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At least 145 records · Page 8

GPS-Based Navigation and Orbit Determination for the AMSAT Phase 3D Satellite

This paper summarizes the results of processing GPS data from the AMSAT Phase 3D (AP3) satellite for real-time navigation and post-processed orbit determination experiments. AP3 was launched into a geostationary transfer orbit (GTO) on November 16, 2000 from Kourou, French Guiana, and then was maneuvered into its HEO over the next several months. It carries two Trimble TANS Vector GPS receivers for signal reception at apogee and at perigee. Its spin stabilization mode currently makes it favorable to track GPS satellites from the backside of the constellation while at perigee, and to track GPS satellites from below while at perigee. To date, the experiment has demonstrated that it is feasible to use GPS for navigation and orbit determination in HEO, which will be of great benefit to planned and proposed missions that will utilize such orbits for science observations. It has also shown that there are many important operational considerations to take into account. For example, GPS signals can be tracked above the constellation at altitudes as high as 58000 km, but sufficient amplification of those weak signals is needed. Moreover, GPS receivers can track up to 4 GPS satellites at perigee while moving as fast as 9.8 km/sec, but unless the receiver can maintain lock on the signals long enough, point solutions will be difficult to generate. The spin stabilization of AP3, for example, appears to cause signal levels to fluctuate as other antennas on the satellite block the signals. As a result, its TANS Vectors have been unable to lock on to the GPS signals long enough to down load the broadcast ephemeris and then generate position and velocity solutions. AP3 is currently in its eclipse season, and thus most of the spacecraft subsystems have been powered off. In Spring 2002, they will again be powered up and AP3 will be placed into a three-axis stabilization mode. This will significantly enhance the likelihood that point solutions can be generated, and perhaps more important, that the receiver clock can be synchronized to GPS time. This is extremely important for real-time and post-processed orbit determination, where removal of receiver clock bias from the data time tags is needed, for time-tagging of science observations. Current analysis suggests that the inability to generate point solutions has allowed the TANS Vector clock bias to drift freely, being perhaps as large as 5-7 seconds by October, 2001, thus causing up to 50 km of along-track orbit error. The data collected in May, 2002 while in three-axis stabilized mode should provide a significant improvement in the orbit determination results.

Davis, George↗

Evaluation of the Relative Contribution of Observing Systems in Reanalyses: Aircraft Temperature Bias and Analysis Innovations

Reanalyses have become important sources of data in weather and climate research. While observations are the most crucial component of the systems, few research projects consider carefully the multitudes of assimilated observations and their impact on the results. This is partly due to the diversity of observations and their individual complexity, but also due to the unfriendly nature of the data formats. Here, we discuss the NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) and a companion dataset, the Gridded Innovations and Observations (GIO). GIO is simply a post-processing of the assimilated observations and their innovations (forecast error and analysis error) to a common spatio-temporal grid, following that of the MERRA analysis fields. This data includes in situ, retrieved and radiance observations that are assimilated and used in the reanalysis. While all these disparate observations and statistics are in a uniform easily accessible format, there are some limitations. Similar observations are binned to the grid, so that multiple observations are combined in the gridding process. The data is then implicitly thinned. Some details in the meta data may also be lost (e.g. aircraft or station ID). Nonetheless, the gridded observations should provide easy access to all the observations input to the reanalysis. To provide an example of the GIO data, a case study evaluating observing systems over the United States and statistics is presented, and demonstrates the evaluation of the observations and the data assimilation. The GIO data is used to collocate 200mb Radiosonde and Aircraft temperature measurements from 1979-2009. A known warm bias of the aircraft measurements is apparent compared to the radiosonde data. However, when larger quantities of aircraft data are available, they dominate the analysis and the radiosonde data become biased against the forecast. When AMSU radiances become available the radiosonde and aircraft analysis and forecast error take on an annual cycle. While this supports results of previous work that recommend bias corrections for the aircraft measurements, the interactions with AMSU radiances will also require further investigation. This also provides an example for reanalysis users in examining the available observations and their impact on the analysis. GIO data is presently available alongside the MERRA reanalysis.

Bosilovich, Michael G.↗

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↗

Comparison of three thrust calculation methods using in-flight thrust data

The gross thrust of an experimental airplane was determined by each method using the same flight maneuvers and generally the same data parameters. Coefficients determined from thrust stand calibrations for each of the three methods were then extrapolated to cruise flight conditions. The values of total aircraft gross thrust calculated by the three methods for cruise flight conditions agreed within + or - 3 percent. The disagreement in the values of thrust calculated by the different techniques manifested itself as a bias in the data. There was little scatter (0.5 percent) for the thrust levels examined in flight.

Hughes, D. L.↗

An empirical determination of the effects of sea state bias on Seasat altimetry

A linear empirical model has been developed for the correction of sea state bias effects, in Seasat altimetry data altitude measurements, that are due to (1) electromagnetic bias caused by the fact that ocean wave troughs reflect the altimeter signal more strongly than the crests, shifting the apparent mean sea level toward the wave troughs, and (2) an independent instrument-related bias resulting from the inability of height corrections applied in the ground processor to compensate for simplifying assumptions made for the processor aboard Seasat. After applying appropriate corrections to the altimetry data, an empirical model for the sea state bias is obtained by differencing significant wave height and height measurements from coincident ground tracks. Height differences are minimized by solving for the coefficient of a linear relationship between height differences and wave height differences that minimize the height differences. In more than 50% of the 36 cases examined, 7% of the value of significant wave height should be subtracted for sea state bias correction.

Born, G. H.↗

Carrier phase ambiguity resolution for the Global Positioning System applied to geodetic baselines up to 2000 km

A technique for resolving the ambiguities in the GPS carrier phase data (which are biased by an integer number of cycles) is described which can be applied to geodetic baselines up to 2000 km in length and can be used with dual-frequency P code receivers. The results of such application demonstrated that a factor of 3 improvement in baseline accuracy could be obtained, giving centimeter-level agreement with coordinates inferred by very-long-baseline interferometry in the western United States. It was found that a method using pseudorange data is more reliable than one using ionospheric constraints for baselines longer than 200 km. It is recommended that future GPS networks have a wide spectrum of baseline lengths (ranging from baselines shorter than 100 km to those longer than 1000 km) and that GPS receivers be used which can acquire dual-frequency P code data.

Blewitt, Geoffrey↗

Trends in the Sea Ice Cover Using Enhanced and Compatible AMSR-E, SSM/I and SMMR Data

Arguably, the most remarkable manifestation of change in the polar regions is the rapid decline (of about -10 %/decade) in the Arctic perennial ice cover. Changes in the global sea ice cover, however, are more modest, being slightly positive in the Southern Hemisphere and slightly negative in the Northern Hemisphere, the significance of which has not been adequately assessed because of unknown errors in the satellite historical data. We take advantage of the recent and more accurate AMSR-E data to evaluate the true seasonal and interannual variability of the sea ice cover, assess the accuracy of historical data, and determine the real trend. Consistently derived ice concentrations from AMSR-E, SSM/I, and SMMR data were analyzed and a slight bias is observed between AMSR-E and SSM/I data mainly because of differences in resolution. Analysis of the combine SMMR, SSM/I and AMSR-E data set, with the bias corrected, shows that the trends in extent and area of sea ice in the Arctic region is -3.4 +/- 0.2 and -4.0 +/- 0.2 % per decade, respectively, while the corresponding values for the Antarctic region is 0.9 +/- 0.2 and 1.7 .+/- 0.3 % per decade. The higher resolution of the AMSR-E provides an improved determination of the location of the ice edge while the SSM/I data show an ice edge about 6 to 12 km further away from the ice pack. Although the current record of AMSR-E is less than 5 years, the data can be utilized in combination with historical data for more accurate determination of the variability and trends in the ice cover.

Comiso, Josefino C.↗

Exploration Analysis of Carbon Dioxide Levels and Ultrasound Measures of the Eye During ISS Missions

Enhanced screening for the Visual Impairment/Intracranial Pressure (VIIP) Syndrome, including in-flight ultrasound, was implemented in 2010 to better characterize the changes in vision observed in some long-duration crewmembers. Suggested possible risk factors for VIIP include cardiovascular changes, diet, anatomical and genetic factors, and environmental conditions. As a potent vasodilator, carbon dioxide (CO (sub 2)), which is chronically elevated on the International Space Station (ISS) relative to typical indoor and outdoor ambient levels on Earth, seems a plausible contributor to VIIP. In an effort to understand the possible associations between CO (sub 2) and VIIP, this study analyzes the relationship between ambient CO (sub 2) levels on ISS and ultrasound measures of the eye obtained from ISS fliers. CO (sub 2) measurements will be pulled directly from Operational Data Reduction Complex for the Lab and Node 3 major constituent analyzers (MCAs) on ISS or from sensors located in the European Columbus module, as available. CO (sub 2) measures between ultrasound sessions will be summarized using standard time series class metrics in MATLAB including time-weighted means and variances. Cumulative CO (sub 2) exposure metrics will also be developed. Regression analyses will be used to quantify the relationships between the CO (sub 2) metrics and specific ultrasound measures. Generalized estimating equations will adjust for the repeated measures within individuals. Multiple imputation techniques will be used to adjust for any possible biases in missing data for either CO (sub 2) or ultrasound measures. These analyses will elucidate the possible relationship between CO (sub 2) and changes in vision and also inform future analysis of inflight VIIP data.

Young, M.↗

Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter

An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.

Klein, V.↗

Evaluation of an infrared horizon scanner bias determination algorithm for earth-oriented spacecraft

An algorithm for estimating infrared horizon scanner biases for earth-oriented spacecraft is presented. A mathematical description of the proposed algorithm is given, and the algorithm is evaluated for use by two earth-oriented spacecraft: the Applications Explorer Missions-A/Heat Capacity Mapping Mission (AEM-A/HCMM) and Seasat-A. The results of this study indicate that scanner alignment and calibration errors appear as nearly constant biases in the scanner pitch and roll data and that these constant biases can be estimated to within 0.05 degree for AEM-A and 0.03 degree for Seasat-A.

Hotovy, S. G.↗

Characterization of Space Shuttle Reusable Rocket Motor Static Test Stand Thrust Measurements

Space Shuttle Reusable Solid Rocket Motors (RSRM) are static tested at two ATK Thiokol Propulsion facilities in Utah, T-24 and T-97. The newer T-97 static test facility was recently upgraded to allow thrust measurement capability. All previous static test motor thrust measurements have been taken at T-24; data from these tests were used to characterize thrust parameters and requirement limits for flight motors. Validation of the new T-97 thrust measurement system is required prior to use for official RSRM performance assessments. Since thrust cannot be measured on RSRM flight motors, flight motor measured chamber pressure and a nominal thrust-to-pressure relationship (based on static test motor thrust and pressure measurements) are used to reconstruct flight motor performance. Historical static test and flight motor performance data are used in conjunction with production subscale test data to predict RSRM performance. The predicted motor performance is provided to support Space Shuttle trajectory and system loads analyses. Therefore, an accurate nominal thrust-to-pressure (F/P) relationship is critical for accurate RSRM flight motor performance and Space Shuttle analyses. Flight Support Motors (FSM) 7, 8, and 9 provided thrust data for the validation of the T-97 thrust measurement system. The T-97 thrust data were analyzed and compared to thrust previously measured at T-24 to verify measured thrust data and identify any test-stand bias. The T-97 FIP data were consistent and within the T-24 static test statistical family expectation. The FSMs 7-9 thrust data met all NASA contract requirements, and the test stand is now verified for future thrust measurements.

Mart L. Cook↗

Total Ionizing Dose Response of SDRAM, DDR2 and DDR3 Memories

Total Ionizing Dose response (ID) of SDRAM (Synchronous Dynamic Random Access Memory), DDR2 (Double Data Rate2) and DDR3 (Double Data Rate3) memories is reported in static bias, and auto refresh modes. Data analysis reveals some types of memory have significant increases in stuck bits during TID exposure when refreshed.

Amrbar, Mehran↗

The Updated GEO Population for ORDEM 3.1

The limited availability of data for satellite fragmentations and debris in the geosynchronous orbit (GEO) region creates challenges to building accurate models for the orbital debris environment at such altitudes. Updated methods to properly incorporate and extrapolate measurement data have become a cornerstone of the GEO component in the newest version of the NASA Orbital Debris Engineering Model (ORDEM), ORDEM 3.1. For the GEO region, the Space Surveillance Network (SSN) catalog provides coverage down to a limit of approximately 1 m. A more statistically complete representation of the GEO population for smaller objects, which can pose a high risk to operational spacecraft, is thus dependent on dedicated observations by instruments optimized to observe debris smaller than the SSN cataloging threshold. For ORDEM 3.1, optical data from the Michigan Orbital DEbris Survey Telescope (MODEST) provided the input for building the GEO population down to approximately 30 cm (converting absolute magnitude to size). For smaller sizes, the size distribution of debris in the MODEST dataset was extrapolated down to 10 cm, and orbital parameters were estimated based on the orbits of the larger objects. When compared to previous versions of the model, significant improvements were made to the process of building the GEO population in ORDEM 3.1, both in the assessment of fragmentation debris in the data and assignment of orbital elements within the model. A so-called “debris ring filter,” based on a range of angles between an orbit’s angular momentum vector and that of the stable Laplace plane, was applied to the data to reduce biases from non- GEO objects, such as objects in a GEO-transfer orbit. In addition, a new approach was implemented to assign noncircular mean motions and eccentricities to the fragmentation debris observed by MODEST because the short observation window (5 min) in GEO limits orbit resolution to a circular orbit assumption for assigning orbital parameters. For ORDEM 3.1, non-circular orbital elements were assigned using relationships that were identified between mean motion and the angle between the orbit plane and the stable Laplace plane, as well as between mean motion and eccentricity, based on breakup clouds modeled by the NASA Standard Breakup Model. This approach has yielded a high-fidelity GEO model that has been validated with data from more recent MODEST observation campaigns.

Manis, A.↗

Comparison Of Downscaled CMIP5 Precipitation Datasets For Projecting Changes In Extreme Precipitation In The San Francisco Bay Area.

Water resource managers planning for the adaptation to future events of extreme precipitation now have access to high resolution downscaled daily projections derived from statistical bias correction and constructed analogs. We also show that along the Pacific Coast the Northern Oscillation Index (NOI) is a reliable predictor of storm likelihood, and therefore a predictor of seasonal precipitation totals and likelihood of extremely intense precipitation. Such time series can be used to project intensity duration curves into the future or input into stormwater models. However, few climate projection studies have explored the impact of the type of downscaling method used on the range and uncertainty of predictions for local flood protection studies. Here we present a study of the future climate flood risk at NASA Ames Research Center, located in South Bay Area, by comparing the range of predictions in extreme precipitation events calculated from three sets of time series downscaled from CMIP5 data: 1) the Bias Correction Constructed Analogs method dataset downscaled to a 1/8 degree grid (12km); 2) the Bias Correction Spatial Disaggregation method downscaled to a 1km grid; 3) a statistical model of extreme daily precipitation events and projected NOI from CMIP5 models. In addition, predicted years of extreme precipitation are used to estimate the risk of overtopping of the retention pond located on the site through simulations of the EPA SWMM hydrologic model. Preliminary results indicate that the intensity of extreme precipitation events is expected to increase and flood the NASA Ames retention pond. The results from these estimations will assist flood protection managers in planning for infrastructure adaptations.

Storm↗

Improved SIFTER v2 algorithm for long-term GOME-2A satellite retrievals of fluorescence with a correction for instrument degradation

Solar-induced fluorescence (SIF) data from satellites are increasingly used as a proxy for photosynthetic activity by vegetation, and as a constraint on gross primary production. Here we report on improvements in the algorithm to retrieve mid-morning (09:30 hrs local time) SIF estimates on the global scale from GOME-2 sensor on the Metop-A satellite (GOME-2A) for the period 2007-2019. Our new SIFTER (Sun-Induced Fluorescence of Terrestrial Ecosystems Retrieval) v2 algorithm improves over a previous version by using a narrower spectral window that avoids strong oxygen absorption and is less sensitive to water vapour absorption, by constructing stable reference spectra from a 6-year period (2007-2012) of atmospheric spectra over the Sahara, and by applying a latitude-dependent zero-level adjustment that accounts for biases in the data product. We generated stable, good-quality SIF retrievals between January 2007 and June 2013, when GOME-2A degradation in the near infrared was still limited. After the narrowing of the GOME-2A swath in July 2013, we characterized the throughput degradation of the level-1 data in order to derive reflectance corrections and apply these for the SIF retrievals between July 2013 and December 2018. SIFTER v2 data compares well with the independent NASA v2.8 data product. Especially in the evergreen tropics, SIFTER v2 no longer shows the underestimates against other satellite products that were seen in SIFTER v1. The new data product includes uncertainty estimates for individual observations, and is best used for mostly clear-sky scenes, and when spectral residuals remain below a certain spectral autocorrelation threshold. Our results support the use of SIFTER v2 data to be used as an independent constraint on photosynthetic activity on regional to global scales.

Solar-induced fluorescence (SIF)↗

Assessment of Geo-Kompsat-2A Atmospheric Motion Vector Data and Its Assimilation Impact in the GEOS Atmospheric Data Assimilation System

Korea’s second geostationary meteorological satellite, Geo-Kompsat-2A (Geostationary-Korean Multi-Purpose Satellite-2A, GK2A), was successfully launched on 4 December 2018. GK2Agenerates Atmospheric Motion Vectors (AMVs) every 10 min in the full disk area. This data hasbeen disseminated via Global Telecommunication System (GTS) since 25 October 2019. This articleevaluates the quality of GK2A AMVs in the Goddard Earth Observing System (GEOS) atmosphericdata assimilation system (ADAS). The data show slow wind speed biases at 200–300 hPa and 600–800hPa in the northern and southern hemispheres. These biases are caused by observation heightassignment errors near jet streams. The Equivalent Blackbody Temperature (EBBT) method of GK2Atends to assign clouds at higher altitude, which mainly causes slow wind speed biases, especially inthe lower atmosphere. The IR/WV intercept method of GK2A assigns clouds slightly lower in theatmospheric layers below the altitude of 400 hPa, which causes positive biases. Quality control (QC)criteria to select the most suitable GK2A AMV data for assimilation are presented based on thesequality assessments. A new QC criterion utilizing height errors within the GEOS ADAS is introducedto exclude data with slow wind speed biases and large errors. GEOS forecast accuracy is slightlyimproved after assimilating GK2A AMVs along with other conventional, radiance, and satellitewinds which include AMVs made by the Himawari-8 satellite in nearly the same observational areaof GK2A. Additionally, the present work shows that GEOS forecasts can be significantly improved,especially in the tropics and southern hemisphere after assimilating GK2A data in the absence ofHimawari-8 AMVs. This study demonstrates that GK2A AMV data is a valuable data source toenhance the robustness of GEOS ADAS.

Atmospheric Motion Vectors↗

Tropospheric Ozone Assessment Report: Tropospheric Ozone From 1877 to 2016, Observed Levels, Trends and Uncertainties

From the earliest observations of ozone in the lower atmosphere in the 19th century, both measurement methods and the portion of the globe observed have evolved and changed. These methods have different uncertainties and biases, and the data records differ with respect to coverage (space and time), information content, and representativeness. In this study, various ozone measurement methods and ozone datasets are reviewed and selected for inclusion in the historical record of background ozone levels, based on relationship of the measurement technique to the modern UV absorption standard, absence of interfering pollutants, representativeness of the well-mixed boundary layer and expert judgement of their credibility. There are significant uncertainties with the 19th and early 20th-century measurements related to interference of other gases. Spectroscopic methods applied before 1960 have likely underestimated ozone by as much as 11% at the surface and by about 24% in the free troposphere, due to the use of differing ozone absorption coefficients. There is no unambiguous evidence in the measurement record back to 1896 that typical mid-latitude background surface ozone values were below about 20 nmol mol–1, but there is robust evidence for increases in the temperate and polar regions of the northern hemisphere of 30–70%, with large uncertainty, between the period of historic observations, 1896–1975, and the modern period (1990–2014). Independent historical observations from balloons and aircraft indicate similar changes in the free troposphere. Changes in the southern hemisphere are much less. Regional representativeness of the available observations remains a potential source of large errors, which are difficult to quantify. The great majority of validation and intercomparison studies of free tropospheric ozone measurement methods use ECC ozonesondes as reference. Compared to UV-absorption measurements they show a modest (~1–5% ±5%) high bias in the troposphere, but no evidence of a change with time. Umkehr, lidar, and FTIR methods all show modest low biases relative to ECCs, and so, using ECC sondes as a transfer standard, all appear to agree to within one standard deviation with the modern UV-absorption standard. Other sonde types show an increase of 5–20% in sensitivity to tropospheric ozone from 1970–1995. Biases and standard deviations of satellite retrieval comparisons are often 2–3 times larger than those of other free tropospheric measurements. The lack of information on temporal changes of bias for satellite measurements of tropospheric ozone is an area of concern for long-term trend studies.

UV absorption standard↗

Prediction of electron concentration reductions in re-entry flow fields due to electrophilic liquid and water injection.

Discussion of an analytical model which leads to predictions of reductions in electron concentrations in reentry flow fields due to the injection of electrophilic liquids and water. The processes incorporated into the model are: penetration and breakup of the liquid jet, droplet acceleration and vaporization, expansion of the liquid spray due to droplet vaporization, electrophilic vapor diffusion, heterogeneous and homogeneous charged species recombination kinetics and homogeneous electron attachment kinetics. Spray boundary calculations are shown to be in good agreement with photographic observations of water and Freon E-3 sprays in wind tunnel tests of a scale model RAM C-III flight vehicle. Fixed-bias electrostatic probe data taken during the RAM C-III flight are interpreted in terms of effective jet penetration distances - which are shown to be consistent with calculations using the present model.

Pergament, H. S.↗