing insight into the behavioral implications of any resulting deficits in visual/visuomotor function.

eye movements↗

Observations of vertical winds and the origin of thermospheric gravity waves launched by auroral substorms and westward travelling surges

Several sequences of observations of strong vertical winds in the upper thermosphere are discussed, in conjunction with models of the generation of such winds. In the auroral oval, the strongest upward winds are observed in or close to regions of intense auroral precipitation and strong ionospheric currents. The strongest winds, of the order of 100 to 200 m/sec are usually upward, and are both localized and of relatively short duration (10 to 20 min). In regions adjacent to those displaying strong upward winds, and following periods of upward winds, downward winds of rather lower magnitude (40 to about 80 m/sec) may be observed. Strong and rapid changes of horizontal winds are correlated with these rapid vertical wind variations. Considered from a large scale viewpoint, this class of strongly time dependent winds propagate globally, and may be considered to be gravity waves launched from an auroral source. During periods of very disturbed geomagnetic activity, there may be regions within and close to the auroral oval where systematic vertical winds of the order of 50 m/sec will occur for periods of several hours. Such persistent winds are part of a very strong large scale horizontal wind circulation set up in the polar regions during a major geomagnetic disturbance. This second class of strong horizontal and vertical winds corresponds more to a standing wave than to a gravity wave, and it is not as effective as the first class in generating large scale propagating gravity waves and correlated horizontal and vertical oscillations. A third class of significant (10 to 30 m/sec) vertical winds can be associated with systematic features of the average geomagnetic energy and momentum input to the polar thermosphere, and appear in statistical studies of the average vertical wind as a function of Universal Time at a given location.

Rees, D.↗

A Test of Macromolecular Crystallization in Microgravity: Large, Well-Ordered Insulin Crystals

Crystals of insulin grown in microgravity on space shuttle mission STS-95 were extremely well-ordered and unusually large (many > 2 mm). The physical characteristics of six microgravity and six earth-grown crystals were examined by X-ray analysis employing superfine f slicing and unfocused synchrotron radiation. This experimental setup allowed hundreds of reflections to be precisely examined for each crystal in a short period of time. The microgravity crystals were on average 34 times larger, had 7 times lower mosaicity, had 54 times higher reflection peak heights and diffracted to significantly higher resolution than their earth grown counterparts. A single mosaic domain model could account for reflections in microgravity crystals whereas reflections from earth crystals required a model with multiple mosaic domains. This statistically significant and unbiased characterization indicates that the microgravity environment was useful for the improvement of crystal growth and resultant diffraction quality in insulin crystals and may be similarly useful for macromolecular crystals in general.

Borgstahl, Gloria E. O.↗

Investigating Response from Turbulent Boundary Layer Excitations on a Real Launch Vehicle using SEA

Statistical Energy Analysis (SEA) response has been fairly well anchored to test observations for Diffuse Acoustic Field (DAF) loading by others. Meanwhile, not many examples can be found in the literature anchoring the SEA vehicle panel response results to Turbulent Boundary Layer (TBL) fluctuating pressure excitations. This deficiency is especially true for supersonic trajectories such as those required by this nation s launch vehicles. Space Shuttle response and excitation data recorded from vehicle flight measurements during the development flights were used in a trial to assess the capability of the SEA tool to predict similar responses. Various known/measured inputs were used. These were supplemented with a range of assumed values in order to cover unknown parameters of the flight. This comparison is presented as "Part A" of the study. A secondary, but perhaps more important, objective is to provide more clarity concerning the accuracy and conservatism that can be expected from response estimates of TBL-excited vehicle models in SEA (Part B). What range of parameters must be included in such an analysis in order to land on the conservative side in response predictions? What is the sensitivity of changes in these input parameters on the results? The TBL fluid structure loading model used for this study is provided by the SEA module of the commercial code VA One.

Harrison, Phillip↗

The Herschel Multi-tiered Extragalactic Survey: HerMES

The Herschel Multi-tiered Extragalactic Survey, HerMES, is a legacy program designed to map a set of nested fields totalling approx. 380 deg(exp 2). Fields range in size from 0.01 to approx. 20 deg (exp 2), using Herschel-SPIRE (at 250, 350 and 500 micron), and Herschel-PACS (at 100 and 160 micron), with an additional wider component of 270 deg. (exp. 2) with SPIRE alone. These bands cover the peak of the redshifted thermal spectral energy distribution from interstellar dust and thus capture the re-processed optical and ultra-violet radiation from star formation that has been absorbed by dust, and are critical for forming a complete multi-wavelength understanding of galaxy formation and evolution. The survey will detect of order 100,000 galaxies at 5-sigma in some of the best studied fields in the sky. Additionally, HerMES is closely coordinated with the PACS Evolutionary Probe survey. Making maximum use of the full spectrum of ancillary data, from radio to X-ray wavelengths, it is designed to: facilitate redshift determination; rapidly identify unusual objects; and understand the relationships between thermal emission from dust and other processes. Scientific questions HerMES will be used to answer include: the total infrared emission of galaxies; the evolution of the luminosity function; the clustering properties of dusty galaxies; and the properties of populations of galaxies which lie below the confusion limit through lensing and statistical techniques. This paper defines the survey observations and data products, outlines the primary scientific goals of the HerMES team, and reviews some of the early results.

multi-tiered↗

A summary of whistlers observed by Voyager 1 at Jupiter

We summarize the Voyager 1 observations of whistlers at Jupiter in order to provide a basis for further analyses of the density profile of the Io plasma torus as well as to support studies of atmospheric lightning at Jupiter. All the whistlers detected by Voyager 1 fell into three general regions in the torus at radial distances ranging beteen 5 and 6 R sub J. An analysis of the broadband wave amplitudes measured by the Voyayer 1 plasma wave instrument and estimates of the peak whistler amplitudes imply the grouping of whistlers was due to variations in the sensitivity of the receiver to whistlers and not to variations in the source or propagation paths of the whistlers. The whistler dispersions are presented in statistical form for each of the three groups of events and analyzed in view of the structure of the Io plasma torus as determined by plasma probe measurements. The results of these analyses give source locations for the whistlers at the foot of the magnetic field lines threading the torus in both hemispheres and over a range of longitudes.

Kurth, W. S.↗

Variability of rainfall over small areas

A preliminary investigation was made to determine estimates of the number of raingauges needed in order to measure the variability of rainfall in time and space over small areas (approximately 40 sq miles). The literature on rainfall variability was examined and the types of empirical relationships used to relate rainfall variations to meteorological and catchment-area characteristics were considered. Relations between the coefficient of variation and areal-mean rainfall and area have been used by several investigators. These parameters seemed reasonable ones to use in any future study of rainfall variations. From a knowledge of an appropriate coefficient of variation (determined by the above-mentioned relations) the number rain gauges needed for the precise determination of areal-mean rainfall may be calculated by statistical estimation theory. The number gauges needed to measure the coefficient of variation over a 40 sq miles area, with varying degrees of error, was found to range from 264 (10% error, mean precipitation = 0.1 in) to about 2 (100% error, mean precipitation = 0.1 in).

Runnels, R. C.↗

Radio properties of type 1.8 and 1.9 Seyfert galaxies

A number of type 1.8 and 1.9 Seyfert galaxies have been observed at the VLA in order to compare their properties with those of the other types of Seyfert galaxy. The observed types have radio luminosities in the range of 10 to the 39th-40.5th args/s, with the median near 10 to the 40th ergs/s. Most of these galaxies have radio sources with diameters of about 500 pc or less. The ratio of radio luminosity to featureless optical continuum luminosity in the Seyfert 1.8/12.9 galaxies and Seyfert 1.2/1.5 galaxies is intermediate between the values for Seyfert 1 and Seyfert 2 galaxies. The infrared-to-radio ratio decreases along the sequence from Seyfert 1 galaxies, through intermediate Seyfert galaxies, to Seyfert 2 galaxies. This systematic statistical difference in the ratio of two aspect-independent quantities implies that the differences among the Seyfert classes cannot be attributed solely to differences in viewing angle.

Ulvestad, James S.↗

DNS and LES of a Shear-Free Mixing Layer

The purpose of this work is twofold. First, given the computational resources available today, it is possible to reach, using DNS, higher Reynolds numbers than in Briggs et al.. In the present study, the microscale Reynolds numbers reached in the low- and high-energy homogeneous regions are, respectively, 32 and 69. The results reported earlier can thus be complemented and their robustness in the presence of increased turbulence studied. The second aim of this work is to perform a detailed and documented LES of the shear-free mixing layer. In that respect, the creation of a DNS database at higher Reynolds number is necessary in order to make meaningful LES assessments. From the point of view of LES, the shear-free mixing-layer is interesting since it allows one to test how traditional LES models perform in the presence of an inhomogeneity without having to deal with difficult numerical issues. Indeed, as argued in Briggs et al., it is possible to use a spectral code to study the shear-free mixing layer and one can thus focus on the accuracy of the modelling while avoiding contamination of the results by commutation errors etc. This paper is organized as follows. First we detail the initialization procedure used in the simulation. Since the flow is not statistically stationary, this initialization procedure has a fairly strong influence on the evolution. Although we will focus here on the shear-free mixing layer, the method proposed in the present work can easily be used for other flows with one inhomogeneous direction. The next section of the article is devoted to the description of the DNS. All the relevant parameters are listed and comparison with the Veeravalli & Warhaft experiment is performed. The section on the LES of the shear-free mixing layer follows. A detailed comparison between the filtered DNS data and the LES predictions is presented. It is shown that simple eddy viscosity models perform very well for the present test case, most probably because the flow seems to be almost isotropic in the small-scale range that is not resolved by the LES.

Knaepen, B.↗

The Bombardment History of 4 Vesta as Told by Sample Geochronology

The Dawn mission showed asteroid 4 Vesta to be an extensively cratered body, ancient in age, with craters in a variety of morphologies and preservation states [1-3]. Tying Vesta's relative crater ages to an absolute impact history can be accomplished through investigations of the HED (howardite, eucrite, diogenite) meteorites. Eucrites are crustal basalts and gabbros, diogenites are mostly orthopyroxenites representing lower crust or upper mantle materials, and howardites are mixed breccias containing both lithologies. Eucrite 53Mn-53Cr systematics show that the HED parent body globally differentiated by ~4.56 Ga and fully crystallized soon afterwards [4]. Much later, many eucrites were brecciated and heated by large impacts into the parent body surface. Disturbance ages in eucrites show that multiple large impacts occurred within 1 Gyr after crystallization, showing a history that largely resembles that of the Moon [5-7]. Dawn images also showed that Vesta is covered with a well-developed regolith that is spectrally similar to howardite meteorites [8]. Howardites are polymict regolith breccias made up mostly of clasts of eucrites and diogenites, but which also contain clasts formed by melting of the regolith by relatively large, energetic impact events. Impact-melt clast ages from howardites extend our knowledge of the impact history of Vesta, expanding on eucrite disturbance ages and helping give absolute age context to the observed crater-counts produced using Dawn data. The distribution of 40Ar-39Ar ages of impact-melt clasts in howardites shows that they formed within the time period 3.3-3.8 Ga [9]. These, and other impact-melted HED materials, have distinct age and compositional characteristics that suggest they formed in discrete impact events. In order to create these crystalline impact-melt products on the surface of Vesta, the impacts during this time period must have had velocities much higher than 5 km/s, the main belt average [10]. This is inconsistent with formation by a normal distribution of impact velocities and points instead to a unique period where high-velocity collisions were more frequent than currently observed. Until now, impact-reset ages in the HED meteorites have been be interpreted under the umbrella of the canonical lunar cataclysm where an increase in the absolute number of bombarding objects is responsible for creating larger absolute amounts of impact-affected and impact-melted rocks, statistically increasing their chances of being found on Earth and dated. However, the distribution of age among the howardite impact-melt clasts may not necessarily result from an increased number of impacts, but rather result from impacts of higher velocity. The changeover from a typical main belt velocity profile to this regime of increased velocity population at Vesta occurs contemporaneously with a similar transition at the Moon, indicating that howardite impact-melt clast ages reinforce the notion of a dynamically unusual episode of bombardment in the inner solar system beginning at around 4.0 Ga.

Cohen, B. A.↗

Elastomeric Seal Performance after Terrestrial Ultraviolet Radiation Exposure

Ultraviolet radiation was evaluated to determine its negative effects on the performance of elastomeric gas pressure seals. The leak rates of the silicone elastomer S0383-70 O-ring test articles were used to quantify the degradation of the seals after exposure to vacuum-ultraviolet and/or middle-to-near-ultraviolet wavelength radiation. Three groups of seals were exposed in terrestrial facilities to 115-165 nm wavelength radiation, 230-500 nm wavelength radiation, or both spectrums, for an orbital spaceflight equivalent of 125 hours. The leak rates of the silicone elastomer S0383-70 seals were quantified and compared to samples that received no radiation. Each lot contained six samples and statistical t-tests were used to determine the separate and combined influences of exposure to the two wavelength ranges. A comparison of the mean leak rates of samples exposed to 115-165 nm wavelength radiation to the control specimens showed no difference, suggesting that spectrum was not damaging. The 230-500 nm wavelength appeared to be damaging, as the mean leak rates of the specimens exposed to that range of wavelengths, and those exposed to the combined 115-165 nm and 230-500 nm spectrums, were significantly different from the leak rates of the control specimens. Most importantly, the test articles exposed to both wavelength spectrums exhibited mean leak rates two orders of magnitude larger than any other exposed specimens, which suggested that both wavelength spectrums are important when simulating the orbital environment.

leakage↗

Recent Changes in Arctic Sea Ice Melt Onset, Freeze-Up, and Melt Season Length

In order to explore changes and trends in the timing of Arctic sea ice melt onset and freeze-up and therefore melt season length, we developed a method that obtains this information directly from satellite passive microwave data, creating a consistent data set from 1979 through present. We furthermore distinguish between early melt (the first day of the year when melt is detected) and the first day of continuous melt. A similar distinction is made for the freeze-up. Using this method we analyze trends in melt onset and freeze-up for 10 different Arctic regions. In all regions except for the Sea of Okhotsk, which shows a very slight and statistically insignificant positive trend (O.4 days/decade), trends in melt onset are negative, i.e. towards earlier melt. The trends range from -1.0day/decade for the Bering Sea to -7.3 days/decade for the East Greenland Sea. Except for the Sea of Okhotsk all areas also show a trend towards later autumn freeze onset. The Chukchi/Beaufort Seas and Laptev/East Siberian Seas observe the strongest trends with 7 days/decade. For the entire Arctic, the melt season length has increased by about 20 days over the last 30 years. Largest trends of over 1O days/decade are seen for Hudson Bay, the East Greenland Sea the Laptev/East Siberian Seas, and the Chukchi/Beaufort Seas. Those trends are statistically significant a1 the 99% level.

Markus, Thorsten↗

I/O Performance Characterization of Lustre and NASA Applications on Pleiades

In this paper we study the performance of the Lustre file system using five scientific and engineering applications representative of NASA workload on large-scale supercomputing systems such as NASA s Pleiades. In order to facilitate the collection of Lustre performance metrics, we have developed a software tool that exports a wide variety of client and server-side metrics using SGI's Performance Co-Pilot (PCP), and generates a human readable report on key metrics at the end of a batch job. These performance metrics are (a) amount of data read and written, (b) number of files opened and closed, and (c) remote procedure call (RPC) size distribution (4 KB to 1024 KB, in powers of 2) for I/O operations. RPC size distribution measures the efficiency of the Lustre client and can pinpoint problems such as small write sizes, disk fragmentation, etc. These extracted statistics are useful in determining the I/O pattern of the application and can assist in identifying possible improvements for users applications. Information on the number of file operations enables a scientist to optimize the I/O performance of their applications. Amount of I/O data helps users choose the optimal stripe size and stripe count to enhance I/O performance. In this paper, we demonstrate the usefulness of this tool on Pleiades for five production quality NASA scientific and engineering applications. We compare the latency of read and write operations under Lustre to that with NFS by tracing system calls and signals. We also investigate the read and write policies and study the effect of page cache size on I/O operations. We examine the performance impact of Lustre stripe size and stripe count along with performance evaluation of file per process and single shared file accessed by all the processes for NASA workload using parameterized IOR benchmark.

Saini, Subhash↗

Space/Time Statistics of Polar Ice Motion

Ice motions have been computed from passive microwave imagery (SMMR and SSM/I) on a daily basis for both Polar Regions. In the Arctic these daily motions have been merged with daily motions from AVHRR imagery and the Arctic buoy program. In the Antarctic motion only from the AVHRR were available for merging with the passive microwave vectors. Long-term means, monthly means and weekly means have all been computed from the resulting 22-year time series of polar ice motion. Papers are in preparation that present the long term (22 year) means, their variability and show animations of the monthly means over this time period for both Polar Regions. These papers will have links to "enhanced objects" that allow the reader to view the animations as part of the paper. The first paper presents the ice motion results from each of the Polar Regions. The second paper looks only at ice motion in the Arctic in order to develop a time series of ice age in the Arctic. Starting with the first full SMMR year in 1979 we keep track of each individual "ice element" (resolution of the sensor) and track it in the subsequent monthly time series. After a year we "age" each "particle" and we thus can keep track of the age of the ice starting in 1979. We keep track of ice age classes between one and five years and thus we can see the evolution of the ice as it ages after the initial 5-year period. This calculation shows how we are losing the older ice through Fram Strait at a rather alarming rate particularly in the past 15 years. This loss of older ice has resulted in an overall decrease in the thickest, oldest ice, which is now limited to a region just north of the Canadian Archipelago with tongues extending out across the pole towards the Siberian Shelf. This loss of old ice is consistent with the effects of global warming which provides the heat needed to melt, move and disperse this oldest ice through Fram Strait. This is the first step in a progression that may eventually open the Arctic ice pack and lead to an ice-free Arctic Ocean.

Emery, William J.↗

Determination of use of a real time tone tracker to obtain same beam interferometry data

The radio metric tracking technique known as Same-Beam Interferometry (SBI) has been shown to improve orbit determination accuracy for the Magellan and Pioneer 12 orbiter. Previous efforts to explore the technique were carried out by making open loop recordings of the carrier signals from the two spacecraft and extracting their phases through post processing. This paper reports on the use of a closed loop receiver to simultaneously measure the carrier signals from two spacecraft in order to produce SBI data in near real time. The Experiment Tone Tracker is a digital closed loop receiver installed in two of NASA's Deep Space Network stations which can simultaneously extract the phase of up to eight tones. The receivers were used in late September and October of 1992 to collect Doppler and SBI data from Pioneer 12 and Magellan. The demise of the Pionner 12 on October 8th during the start-up phase of our tests precluded the collection of an extensive set of SBI data, however two passes of SBI and several arcs of single spacecraft Doppler data were recorded. The SBI data were analyzed and determined to have statistical errors consistent with error models and similar to open loop data.

Nandi, S.↗

Accuracy assessment: The statistical approach to performance evaluation in LACIE

A statistical methodology was developed to check the accuracy of the products of the experimental operations throughout crop growth and to determine whether the procedures are adequate to accomplish the desired accuracy and reliability goals. It has allowed the identification and isolation of key problems in wheat area yield estimation, some of which have been corrected and some of which remain to be resolved. The major unresolved problem in accuracy assessment is that of precisely estimating the bias of the LACIE production estimator. Topics covered include: (1) evaluation techniques; (2) variance and bias estimation for the wheat production estimate; (3) the 90/90 evaluation; (4) comparison of the LACIE estimate with reference standards; and (5) first and second order error source investigations.

Houston, A. G.↗