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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Trends in the Southern Hemisphere

The station data of monthly mean sea level pressure, surface air temperature as well as monthly mean upper air rawinsonde observations were used to study the trends in the southern winter (June, July and August) and summer (December, January and February). This study covers the period 1951 to 1981. Most of the surface data have continuous 31 year records, however, for some high latitude stations, both surface and upper air records started in 1957 or even later. The normalized anomaly for a given variable Z is defined as the departure from the 1951 to 1981 grand mean divided by the standard deviation during the same period. To eliminate the large fluctuations in the data, the 1-3-1 smoothing was applied to the time series of normalized anomalies. The trends of monthly mean temperatures and height from the surface to 200 mb level is documented.

Mo, K. C.↗
NASA NTRS1986

Compensation for Primary Reflector Wavefront Error

The object of the invention is to compensate for errors in a large telescope primary reflector by making certain compensating deviations in a smaller, auxiliary reflector of the telescope. At least one intermediate element forms an image of the primary surface onto the secondary surface, so each point on the secondary surface corresponds to a point on the primary surface. The secondary surface is formed with a deviation from an ideal secondary surface, with the piston distance of each point on the actual secondary surface equal to the piston distance of a corresponding piston on the actual primary surface from the ideal primary surface. It is found that this results in electromagnetic (e.g., light) rays which strike a deviating area of the actual primary surface being brought to the same focus as if the actual primary surface did not have a diviation from an ideal primary surface.

Meinel, A. B.↗
NASA NTRS1986

Lithologic mapping of silicate rocks using TIMS

Common rock-forming minerals have thermal infrared spectral features that are measured in the laboratory to infer composition. An airborne Daedalus scanner (TIMS) that collects six channels of thermal infrared radiance data (8 to 12 microns), may be used to measure these same features for rock identification. Previously, false-color composite pictures made from channels 1, 3, and 5 and emittance spectra for small areas on these images were used to make lithologic maps. Central wavelength, standard deviation, and amplitude of normal curves regressed on the emittance spectra are related to compositional information for crystalline igneous silicate rocks. As expected, the central wavelength varies systematically with silica content and with modal quartz content. Standard deviation is less sensitive to compositional changes, but large values may result from mixed admixture of vegetation. Compression of the six TIMS channels to three image channels made from the regressed parameters may be effective in improving geologic mapping from TIMS data, and these synthetic images may form a basis for the remote assessment of rock composition.

Gillespie, A. R.↗
NASA NTRS1999

The NASA/MSFC Global Reference Atmospheric Model: 1999 Version (GRAM-99)

The latest version of Global Reference Atmospheric Model (GRAM-99) is presented and discussed. GRAM-99 uses either (binary) Global Upper Air Climatic Atlas (GUACA) or (ASCII) Global Gridded Upper Air Statistics (GGUAS) CD-ROM data sets, for 0-27 km altitudes. As with earlier versions, GRAM-99 provides complete geographical and altitude coverage for each month of the year. GRAM-99 uses a specially-developed data set, based on Middle Atmosphere Program (MAP) data, for 20-120 km altitudes, and NASA's 1999 version Marshall Engineering Thermosphere (MET-99) model for heights above 90 km. Fairing techniques assure smooth transition in overlap height ranges (20-27 km and 90-120 km). GRAM-99 includes water vapor and 11 other atmospheric constituents (O3, N2O, CO, CH4, CO2, N2, O2, O, A, He and H). A variable-scale perturbation model provides both large-scale (wave) and small-scale (stochastic) deviations from mean values for thermodynamic variables and horizontal and vertical wind components. The small-scale perturbation model includes improvements in representing intermittency ("patchiness"). A major new feature is an option to substitute Range Reference Atmosphere (RRA) data for conventional GRAM climatology when a trajectory passes sufficiently near any RRA site. A complete user's guide for running the program, plus sample input and output, is provided. An example is provided for how to incorporate GRAM-99 as subroutines in other programs (e.g., trajectory codes).

Justus, C. G.↗
NASA NTRS2006

Visualization of a Capsule Entry Vehicle Reaction-Control System (RCS) Thruster

Planar laser-induced fluorescence (PLIF) was used to visualize the reaction control system (RCS) jet flow emanating from the aft-body of an Apollo-geometry capsule test article in the NASA Langley Research Center 31-Inch Mach 10 Air wind tunnel. The RCS jet was oriented normal to the aft surface of the model and had a nominal Mach number of 2.94. The composition of the jet gas by mass was 95% nitrogen (N2) and 5% nitric oxide (NO). The RCS jet flowrate varied between zero and 0.5 standard liters per minute and the angle of attack and tunnel stagnation pressure were also varied. PLIF was used to excite the NO molecules for flow visualization. These flow visualization images were processed to determine the trajectory and to quantify the flapping of the RCS jet. The spatial resolution of the jet trajectory measurement was about 1 mm and the single-shot precision of the measurement was estimated to be 0.02 mm in the far field of the jet plume. The jet flapping, measured by the standard deviation of the jet centerline position was as large as 0.9 mm, while the jet was 1.5-4 mm in diameter (full width at half maximum). Schlieren flow visualization images were obtained for comparison with the PLIF. Surface pressures were also measured and presented. Virtual Diagnostics Interface (VIDI) technology developed at NASA Langley was used to superimpose and visualize the data sets. The measurements demonstrate some of the capabilities of the PLIF method while providing a test case for computational fluid dynamics (CFD) validation.

Danehy, P. M.↗
NASA NTRS2016

Soil Moisture Active Passive Mission L4_SM Data Product Assessment (Version 2 Validated Release)

During the post-launch SMAP calibration and validation (Cal/Val) phase there are two objectives for each science data product team: 1) calibrate, verify, and improve the performance of the science algorithm, and 2) validate the accuracy of the science data product as specified in the science requirements and according to the Cal/Val schedule. This report provides an assessment of the SMAP Level 4 Surface and Root Zone Soil Moisture Passive (L4_SM) product specifically for the product's public Version 2 validated release scheduled for 29 April 2016. The assessment of the Version 2 L4_SM data product includes comparisons of SMAP L4_SM soil moisture estimates with in situ soil moisture observations from core validation sites and sparse networks. The assessment further includes a global evaluation of the internal diagnostics from the ensemble-based data assimilation system that is used to generate the L4_SM product. This evaluation focuses on the statistics of the observation-minus-forecast (O-F) residuals and the analysis increments. Together, the core validation site comparisons and the statistics of the assimilation diagnostics are considered primary validation methodologies for the L4_SM product. Comparisons against in situ measurements from regional-scale sparse networks are considered a secondary validation methodology because such in situ measurements are subject to up-scaling errors from the point-scale to the grid cell scale of the data product. Based on the limited set of core validation sites, the wide geographic range of the sparse network sites, and the global assessment of the assimilation diagnostics, the assessment presented here meets the criteria established by the Committee on Earth Observing Satellites for Stage 2 validation and supports the validated release of the data. An analysis of the time average surface and root zone soil moisture shows that the global pattern of arid and humid regions are captured by the L4_SM estimates. Results from the core validation site comparisons indicate that "Version 2" of the L4_SM data product meets the self-imposed L4_SM accuracy requirement, which is formulated in terms of the ubRMSE: the RMSE (Root Mean Square Error) after removal of the long-term mean difference. The overall ubRMSE of the 3-hourly L4_SM surface soil moisture at the 9 km scale is 0.035 cubic meters per cubic meter requirement. The corresponding ubRMSE for L4_SM root zone soil moisture is 0.024 cubic meters per cubic meter requirement. Both of these metrics are comfortably below the 0.04 cubic meters per cubic meter requirement. The L4_SM estimates are an improvement over estimates from a model-only SMAP Nature Run version 4 (NRv4), which demonstrates the beneficial impact of the SMAP brightness temperature data. L4_SM surface soil moisture estimates are consistently more skillful than NRv4 estimates, although not by a statistically significant margin. The lack of statistical significance is not surprising given the limited data record available to date. Root zone soil moisture estimates from L4_SM and NRv4 have similar skill. Results from comparisons of the L4_SM product to in situ measurements from nearly 400 sparse network sites corroborate the core validation site results. The instantaneous soil moisture and soil temperature analysis increments are within a reasonable range and result in spatially smooth soil moisture analyses. The O-F residuals exhibit only small biases on the order of 1-3 degrees Kelvin between the (re-scaled) SMAP brightness temperature observations and the L4_SM model forecast, which indicates that the assimilation system is largely unbiased. The spatially averaged time series standard deviation of the O-F residuals is 5.9 degrees Kelvin, which reduces to 4.0 degrees Kelvin for the observation-minus-analysis (O-A) residuals, reflecting the impact of the SMAP observations on the L4_SM system. Averaged globally, the time series standard deviation of the normalized O-F residuals is close to unity, which would suggest that the magnitude of the modeled errors approximately reflects that of the actual errors. The assessment report also notes several limitations of the "Version 2" L4_SM data product and science algorithm calibration that will be addressed in future releases. Regionally, the time series standard deviation of the normalized O-F residuals deviates considerably from unity, which indicates that the L4_SM assimilation algorithm either over- or under-estimates the actual errors that are present in the system. Planned improvements include revised land model parameters, revised error parameters for the land model and the assimilated SMAP observations, and revised surface meteorological forcing data for the operational period and underlying climatological data. Moreover, a refined analysis of the impact of SMAP observations will be facilitated by the construction of additional variants of the model-only reference data. Nevertheless, the “Version 2” validated release of the L4_SM product is sufficiently mature and of adequate quality for distribution to and use by the larger science and application communities.

SMAP L4_SM↗
NASA NTRS2022

Determining the Primary Sources of Uncertainty in Retrieval of Marine Remote Sensing Reflectance From Satellite Ocean Color Sensors

Uncertainties in the retrieval of the remote sensing reflectance, R_rs, from Ocean Color (OC) satellite sensors have a strong impact on the performance of algorithms for the estimation of chlorophyll-a, mineral concentrations, and inherent optical properties (IOPs). The uncertainties are highest in the blue bands. The total radiance measured at the top of the atmosphere captures the instantaneous state of the atmosphere-ocean system: the in-water conditions, sky and Sun glint reflected from the wind-roughened ocean surface, as well as light scattered from molecules and aerosols in the atmosphere. Each of these components has associated uncertainties, and when combined with the additional uncertainties from the instrument noise and the atmospheric correction process, they contribute to the total uncertainty budget for the retrieved R_rs. We analyzed the contribution of each component uncertainties to the total R_rs uncertainties in SNPP-VIIRS level 2 products, taking advantage of the spectral differences between the components. We examined multiple scenes in the open ocean and coastal waters at spatial resolutions ranging from 2250 to 5250 m by comparing the retrieved R_rs to in situ measurements made at several AERONET-OC sites and at the MOBY site. It was shown that uncertainties associated with the molecular (Rayleigh) scattering play the most significant role, while the contributions of other components are usually smaller. Uncertainties in Rayleigh scattering are primarily attributed to the variability of Rayleigh optical thickness (ROT) with a standard deviation of approximately 1.5% of ROT, which can largely explain the frequency of negative R_rs retrievals as observed using the current standard atmospheric correction process employed by NASA. Variability of the sky light reflected from the ocean surface in some conditions also contributed to uncertainties in the blue; water variability proportional to R_rs had a very pronounced peak in the green at coastal sites.

remote sensing reflectance↗
DOE OSTI2019

Phenomenology of large scale structure in scalar-tensor theories: Joint prior covariance of w DE , Σ, and μ in Horndeski theories

Ongoing and upcoming cosmological surveys will significantly improve our ability to probe the equation of state of dark energy, w DE , and the phenomenology of large scale structure. They will allow us to constrain deviations from the Λ cold dark matter predictions for the relations between the matter density contrast and the weak lensing and the Newtonian potential, described by the functions Σ and μ, respectively. In this work, we derive the theoretical prior for the joint covariance of w DE , Σ and μ, expected in general scalar-tensor theories with second order equations of motion (Horndeski gravity), focusing on their time-dependence at certain representative scales. We employ Monte Carlo methods to generate large ensembles of statistically independent Horndeski models, focusing on those that are physically viable and in broad agreement with local tests of gravity, the observed cosmic expansion history and the measurement of the speed of gravitational waves from a binary neutron star merger. Here, we identify several interesting features and trends in the distribution functions of w DE , Σ and μ, as well as in their covariances; we confirm the high degree of correlation between Σ and μ in scalar-tensor theories. The derived prior covariance matrices will allow us to reconstruct jointly w DE , Σ and μ in a nonparametric way.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

How Far Is Quasar UV/Optical Variability from a Damped Random Walk at Low Frequency?

Studies have shown that UV/optical light curves of quasars can be described using the prevalent damped random walk (DRW) model, also known as the Ornstein–Uhlenbeck process. A white noise power spectral density (PSD) is expected at low frequency in this model; however, a direct observational constraint to the low-frequency PSD slope is difficult due to the limited lengths of the light curves available. Meanwhile, quasars show scatter in their DRW parameters that is too large to be attributed to uncertainties in the measurements and dependence on the variation of known physical factors. In this work we present simulations showing that, if the low-frequency PSD deviates from the DRW, the red noise leakage can naturally produce large scatter in the variation parameters measured from simulated light curves. The steeper the low-frequency PSD slope, the larger scatter we expect. Based on observations of SDSS Stripe 82 quasars, we find that the low-frequency PSD slope should be no steeper than −1.3. The actual slope could be flatter, which consequently requires that the quasar variabilities should be influenced by other unknown factors. We speculate that the magnetic field and/or metallicity could be such additional factors.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2016

Conjunction Assessment Late-Notice High-Interest Event Investigation: Space Weather Aspects

Late-notice events usually driven by large changes in primary (protected) object or secondary object state. Main parameter to represent size of state change is component position difference divided by associated standard deviation (epsilon divided by sigma) from covariance. Investigation determined actual frequency of large state changes, in both individual and combined states. Compared them to theoretically expected frequencies. Found that large changes ( (epsilon divided by sigma) is greater than 3) in individual object states occur much more frequently than theory dictates. Effect is less pronounced in radial components and in events with probability of collision (Pc) greater than 1 (sup -5) (1e-5). Found combined state matched much closer to theoretical expectation, especially for radial and cross-track. In-track is expected to be the most vulnerable to modeling errors, so not surprising that non-compliance largest in this component.

Conjunction↗
DOE OSTI2023

Rotor and wake aerodynamic analysis of the Hybrid-Lambda concept - an offshore low-specific-rating rotor concept

The low-specific-rating rotor concept Hybrid-Lambda introduces a blade design with nonuniform distribution of design variables (design tip speed ratio and axial induction) along the blade span to alleviate loads of the outboard section in strong winds. In this paper, we validate aerodynamic design calculations, which were carried out with the blade element momentum theory by comparing the results to free vortex wake investigations (FVW). Furthermore, we investigate the wake behaviour with FVW and large-eddy simulations. The results show good agreements between the blade element momentum theory and FVW for integrated rotor quantities (power and thrust). Small deviations are present when the gradients of axial induction along the span are large. The wake of the Hybrid-Lambda Rotor shows advantages in the near-wake region (up to 4 diameters [D] downstream), especially in the outer wake annulus and in low turbulence scenarios. For further downstream positions, the wake is comparable to that of the reference turbine.

17 WIND ENERGY↗
DOE OSTI2023

Frequency Recovery in Power Grids Using High-Performance Computing

Maintaining electric power system stability is paramount, especially in extreme contingencies involving unexpected outages of multiple generators or transmission lines that are typical during severe weather events. Such outages often lead to large supply-demand mismatches followed by subsequent system frequency deviations from their nominal value. The extent of frequency deviations is an important metric of system resilience, and its timely mitigation is a central goal of power system operation and control. This paper develops a novel nonlinear model predictive control (NMPC) method to minimize frequency deviations when the grid is affected by an unforeseen loss of multiple components. Our method is based on a novel multi-period alternating current optimal power flow (ACOPF) formulation that accurately models both nonlinear electric power flow physics and the primary and secondary frequency response of generator control mechanisms. We develop a distributed parallel Julia package for solving the large-scale nonlinear optimization problems that result from our NMPC method and thereby address realistic test instances on existing high-performance computing architectures. Our method demonstrates superior performance in terms of frequency recovery over existing industry practices, where generator levels are set based on the solution of single-period classical ACOPF models.

nonlinear model predictive control↗
NASA NTRS1984

A statistical study of F region ion temperatures at high latitudes based on Atmosphere Explorer C data

The ion-energy balance in the high-latitude F region was studied using 40,000 simultaneous ion-temperature and drift measurements on Atmosphere Explorer C. The large number of measurements revealed how the mean ion temperature, and the average deviation from that mean, change as a function of ion drift speed during solar-minimum conditions. It was found that, in spite of an apparent large scatter in the data, the measurements could always be reasonably explained in terms of fluctuations in the neutral dynamical properties, to which the ion energy is coupled. The results also provide evidence for increased neutral drifts as the ion E x B drift increases. Evidence for systematic ion-drag effects can also be found, on the average, for dc electric fields stronger than 60 mV/m.

St.-Maurice, J.-P.↗
DOE OSTI2015

Radiotherapy Quality Assurance Report From Children's Oncology Group AHOD0031

Purpose: A phase 3 trial assessing response-based therapy in intermediate-risk Hodgkin lymphoma mandated real-time central review of involved field radiation therapy (IFRT) and imaging records by a centralized review center to maximize protocol compliance. We report the impact of centralized radiation therapy review on protocol compliance. Methods and Materials: Review of simulation films, port films, and dosimetry records was required before and after treatment. Records were reviewed by study-affiliated or review center–affiliated radiation oncologists. A deviation of 6% to 10% from protocol-specified dose was scored as “minor”; a deviation of >10% was “major.” A volume deviation was scored as “minor” if margins were less than specified or “major” if fields transected disease-bearing areas. Interventional review and final compliance review scores were assigned to each radiation therapy case and compared. Results: Of 1712 patients enrolled, 1173 underwent IFRT at 256 institutions in 7 countries. An interventional review was performed in 88% of patients and a final review in 98%. Overall, minor and major deviations were found in 12% and 6% of patients, respectively. Among the cases for which ≥1 pre-IFRT modification was requested by the Quality Assurance Review Center and subsequently made by the treating institution, 100% were made compliant on final review. By contrast, among the cases for which ≥1 modification was requested but not made by the treating institution, 10% were deemed compliant on final review. Conclusions: In a large trial with complex treatment pathways and heterogeneous radiation therapy fields, central review was performed in a large percentage of cases before IFRT and identified frequent potential deviations in a timely manner. When suggested modifications were performed by the institutions, deviations were almost eliminated.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1993

Radio metric errors due to mismatch and offset between a DSN antenna beam and the beam of a troposphere calibration instrument

Two components of the error of a troposphere calibration measurement were quantified by theoretical calculations. The first component is a beam mismatch error, which occurs when the calibration instrument senses a conical volume different from the cylindrical volume sampled by a Deep Space Network (DSN) antenna. The second component is a beam offset error, which occurs if the calibration instrument is not mounted on the axis of the DSN antenna. These two error sources were calculated for both delay (e.g., VLBI) and delay rate (e.g., Doppler) measurements. The beam mismatch error for both delay and delay rate drops rapidly as the beamwidth of the troposphere calibration instrument (e.g., a water vapor radiometer or an infrared Fourier transform spectrometer) is reduced. At a 10-deg elevation angle, the instantaneous beam mismatch error is 1.0 mm for a 6-deg beamwidth and 0.09 mm for a 0.5-deg beam (these are the full angular widths of a circular beam with uniform gain out to a sharp cutoff). Time averaging for 60-100 sec will reduce these errors by factors of 1.2-2.2. At a 20-deg elevation angle, the lower limit for current Doppler observations, the beam-mismatch delay rate error is an Allan standard deviation over 100 sec of 1.1 x 10(exp -14) with a 4-deg beam and 1.3 x 10(exp -l5) for a 0.5-deg beam. A 50-m beam offset would result in a fairly modest (compared to other expected error sources) delay error (less than or equal to 0.3 mm for 60-sec integrations at any elevation angle is greater than or equal to 6 deg). However, the same offset would cause a large error in delay rate measurements (e.g., an Allan standard deviation of 1.2 x 10(exp -14) over 100 sec at a 20-deg elevation angle), which would dominate over other known error sources if the beamwidth is 2 deg or smaller. An on-axis location is essential for accurate troposphere calibration of delay rate measurements. A half-power beamwidth (for a beam with a tapered gain profile) of 1.2 deg or smaller is desired for calibration of all types of radio metrics. A water-vapor radiometer calibration beam of this size with very low sidelobes would require a clear aperture antenna with a diameter of at least 1.5 m if the primary water vapor sensing channel were in the 20-22 GHz range.

R P Linfield↗
DOE OSTI2016

SU-F-J-29: Dosimetric Effect of Image Registration ROI Size and Focus in Automated CBCT Registration for Spine SBRT

Purpose: Spinal stereotactic body radiotherapy (SBRT) involves highly conformal dose distributions and steep dose gradients due to the proximity of the spinal cord to the treatment volume. To achieve the planning goals while limiting the spinal cord dose, patients are setup using kV cone-beam CT (kV-CBCT) with 6 degree corrections. The kV-CBCT registration with the reference CT is dependent on a user selected region of interest (ROI). The objective of this work is to determine the dosimetric impact of ROI selection. Methods: Twenty patients were selected for this study. For each patient, the kV-CBCT was registered to the reference CT using three ROIs including: 1) the external body, 2) a large anatomic region, and 3) a small region focused in the target volume. Following each registration, the aligned CBCTs and contours were input to the treatment planning system for dose evaluation. The minimum dose, dose to 99% and 90% of the tumor volume (D99%, D90%), dose to 0.03cc and the dose to 10% of the spinal cord subvolume (V10Gy) were compared to the planned values. Results: The average deviations in the tumor minimum dose were 2.68%±1.7%, 4.6%±4.0%, 14.82%±9.9% for small, large and the external ROIs, respectively. The average deviations in tumor D99% were 1.15%±0.7%, 3.18%±1.7%, 10.0%±6.6%, respectively. The average deviations in tumor D90% were 1.00%±0.96%, 1.14%±1.05%, 3.19%±4.77% respectively. The average deviations in the maximum dose to the spinal cord were 2.80%±2.56%, 7.58%±8.28%, 13.35%±13.14%, respectively. The average deviation in V10Gy to the spinal cord were 1.69%±0.88%, 1.98%±2.79%, 2.71%±5.63%. Conclusion: When using automated registration algorithms for CBCT-Reference alignment, a small target-focused ROI results in the least dosimetric deviation from the plan. It is recommended to focus narrowly on the target volume to keep the spinal cord dose below tolerance.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2013

The Evolving Polarized Jet of Black Hole Candidate Swift J1745-26

Swift J1745−26 is an X-ray binary towards the Galactic Centre that was detected when it went into outburst in September 2012. This source is thought to be one of a growing number of sources that display "failed outbursts", in which the self-absorbed radio jets of the transient source are never fully quenched and the thermal emission from the geometrically-thin inner accretion disk never fully dominates the X-ray flux. We present multifrequency data from the Very Large Array, Australia Telescope Compact Array and Karoo Array Telescope (KAT- 7) radio arrays, spanning the entire period of the outburst. Our rich data set exposes radio emission that displays a high level of large scale variability compared to the X-ray emission and deviations from the standard radio-X-ray correlation that are indicative of an unstable jet and confirm the outburst's transition from the canonical hard state to an intermediate state. We also observe steepening of the spectral index and an increase of the linear polarization to a large fraction (is approx. equal to 50%) of the total flux, as well as a rotation of the electric vector position angle. These are consistent with a transformation from a self-absorbed compact jet to optically-thin ejecta - the first time such a discrete ejection has been observed in a failed outburst - and may imply a complex magnetic field geometry.

black↗
DOE OSTI2015

Extension of structure-reactivity correlations for the hydrogen abstraction reaction by bromine atom and comparison to chlorine atom and hydroxyl radical

Recently we presented structure-reactivity correlations for the gas-phase ambient-temperature rate constants for hydrogen abstraction from sp 3 -hybridized carbon by chlorine atom and hydroxyl radical (Cl•/HO• + HCR 3 → HCl/HOH + •CR 3 ); the reaction enthalpy effect was represented by the independent variable Δ r H and the polar effect by the independent variables F and R, the Hammett constants for field/inductive and resonance effects. Both these reactions are predominantly exothermic and have early transition states. Here we present a parallel treatment for Br• whose reaction is significantly endothermic with a correspondingly late transition state. In spite of lower expectations because the available data base is less extensive and much more scattered and because long temperature extrapolations are often required, the resulting least-squares fit (log k 298,Br = –0.147 Δ r H –4.32 ΣF –4.28 ΣR –12.38 with r 2 = 0.92) was modestly successful and useful for initial predictions. The coefficient of Δ r H was ~4-fold greater, indicative of the change from an early to a late transition state; meanwhile the sizable coefficients of ΣF and ΣR indicate the persistence of the polar effect. Although the mean unsigned deviation of 0.79 log k 298 units is rather large, it must be considered in the context of a total span of over 15 log units in the data set. Lastly, the major outliers are briefly discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗