Transit timing variation analysis of the low-mass brown dwarf KELT-1 b
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Masses of the Kepler-419 planets from transit timing variations analysis
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X Saad-Olivera↗
Solid-propellant rocket motor internal ballistic performance variation analysis, phase 2
The Monte Carlo method was used to investigate thrust imbalance and its first time derivative throughtout the burning time of pairs of solid rocket motors firing in parallel. Results obtained compare favorably with Titan 3 C flight performance data. Statistical correlations of the thrust imbalance at various times with corresponding nominal trace slopes suggest several alternative methods of predicting thrust imbalance. The effect of circular-perforated grain deformation on internal ballistics is discussed, and a modified design analysis computer program which permits such an evaluation is presented. Comparisons with SRM firings indicate that grain deformation may account for a portion of the so-called scale factor on burning rate between large motors and strand burners or small ballistic test motors. Thermoelastic effects on burning rate are also investigated. Burning surface temperature is calculated by coupling the solid phase energy equation containing a strain rate term with a model of gas phase combustion zone using the Zeldovich-Novozhilov technique. Comparisons of solutions with and without the strain rate term indicate a small but possibly significant effect of the thermoelastic coupling.
Sforzini, R. H.↗
Solid propellant rocket motor internal ballistics performance variation analysis, phase 3
Results of research aimed at improving the predictability of off nominal internal ballistics performance of solid propellant rocket motors (SRMs) including thrust imbalance between two SRMs firing in parallel are reported. The potential effects of nozzle throat erosion on internal ballistic performance were studied and a propellant burning rate low postulated. The propellant burning rate model when coupled with the grain deformation model permits an excellent match between theoretical results and test data for the Titan IIIC, TU455.02, and the first Space Shuttle SRM (DM-1). Analysis of star grain deformation using an experimental model and a finite element model shows the star grain deformation effects for the Space Shuttle to be small in comparison to those of the circular perforated grain. An alternative technique was developed for predicting thrust imbalance without recourse to the Monte Carlo computer program. A scaling relationship used to relate theoretical results to test results may be applied to the alternative technique of predicting thrust imbalance or to the Monte Carlo evaluation. Extended investigation into the effect of strain rate on propellant burning rate leads to the conclusion that the thermoelastic effect is generally negligible for both steadily increasing pressure loads and oscillatory loads.
Sforzini, R. H.↗
Variational analysis of temperature and moisture advection in a severe storm environment
Horizontal wind components, potential temperature, and mixing ratio fields associated with a severe storm environment in the south central United States were objectively analyzed from synoptic upper air observations with a nonhomogeneous anisotropic weighting function. The particular case study discussed here is the tornado producting squall line which moved through eastern Oklahoma 26 May 1973. The synoptic situation which preceded squall line development was cyclogenesis and frontogenesis in the lee-of-mountain trough, which produced a well-defined surface dry line (or dew point front) and a pronounced mid-level dry air intrusion. It is shown that the intrusion was also characterized by warm air, with a lapse rate approaching the dry adiabatic.
Mcfarland, M. J.↗
Solid-propellant rocket motor internal ballistics performance variation analysis, phase 5
The results of research aimed at improving the predictability of internal ballistics performance of solid-propellant rocket motors (SRM's) including thrust imbalance between two SRM's firing in parallel are presented. Static test data from the first six Space Shuttle SRM's is analyzed using a computer program previously developed for this purpose. The program permits intentional minor design biases affecting the imbalance between any two SMR's to be removed. Results for the last four of the six SRM's, with only the propellant bulk temperature as a non-random variable, are generally within limits predicted by theory. Extended studies of internal ballistic performance of single SRM's are presented based on an earlier developed mathematical model which includes an assessment of grain deformation. The erosive burning rate law used in the model is upgraded and made more general. Excellent results are obtained in predictions of the performances of five different SRM's of quite different sizes and configurations. These SRM's all employ PBAN type propellants with ammonium perchlorate oxidizer and 16 to 20% aluminum except one which uses carboxyl terminated butadiene binder. The only non-calculated parameters in the burning rate equations that are changed for the different SRM's are the zero crossflow velocity burning rate coefficients and exponents. The results, in general, confirm the importance of grain deformation. The improved internal ballistic model makes practical development of an effective computer program for application of an optimization technique to SRM design which is also demonstrated. The program uses a pattern search technique to minimize the difference between a desired thrust-time trace and one calculated based on the internal ballistic model.
Sforzini, R. H.↗
Mapping ERS-1 wind fields over north west Atlantic using a variational objective analysis
A variational method is implemented to produce five day mean gridded ERS-1 analyzed wind fields in the north west Atlantic with the aim of providing for wind forcing of basin scale ocean models. The method consists of minimizing a cost functional, designed to measure misfits to prescribed weighted constraints which express a smoothed behavior and the proximity to input data vectors and curl. The weights are empirically determined by comparison with independent ship and buoy data over four five day periods. Root mean square differences between analyzed winds and independent data are thus further decreased: they range from 0.8 up to 1.8 m/s. Some problems present in the initial data remain; they are principally due to incomplete data coverage (instrumental problems), and possibly unresolved ambiguities. The resulting curl fields are smoothed and show coherent patterns. A comparison with the European Center for Medium range Weather Forecasting (ECMWF) analysis is encouraging.
Siefridt, L.↗
Preparation of satellite soundings for insertion in a variational objective analysis model
The performance of a variational analysis model being developed at the Illinois State Water Survey, which allows blending of satellite and conventional soundings in a way which preserves the information content of both data sources, requires preparation of the input data before insertion into the model. Using operationally retrieved Tiros-N TOVS soundings and rawinsonde data, four procedures to prepare satellite soundings for model insertion are demonstrated: (1) determination and removal of biases, (2) determination of standard errors of the satellite temperatures to assist in the assignment of weights in the model, (3) conversion of layer mean temperatures to level temperatures, and (4) determination of the action necessary for correcting for the nonsynoptic nature of the satellite data.
Kidder, Stanley Q.↗
Global ozone long-term trends from satellite measurements and the response to solar activity variations
Analysis of global ozone variations for the period April 1970 to December 1975 was performed by using the reprocessed Nimbus 4 backscattered ultraviolet (BUV) measurements of total ozone. A correlation coefficient of 0.97 is found between the 6-month running mean of global mean total ozone (filtered for mean semiannual, annual, and quasibiennial variations) and the 10.7-cm solar activity index. Correcting ozone for a time-dependent latitudinal bias relative to Dobson ozone measurements reduces to 2-3% the global mean ozone variation over the solar cycle. The solar ultraviolet variability required in a one-dimensional time-dependent radiative photochemical model to account for the observed ozone variation appears to be consistent with recent solar UV observations.
Keating, G. M.↗
Some New Mathematical Methods for Variational Objective Analysis
New and/or improved variational methods for simultaneously combining forecast, heterogeneous observational data, a priori climatology, and physics to obtain improved estimates of the initial state of the atmosphere for the purpose of numerical weather prediction are developed. Cross validated spline methods are applied to atmospheric data for the purpose of improved description and analysis of atmospheric phenomena such as the tropopause and frontal boundary surfaces.
Wahba, G.↗
Variational optimization analysis of temperature and moisture advection in a severe storm environment
Horizontal wind components, potential temperature, and mixing ratio fields associated with a severe storm environment in the south central U.S. were analyzed from synoptic upper air observations with a nonhomogeneous, anisotropic weighting function. Each data field was filtered with variational optimization analysis techniques. Variational optimization analysis was also performed on the vertical motion field and was used to produce advective forecasts of the potential temperature and mixing ratio fields. Results show that the dry intrusion is characterized by warm air, the advection of which produces a well-defined upward motion pattern. A corresponding downward motion pattern comprising a deep vertical circulation in the warm air sector of the low pressure system was detected. The axes alignment of maximum dry and warm advection with the axis of the tornado-producing squall line also resulted.
Mcfarland, M. J.↗
Variational global analysis of satellite temperature soundings
A variational spherical harmonic analysis is developed for the production of global geopotential height and geostropic wind fields from the TIROS-N spacecraft's temperature sounding profiles. This scheme is based on Tykhonov's (1964) regularization method, and the smoothing parameter is determined by cross validation. The scheme is noted to be stable and computationally efficient, and it does not depend on a priori information. Its applications to three-dimensional temperature retrievals and to four-dimensional spectral analyses are illustrated.
Halem, M.↗
Some new mathematical methods for variational objective analysis
Numerous results were obtained relevant to remote sensing, variational objective analysis, and data assimilation. A list of publications relevant in whole or in part is attached. The principal investigator gave many invited lectures, disseminating the results to the meteorological community as well as the statistical community. A list of invited lectures at meetings is attached, as well as a list of departmental colloquia at various universities and institutes.
Wahba, Grace↗
Variational mechanics analysis of the stresses in microdrop debond specimens
A recently derived variational mechanics analysis of stresses in single-fiber model composites has been applied to the analysis of the stresses in the microdrop debond specimen. The new analysis is more accurate than the commonly applied shear-lag or elastic-plastic analyses. The results from a sample stress state calculation suggest that interfacial failure between the fiber and the microdrop is by mode I or opening mode failure at the beginning of the microdrop. The opening mode failure is caused by a large tensile radial stress at the fiber/matrix interface. Previous analyses of microdrop debond data have been in terms of a shear strength. It is suggested that these analyses misrepresent microdrop debond results and recommend instead a failure analysis based on energy release rate and interfacial fracture toughness. A procedure for calculating the energy release rate for the growth of an interfacial crack is described.
Scheer, Robert J.↗
Comparison of turbine annulus mass flow computed by one- and two-dimensional analysis
Variations in specific heat ratio, flow angle, critical velocity ratio, swirl distribution exponent, and radius ratio were considered in computing the mass flow. Variations in specific heat ratio had no significant effect and variations in critical velocity ratio had only small effect on computed mass flow between a one- and two-dimensional analysis. All non-free-vortex cases considered showed larger differences in computed mass flow between one- and two-dimensional analysis than for free vortex flow. For the non-free-vortex cases, decreasing radius ratio and increasing flow angle resulted in larger differences in mass flow as computed by the two methods.
Wasserbauer, C. A.↗
Hybrid Data Assimilation without Ensemble Filtering
The Global Modeling and Assimilation Office is preparing to upgrade its three-dimensional variational system to a hybrid approach in which the ensemble is generated using a square-root ensemble Kalman filter (EnKF) and the variational problem is solved using the Grid-point Statistical Interpolation system. As in most EnKF applications, we found it necessary to employ a combination of multiplicative and additive inflations, to compensate for sampling and modeling errors, respectively and, to maintain the small-member ensemble solution close to the variational solution; we also found it necessary to re-center the members of the ensemble about the variational analysis. During tuning of the filter we have found re-centering and additive inflation to play a considerably larger role than expected, particularly in a dual-resolution context when the variational analysis is ran at larger resolution than the ensemble. This led us to consider a hybrid strategy in which the members of the ensemble are generated by simply converting the variational analysis to the resolution of the ensemble and applying additive inflation, thus bypassing the EnKF. Comparisons of this, so-called, filter-free hybrid procedure with an EnKF-based hybrid procedure and a control non-hybrid, traditional, scheme show both hybrid strategies to provide equally significant improvement over the control; more interestingly, the filter-free procedure was found to give qualitatively similar results to the EnKF-based procedure.
Kalman Filter↗
Mesospheric effects of solar ultraviolet variations - Further analysis of SME IR ozone and Nimbus 7 SAMS temperature data
In order to improve the constraints on models of the mesospheric response to solar UV variations, an analysis is conducted of the Solar Mesosphere Explorer (SME) IR ozone data and Nimbus 7 stratosphere and mesosphere sounder (SAMS) temperature data. Maximum low-altitude ozone and temperature-response amplitudes occur at about the same altitude, where a strong coupling between photochemical and thermal components of the mesospheric response is suggested by the simultaneous positive temperature and negative ozone response maxima. Increased Lyman-alpha dissociation of water vapor and temperature feedback are theorized to account for the negative ozone response. HO(x) chemical heating can increase as ozone destruction increases, and can therefore account for the positive temperature response.
Hood, L. L.↗
Use of a transcendental approximation in transient conduction analysis
Variation method applied to transient thermal conductivity in semiinfinite slab with nonlinear boundary condition
TRANSIENT HEATING↗