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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Kinetic energy equations for the average-passage equation system

Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

Johnson, Richard W.↗
NASA NTRS1990

On the average rate of growth in sunspot number and the size of the sunspot cycle

The average rate of growth in sunspot number over selected time intervals and the maximum average value as they both relate to the size of the cycle are examined, in order to predict the size of cycle 22. The predictions are compared with those of Wilson (1990) to determine whether a consensus is apparent. The average rate of growth during the ascending portion of the sunspot cycle, defined as the difference in smoothed sunspot number values between elapsed time t and sunspot minimum divided by t, is shown to correlate with the size of the sunspot cycle, especially for t greater or equal to 18 months. The maximum value of the average rate of growth is also shown to highly correlate (r = 0.98) with the size of the cycle. Using 4.5 as the maximum value of the average rate of growth, a lower limit for R(M) is estimated. The results show that the findings are consistent with the previous single variate predictions for R(M) for cycle 22.

Wilson, Robert M.↗
NASA NTRS1991

Global average ozone change from November 1978 to May 1990

A recent recalibration and reprocessing of the total ozone mapping spectrometer (TOMS) data have made possible a new determination of the global average total ozone decrease of 3.5 percent over the 11-year period, January 1, 1979, to December 31, 1989, with a 2 sigma error of 1.4 percent. The revised TOMS ozone trend data are in agreement, within error limits, with the average of 39 ground-based Dobson stations and with the world standard Dobson spectrometer 83 at Mauna Loa, Hawaii. Superimposed on the 11-year ozone trend is a possible solar cycle effect, quasi-biennial oscillation (QBO), annual, and semiannual cycles. Using solar 10-7-cm flux data and 30-mbar Singapore wind data (QBO), a time series has been constructed that reproduces the long-term behavior of the globally averaged ozone. Removal of the apparent solar cycle effect from the global average reduces the net ozone loss to 2.66 + or - 1.4 percent per decade. The precise value of the global average ozone trend depends on the latitude range selected, with ranges greater than + or - 69 emphasizing the larger variations at high latitudes.

Herman, J. R.↗
NASA NTRS1992

Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem

Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.

Deissler, Robert G.↗
NASA NTRS1992

Are repeaters responsible for gamma-ray burst average V/V(max) less than 0.5?

We show that gamma-ray bursts, observed by the Konus experiment on Venera 11 and Venera 12, from the three identified sources of short-term repeating bursts have a very low average V/V(max) of only 0.17 +/- 0.10 and are very important contributors to the low average V/V(max) of 0.43 +/- 0.03 found from the entire Konus burst sample. We further point out that the expected number of additional, as yet unidentified, repeating sources is quite sufficient to account for the low Konus average V/V(max), assuming that the average V/V(max) for bursts from all other sources is 0.5. Thus we suggest that the class of short-term repeating gamma-ray burst sources, as yet only partially identified, are a high-luminosity population that could be responsible for the values of average V/V(max) less than 0.5 also found by the BATSE, SMM, and other gamma-ray burst experiments. We note, however, that repeating bursts cannot as yet be identified solely by their spectral and temporal properties.

Lingenfelter, R. E.↗
NASA NTRS1995

Determining GPS average performance metrics

Analytic and semi-analytic methods are used to show that users of the GPS constellation can expect performance variations based on their location. Specifically, performance is shown to be a function of both altitude and latitude. These results stem from the fact that the GPS constellation is itself non-uniform. For example, GPS satellites are over four times as likely to be directly over Tierra del Fuego than over Hawaii or Singapore. Inevitable performance variations due to user location occur for ground, sea, air and space GPS users. These performance variations can be studied in an average relative sense. A semi-analytic tool which symmetrically allocates GPS satellite latitude belt dwell times among longitude points is used to compute average performance metrics. These metrics include average number of GPS vehicles visible, relative average accuracies in the radial, intrack and crosstrack (or radial, north/south, east/west) directions, and relative average PDOP or GDOP. The tool can be quickly changed to incorporate various user antenna obscuration models and various GPS constellation designs. Among other applications, tool results can be used in studies to: predict locations and geometries of best/worst case performance, design GPS constellations, determine optimal user antenna location and understand performance trends among various users.

Moore, G. V.↗
NASA NTRS1995

The effect of sensor sheltering and averaging techniques on wind measurements at the Shuttle Landing Facility

This document presents results of a field study of the effect of sheltering of wind sensors by nearby foliage on the validity of wind measurements at the Space Shuttle Landing Facility (SLF). Standard measurements are made at one second intervals from 30-feet (9.1-m) towers located 500 feet (152 m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. A companion study, Merceret (1995), quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. This work examines the effect of nearby foliage on the accuracy of the measurements made by any one sensor, and the effects of averaging on interpretation of the measurements. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions as a function of distance from the obstructing foliage. Appropriate statistics were computed. The results suggest that accurate measurements require foliage be cut back to OFCM standards. Analysis of averaging techniques showed that there is no significant difference between vector and scalar averages. Longer averaging periods reduce measurement error but do not otherwise change the measurement in reasonably steady flow regimes. In rapidly changing conditions, shorter averaging periods may be required to capture trends.

Merceret, Francis J.↗
NASA NTRS1996

The Average Intensity and Spectral Evolution of Batse Cosmic Gamma-Ray Bursts

Statistical studies of BATSE gamma-ray bursts are presented: we average the time profiles, aligning the events at their highest peaks. Using the time histories in different energy channels, we summarize the general features of the average intensity and spectral evolution of gamma-ray bursts (GRBS) and compare the average evolution of bright and dim events. While no differences are found between the average intensity histories, the average hardness ratio histories demonstrate a hardness/brightness correlation. The observed lack of differences between the intensity histories of bright and dim bursts is incompatible with cosmological time dilation effects predicted by simple cosmological models. The combined results of no intensity history difference but a hardness history difference between bright and dim bursts places constraints on galactic models for the origin of GRBS.

Mitrofanov, Igor G.↗
NASA NTRS2000

Three Averaging Techniques for Reduction of Antenna Temperature Variance Measured by a Dicke Mode, C-Band Radiometer

As new radiometer technologies provide the possibility of greatly improved spatial resolution, their performance must also be evaluated in terms of expected sensitivity and absolute accuracy. As aperture size increases, the sensitivity of a Dicke mode radiometer can be maintained or improved by application of any or all of three digital averaging techniques: antenna data averaging with a greater than 50% antenna duty cycle, reference data averaging, and gain averaging. An experimental, noise-injection, benchtop radiometer at C-band showed a 68.5% reduction in Delta-T after all three averaging methods had been applied simultaneously. For any one antenna integration time, the optimum 34.8% reduction in Delta-T was realized by using an 83.3% antenna/reference duty cycle.

Mackenzie, Anne I.↗
NASA NTRS1997

Steady-State Pursuit Is Driven by Object Motion Rather Than the Vector Average of Local Motions

We have previously shown that humans can pursue the motion of objects whose trajectories can be recovered only by spatio-temporal integration of local motion signals. We now explore the integration rule used to derive the target-motion signal driving pursuit. We measured the pursuit response of 4 observers (2 naive) to the motion of a line-figure diamond viewed through two vertical bar apertures (0.2 cd/square m). The comers were always occluded so that only four line segments (93 cd/square m) were visible behind the occluding foreground (38 cd/square m). The diamond was flattened (40 & 140 degree vertex angles) such that vector averaging of the local normal motions and vertical integration (e.g. IOC) yield very I or different predictions, analogous to using a Type II plaid. The diamond moved along Lissajous-figure trajectories (Ax = Ay = 2 degrees; TFx = 0.8 Hz; TFy = 0.4 Hz). We presented only 1.25 cycles and used 6 different randomly interleaved initial relative phases to minimize the role of predictive strategies. Observers were instructed to track the diamond and reported that its motion was always coherent (unlike type II plaids). Saccade-free portions of the horizontal and vertical eye-position traces sampled at 240 Hz were fit by separate sinusoids. Pursuit gain with respect to the diamond averaged 0.7 across subjects and directions. The ratio of the mean vertical to horizontal amplitude of the pursuit response was 1.7 +/- 0.7 averaged across subjects (1SD). This is close to the prediction of 1.0 from vertical motion-integration rules, but far from 7.7 predicted by vector averaging and infinity predicted by segment- or terminator-tracking strategies. Because there is no retinal motion which directly corresponds to the diamond's motion, steady-state pursuit of our "virtual" diamond is not closed-loop in the traditional sense. Thus, accurate pursuit is unlikely to result simply from local retinal negative feedback. We conclude that the signal driving steady-state pursuit is not the vector average of local motion signals, but rather a more vertical estimate of object motion, derived in extrastriate cortical areas beyond V1, perhaps NIT or MST.

Stone, Leland S.↗
NASA NTRS2002

A Stochastic Model of Space-Time Variability of Tropical Rainfall: I. Statistics of Spatial Averages

Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by rain decreases, as the size of a pixel becomes smaller. This means that within what looks like a patch of rainy area in a coarse resolution view with larger pixel size, one finds clusters of rainy and dry patches when viewed on a finer scale. The model makes definite predictions about how these and other related statistics depend on the pixel size. These predictions were found to agree well with data. In a subsequent second part of the work we plan to test the model with rain gauge data collected during the TRMM (Tropical Rainfall Measuring Mission) ground validation campaign.

Kundu, Prasun K.↗
NASA NTRS2004

The Average Quality Factors by TEPC for Charged Particles

The quality factor used in radiation protection is defined as a function of LET, Q(sub ave)(LET). However, tissue equivalent proportional counters (TEPC) measure the average quality factors as a function of lineal energy (y), Q(sub ave)(Y). A model of the TEPC response for charged particles considers energy deposition as a function of impact parameter from the ion s path to the volume, and describes the escape of energy out of sensitive volume by delta-rays and the entry of delta rays from the high-density wall into the low-density gas-volume. A common goal for operational detectors is to measure the average radiation quality to within accuracy of 25%. Using our TEPC response model and the NASA space radiation transport model we show that this accuracy is obtained by a properly calibrated TEPC. However, when the individual contributions from trapped protons and galactic cosmic rays (GCR) are considered; the average quality factor obtained by TEPC is overestimated for trapped protons and underestimated for GCR by about 30%, i.e., a compensating error. Using TEPC's values for trapped protons for Q(sub ave)(y), we obtained average quality factors in the 2.07-2.32 range. However, Q(sub ave)(LET) ranges from 1.5-1.65 as spacecraft shielding depth increases. The average quality factors for trapped protons on STS-89 demonstrate that the model of the TEPC response is in good agreement with flight TEPC data for Q(sub ave)(y), and thus Q(sub ave)(LET) for trapped protons is overestimated by TEPC. Preliminary comparisons for the complete GCR spectra show that Q(sub ave)(LET) for GCR is approximately 3.2-4.1, while TEPC measures 2.9-3.4 for QQ(sub ave)(y), indicating that QQ(sub ave)(LET) for GCR is underestimated by TEPC.

Kim, Myung-Hee Y.↗
NASA NTRS2007

Comparison of Integrated Radiation Transport Models with TEPC Measurements for the Average Quality Factors in Spaceflights

The purpose of this work is to test our theoretical model for the interpretation of radiation data measured in space. During the space missions astronauts are exposed to the complex field of radiation type and kinetic energies from galactic cosmic rays (GCR), trapped protons, and sometimes solar particle events (SPEs). The tissue equivalent proportional counter (TEPC) is a simple time-dependent approach for radiation monitoring for astronauts on board the International Space Station. Another and a newer approach to Microdosimetry is the use of silicon-on-insulator (SOI) technology launched on the MidSTAR-1 mission in low Earth orbit (LEO). In the radiation protection practice, the average quality factor of a radiation field is defined as a function of linear energy transfer (LET), Q(sub ave)(LET). However, TEPC measures the average quality factor as a function of the lineal energy y, Q(sub ave)(y), defined as the average energy deposition in a volume divided by the average chord length of the volume. Lineal energy, y, deviates from LET due to energy straggling, delta-ray escape or entry, and nuclear fragments produced in the detector volume. Monte Carlo track structure simulation was employed to obtain the response of a TEPC irradiated with charged particle for an equivalent site diameter of 1 micron of wall-less counter. The calculated data of the energy absorption in the wall-less counter were compiled for various y values for several ion types at various discrete projectile energy levels. For the simulation of TEPC response from the mixed radiation environments inside a spacecraft, such as, Space Shuttle and International Space Station, the complete microdosimetric TEPC response, f( y, E, Z), were calculated with the Monte Carlo theoretical results by using the first order Lagrangian interpolation for a monovariate function at a given y value (y = 0.1 keV/micron 5000 keV/micron) at any projectile energy level (E = 0.01 MeV/u to 50,000 MeV/u) of each specific radiation type (Z = 1 to 28). Because the anomalous response has been observed at large event sizes in the experiment due to the escape of energy out of sensitive volume by delta-rays and the entry of delta-rays from the high-density wall into the low-density gas-volume cavity, Monte Carlo simulation was also made for the response of a walled-TEPC with wall thickness 2 mm and density 1 g/cm(exp 3). The radius of cavity was set to 6.35 mm and a gas density 7.874 x 10(exp -5) g/cm(exp 3). The response of the walled- and the wall-less counters were compared. The average quality factor Q(sub ave)(y) for trapped protons on STS-89 demonstrated the good agreement between the model calculations and flight TEPC data as shown. Using an integrated space radiation model (this includes the transport codes HZETRN and BRYNTRN, the quantum nuclear interaction model QMSFRG) and the resultant response distribution functions of walled-TEPC from Monte-Carlo track simulations, we compared model calculations with walled-TEPC measurements from NASA missions in LEO and made predictions for the lunar and the Mars missions. The Q(sub ave)(y) values for the trapped or the solar protons ranged from 1.9-2.5. This over-estimates the Qave(LET) values which ranged from 1.4-1.6. Both quantities increase with shield thickness due to nuclear fragmentation. The Q(sub ave)(LET) for the complete GCR spectra was found to be 3.5-4.5, while flight TEPCs measured 2.9-3.4 for Q(sub ave)(y). The GCR values are decreasing with the shield thickness. Our analysis for a proper interpretation of data supports the use of TEPCs for monitoring space radiation environment.

Kim, Myung-Hee Y.↗
NASA NTRS1990

Threaded average temperature thermocouple

A threaded average temperature thermocouple 11 is provided to measure the average temperature of a test situs of a test material 30. A ceramic insulator rod 15 with two parallel holes 17 and 18 through the length thereof is securely fitted in a cylinder 16, which is bored along the longitudinal axis of symmetry of threaded bolt 12. Threaded bolt 12 is composed of material having thermal properties similar to those of test material 30. Leads of a thermocouple wire 20 leading from a remotely situated temperature sensing device 35 are each fed through one of the holes 17 or 18, secured at head end 13 of ceramic insulator rod 15, and exit at tip end 14. Each lead of thermocouple wire 20 is bent into and secured in an opposite radial groove 25 in tip end 14 of threaded bolt 12. Resulting threaded average temperature thermocouple 11 is ready to be inserted into cylindrical receptacle 32. The tip end 14 of the threaded average temperature thermocouple 11 is in intimate contact with receptacle 32. A jam nut 36 secures the threaded average temperature thermocouple 11 to test material 30.

Ward, Stanley W.↗
NASA NTRS2008

On the Relationship between Solar Wind Speed, Earthward-Directed Coronal Mass Ejections, Geomagnetic Activity, and the Sunspot Cycle Using 12-Month Moving Averages

For 1996 .2006 (cycle 23), 12-month moving averages of the aa geomagnetic index strongly correlate (r = 0.92) with 12-month moving averages of solar wind speed, and 12-month moving averages of the number of coronal mass ejections (CMEs) (halo and partial halo events) strongly correlate (r = 0.87) with 12-month moving averages of sunspot number. In particular, the minimum (15.8, September/October 1997) and maximum (38.0, August 2003) values of the aa geomagnetic index occur simultaneously with the minimum (376 km/s) and maximum (547 km/s) solar wind speeds, both being strongly correlated with the following recurrent component (due to high-speed streams). The large peak of aa geomagnetic activity in cycle 23, the largest on record, spans the interval late 2002 to mid 2004 and is associated with a decreased number of halo and partial halo CMEs, whereas the smaller secondary peak of early 2005 seems to be associated with a slight rebound in the number of halo and partial halo CMEs. Based on the observed aaM during the declining portion of cycle 23, RM for cycle 24 is predicted to be larger than average, being about 168+/-60 (the 90% prediction interval), whereas based on the expected aam for cycle 24 (greater than or equal to 14.6), RM for cycle 24 should measure greater than or equal to 118+/-30, yielding an overlap of about 128+/-20.

Wilson, Robert M.↗
NASA NTRS2018

Average Versus High Surface Ozone Levels over the Continental USA: Model Bias, Background Influences, and Interannual Variability

US background ozone (O3) includes O3 produced from anthropogenic O3 precursors emitted outside of the USA, from global methane, and from any natural sources. Using a suite of sensitivity simulations in the GEOS-Chem global chemistry transport model, we estimate the influence from individual background sources versus US anthropogenic sources on total surface O3 over 10 continental US regions from 2004 to 2012. Evaluation with observations reveals model biases of +0-19ppb in seasonal mean maximum daily 8h average (MDA8) O3, highest in summer over the eastern USA. Simulated high-O3 events cluster too late in the season. We link these model biases to excessive regional O3 production (e.g., US anthropogenic, biogenic volatile organic compounds (BVOCs), and soil NOx, emissions), or coincident missing sinks. On the 10 highest observed O3 days during summer (O3_top10obs_JJA), US anthropogenic emissions enhance O3 by 5-11ppb and by less than 2ppb in the eastern versus western USA. The O3 enhancement from BVOC emissions during summer is 1-7 ppb higher on O3_top10obs_JJA days than on average days, while intercontinental pollution is up to 2ppb higher on average versus on O3_top10obs_JJA days. During the summers of 2004-2012, monthly regional mean US background O3 MDA8 levels vary by up to 15ppb from year to year. Observed and simulated summertime total surface O3 levels on O3_top10obs_JJA days decline by 3ppb (averaged over all regions) from 2004-2006 to 2010-2012, reflecting rising US background (+2ppb) and declining US anthropogenic O3 emissions (6ppb) in the model. The model attributes interannual variability in US background O3 on O3_top10obs days to natural sources, not international pollution transport. We find that a 3-year averaging period is not long enough to eliminate interannual variability in background O3 on the highest observed O3 days.

Guo, Jean J.↗
DOE OSTI2024

Average and Marginal Capacity Credit Values of Renewable Energy and Battery Storage in the United States Power System

As deployment of renewable resources and storage continue to significantly grow in the coming decades, these technologies will play increasingly important roles in maintaining power systems' resource adequacy. Few analyses so far offer comprehensive comparisons of forward-looking average and marginal capacity credits of variable renewable energy and storage in the U.S. interconnections across a wide range of possible futures. To fill this research gap, we quantify the average and marginal capacity credits of solar PV, onshore and offshore wind, and batteries between 2026 and 2050 across the U.S power systems to examine the temporal trends, spatial patterns, and trade-offs between these two capacity accreditation approaches. Across technologies, capacity credits of solar PV most clearly follow downward trends over time, reflecting the significant rise in solar PV generation share as the grid decarbonizes. While battery storages' generation shares also rise significantly over time, their capacity credits always remain stably high due to their capabilities to be dispatched strategically during critical periods to maintain reliability. On the other hand, capacity credits of wind technologies in general follow slight upward trends as their generation shares level off. There are strong spatial variabilities of both average and marginal capacity credits across technologies, but capacity credits of solar PV displaying the most obvious spatial patterns with high capacity credits concentrating in wind-rich, solar-poor regions in SPP, PJM, and MISO, suggesting potential reliability benefits of interconnection-wide planning for renewable energy deployments. Additionally, except for offshore wind, average capacity credits of all other renewable technologies tend to be higher than their marginal capacity credits, indicating that existing renewable resources tend to be accredited higher than new resources at almost any time.

25 ENERGY STORAGE↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗