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DOE OSTI2024

Hyperspectral Reflectance-Based High Throughput Phenotyping to Assess Water-Use Efficiency in Cotton

Cotton is a pivotal global commodity underscored by its economic value and widespread use. In the face of climate change, breeding resilient cultivars for variable environmental conditions becomes increasingly essential. However, the process of phenotyping, crucial to breeding programs, is often viewed as a bottleneck due to the inefficiency of traditional, low-throughput methods. To address this limitation, this study utilizes hyperspectral remote sensing, a promising tool for assessing crucial crop traits across forty cotton varieties. The results from this study demonstrated the effectiveness of four vegetation indices (VIs) in evaluating these varieties for water-use efficiency (WUE). The prediction accuracy for WUE through VIs such as the simple ratio water index (SRWI) and normalized difference water index (NDWI) was higher (up to R2 = 0.66), enabling better detection of phenotypic variations (p < 0.05) among the varieties compared to physiological-related traits (from R2 = 0.21 to R2 = 0.42), with high repeatability and a low RMSE. These VIs also showed high Pearson correlations with WUE (up to r = 0.81) and yield-related traits (up to r = 0.63). We also selected high-performing varieties based on the VIs, WUE, and fiber quality traits. This study demonstrated that the hyperspectral-based proximal sensing approach helps rapidly assess the in-season performance of varieties for imperative traits and aids in precise breeding decisions.

Agriculture↗

DOE OSTI2023

Refractivity Observations from Radar Phase Measurements: The 22 May 2002 Dryline Case during IHOP Project

The dryline, often associated with the development of severe storms in the Southern Great Plains of the United States of America, is a boundary layer phenomenon that occurs when a warm and moist air mass from the Gulf of Mexico meets a hot and dry air mass from the southwest desert area. An accurate knowledge of the water vapor spatio-temporal variability in the lower part of the atmosphere is crucial for a better understanding of the evolution of the dryline. The tropospheric refractivity, directly related to water vapor content, is a proxy for the water vapor content of the troposphere. It has already been demonstrated that the refractivity and the refractivity vertical gradient can be jointly estimated from radar phase measurements. In fact, it has been shown that using kriging interpolation techniques, accurate refractivity maps within the coverage area of the radar can be obtained with high temporal resolution. In this paper, a detailed analysis of the time series of radar-based refractivity maps obtained during a dryline that occurred on the afternoon of 22 May 2002 during the International H 2 O Project is presented. Comparisons between the time series of radar refractivity maps, obtained with the NCAR S-Pol radar, and the refractivity measurements derived from automatic ground-based weather stations and the AERI instrument, placed at different locations within the coverage area of the NCAR S-Pol radar, demonstrate the accuracy of radar refractivity estimates even for highly variable conditions, both in time and space, in the troposphere. Correlation coefficients higher than 0.95 are obtained in all weather station locations. Regarding the RMSE, errors less than 6 N-units are obtained for all cases, being even as low as 2.92 N-units at some locations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1987

The sensing and perception subsystem of the NASA research telerobot

A useful space telerobot for on-orbit assembly, maintenance, and repair tasks must have a sensing and perception subsystem which can provide the locations, orientations, and velocities of all relevant objects in the work environment. This function must be accomplished with sufficient speed and accuracy to permit effective grappling and manipulation. Appropriate symbolic names must be attached to each object for use by higher-level planning algorithms. Sensor data and inferences must be presented to the remote human operator in a way that is both comprehensible in ensuring safe autonomous operation and useful for direct teleoperation. Research at JPL toward these objectives is described.

Wilcox, B.↗

NASA NTRS2010

Vibration Response Predictions for Heavy Panel Mounted Components from Panel Acreage Environment Specifications

The development of new launch vehicles in the Aerospace industry often relies on response measurements taken from previously developed vehicles during various stages of liftoff and ascent, and from wind tunnel models. These measurements include sound pressure levels, dynamic pressures in turbulent boundary layers and accelerations. Rigorous statistical scaling methods are applied to the data to derive new environments and estimate the performance of new skin panel structures. Scaling methods have proven to be reliable, particularly for designs similar to the vehicles used as the basis for scaling, and especially in regions of smooth acreage without exterior protuberances or heavy components mounted to the panel. To account for response attenuation of a panel-mounted component due to its apparent mass at higher frequencies, the vibroacoustics engineer often reduces the acreage vibration according to a weight ratio first suggested by Barrett. The accuracy of the reduction is reduced with increased weight of the panel-mounted component, and does not account for low-frequency amplification of the component/panel response as a system. A method is proposed that combines acreage vibration from scaling methods with finite element analysis to account for the frequency-dependent dynamics of heavy panel-mounted components. Since the acreage and mass-loaded skins respond to the same dynamic input pressure, such pressure may be eliminated in favor of a frequency-dependent scaling function applied to the acreage vibration to predict the mass-loaded panel response. The scaling function replaces the Barrett weight ratio, and contains all of the dynamic character of the loaded and unloaded skin panels. The solution simplifies for spatially uncorrelated and fully correlated input pressures. Since the prediction uses finite element models of the loaded and unloaded skins, a rich suite of response data are available to the design engineer, including interface forces, stress and strain, as well as acceleration and displacement. An extension of the method is also developed to incorporate the effect of a local protuberance near a heavy component. Acreage environments from traditional scaling methods with and without protuberance effects serve as the basis for the extension. Authors:

Harrison, Phillip↗

NASA NTRS2011

Determining Trends in Impervious Cover for the Mobile Bay, AL Region for 1974-2008, Based on a Landsat Time Series

This presentation will discuss the development and use of Landsat-based impervious cover products in conjunction with land use land cover change products to assess multi-decadal urbanization across the Mobile Bay region at regional and watershed scales. This nationally important coastal region has undergone a variety of ephemeral and permanent land use land cover change since the mid-1970s, including gradual but consequential increases in urban surface cover. This urban sprawl corresponds with increased regional percent impervious cover. The region s coastal zone managers are concerned about the increasing percent impervious cover, since it can negatively influence water quality and is an important consideration for coastal conservation and restoration work. In response, we processed multi-temporal Landsat data to compute maps of percent impervious cover for multiple dates from 1974 through 2008, roughly at 5-year intervals. Each year of product was classified using one single date of leaf-on and leaf-off Landsat data in conjunction with Cubist software. We are assessing Landsat impervious cover product accuracy through comparisons to available reference data, including available NLCD impervious cover products from the USGS, raw Landsat data, plus higher spatial resolution aerial and satellite data. In particular, we are quantitatively comparing the 2008 Landsat impervious cover products to those from QuickBird 2.4-meter multispectral data. Initial visual comparisons with the QuickBird impervious cover product suggest that the 2008 Landsat product tends to underestimate impervious cover for high density urban areas and to overestimate impervious cover in established residential subdivisions mixed with forested cover. Landsat TM and ETM data appears to produce more accurate impervious cover products compared to those using lower resolution Landsat MSS data. Although imperfect, these Landsat impervious cover products have helped the Mobile Bay National Estuary Program visualize basic urbanization trends for multiple HUC-12 watersheds of concern to them and their constituents

Spruce, Joseph P.↗

NASA NTRS2004

Higher-Order Finite Elements for Computing Thermal Radiation

Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other unrealistic physical conditions are assumed. Instead, the equations of radiative heat transfer are integrated numerically over the parent finite elements by use of a computationally efficient Gaussian integration scheme.

Gould, Dana C.↗

NASA NTRS2012

Celestial Reference Frames at Multiple Radio Wavelengths

In 1997 the IAU adopted the International Celestial Reference Frame (ICRF) built from S/X VLBI data. In response to IAU resolutions encouraging the extension of the ICRF to additional frequency bands, VLBI frames have been made at 24, 32, and 43 gigahertz. Meanwhile, the 8.4 gigahertz work has been greatly improved with the 2009 release of the ICRF-2. This paper discusses the motivations for extending the ICRF to these higher radio bands. Results to date will be summarized including evidence that the high frequency frames are rapidly approaching the accuracy of the 8.4 gigahertz ICRF-2. We discuss current limiting errors and prospects for the future accuracy of radio reference frames. We note that comparison of multiple radio frames is characterizing the frequency dependent systematic noise floor from extended source morphology and core shift. Finally, given Gaia's potential for high accuracy optical astrometry, we have simulated the precision of a radio-optical frame tie to be approximately10-15 microarcseconds ((1-sigma) (1-standard deviation), per component).

quasars↗

NASA NTRS2017

Operational Implementation of Sea Ice Concentration Estimates from the AMSR2 Sensor

An operation implementation of a passive microwave sea ice concentration algorithm to support NOAA's operational mission is presented. The NASA team 2 algorithm, previously developed for the NASA advanced microwave scanning radiometer for the Earth observing system (AMSR-E) product suite, is adapted for operational use with the JAXA AMSR2 sensor through several enhancements. First, the algorithm is modified to process individual swaths and provide concentration from the most recent swaths instead of a 24-hour average. A latency (time since observation) field and a 24-hour concentration range (maximum-minimum) are included to provide indications of data timeliness and variability. Concentration from the Bootstrap algorithm is a secondary field to provide complementary sea ice information. A quality flag is implemented to provide information on interpolation, filtering, and other quality control steps. The AMSR2 concentration fields are compared with a different AMSR2 passive microwave product, and then validated via comparison with sea ice concentration from the Suomi visible and infrared imaging radiometer suite. This validation indicates the AMSR2 concentrations have a bias of 3.9% and an RMSE of 11.0% in the Arctic, and a bias of 4.45% and RMSE of 8.8% in the Antarctic. In most cases, the NOAA operational requirements for accuracy are met. However, in low-concentration regimes, such as during melt and near the ice edge, errors are higher because of the limitations of passive microwave sensors and the algorithm retrieval.

Arctic↗

NASA NTRS2018

Landsat 9 Thermal Infrared Sensor 2 Architecture and Design

The Thermal Infrared Sensor 2 (TIRS-2) will fly aboard the Landsat 9 spacecraft and leverages the Thermal Infrared Sensor (TIRS) design currently flying on Landsat 8. TIRS-2 will provide similar science data as TIRS, but is not a buildto-print rebuild due to changes in requirements and improvements in absolute accuracy. The heritage TIRS design has been modified to reduce the influence of stray light and to add redundancy for higher reliability over a longer mission life. The TIRS-2 development context differs from the TIRS scenario, adding to the changes. The TIRS-2 team has also learned some lessons along the way.

Hair, Jason H.↗

NASA NTRS2019

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will carry into space the Ocean Color Instrument (OCI), a spectrometer measuring at 5 nm spectral resolution in the ultraviolet (UV) to near infrared (NIR) with additional spectral bands in the shortwave infrared (SWIR), and two multi-angle polarimeters that will overlap the OCI spectral range and spatial coverage, i. e., the Spectrometer for Planetary Exploration (SPEXone) and the Hyper-Angular Rainbow Polarimeter (HARP2). These instruments, especially when used in synergy, have great potential for improving estimates of water reflectance in the post Earth Observing System (EOS) era. Extending the top-of-atmosphere (TOA) observations to the UV, where aerosol absorption is effective, adding spectral bands in the SWIR, where even the most turbid waters are black and sensitivity to the aerosol coarse mode is higher than at shorter wavelengths, and measuring in the oxygen A-band to estimate aerosol altitude will enable greater accuracy in atmospheric correction for ocean color science. The multi-angular and polarized measurements, sensitive to aerosol properties (e.g., size distribution, index of refraction), can further help to identify or constrain the aerosol model, or to retrieve directly water reflectance. Algorithms that exploit the new capabilities are presented, and their ability to improve accuracy is discussed. They embrace a modern, adapted heritage two-step algorithm and alternative schemes (deterministic, statistical) that aim at inverting the TOA signal in a single step. These schemes, by the nature of their construction, their robustness, their generalization properties, and their ability to associate uncertainties, are expected to become the new standard in the future. A strategy for atmospheric correction is presented that ensures continuity and consistency with past and present ocean-color missions while enabling full exploitation of the new dimensions and possibilities. Despite the major improvements anticipated with the PACE instruments, gaps/issues remain to be filled/tackled. They include dealing properly with whitecaps, taking into account Earth-curvature effects, correcting for adjacency effects, accounting for the coupling between scattering and absorption, modeling accurately water reflectance, and acquiring a sufficiently representative dataset of water reflectance in the UV to SWIR. Dedicated efforts, experimental and theoretical, are in order to gather the necessary information and rectify inadequacies. Ideas and solutions are put forward to address the unresolved issues. Thanks to its design and characteristics, the PACE mission will mark the beginning of a new era of unprecedented accuracy in ocean-color radiometry from space.

Robert J Frouin↗

NASA NTRS2019

Evaluation of Satellite-Based Rainfall Estimates in the Lower Mekong River Basin (Southeast Asia)

Satellite-based precipitation is an essential tool for regional water resource applications that requires frequent observations of meteorological forcing, particularly in areas that have sparse rain gauge networks. To fully realize the utility of remotely sensed precipitation products in watershed modeling and decision-making, a thorough evaluation of the accuracy of satellite-based rainfall and regional gauge network estimates is needed. In this study, Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA) 3B42 v.7 and Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) daily rainfall estimates were compared with daily rain gauge observations from 2000 to 2014 in the Lower Mekong River Basin (LMRB) in Southeast Asia. Monthly, seasonal, and annual comparisons were performed, which included the calculations of correlation coefficient, coefficient of determination, bias, root mean square error (RMSE), and mean absolute error (MAE). Our validation test showed TMPA to correctly detect precipitation or no-precipitation 64.9% of all days and CHIRPS 66.8% of all days, compared to daily in-situ rainfall measurements. The accuracy of the satellite-based products varied greatly between the wet and dry seasons. Both TMPA and CHIRPS showed higher correlation with in-situ data during the wet season (June–September) as compared to the dry season (November–January). Additionally, both performed better on a monthly than an annual time-scale when compared to in-situ data. The satellite-based products showed wet biases during months that received higher cumulative precipitation. Based on a spatial correlation analysis, the average r-value of CHIRPS was much higher than TMPA across the basin. CHIRPS correlated better than TMPA at lower elevations and for monthly rainfall accumulation less than 500 mm. While both satellite-based products performed well, as compared to rain gauge measurements, the present research shows that CHIRPS might be better at representing precipitation over the LMRB than TMPA.

Dandridge, Chelsea↗

NASA NTRS2019

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era

ocean color↗

DOE OSTI2023

A Medium-/Low-Voltage Joint State Estimator Through Linear Uncertainty Propagation

Traditionally, distribution system state estimations (DSSE) are challenged by the lack of measurements at both primary and secondary sides of the system. The widely available cable television (CATV) voltage sensors installed in low-voltage (LV) networks bring opportunities to achieve higher quality DSSE covering a broader area of the distribution network. This study proposes a medium-/low-voltage (MV/LV) joint distribution system state estimation approach using the untapped CATV measurements. It aims at addressing the need for system situational awareness at the grid edge while improving the estimation accuracy at both the primary and secondary sides compared to its disjointed counterpart. Linearized measurement functions and boundary condition uncertainty propagation rules are derived to ensure the computational efficiency and accuracy of the joint state estimator. Numerical experiments are conducted on an IEEE test feeder to demonstrate the efficacy of the proposed method and the value of CATV measurements.

joint state estimation↗

DOE OSTI2023

AI ensemble for signal detection of higher order gravitational wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

We introduce spatiotemporal-graph models that concurrently process data from the twin advanced LIGO detectors and the advanced Virgo detector. We trained these AI classifiers with 2.4 million IMRPhenomXPHM waveforms that describe quasi-circular, spinning, non-precessing binary black hole mergers with component masses m{1,2}∈[3M⊙,50M⊙], and individual spins sz{1,2}∈[−0.9,0.9]; and which include the (ℓ,|m|)={(2,2),(2,1),(3,3),(3,2),(4,4)} modes, and mode mixing effects in the ℓ=3,|m|=2 harmonics. We trained these AI classifiers within 22 hours using distributed training over 96 NVIDIA V100 GPUs in the Summit supercomputer. We then used transfer learning to create AI predictors that estimate the total mass of potential binary black holes identified by all AI classifiers in the ensemble. We used this ensemble, 3 classifiers for signal detection and 2 total mass predictors, to process a year-long test set in which we injected 300,000 signals. This year-long test set was processed within 5.19 minutes using 1024 NVIDIA A100 GPUs in the Polaris supercomputer (for AI inference) and 128 CPU nodes in the ThetaKNL supercomputer (for post-processing of noise triggers), housed at the Argonne Leadership Computing Facility. These studies indicate that our AI ensemble provides state-of-the-art signal detection accuracy, and reports 2 misclassifications for every year of searched data. This is the first AI ensemble designed to search for and find higher order gravitational wave mode signals.

Tian, Minyang↗

NASA NTRSDate not supplied

X-57 “Maxwell” High-Lift Propeller Testing and Model Development

NASA’s X-57 “Maxwell” distributed electric propulsion flight demonstrator has a high-lift system that includes 12 fixed-pitch high-lift propellers located upstream of the wing leading edge for lift augmentation at low speeds. These high-lift propellers are not required at higher speeds and are folded conformally along the nacelles to reduce drag when not in operation. Aircraft performance models and flight simulations incorporate propeller performance to predict thrust, moments, and power consumption and propeller model accuracy is important in identifying safe operating regimes for this aircraft. Current high-lift propeller performance models have been verified and calibrated against numerous computational fluid dynamics analyses under a variety of flight conditions. We performed a series of full-scale wind tunnel tests at the NASA Langley Research Center Low Speed Aeroacoustic Wind Tunnel to further validate these models, to identify any adverse operating conditions for these propellers, and to assess the accuracy of the facility’s new Propeller Test Stand. The results indicate that the models accurately predicted performance and that the right-handed propeller showed lower torque and thrust for a given propeller speed compared to the left-handed version. Acoustic data support these measurements, showing higher tonal noise for the left versus right propeller. We suspect this is due to slight differences in the material properties between the early production (right) and more recent (left) blade sets leading to greater detwisting in the right-handed blades under load. Both propellers demonstrated very stable operation throughout the test including during deployment, stowing, and windmilling. Furthermore, high-speed imagery of the spinning propeller indicated no blade oscillations or instabilities for any test case. We also leveraged these images to analyze the effects of propeller loading on blade detwisting and tip position. Unfortunately, the thrust measurements varied significantly during the test due to cross-loading of the Propeller Test Stand load cell, though trends in the thrust data were still observable. The torque measurement, however, remained very precise for all test points and was used for performance comparisons. As a result of this test, we validated and improved the X-57 high-lift propeller performance models, obtained detailed propeller acoustic data and high-speed imagery, observed the propeller operating safely during a variety of dynamic events, and identified two potentially adverse, low-propeller-speed conditions which will be avoided during normal aircraft operation.

X-57↗

NASA NTRS2021

Evaluation of Higher-order Quadrature Schemes in Improving Computational Efficiency for Orientation-averaged Single-Scattering Properties of Nonspherical Ice Particles

We evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation-averaged SSPs derived from realistic hydrometeors as input to radiative transfer Models (RTMs). The DDA has been a popular choice for single-scattering calculations, due to its versatility with respect to target geometry. However, being iterative-solver-based (ISB), the most used DDA codes, e.g. DDSCAT and ADDA, must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation-averages can increase drastically and so does the computation cost incurred by the ISB-DDA methods. MIDAS is a Direct-Solver-Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB-DDA methods. MIDAS, when combined with high-order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM-ready SSPs of complex-shaped hydrometeors than existing ISB-DDA methods, with the native quadrature schemes they offer.

Ines Fenni↗

NASA NTRS1998

The Software Design for the Wide-Field Infrared Explorer Attitude Control System

The Wide-Field Infrared Explorer (WIRE), currently scheduled for launch in September 1998, is the fifth of five spacecraft in the NASA/Goddard Small Explorer (SMEX) series. This paper presents the design of WIRE's Attitude Control System flight software (ACS FSW). WIRE is a momentum-biased, three-axis stabilized stellar pointer which provides high-accuracy pointing and autonomous acquisition for eight to ten stellar targets per orbit. WIRE's short mission life and limited cryogen supply motivate requirements for Sun and Earth avoidance constraints which are designed to prevent catastrophic instrument damage and to minimize the heat load on the cryostat. The FSW implements autonomous fault detection and handling (FDH) to enforce these instrument constraints and to perform several other checks which insure the safety of the spacecraft. The ACS FSW implements modules for sensor data processing, attitude determination, attitude control, guide star acquisition, actuator command generation, command/telemetry processing, and FDH. These software components are integrated with a hierarchical control mode managing module that dictates which software components are currently active. The lowest mode in the hierarchy is the 'safest' one, in the sense that it utilizes a minimal complement of sensors and actuators to keep the spacecraft in a stable configuration (power and pointing constraints are maintained). As higher modes in the hierarchy are achieved, the various software functions are activated by the mode manager, and an increasing level of attitude control accuracy is provided. If FDH detects a constraint violation or other anomaly, it triggers a safing transition to a lower control mode. The WIRE ACS FSW satisfies all target acquisition and pointing accuracy requirements, enforces all pointing constraints, provides the ground with a simple means for reconfiguring the system via table load, and meets all the demands of its real-time embedded environment (16 MHz Intel 80386 processor with 80387 coprocessor running under the VRTX operating system). The mode manager organizes and controls all the software modules used to accomplish these goals, and in particular, the FDH module is tightly coupled with the mode manager.

Anderson, Mark O.↗

NASA NTRS1996

Elevation correction factor for absolute pressure measurements

With the arrival of highly accurate multi-port pressure measurement systems, conditions that previously did not affect overall system accuracy must now be scrutinized closely. Errors caused by elevation differences between pressure sensing elements and model pressure taps can be quantified and corrected. With multi-port pressure measurement systems, the sensing elements are connected to pressure taps that may be many feet away. The measurement system may be at a different elevation than the pressure taps due to laboratory space or test article constraints. This difference produces a pressure gradient that is inversely proportional to height within the interface tube. The pressure at the bottom of the tube will be higher than the pressure at the top due to the weight of the tube's column of air. Tubes with higher pressures will exhibit larger absolute errors due to the higher air density. The above effect is well documented but has generally been taken into account with large elevations only. With error analysis techniques, the loss in accuracy from elevation can be easily quantified. Correction factors can be applied to maintain the high accuracies of new pressure measurement systems.

Panek, Joseph W.↗