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NASA NTRS1973

The random coding bound is tight for the average code.

The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.

Gallager, R. G.↗

NASA NTRS1973

Total-pressure-tube averaging in pulsating flows.

A number of total-pressure tubes were tested in a nonsteady flow generator in which the fraction of period that pressure is a maximum is approximately 0.8, thereby simulating turbomachine-type flow conditions. The tests were performed at a pressure level of 1 bar, for Mach numbers up to near 1, and frequencies up to 3 kHz. Most of the tubes indicated a pressure which was higher than the true average. Organ-pipe resonances which further increased the indicated pressure were encountered within the tubes at discrete frequencies. There was no obvious combination of tube diameter, length, and/or geometry variation used in the tests which resulted in negligible averaging error. A pneumatic-type probe was found to measure true average pressure, and is suggested as a comparison instrument to determine whether nonlinear averaging effects are serious in unknown pulsation profiles.

Krause, L. N.↗

NASA NTRS1974

A review of averaging techniques and their application to orbit determination systems

The theory of numerical averaging and analytical averaging will be reviewed and the application of these techniques to orbit and parameter estimation problems will be presented. Comparisons will be made between utilizing mean elements versus tracking data as the observation types. Results will be presented comparing the accuracy and efficiency of the combined orbit estimation and orbit prediction problem using averaged equations of motion, the Cowell equations of motion and the Brouwer general perturbation theory. The problem of converting the averaged element space back to osculating element space for orbit operations will also be discussed.

Velez, C. E.↗

NASA NTRS1978

Development and evaluation of a hybrid averaged orbit generator

A rapid orbit generator based on a first-order application of the Generalized Method of Averaging has been developed for the Research and Development (R&D) version of the Goddard Trajectory Determination System (GTDS). The evaluation of the averaged equations of motion can use both numerically averaged and recursively evaluated, analytically averaged perturbation models. These equations are numerically integrated to obtain the secular and long-period motion. Factors affecting efficient orbit prediction are discussed and guidelines are presented for treatment of each major perturbation. Guidelines for obtaining initial mean elements compatible with the theory are presented. An overview of the orbit generator is presented and comparisons with high precision methods are given.

Mcclain, W. D.↗

NASA NTRS1980

Estimating monthly-averaged air-sea transfers of heat and momentum using the bulk aerodynamic method

Air-sea transfers of sensible heat, latent heat, and momentum are computed from twenty-five years of middle-latitude and subtropical ocean weather ship data in the North Atlantic and North Pacific using the bulk aerodynamic method. The results show that monthly-averaged wind speeds, temperatures, and humidities can be used to estimate the monthly-averaged sensible and latent heat fluxes computed from the bulk aerodynamic equations to within a relative error of approximately 10%. The estimate of monthly-averaged wind stress under the assumption of neutral stability are shown to be within approximately 5% of the monthly-averaged non-neutral values.

Esbensen, S. K.↗

NASA NTRS1981

Estimating monthly averaged air-sea transfers of heat and momentum using the bulk aerodynamic method

Air-sea transfers of sensible heat, latent heat and momentum are computed from 25 years of middle-latitude and subtropical ocean weather ship data in the North Atlantic and North Pacific using the bulk aerodynamic method. The results show that monthly averaged wind speeds, temperatures and humidities can be used to estimate the monthly averaged sensible and latent heat fluxes from the bulk aerodynamic equations to within a relative error of approximately 10%. The estimates of monthly averaged wind stress under the assumption of neutral stability are shown to be within approximately 5% of the monthly averaged nonneutral values.

Esbensen, S. K.↗

NASA NTRS1982

The latitude dependence of the variance of zonally averaged quantities

Geometric characteristics of the spherical earth are shown to be responsible for the increase of variance with latitude of zonally averaged meteorological statistics. An analytic model is constructed to display the effect of a spherical geometry on zonal averages, employing a sphere labeled with radial unit vectors in a real, stochastic field expanded in complex spherical harmonics. The variance of a zonally averaged field is found to be expressible in terms of the spectrum of the vector field of the spherical harmonics. A maximum variance is then located at the poles, and the ratio of the variance to the zonally averaged grid-point variance, weighted by the cosine of the latitude, yields the zonal correlation typical of the latitude. An example is provided for the 500 mb level in the Northern Hemisphere compared to 15 years of data. Variance is determined to increase north of 60 deg latitude.

North, G. R.↗

NASA NTRS1982

Limitations of signal averaging due to temporal correlation in laser remote-sensing measurements

Laser remote sensing involves the measurement of laser-beam transmission through the atmosphere and is subject to uncertainties caused by strong fluctuations due primarily to speckle, glint, and atmospheric-turbulence effects. These uncertainties are generally reduced by taking average values of increasing numbers of measurements. An experiment was carried out to directly measure the effect of signal averaging on back-scattered laser return signals from a diffusely reflecting target using a direct-detection differential-absorption lidar (DIAL) system. The improvement in accuracy obtained by averaging over increasing numbers of data points was found to be smaller than that predicted for independent measurements. The experimental results are shown to be in excellent agreement with a theoretical analysis which considers the effect of temporal correlation. The analysis indicates that small but long-term temporal correlation severely limits the improvement available through signal averaging.

Menyuk, N.↗

NASA NTRS1983

Statistical theory for estimating sampling errors of regional radiation averages based on satellite measurements

The processes which determine the weather and climate are driven by the radiation received by the earth and the radiation subsequently emitted. A knowledge of the absorbed and emitted components of radiation is thus fundamental for the study of these processes. In connection with the desire to improve the quality of long-range forecasting, NASA is developing the Earth Radiation Budget Experiment (ERBE), consisting of a three-channel scanning radiometer and a package of nonscanning radiometers. A set of these instruments is to be flown on both the NOAA-F and NOAA-G spacecraft, in sun-synchronous orbits, and on an Earth Radiation Budget Satellite. The purpose of the scanning radiometer is to obtain measurements from which the average reflected solar radiant exitance and the average earth-emitted radiant exitance at a reference level can be established. The estimate of regional average exitance obtained will not exactly equal the true value of the regional average exitance, but will differ due to spatial sampling. A method is presented for evaluating this spatial sampling error.

Smith, G. L.↗

NASA NTRS1984

Phase average measurements of the coherent structure in a Mach number 0.6 jet

Phase averaged measurements of the axial mass velocity, radial velocity, and the product of the two have been made in an artificially excited cold air jet. The radial velocity fluctuations had a lower amplitude for both the full wave and phase averaged fluctuations compared to the axial mass velocity fluctuations. The Reynolds stress tended to decay faster in amplitude than the axial mass velocity and radial velocity fluctuations for both the full wave and phase averaged components. The radial velocity fluctuations possessed higher levels of coherence than the axial mass velocity fluctuation and the Reynolds stress. When the jet was excited at the frequency of St = 0.474, a high amplitude component at that frequency dominated the entire phase averaged flowfield from X/D = 1 to 10. This fundamental frequency was accompanied by several relatively high amplitude harmonics. These harmonics were more pronounced in the radial velocity fluctuations than for the axial fluctuations or the Reynolds stress.

Emami, S.↗

NASA NTRS1985

Geologic analysis of averaged magnetic satellite anomalies

To investigate relative advantages and limitations for quantitative geologic analysis of magnetic satellite scalar anomalies derived from arithmetic averaging of orbital profiles within equal-angle or equal-area parallelograms, the anomaly averaging process was simulated by orbital profiles computed from spherical-earth crustal magnetic anomaly modeling experiments using Gauss-Legendre quadrature integration. The results indicate that averaging can provide reasonable values at satellite elevations, where contributing error factors within a given parallelogram include the elevation distribution of the data, and orbital noise and geomagnetic field attributes. Various inversion schemes including the use of equivalent point dipoles are also investigated as an alternative to arithmetic averaging. Although inversion can provide improved spherical grid anomaly estimates, these procedures are problematic in practice where computer scaling difficulties frequently arise due to a combination of factors including large source-to-observation distances ( 400 km), high geographic latitudes, and low geomagnetic field inclinations.

Goyal, H. K.↗

NASA NTRS1986

An average interstellar extinction curve for the Large Magellanic Cloud

LMC regions located more than 0.5 deg from the center of the 30 Doradus nebula have an average UV extinction curve that is about 2 units higher in the far UV than the average Galactic curve. Within the 30 Doradus region, the normalized far-UV extinction is much steeper than the average Galactic or average LMC curves, yet has been considered to be representative of the LMC in general in the past. The present results show typical LMC extinction properties to have much more in common with those in the Milky Way.

Fitzpatrick, Edward L.↗

NASA NTRS1987

Conditionally-averaged structures in wall-bounded turbulent flows

The quadrant-splitting and the wall-shear detection techniques were used to obtain ensemble-averaged wall layer structures. The two techniques give similar results for Q4 events, but the wall-shear method leads to smearing of Q2 events. Events were found to maintain their identity for very long times. The ensemble-averaged structures scale with outer variables. Turbulence producing events were associated with one dominant vortical structure rather than a pair of counter-rotating structures. An asymmetry-preserving averaging scheme was devised that allowed a picture of the average structure which more closely resembles the instantaneous one, to be obtained.

Guezennec, Yann G.↗

NASA NTRS1988

Does subduction zone magmatism produce average continental crust

The question of whether present day subduction zone magmatism produces material of average continental crust composition, which perhaps most would agree is andesitic, is addressed. It was argued that modern andesitic to dacitic rocks in Andean-type settings are produced by plagioclase fractionation of mantle derived basalts, leaving a complementary residue with low Rb/Sr and a positive Eu anomaly. This residue must be removed, for example by delamination, if the average crust produced in these settings is andesitic. The author argued against this, pointing out the absence of evidence for such a signature in the mantle. Either the average crust is not andesitic, a conclusion the author was not entirely comfortable with, or other crust forming processes must be sought. One possibility is that during the Archean, direct slab melting of basaltic or eclogitic oceanic crust produced felsic melts, which together with about 65 percent mafic material, yielded an average crust of andesitic composition.

Ellam, R. M.↗

NASA NTRS1990

Cell averaging Chebyshev methods for hyperbolic problems

A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods presented are proven stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods.

Wei, Cai↗

NASA NTRS1992

Signal Quality Influence on Averaging Procedure for DIAL Pollution Monitoring

Presented here is an analysis of the relative effect of each stochastic phenomenon on the accuracy of LIDAR measurements. The preferred averaging procedure to be applied is noted. The analysis takes into account the temporal correlation of the transmitted power variations which are associated with laser modal noise, short term temporal correlation of atmospheric turbulence, and 'white' additive noise. A distinction is made between two types of systems, one that transmits a sequence of pulses tuned into two wavelengths, but with a relatively large time separation, and another that transmits pulses in two wavelengths almost coincidentally. This distinction is important because the effect of speckle noise can be minimized when the pulses at two wavelengths are sent within the correlation time of the atmospheric turbulence. The presented analysis compares the signal to noise ratio in the calculation of the ratio beta (sub 1)/beta (sub 2), as achieved by using two methods of calculations: first averaging the data related to each wavelength and then taking the ratio, and first taking the ratio and then averaging. For both methods, normalization with respect to the transmitted power is considered, either prior to or after the averaging of the signals in each wavelength.

Egert, S.↗

NASA NTRS1993

Effects of spatial variability and scale on areal -average evapotranspiration

This paper explores the effect of spatial variability and scale on areally-averaged evapotranspiration. A spatially-distributed water and energy balance model is employed to determine the effect of explicit patterns of model parameters and atmospheric forcing on modeled areally-averaged evapotranspiration over a range of increasing spatial scales. The analysis is performed from the local scale to the catchment scale. The study area is King's Creek catchment, an 11.7 sq km watershed located on the native tallgrass prairie of Kansas. The dominant controls on the scaling behavior of catchment-average evapotranspiration are investigated by simulation, as is the existence of a threshold scale for evapotranspiration modeling, with implications for explicit versus statistical representation of important process controls. It appears that some of our findings are fairly general, and will therefore provide a framework for understanding the scaling behavior of areally-averaged evapotranspiration at the catchment and larger scales.

Famiglietti, J. S.↗

NASA NTRS1995

Average motion, structure and orientation of the distant magnetotail determined from remote sensing of the edge of the plasma sheet boundary layer with E greater than 35 keV ions

We study gradients of the energetic ion intesity observed at the edge of the plasma sheet boundary layer (PSBL) by the energetic ion anisotropy spectrometer (EPAS) on International Sun Earth Explorer 3 (ISEE 3). In particular, we have determined the velocity of the boundary relative to the spacecraft in the direction perpendicular to the tail axis and the angle which the boundary normal makes to the spacecraft spin axis for 1160 PSBL encounters at X(sub GSM) greater than -240 R(sub E). By asuming that, on average, the edge of the PSBL is parallel to the cross-tail current sheet, we are then able to determine a number of properties of the structure, orientation and motion of the deep geomagnetic tail. We conclude the following: (1) Most crossings of the edge of the PSBL are caused by transverse motuion of the entire tail induced by solar wind direction variations, although some are caused by reconfiguration of the tail due to geomagnetic activity. (2) The typical velocity of the PSBL (and hence of the tail) in the direction perpendicular to the tail axis is 50-85 km/s. (3) The average twist of the tail is near zero, with the edge of the PSBL (and by inference the cross-tail current sheet) lying parallel to the ecliptic plane (however, large twists are found in individual events and the distribution of twists is broad, with one standard deviation of approximately 50 deg. (4) The width of the distribution decreases with downtail distance. (5) The variation of the distributions with cross-tail position reveals that this decreas in width is most likely due to the edge of the PSBL being concave, or significantly flared at the tail flanks, in the near-Earth region. (6) During days on which the Interplanetary Magnetic Field (IMF) has 'away' sector structure, the north lobe of the trail is twisted on average towards dawn by 7.0 +/-2.4 deg. (7) During days on which the IMF has 'toward' sector structure, the north lobe is tilted towards duskby 3.8 +/- 2.3. (8) A subset of events for which IMP 8 solar wind data are available show that, for southward IMF BH(sub z) the tail has a mean twist of -12.3 +/- 5.0 deg for IMF B(sub Y) greater than 0 and 5.5 +/- 3.8 deg for IMF B(sub Y) less than 0 (positive twist angles correspond to a tilt of the northern lobe towards dusk). (9) For northward IMF B(sub z) the tail has a twist of -23.9 +/- 5.0 deg for IMF B(sub Y) greater than 0 and 13.4 +/- 6.0 deg for IMF B(sub y) less than 0. Hence the tail appears more twisted on average for the IMF B(sub Z) northward case. (10) The distribution of tail twist is wider for lower levels of geomagnetic activity, indicating that the tail is able to twist more at lower levels of activity. (11) The data set reveals no evident effect of the earth's dipole wobble; tail orientation appears to be controlled by the solar wind and IMF, such that the GSE coordinate system may be appropriate for the study of field and plasma structures in the distant tail region.

Owen, C. J.↗