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Particle Acceleration in Active Galactic Nuclei

The investigation of stochastic particle acceleration through resonant interactions with plasma waves that populate the magnetosphere surrounding an accreting black hole is presented. Stochastic acceleration has been successfully applied to the problem of ion and electron energization in solar flares, and is capable of accounting for a wide range of both neutral and charged particle emissions. It is also a component in diffusive shock acceleration, since pitch-angle scattering (which is necessary for multiple shock crossings) is accompanied by diffusion in momentum space, which in turn yields a net systematic energy gain; however, stochastic energization will dominate the first-order shock process only in certain parameter regimes. Although stochastic acceleration has been applied to particle energization in the lobes of radio galaxies, its application to the central regions of AGNs (active galactic nuclei) has only recently been considered, but not in detail. We proposed to systematically investigate the plasma processes responsible for stochastic particle acceleration in black hole magnetospheres along with the energy-loss processes which impede particle energization. To this end, we calculated acceleration rates and escape time scales for protons and electrons resonating with Alfven waves, and for electrons resonating with whistlers. We also considered the "hot" topic of gamma-ray line emission from the Orion complex. We proposed that the observed gamma-ray lines are produced by energetic ions that are stochastically accelerated by cascading Alfven waves in the accretion plasma near a black hole. Related research papers that were published in journals are listed.

Miller, James A.↗

Advanced Water Vapor Lidar Detection System

In the present water vapor lidar system, the detected signal is sent over long cables to a waveform digitizer in a CAMAC crate. This has the disadvantage of transmitting analog signals for a relatively long distance, which is subjected to pickup noise, leading to a decrease in the signal to noise ratio. Generally, errors in the measurement of water vapor with the DIAL method arise from both random and systematic sources. Systematic errors in DIAL measurements are caused by both atmospheric and instrumentation effects. The selection of the on-line alexandrite laser with a narrow linewidth, suitable intensity and high spectral purity, and its operation at the center of the water vapor lines, ensures minimum influence in the DIAL measurement that are caused by the laser spectral distribution and avoid system overloads. Random errors are caused by noise in the detected signal. Variability of the photon statistics in the lidar return signal, noise resulting from detector dark current, and noise in the background signal are the main sources of random error. This type of error can be minimized by maximizing the signal to noise ratio. The increase in the signal to noise ratio can be achieved by several ways. One way is to increase the laser pulse energy, by increasing its amplitude or the pulse repetition rate. Another way, is to use a detector system with higher quantum efficiency and lower noise, on the other hand, the selection of a narrow band optical filter that rejects most of the day background light and retains high optical efficiency is an important issue. Following acquisition of the lidar data, we minimize random errors in the DIAL measurement by averaging the data, but this will result in the reduction of the vertical and horizontal resolutions. Thus, a trade off is necessary to achieve a balance between the spatial resolution and the measurement precision. Therefore, the main goal of this research effort is to increase the signal to noise ratio by a factor of 10 over the current system, using a newly evaluated, very low noise avalanche photo diode detector and constructing a 10 MHz waveform digitizer which will replace the current CAMAC system.

Elsayed-Ali, Hani↗

Radial Velocity Detection of Extra-Solar Planetary Systems

The McDonald Observatory Planetary Search (MOPS) was designed to search for Jovian-mass planets in orbit around solar-type stars by making high-precision measurements of the Radial Velocity (RV) of a star, to attempt to detect the reflex orbital motion of the star around the star-planet barycenter. In our solar system, the velocity of the Sun around the Sun-Jupiter barycenter averages 12.3 m/ s. The MOPS survey started operation in September 1987, and searches 36 bright, nearby, solar-type dwarfs to 10 m/s precision. The survey was started using telluric O2 absorption lines as the velocity reference metric. Observations use the McDonald Observatory 2.7-m Harlan Smith Telescope coude spectrograph with the six-foot camera. This spectrograph configuration isolates a single order of the echelle grating on a Texas Instruments 800 x 800 CCD. The telluric line method gave us a routine radial velocity precision of about 15 m/s for stars down to about 5-th magnitude. However, the data obtained with this technique suffered from some source of long-term systematic errors, which was probably the intrinsic velocity variability of the terrestrial atmosphere, i.e. winds. In order to eliminate this systematic error and to improve our overall measurement precision, we installed a stabilized I2 gas absorption cell as the velocity metric for the MOPS in October 1990. In use at the telescope, the cell is placed directly in front of the spectrograph entrance slit, with starlight passing through the cell. The use of this sealed stabilized I2 cell removes potential problems with possible long-term drifts in the velocity metric. The survey now includes a sample of 36 nearby F, G, and K type stars of luminosity class V or IV-V.

Cochran, William D.↗

Atmospheric Condensational Properties of Ultrafine Chain and Fractal Aerosol Particles

The purpose for the research sponsored by this grant was to lay the foundations for qualitative understanding and quantitative description of the equilibrium vapor pressure of water vapor over the irregularly shaped, carbonaceous particles that are present in the atmosphere. This work apparently was the first systematic treatment of the subject. Research was conducted in two complementary components: 1. Calculations were performed of the equilibrium vapor pressure of water over particles comprised of aggregates of spheres in the 50-200 nm radius range. The purposes of this work were two-fold. First, since no systematic treatment of this subject had previously been conducted, its availability would be directly useful for quantitative treatment for a limited range of atmospheric aerosols. Second, it would provide qualitative indications of the effects of highly irregular particle shape on equilibrium vapor pressure of aggregates comprised of smaller spheres.

Marlow, William H.↗

Particle Acceleration in Active Galactic Nuclei

The high efficiency of energy generation inferred from radio observations of quasars and X-ray observations of Seyfert active galactic nuclei (AGNs) is apparently achieved only by the gravitational conversion of the rest mass energy of accreting matter onto supermassive black holes. Evidence for the acceleration of particles to high energies by a central engine is also inferred from observations of apparent superluminal motion in flat spectrum, core-dominated radio sources. This phenomenon is widely attributed to the ejection of relativistic bulk plasma from the nuclei of active galaxies, and accounts for the existence of large scale radio jets and lobes at large distances from the central regions of radio galaxies. Reports of radio jets and superluminal motion from galactic black hole candidate X-ray sources indicate that similar processes are operating in these sources. Observations of luminous, rapidly variable high-energy radiation from active galactic nuclei (AGNs) with the Compton Gamma Ray Observatory show directly that particles are accelerated to high energies in a compact environment. The mechanisms which transform the gravitational potential energy of the infalling matter into nonthermal particle energy in galactic black hole candidates and AGNs are not conclusively identified, although several have been proposed. These include direct acceleration by static electric fields (resulting from, for example, magnetic reconnection), shock acceleration, and energy extraction from the rotational energy of Kerr black holes. The dominant acceleration mechanism(s) operating in the black hole environment can only be determined, of course, by a comparison of model predictions with observations. The purpose of the work proposed for this grant was to investigate stochastic particle acceleration through resonant interactions with plasma waves that populate the magnetosphere surrounding an accreting black hole. Stochastic acceleration has been successfully applied to the problem of ion and electron energization in solar flares, and is capable of accounting for a wide range of both neutral and charged particle emissions. It is also a component in diffusive shock acceleration, since pitch-angle scattering (which is necessary for multiple shock crossings) is accompanied by diffusion in momentum space, which in turn yields a net systematic energy gain; however, stochastic energization will dominate the first-order shock process only in certain parameter regimes. Although stochastic acceleration has been applied to particle energization in the lobes of radio galaxies, its application to the central regions of AGNs has only recently been considered, but not in detail. We proposed to systematically investigate the plasma processes responsible for stochastic particle acceleration in black hole magnetospheres along with the energy-loss processes which impede particle energization. To this end we calculated acceleration rates and escape time scales for protons and electrons resonating with Alfven waves, and for electrons resonating with whistlers. Assuming either a Kolmogorov or Kraichnan wave spectrum, accretion at the Eddington limit, magnetic field strengths near equipartition, and turbulence energy densities approx. 10% of the total magnetic field energy density, we find that Alfven waves accelerate protons to Lorentz factors approx, equals 10(exp 4) - 10(exp 6) before they escape from the system. Acceleration of electrons by fast mode and whistler waves can produce a nonthermal population of relativistic electrons whose maximum energy is determined by a competition with radiation losses.

Miller, James A.↗

[MODIS Investigation]

The objective of the last six months were: (1) Continue analysis of Hawaii Ocean Time-series (HOT) bio-optical mooring data, and Southern Ocean bio-optical drifter data; (2) Complete development of documentation of MOCEAN algorithms and software for use by MOCEAN team and GLI team; (3) Deploy instrumentation during JGOFS cruises in the Southern Ocean; (4) Participate in test cruise for Fast Repetition Rate (FRR) fluorometer; (5) Continue chemostat experiments on the relationship of fluorescence quantum yield to environmental factors; and (6) Continue to develop and expand browser-based information system for in situ bio-optical data. We are continuing to analyze bio-optical data collected at the Hawaii Ocean Time Series mooring as well as data from bio-optical drifters that were deployed in the Southern Ocean. A draft manuscript has now been prepared and is being revised. A second manuscript is also in preparation that explores the vector wind fields derived from NSCAT measurements. The HOT bio-optical mooring was recovered in December 1997. After retrieving the data, the sensor package was serviced and redeployed. We have begun preliminary analysis of these data, but we have only had the data for 3 weeks. However, all of the data were recovered, and there were no obvious anomalies. We will add second sensor package to the mooring when it is serviced next spring. In addition, Ricardo Letelier is funded as part of the SeaWiFS calibration/validation effort (through a subcontract from the University of Hawaii, Dr. John Porter), and he will be collecting bio-optical and fluorescence data as part of the HOT activity. This will provide additional in situ measurements for MODIS validation. As noted in the previous quarterly report, we have been analyzing data from three bio-optical drifters that were deployed in the Southern Ocean in September 1996. We presented results on chlorophyll and drifter speed. For the 1998 Ocean Sciences meeting, a paper will be presented on this data set, focusing on the diel variations in fluorescence quantum yield. Briefly, there are systematic patterns in the apparent quantum yield of fluorescence (defined as the slope of the line relating fluorescence/chlorophyll and incoming solar radiation). These systematic variations appear to be related to changes in the circulation of the Antarctic Polar Front which force nutrients into the upper ocean. A more complete analysis will be provided in the next Quarterly report.

Abbott, Mark R.↗

Analysis of Gamma-Ray Data from Solar Flares in Cycles 21 and 22

One of our primary accomplishments under grant NAGW-35381 was the systematic derivation and compilation, for the first time, of physical parameters for all gamma-ray flares detected by the SMM GRS during its ten year lifetime. The flare parameters derived from the gamma-ray spectra include: bremsstrahlung fluence and best-fit power-law parameters, narrow nuclear line fluence, positron annihilation line fluence, neutron capture line fluence, and an indication of whether or not greater than 10 MeV emissions were present. We combined this compilation of flare parameters with our plots of counting rate time histories and flare spectra to construct an atlas of gamma-ray flare characteristics. The atlas time histories display four energy bands: 56-199 kev, 298526 keV, 4-8 MeV, and 10-25 MeV. These energy bands respectively measure nonrelativistic bremsstrahlung, trans-relativistic bremsstrahlung, nuclear de-excitation, and ultra-relativistic bremsstrahlung. The atlas spectra show the integrated high-energy spectra measured for all GRS flares and dissects them into electron bremsstrahlung, positron annihilation and nuclear emission components. The atlas has been accepted for publication in the Astrophysical Journal Supplements and is currently in press. The atlas materials were also supplied to the Solar Data Analysis Center at Goddard Space Flight Center and were made available through a web site at the University of New Hampshire. Since a uniform methodology was adopted for deriving the flare parameters, this atlas will be very useful for future statistical and correlative studies of solar flares-three independent groups are presently using it to correlate interplanetary energetic particle measurements with our gamma-ray measurements. A better model for the response of the GRS instrument to high energy radiation was also developed. A refined response model was needed because the old model was not adequate for predicting the first and second escape peaks associated with strong nuclear lines nor could it accurately describe the Compton continuum shape. The new response was developed using a GEANT based simulation code and tested against preflight calibration data. The refinement of the response model and the removal of systematic errors now allow more detailed spectral studies of the GRS gamma-ray measurements. This refined response function was supplied to the Solar DAC at Goddard and was also made available via a web site at the University of New Hampshire.

Vestrand, W. Thomas↗

Global Warming Estimation from MSU

In this study, we have developed time series of global temperature from 1980-97 based on the Microwave Sounding Unit (MSU) Ch 2 (53.74 GHz) observations taken from polar-orbiting NOAA operational satellites. In order to create these time series, systematic errors (approx. 0.1 K) in the Ch 2 data arising from inter-satellite differences are removed objectively. On the other hand, smaller systematic errors (approx. 0.03 K) in the data due to orbital drift of each satellite cannot be removed objectively. Such errors are expected to remain in the time series and leave an uncertainty in the inferred global temperature trend. With the help of a statistical method, the error in the MSU inferred global temperature trend resulting from orbital drifts and residual inter-satellite differences of all satellites is estimated to be 0.06 K decade. Incorporating this error, our analysis shows that the global temperature increased at a rate of 0.13 +/- 0.06 K decade during 1980-97.

Prabhakara, C.↗

Efficient Methods to Assimilate Satellite Retrievals Based on Information Content: Suboptimal Retrieval Assimilation - Part 2

One of the outstanding problems in data assimilation has been and continues to be how best to utilize satellite data while balancing the tradeoff between accuracy and computational cost. A number of weather prediction centers have recently achieved remarkable success in improving their forecast skill by changing the method by which satellite data are assimilated into the forecast model from the traditional approach of assimilating retrievals to the direct assimilation of radiances in a variational framework. The operational implementation of such a substantial change in methodology involves a great number of technical details, e.g., pertaining to quality control procedures, systematic error correction techniques, and tuning of the statistical parameters in the analysis algorithm. Although there are clear theoretical advantages to the direct radiance assimilation approach, it is not obvious at all to what extent the improvements that have been obtained so far can be attributed to the change in methodology, or to various technical aspects of the implementation. The issue is of interest because retrieval assimilation retains many practical and logistical advantages which may become even more significant in the near future when increasingly high-volume data sources become available. The central question we address here is: how much improvement can we expect from assimilating radiances rather than retrievals, all other things being equal? We compare the two approaches in a simplified one-dimensional theoretical framework, in which problems related to quality control and systematic error correction are conveniently absent. By assuming a perfect radiative transfer model and perfect knowledge of radiance and background error covariances, we are able to formulate a nonlinear local error analysis for each assimilation method. Direct radiance assimilation is optimal in this idealized context, while the traditional method of assimilating retrievals is suboptimal because it ignores the cross-covariances between background errors and retrieval errors. We show that interactive retrieval assimilation (where the same background used for assimilation is also used in the retrieval step) is equivalent to direct assimilation of radiances with suboptimal analysis weights. We illustrate and extend these theoretical arguments with several one-dimensional assimilation experiments, where we estimate vertical atmospheric profiles using simulated data from both the High-resolution InfraRed Sounder 2 (HIRS2) and the future Atmospheric InfraRed Sounder (AIRS).

Joiner, J.↗

The Problem of Hipparcos Distances to Open Clusters: Constraints from Multicolor a Main-Sequence Fitting - Report 1

Parallax data from the Hipparcos mission allow the direct distance to open clusters to be compared with the distance inferred from main-sequence (MS) fitting. There are surprising differences between the two distance measurements. indicating either the need for changes in the cluster compositions or reddening, underlying problems with the technique of MS fitting, or systematic errors in the Hipparcos parallaxes at the 1 mas level. We examine the different possibilities, focusing on MS fitting in both metallicity-sensitive B-V and metallicity-insensitive V-I for five well-studied systems (the Hyades, Pleiades, alpha Per, Praesepe, and Coma Ber). The Hipparcos distances to the Hyades and alpha Per are within 1 sigma of the MS-fitting distance in B-V and V-I, while the Hipparcos distances to Coma Ber and the Pleiades are in disagreement with the MS-fitting distance at more than the 3 sigma level. There are two Hipparcos measurements of the distance to Praesepe; one is in good agreement with the MS-fitting distance and the other disagrees at the 2 sigma level. The distance estimates from the different colors are in conflict with one another for Coma but in agreement for the Pleiades. Changes in the relative cluster metal abundances, age related effects, helium, and reddening are shown to be unlikely to explain the puzzling behavior of the Pleiades. We present evidence for spatially dependent systematic errors at the 1 mas level in the parallaxes of Pleiades stars. The implications of this result are discussed.

Pinsonneault, Marc H.↗

An Evidenced-Based Approach for Estimating Decompression Sickness Risk in Aircraft Operations

Estimating the risk of decompression Sickness (DCS) in aircraft operations remains a challenge, making the reduction of this risk through the development of operationally acceptable denitrogenation schedules difficult. In addition, the medical recommendations which are promulgated are often not supported by rigorous evaluation of the available data, but are instead arrived at by negotiation with the aircraft operations community, are adapted from other similar aircraft operations, or are based upon the opinion of the local medical community. We present a systematic approach for defining DCS risk in aircraft operations by analyzing the data available for a specific aircraft, flight profile, and aviator population. Once the risk of DCS in a particular aircraft operation is known, appropriate steps can be taken to reduce this risk to a level acceptable to the applicable aviation community. Using this technique will allow any aviation medical community to arrive at the best estimate of DCS risk for its specific mission and aviator population and will allow systematic reevaluation of the decisions regarding DCS risk reduction when additional data are available.

Robinson, Ronald R.↗

Form and Objective of the Decision Rule in Absolute Identification

In several conditions of a line length identification experiment, the subjects' decision making strategies were systematically biased against the responses on the edges of the stimulus range. When the range and number of the stimuli were small, the bias caused the percentage of correct responses to be highest in the center and lowest on the extremes of the range. Two general classes of decision rules that would explain these results are considered. The first class assumes that subjects intend to adopt an optimal decision rule, but systematically misrepresent one or more parameters of the decision making context. The second class assumes that subjects use a different measure of performance than the one assumed by the experimenter: instead of maximizing the chances of a correct response, the subject attempts to minimize the expected size of the response error (a "fidelity criterion"). In a second experiment, extended experience and feedback did not diminish the bias effect, but explicitly penalizing all response errors equally, regardless of their size, did reduce or eliminate it in some subjects. Both results favor the fidelity criterion over the optimal rule.

Balakrishnan, J. D.↗

The Sunyaev-Zel'dovich Effect in Abell 370

We present interferometric measurements of the Sunyaev-Zel'dovich (SZ) effect towards the galaxy cluster Abell 370. These measurements, which directly probe the pressure of the cluster's gas, show the gas is strongly aspherical, on agreement with the morphology revealed by x-ray and gravitational lensing observations. We calculate the cluster's gas mass fraction by comparing the gas mass derived from the SZ measurements to the lensing-derived gravitational mass near the critical lensing radius. We also calculate the gas mass fraction from the SZ data by deriving the total mass under the assumption that the gas is in hydrostatic equilibrium (HSE). We test the assumptions in the HSE method by comparing the total cluster mass implied by the two methods. The Hubble constant derived for this cluster, when the known systematic uncertainties are included, has a very wide range of values and therefore does not provide additional constraints on the validity of the assumptions. We examine carefully the possible systematic errors in the gas fraction measurement. The gas fraction is a lower limit to the cluster's baryon fraction and so we compare the gas mass fraction, calibrated by numerical simulations to approximately the virial radius, to measurements of the global mass fraction of baryonic matter, OMEGA(sub B)/OMEGA(sub matter). Our lower limit to the cluster baryon fraction is f(sub B) = (0.043 +/- 0.014)/h (sub 100). From this, we derive an upper limit to the universal matter density, OMEGA(sub matter) <= 0.72/h(sub 100), and a likely value of OMEGA(sub matter) <= (0.44(sup 0.15, sub -0.12)/h(sub 100).

Grego, Laura↗

Calibration of the Microwave Limb Sounder on the Upper Atmosphere Research Satellite

The Microwave Limb Sounder (MLS) is a three-radiometer, passive, limb emission instrument onboard the Upper Atmosphere Research Satellite (UARS). Radiometric, spectral and field-of-view calibrations of the MLS instrument are described in this paper. In-orbit noise performance, gain stability, spectral baseline and dynamic range are described, as well as use of in-flight data for validation and refinement of prelaunch calibrations. Estimated systematic scaling uncertainties (3 sigma) on calibrated limb radiances from prelaunch calibrations are 2.6% in bands 1 through 3, 3.4% in band 4, and 6% in band 5. The observed systematic errors in band 6 are about 15%, consistent with prelaunch calibration uncertainties. Random uncertainties on individual limb radiance measurements are very close to the levels predicted from measured radiometer noise temperature, with negligible contribution from noise and drifts on the regular in-flight gain calibration measurements.

Jarnot, R. F.↗

Moisture Forecast Bias Correction in GEOS DAS

Data assimilation methods rely on numerous assumptions about the errors involved in measuring and forecasting atmospheric fields. One of the more disturbing of these is that short-term model forecasts are assumed to be unbiased. In case of atmospheric moisture, for example, observational evidence shows that the systematic component of errors in forecasts and analyses is often of the same order of magnitude as the random component. we have implemented a sequential algorithm for estimating forecast moisture bias from rawinsonde data in the Goddard Earth Observing System Data Assimilation System (GEOS DAS). The algorithm is designed to remove the systematic component of analysis errors and can be easily incorporated in an existing statistical data assimilation system. We will present results of initial experiments that show a significant reduction of bias in the GEOS DAS moisture analyses.

Dee, D.↗

Landsat 7: An Early Look at On-Orbit Performance

As this article was being submitted in mid-March, 1999, Landsat 7 had been cleared for an official launch date of April 15, 1999, approximately 2 and 1/2 months prior to the 21st Canadian Symposium on Remote Sensing. Since it is impossible to discuss "early on-orbit performance" prior to the actual launch of the satellite, we have chosen to briefly summarize the major features of the Landsat 7 program. Additional information can be found at several web sites which will summarized at the end of this paper. At this time, the Landsat Project Science Office is pleased to report that the performance of the ETM+ instrument appears to be very good. In addition to excellent instrument performance, a robust data acquisition plan has been developed with the goal of acquiring and systematically refreshing a global archive of land observations at the EROS Data Center annually. A ground processing system is being implemented at EROS that will be capable of capturing, processing and archiving 250 Landsat scenes per day, and delivering 100 scene products to users daily. In addition, the cost of a systematically-processed Level 1 product will be less than $600, and there will be no copyright protection on the data. The net result is that the use of remote sensing data in our daily lives is expected to grow dramatically. This growth is expected to benefit all facets of the land remote sensing community.

Williams, D. L.↗

The Error Distribution of BATSE GRB Location

We develop empirical probability models for BATSE GRB location errors by a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the InterPlanetary Network (IPN). Models are compared and their parameters estimated using 394 GRBs with single IPN annuli and 20 GRBs with intersecting IPN annuli. Most of the analysis is for the 4B (rev) BATSE catalog; earlier catalogs are also analyzed. The simplest model that provides a good representation of the error distribution has 78% of the locations in a 'core' term with a systematic error of 1.85 degrees and the remainder in an extended tail with a systematic error of 5.36 degrees, implying a 68% confidence region for bursts with negligible statistical errors of 2.3 degrees. There is some evidence for a more complicated model in which the error distribution depends on the BATSE datatype that was used to obtain the location. Bright bursts are typically located using the CONT datatype, and according to the more complicated model, the 68% confidence region for CONT-located bursts with negligible statistical errors is 2.0 degrees.

Briggs, Michael S.↗

The Influence of Airmass Histories on Radical Species during POLARIS

The Goddard trajectory chemistry model was used with ER-2 aircraft data to test our current knowledge of radical photochemistry during the POLARIS (Polar Ozone Loss in the Arctic Region In Summer) campaign. The results of the trajectory chemistry model with and without trajectories are used to identify cases where steady state does not accurately describe the measurements. Over the entire mission, using trajectory chemistry reduces the variability in the modeled NO(x) comparisons to data by 25% with respect to the same model simulating steady state. Although the variability is reduced, NO(x)/NO(y) trajectory model results were found to be systematically low relative to the observations by 20-30% as seen in previous studies. Using new rate constants for reactions important in NO(y) partitioning improves the agreement of NO(x)/NO(y) with the observations but a 5-10% bias still exists. OH and HO2 individually are underpredicted by 15% of the standard steady state model and worsen with the new rate constants. Trajectory chemistry model results of OH/HO2 were systematically low by 10-20% but improve using the new rates constants because of the explicit dependence on NO. This suggests that our understanding of NO(x) is accurate to the 20% level and HO(x) chemistry is accurate to the 30% level in the lower stratosphere or better for the POLARIS regime. The behavior of the NO(x) and HO(x) comparisons to data using steady state versus trajectory chemistry and with updated rate coefficients is discussed in ten-ns of known chemical mechanisms and lifetimes.

Pierson, J. M.↗