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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Field Penetration in a Rectangular Box Using Numerical Techniques: An Effort to Obtain Statistical Shielding Effectiveness

This paper emphasizes the application of numerical methods to explore the ideas related to shielding effectiveness from a statistical view. An empty rectangular box is examined using a hybrid modal/moment method. The basic computational method is presented followed by the results for single- and multiple observation points within the over-moded empty structure. The statistics of the field are obtained by using frequency stirring, borrowed from the ideas connected with reverberation chamber techniques, and extends the ideas of shielding effectiveness well into the multiple resonance regions. The study presented in this paper will address the average shielding effectiveness over a broad spatial sample within the enclosure as the frequency is varied.

Bunting, Charles F.↗
NASA NTRS1993

Backscatter Characteristics of the Winter Sea Ice Cover in the Beaufort

The microwave backscatter statistics of the sea ice cover in the winter Beaufort Sea were characterized using C-band Synthetic Aperture Radar (SAR) data collected by ERS-1. Sea ice backscatter signatures were sampled from SAR image data collected during the winter of 1991/92 and winter of 1992/93. The spatial and temporal variabilities of the backscatter signatures of different ice types are discussed. The results show considerable seasonal stability of the backscatter signature of multi-year ice as well as first-year ice. Small amplitude regional variations of the multi-year ice backscatter can be observed. Consistent contrast between multiyear ice and first-year ice is maintained throughout the season.

Kwok, R.↗
NASA NTRS2012

Upper-Ocean Heat Balance Processes and the Walker Circulation in CMIP5 Model Projections

Considerable uncertainty remains as to the importance of mechanisms governing decadal and longer variability of the Walker Circulation, its connection to the tropical climate system, and prospects for tropical climate change in the face of anthropogenic forcing. Most contemporary climate models suggest that in response to elevated CO2 and a warmer but more stratified atmosphere, the required upward mass flux in tropical convection will diminish along with the Walker component of the tropical mean circulation as well. Alternatively, there is also evidence to suggest that the shoaling and increased vertical stratification of the thermocline in the eastern Pacific will enable a muted SST increase there-- preserving or even enhancing some of the dynamical forcing for the Walker cell flow. Over the past decade there have been observational indications of an acceleration in near-surface easterlies, a strengthened Pacific zonal SST gradient, and globally-teleconnected dislocations in precipitation. But is this evidence in support of an ocean dynamical thermostat process posited to accompany anthropogenic forcing, or just residual decadal fluctuations associated with variations in warm and cold ENSO events and other stochastic forcing? From a modeling perspective we try to make headway on this question by examining zonal variations in surface energy fluxes and dynamics governing tropical upper ocean heat content evolution in the WCRP CMIP5 model projections. There is some diversity among model simulations; for example, the CCSM4 indicates net ocean warming over the IndoPacific region while the CSIRO model concentrates separate warming responses over the central Pacific and Indian Ocean regions. The models, as with observations, demonstrate strong local coupling between variations in column water vapor, downward surface longwave radiation and SST; but the spatial patterns of changes in the sign of this relationship differ among models and, for models as a whole, with observations. Our analysis focuses initially on probing the inter-model differences in energy fluxes / transports and Walker Circulation response to forcing. We then attempt to identify statistically the El Nino- / La Nina-related ocean heat content variability unique to each model and regress out the associated energy flux, ocean heat transport and Walker response on these shorter time scales for comparison to that of the anthropogenic signals.

Robertson, F. R.↗
NASA NTRS2019

Twentieth Century Redistribution in Climatic Drivers of Global Tree Growth

Energy and water limitations of tree growth remain insufficiently understood at large spatiotemporal scales, hindering model representation of interannual or longer-term ecosystem processes. By assessing and statistically scaling the climatic drivers from 2710 tree-ring sites, we identified the boreal and temperate land areas where tree growth during 1930–1960 CE responded positively to temperature (20.8 ± 3.7 Mio km2; 25.9 ± 4.6%), precipitation (77.5 ± 3.3 Mio km2; 96.4 ± 4.1%), and other parameters. The spatial manifestation of this climate response is determined by latitudinal and altitudinal temperature gradients, indicating that warming leads to geographic shifts in growth limitations. We observed a significant (P < 0.001) decrease in temperature response at cold-dry sites between 1930–1960 and 1960–1990 CE, and the total temperature-limited area shrunk by −8.7 ± 0.6 Mio km2. Simultaneously, trees became more limited by atmospheric water demand almost worldwide. These changes occurred under mild warming, and we expect that continued climate change will trigger a major redistribution in growth responses to climate.

Babst, Flurin↗
DOE OSTI2020

Sea Level Rise in the CESM Large Ensemble: The Role of Individual Climate Forcings and Consequences for the Coming Decades

The emergence of a spatial pattern in the externally forced response (FR) of dynamic sea level (DSL) during the altimeter era has recently been demonstrated using climate models but our understanding of its initial emergence, drivers, and implications for the future is poor. Here the anthropogenic forcings of the DSL pattern are explored using the Community Earth System Model Large Ensemble (CESM-LE) and Single-Forcing Large Ensemble, a newly available set of simulations where values of individual forcing agents remain fixed at 1920 levels, allowing for an estimation of their effects. Statistically significant contributions to the DSL FR are identified for greenhouse gases (GHGs) and industrial aerosols (AERs), with particularly strong contributions resulting from AERs in the mid-twentieth century and GHGs in the late twentieth and twenty-first century. Secondary, but important, contributions are identified for biomass burning aerosols in the equatorial Atlantic Ocean in the mid-twentieth century, and for stratospheric ozone in the Southern Ocean during the late twentieth century. Key to understanding regional DSL patterns are ocean heat content and salinity anomalies, which are driven by surface heat and freshwater fluxes, ocean dynamics, and the spatial structure of seawater thermal expansivity. Finally, potential implications for the interpretation of DSL during the satellite era and the longer records from tide gauges are suggested as a topic for future research.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2020

Synergistic Use of Hyperspectral UV-Visible OMI and Broadband Meteorological Imager MODIS Data for a Merged Aerosol Product

The retrieval of optimal aerosol datasets by the synergistic use of hyperspectral ultraviolet(UV)–visible and broadband meteorological imager (MI) techniques was investigated. The Aura Ozone Monitoring Instrument (OMI) Level 1B (L1B) was used as a proxy for hyperspectral UV–visible instrument data to which the Geostationary Environment Monitoring Spectrometer (GEMS) aerosol algorithm was applied. Moderate-Resolution Imaging Spectroradiometer (MODIS) L1B and dark target aerosol Level 2 (L2) data were used with a broadband MI to take advantage of the consistent time gap between the MODIS and the OMI. First, the use of cloud mask information from the MI infrared (IR) channel was tested for synergy. High-spatial-resolution and IR channels of the MI helped mask cirrus and sub-pixel cloud contamination of GEMS aerosol, as clearly seen in aerosol optical depth (AOD) validation with Aerosol Robotic Network (AERONET) data. Second, dust aerosols were distinguished in the GEMS aerosol-type classification algorithm by calculating the total dust confidence index (TDCI) from MODIS L1B IR channels. Statistical analysis indicates that the Probability of Correct Detection (POCD) between the forward and inversion aerosol dust models (DS) was increased from 72% to 94% by use of the TDCI for GEMS aerosol-type classification, and updated aerosol types were then applied to the GEMS algorithm. Use of the TDCI for DS type classification in the GEMS retrieval procedure gave improved single-scattering albedo (SSA) values for absorbing fine pollution particles (BC) and DS aerosols. Aerosol layer height (ALH) retrieved from GEMS was compared with Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data, which provides high-resolution vertical aerosol profile information. The CALIOP ALH was calculated from total attenuated backscatter data at 1064 nm, which is identical to the definition of GEMS ALH. Application of the TDCI value reduced the median bias of GEMS ALH data slightly. The GEMS ALH bias approximates zero, especially for GEMS AOD values of>~0.4 and GEMS SSA values of<~0.95.Finally, the AOD products from the GEMS algorithm and MI were used in aerosol merging with the maximum-likelihood estimation method, based on a weighting factor derived from the standard deviation of the original AOD products. With the advantage of the UV–visible channel in retrieving aerosol properties over bright surfaces, the combined AOD products demonstrated better spatial data availability than the original AOD products, with comparable accuracy. Furthermore, pixel-level error analysis of GEMS AOD data indicates improvement through MI synergy.

aerosol↗
DOE OSTI2023

A Data-Driven Framework for Direct Local Tensile Property Prediction of Laser Powder Bed Fusion Parts

This article proposes a generalizable, data-driven framework for qualifying laser powder bed fusion additively manufactured parts using part-specific in situ data, including powder bed imaging, machine health sensors, and laser scan paths. To achieve part qualification without relying solely on statistical processes or feedstock control, a sequence of machine learning models was trained on 6299 tensile specimens to locally predict the tensile properties of stainless-steel parts based on fused multi-modal in situ sensor data and a priori information. A cyberphysical infrastructure enabled the robust spatial tracking of individual specimens, and computer vision techniques registered the ground truth tensile measurements to the in situ data. The co-registered 230 GB dataset used in this work has been publicly released and is available as a set of HDF5 files. The extensive training data requirements and wide range of size scales were addressed by combining deep learning, machine learning, and feature engineering algorithms in a relay. The trained models demonstrated a 61% error reduction in ultimate tensile strength predictions relative to estimates made without any in situ information. Lessons learned and potential improvements to the sensors and mechanical testing procedure are discussed.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Classifying unresolved objects from simulated space data.

A multispectral scanner data set gathered at a flight altitude of 10,000 ft. over an agricultural area was modified to simulate the spatial resolution of the spacecraft scanners. Signatures were obtained for several major crops and their proportions were estimated over a large area. For each crop, a map was generated to show its approximate proportion in each resolution element, and hence its distribution over the area of interest. A statistical criterion was developed to identify data points that may not represent a mixture of the specified crops. This allows for great reduction in the effect of unknown or alien objects on the estimated proportions. This criterion can be used to locate special features, such as roads or farm houses. Preliminary analysis indicates a high level of consistency between estimated proportions and available ground truth. Large concentrations of major crops show up especially well on the maps.

Nalepka, R. F.↗
NASA NTRS1986

Statistical corrections to numerical predictions. IV

The National Meteorological Center Barotropic-Mesh Model has been used to test a statistical correction procedure, designated as M-II, that was developed in Schemm et al. (1981). In the present application, statistical corrections at 12 h resulted in significant reductions of the mean-square errors of both vorticity and the Laplacian of thickness. Predictions to 48 h demonstrated the feasibility of applying corrections at every 12 h in extended forecasts. In addition to these improvements, however, the statistical corrections resulted in a shift of error from smaller to larger-scale motions, improving the smallest scales dramatically but deteriorating the largest scales. This effect is shown to be a consequence of randomization of the residual errors by the regression equations and can be corrected by spatially high-pass filtering the field of corrections before they are applied.

Schemm, Jae-Kyung↗
NASA NTRS1988

An all-sky search for molecular cirrus clouds

An all-sky map of IR-excess gas has been produced by subtracting the H I component from the IR brightness. The large IR-excess residuals that are spatially connected are used to define IR-excess clouds. Also, nearby molecular clouds at high Galactic latitude and clouds with local heating sources or a larger dust-to-gas ratio than average are identified. The map and a catalog of 516 significant clouds are presented and statistically analyzed.

Desert, F. X.↗
NASA NTRS1993

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O yields product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants' mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain, indicating a lower reactedness.

Steinberger, C. J.↗
NASA NTRS1994

Acceleration of interstellar pickup ions in the disturbed solar wind observed on Ulysses

Acceleration of interstellar pickup H(+) and He(+) as well as of solar wind protons and alpha particles has been observed on Ulysses during the passage of a corotating interaction region (CIR) at approximately 4.5 AU. Injection efficiencies for both the high thermal speed interstellar pickup ions (H(+) and He(+)) and the low thermal speed solar wind ions (H(+) and He(++) are derived using velocity distribution functions of protons, pickup He(+) and alpha particles from less than 1 to 60 keV/e and of ions (principally protons) above approximately 60 keV. The observed spatial variations of the few keV and the few hundred keV accelerated pickup protons across the forward shock of CIR indicate a two stage acceleration mechanism. Thermal ions are first accelerated to speeds of 3 to 4 times the solar wind speed inside the CIR, presumably by some statistical mechanism, before reaching higher energies by a shock acceleration process. Our results also indicate that (1) the injection efficiencies for pickup ions are almost 100 times higher than they are for solar wind ions, (2) pickup H(+) and He(+) are the two most abundant suprathermal ion species and they carry a large fraction of the particle thermal pressure, (3) the injection efficiency is highest for protons, lowest for He(+), and intermediate for alpha particles, (4) both H(+) and He(+) have identical spectral shapes above the cutoff speed for pickup ions, and (5) the solar wind frame velocity distribution function of protons has the form F(w) = F(sub o)w(sup -4) for 1 is less than w is less than approximately 5, where w is the ion speed divided by the solar wind speed. Above w approximately 5-10 the proton spectrum becomes steeper. These results have important implications concerning acceleration of ions by shocks and CIRs, acceleration of anomalous cosmic rays, and particle dynamics in the outer heliosphere.

Gloeckler, G.↗
NASA NTRS1997

Mathematical and Computational Challenges in Population Biology and Ecosystems Science

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

Levin, Simon A.↗
NASA NTRS1999

Characterization of Climate Change and Variability with GPS

We compared zonal mean specific humidity derived from the 21 June-4 July 1995 Global Positioning System (GPS)/MET occultation observations with that derived from the European Center for Medium-Range Weather Forecasts (ECMWF) global analyses. The GPS/MET results indicate a drier troposphere, especially near the subtropical tradewind inversion. A small, moist bias in the GPS/MET upper northern-hemisphere troposphere compared to ECMWF may be due to a small radiosonde temperature bias. A diagram shows the difference (g/kg) between the GPS/MET zonal mean specific humidity and that for June-August derived from 1963-1973 radiosondes. Although the observing period is short, GPS and ECMWF results both indicate a significantly wetter boundary layer at most latitudes consistent with decadal trends observed in radiosonde data. GPS/MET results exhibit higher tropical convective available potential energy (CAPE), suggesting a more vigorous tropical Hadley circulation. Drier, free troposphere air in the descending branches of the Hadley circulation is due in part to a moist radiosonde bias but may also reflect some negative moisture feedback. Using 1992-1997 ground GPS observations and recent advancements in GPS technology, we removed an apparent altimetric drift (-1.2 +/- 0.4 mm/yr) due to columnar water vapor from the Topography (Ocean) Experiment (TOPEX) microwave radiometer, which brought the TOPEX mean sea level change estimates into better agreement with historical tide gauge records, suggesting global mean sea level is rising at a rate of 1.5-2.0 mm/yr. We can also discern a statistically significant increase of 0.2 +/- 0.1 kg/square m/yr in mean columnar water vapor over the ocean from 1992-1997. Optimal fingerprinting can be used for the detection and attribution of tropospheric warming due to an anthropogenic greenhouse. Optimal fingerprinting distinguishes between different types of signals according to their spatial and temporal patterns, while minimizing the influence of natural climate variability. S. Leroy concludes that the signal-to-noise ratio of global warming detection increases by unity approximately every 10 years if a single oceanic region is chosen. Less time for detection is likely when many global regions are considered simultaneously. GPS occultation constellations allow the possibility of detecting small changes in upper air temperature with inconsequential calibration errors, making occultation an ideal data type for global warming detection studies. Our initial study of a 22-GHz satellite-satellite occultation system predicts upper troposphere moisture sensitivities of 3-5 ppmv and 1-2 percent in the middle and lower troposphere. Additional information contained in original.

Kursinski, R.↗
NASA NTRS2021

Air Pollution Scenario over Pakistan: Characterization and Ranking of Extremely Polluted Cities using Long-Term Concentrations of Aerosols and Trace Gases

Pakistan ranks third in the world in terms of mortality attributable to air pollution, with aerosol mass concentrations (PM2.5) consistently well above WHO (World Health Organization) air quality guidelines (AQG). However, regulation is dependent on a sparse network of air quality monitoring stations and insufficient ground data. This study utilizes long-term observations of aerosols and trace gases to characterize and rank the air pollution scenarios and pollution characteristics of 80 selected cities in Pakistan. Datasets used include (1) the Aqua and Terra (AquaTerra) MODIS (Moderate Resolution Imaging Spectroradiometer) Level 2 Collection 6.1 merged Dark Target and Deep Blue (DTB) aerosol optical depth (AOD) retrieval products; (2) the CAMS (Copernicus Atmosphere Monitoring Service) reanalysis PM1, PM2.5, and PM10 data; (3) the MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) reanalysis PM2.5 data, (4) the OMI (Ozone Monitoring Instrument) tropospheric vertical column density (TVCD) of nitrogen dioxide (NO2), and VCD of sulfur dioxide (SO2) in the Planetary Boundary Layer (PBL), (5) the VIIRS (Visible Infrared Imaging Radiometer Suite) Nighttime Lights data, (6) MODIS Collection 6 Version 2 global monthly fire location data (MCD14ML), (7) population density, (8) MODIS Level 3 Collection 6 land cover types, (9) AERONET (AErosol RObotic NETwork) Version 3 Level 2.0 data, and (10) ground-based PM2.5 concentrations from air quality monitoring stations. Potential Source Contribution Function (PSCF) analyses were performed by integrating with ground-based PM2.5 concentrations and the NOAA (National Oceanic and Atmospheric Administration) HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) air parcel back trajectories to identify potential pollution source areas which are responsible for extreme air pollution in Pakistan. Results show that the ranking of the top polluted cities depends on the type of pollutant considered and the metric used. For example, Jhang, Multan, and Vehari were characterized as the top three polluted cities in Pakistan when considering AquaTerra DTB AOD products; for PM1, PM2.5, and PM10 Lahore, Gujranwala, and Okara were the top three; for tropospheric NO2 VCD Lahore, Rawalpindi, and Islamabad and for PBL SO2 VCD Lahore, Mirpur, and Gujranwala. The results demonstrate that Pakistan’s entire population has been exposed to high PM2.5 concentrations for many years, with a mean annual value of 54.7 μg/cu. m, over all Pakistan from 2003 to 2020. This value exceeds Pakistan’s National Environmental Quality Standards (Pak-NEQS, i.e., <15 μg/cu. m annual mean) for ambient air defined by the Pakistan Environmental Protection Agency (Pak-EPA) as well as the WHO Interim Target-1 (i.e., mean annual PM2.5 <35 μg/cu. m). The spatial analyses of the concentrations of aerosols and trace gases in terms of population density, nighttime lights, land cover types, and fire location data, and the PSCF analysis indicate that Pakistan’s air quality is strongly affected by anthropogenic sources inside of Pakistan, with contributions from surrounding countries. Statistically significant positive (increasing) trends in PM1, PM2.5, PM10, tropospheric NO2 VCD, and SO2 VCD were observed in ~89%, ~67%, ~48%, 91%, and ~88% of the Pakistani cities (80 cities), respectively. This comprehensive analysis of aerosol and trace gas levels, their characteristics in spatio-temporal domains, and their trends over Pakistan, is the first of its kind. Results will be helpful to the Ministry of Climate Change (Government of Pakistan), Pak-EPA, SUPARCO (Pakistan Space and Upper Atmosphere Research Commission), policymakers, and the local research community to mitigate air pollution and its effects on human health.

Muhammad Bilal↗
NASA NTRS2023

Retrieval of Aerosol Optical Properties From GOCI-II Observations: Continuation of Long-Term Geostationary Aerosol Monitoring Over East Asia

Since the Geostationary Ocean Color Imager (GOCI) was successfully launched in 2010, the GOCI Yonsei aerosol retrieval (YAER) algorithm has been continuously updated to retrieve hourly aerosol optical properties. GOCI-II has 4 more channels including UV, finer spatial resolution (250 m), and daily full disk coverage as compared to GOCI, and was launched in February 2020, onboard the GEO-KOMPSAT-2B (GK-2B) satellite. In this study, we extended the YAER algorithm to GOCI-II data based on its improved performance in many aspects and present the first results of aerosol optical properties retrieved from GOCI-II data. Utilizing the overlapping period between the GOCI-II and GOCI in geostationary Earth orbit, we present GOCI-II aerosol retrievals for high aerosol-loading cases over East Asia and show that these have a consistent spatial distribution with those from GOCI. Furthermore, GOCI-II provides AOD at an even higher spatial resolution, revealing finer changes in aerosol concentrations. Validation results for one year data show that the GOCI-II AOD has a correlation coefficient of 0.83 and a ratio within the expected error (EE) of 59.4 % when compared with the aerosol robotic network (AERONET) data. We compared statistical metrics for the GOCI and GOCI-II AODs to assess the consistency between the two datasets. In addition, it was found that there is a strong correlation between the two datasets from the comparison of gridded GOCI and GOCI-II AOD products. It is expected that data from GOCI-II will continue long-term aerosol records with high accuracy that can be used to address air-quality issues over East Asia.

AOD↗
DOE OSTI2020

Spatial Mapping of Riverbed Grain-Size Distribution Using Machine Learning

Recent alluvial sediments in riverbeds play a significant role in controlling hydrologic exchange flows (HEFs) in river systems. The alluvial layer is usually associated with strong heterogeneity in physical properties (e.g., permeability and hydraulic conductivity), which affects local HEFs and therefore biogeochemical processes. The spatial distribution of these physical properties needs to be determined to inform the numerical models used to reveal the realistic hydro-biogeochemical behaviors. Such information can be obtained based on the intrinsic link between sediment grain-size distribution and hydraulic properties where sediment texture information is available. However, grain-size measurements are usually spatially sparse and do not have adequate coverage and resolution, particularly for a relatively large domain such as the Hanford Reach of the Columbia River. In this paper, we adopted machine learning (ML) approaches for categorizing and mapping the spatial distributions of riverbed substrate grain size and filling in missing areas of substrate data using the ML models along the reach. Such ML models for substrate size mapping were trained at 13,372 locations using measured substrate sizes along with observed and simulated attributes, including bathymetric attributes (e.g., elevation, slope, and aspect ratio) from LIDAR and bathymetric surveys, and hydrodynamic properties (e.g., water depth, velocity, shear stress, and their statistical moments). An ensemble bagging-based ML technique, Random Forest, was adopted to identify the most influential factors as predictors to develop the predictive models with over-fitting issues addressed. The models were evaluated with respect to each individual substrate size class and the lumped group, and then used to generate the final substrate size maps covering all the grid cells in the numerical modeling domain.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1975

Study to define unsteady flow fields and their statistical characteristics

Preliminary estimates of space shuttle fluctuating pressure environments were made based on analyses of wind tunnel data, and empirical prediction techniques. Particular emphasis was given to the external tank and solid rocket boosters for the transonic speed regime during launch of a parallel-burn space shuttle configuration. Predicted environments are presented as space-averaged zonal profiles with progressive shading from zone to zone to illustrate spatial variations in the magnitude of the fluctuating pressure coefficient over the surfaces of the external tank and solid rocket boosters. Predictions are provided for the transonic Mach number range from 0.8 equal to or less than M sub infinity equal to or less than 1.5, and for supersonic Mach numbers of 2.0 and 3.0.

Robertson, J. E.↗