Reverse Trajectory Research Articles

Comparison of satellite ozone observations in coincident air masses in early November 1994

Ozone observed by seven satellite instruments, the Atmospheric Trace Molecule Spectroscopy instrument (ATMOS), Stratospheric Aerosol and Gas Experiment (SAGE) II, Polar Ozone and Aerosol Measurement (POAM) II instrument, Halogen Occultation Experiment (HALOE), Microwave Limb Sounder (MLS), Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA), and Millimeter‐wave Atmospheric Sounder (MAS), during early November 1994 is mapped in equivalent latitude/potential temperature (EqL/θ) space to facilitate nearly global comparisons of measurements taken in similar air masses. Ozone from all instruments usually agrees to within 0.5 ppmv (∼5%) in the upper stratosphere and ∼0.25 ppmv in the lower stratosphere; larger differences in the midstratosphere are primarily due to sampling differences. Individual profile comparisons, selected to match meteorological conditions, show remarkably good agreement between all instruments that sample similar latitudes, although some small differences do not appear to be related to sampling differences. In the Southern Hemisphere (SH) midstratosphere, the instruments (ATMOS, SAGE II, and POAM II) with observations confined to high latitudes measured low EqLs in air drawn up from low latitudes that had formed a “low‐ozone pocket”; they measured much lower ozone at low EqL than those that sampled low latitudes. A low‐ozone pocket had also formed in the Northern Hemisphere (NH) midstratosphere (a month earlier than this phenomenon has previously been reported), also resulting in differences between instruments based on their sampling patterns. POAM II sampled only high latitudes in the NH, where extravortex sampling did not include tropical, high‐ozone air, and thus measured lower ozone at a given EqL than other instruments. Ozone laminae appear in coincident profiles from multiple instruments, confirming atmospheric origins for these features and agreement in some detail between ozone observed by several instruments; reverse trajectory calculations indicate such laminae arise from filamentation in and around the polar vortices. Both EqL/θ and profile comparisons indicate overall excellent agreement in ozone observed by all seven instruments in early November 1994. When care is taken to compare similar air masses and to understand sampling effects, much useful information can be obtained from comparisons between instruments with very different observing patterns.

Transition reform in the mineral-rich Caspian region countries

In the absence of a developmental political state, natural resource abundance may impede the economic transition by diminishing the urgency of reform and by distorting the economy (through Dutch disease effects and also rent-seeking behavior and corruption). These problems tend to be especially acute in mineral-rich economies because the socio-economic linkages from mining concentrate revenues on the government and increase the risk of policy failure. This paper tests these hypotheses through a comparison of mineral-rich and resource-poor countries in transition in the Caspian region, all of which failed to evolve developmental political states. It shows that the mineral-rich countries are slower reformers, despite the fact in three of the four resource-poor countries the reforms were adversely impacted by civil strife. Mineral-rich countries also experience a stronger rebound of the real exchange rate and greater shrinkage of employment in the tradeable sector. These differences are reflected in a reverse J-shape post-transition development trajectory for the mineral-rich countries compared to the V-shaped trajectory of the resource-poor countries. However, rent-seeking and corruption do not appear to vary with the natural resource endowment.

Lamination and polar vortex development in fall from ATMOS long‐lived trace gases observed during November 1994

Long‐lived trace‐gas profiles observed by the Atmospheric Trace Molecule Spectroscopy (ATMOS) instrument around the developing polar vortex (the “protovortex”) during early November 1994 show distinctive inversions (laminae). High‐resolution profiles calculated using a reverse trajectory (RT) model reproduce the majority of these laminae, demonstrating that most of these features arise from advection by the large‐scale winds. The relationship between CH4 and N2O sampled in filaments of low‐latitude air changes from the canonical midlatitude correlation to one typical of tropical air, confirming the identification of tropical laminae. N2O/CH4 correlations for laminae in vortex filaments indicate that enough confined descent and mixing has already occurred in the middle and upper stratosphere by early November to alter the tracer relationship in the protovortex from that in midlatitudes. Distributions of laminae in ATMOS observations agree with regions of greater or less filamentation seen in high‐resolution RT maps. There is a deep minimum in laminae occurrence between 30° and 90°E at all levels, extending to about 150°E above ∼35 km. Maxima in lamination in the lower stratosphere near 90°–150°E and 210°–270°E are associated with the main regions where tropical air is drawn up around the developing vortex. Continuous filamentation associated with the developing vortex and anticyclone in early November 1994 shows that transport and mixing processes previously reported during winter are already important during fall.

Physical characteristics of summer sea ice across the Arctic Ocean

Sea ice characteristics were investigated during July and August on the 1994 transect across the Arctic Ocean. Properties examined from ice cores included salinity, temperature, and ice structure. Salinities measured near zero at the surface, increasing to 3–4‰ at the ice‐water interface. Ice crystal texture was dominated by columnar ice, comprising 90% of the ice sampled. Surface albedos of various ice types, measured with radiometers, showed integrated shortwave albedos of 0.1 to 0.3 for melt ponds, 0.5 for bare, discolored ice, and 0.6 to 0.8 for a deteriorated surface or snow‐covered ice. Aerial photography was utilized to document the distribution of open melt ponds, which decreased from 12% coverage of the ice surface in late July at 76°N to almost none in mid‐August at 88°N. Most melt ponds were shallow, and depth bore no relationship to size. Sediment was pervasive from the southern Chukchi Sea to the north pole, occurring in bands or patches. It was absent in the Eurasian Arctic, where it had been observed on earlier expeditions. Calculations of reverse trajectories of the sediment‐bearing floes suggest that the southernmost sediment was entrained during ice formation in the Beaufort Sea while more northerly samples probably originated in the East Siberian Sea, some as far west as the New Siberian Islands.

Analysis of record‐low ozone values during the 1997 winter over Lauder, New Zealand

Record‐low ozone (O3) column densities (with a minimum of 222 DU) were observed over the Lauder NDSC (Network for the Detection of Stratospheric Change) station (45°S, 170°E) in August 1997. Possible causes are examined using height‐resolvedO3measurements over Lauder, and high‐resolution reverse trajectory maps ofO3(initialised with Microwave Limb Sounder measurements) and of potential vorticity. The analysis shows thatO3poor air originated from two regions: Below the 550 K isentrope (∼22 km) subtropical air was observed, while between 600 and 1000 K (∼25–33.5 km) the polar vortex tilted over Lauder for several days. A rapid recovery of theO3column density was observed later, due to anO3rich polar vortex filament moving over Lauder between 18 and 24 km, while simultaneously theO3poor higher vortex moved away.

Ozone depletion in and below the Arctic Vortex for 1997

The winter 1996/97 was quite unusual with late vortex formation and polar stratospheric cloud (PSC) development and subsequent record low temperatures in March. Ozone depletion in the Arctic vortex is determined using ozonesondes. The diabatic cooling is calculated with PV‐theta mapped ozone mixing ratios and the large ozone depletions, especially at the center of the vortex where most PSC existence was predicted, enhances the diabatic cooling by up to 80%. The average vortex chemical ozone depletion from January 6 to April 6 is 33, 46, 46, 43, 35, 33, 32 and 21 % in air masses ending at 375, 400, 425, 450, 475, 500, 525, and 550 K (about 14–22 km). This depletion is corrected for transport of ozone across the vortex edge calculated with reverse domain‐filling trajectories. 375 K is in fact below the vortex, but the calculation method is applicable at this level with small changes. The column integrated chemical ozone depletion amounts to about 92 DU (21%), which is comparable to the depletions observed during the previous four winters.

Efficient calculation of photoelectron angular distribution

AbstractDifferent methods of calculating efficiently the angular distribution of photoelectrons escaping from uniform amorphous and polycrystalline targets are analysed in detail. Comparison has been made between the analytical results and Monte Carlo simulation data. The analytical approach is based on the solution of the kinetic equation in the transport approximation. The Monte Carlo codes comprise the conventional forward simulation algorithm and the reverse trajectory method. The reverse trajectory method employs the reciprocity theorem and allows same statistically significant results to be obtained with less computational effort. The angular distributions of photoelectrons leaving Al, Si, Cu, Ag, Ta and Au samples have been calculated as a function of polar and azimuthal angles for electron energies relevant in quantitative XPS analysis. It has been found that both Monte Carlo methods provide equivalent results. The discrepancies between the transport approximation and the Monte Carlo data do not exceed, as a rule, 5%. The largest deviations of the analytical results from those found by Monte Carlo codes are observed in the vicinity of the emission directions, where the photoelectric differential cross‐section has its minima, and are about 15%. The agreement between the results obtained by different approaches, corresponding to the magic angle geometry, is within 2% for all cases studied.

An improved quasiclassical trajectory method for state to state reactive scattering cross sections and rate constants

A systematic scheme is developed for the incorporation into quasiclassical trajectory (QCT) methodology of recent advances in the understanding of vibrationally adiabatic barriers in collinear atom + diatom reactions. The resulting hybrid QCT method centers on a definite set of rules for optimally combining the results of forward and reverse trajectory calculations. It is argued, and demonstrated by practical examples, that the hybrid method will give a more consistently reliable account of the threshold behavior of collinear reaction cross sections than the conventional QCT method. Extension of the method to the three dimensional F+H2 reaction gives similarly encouraging results, both for state to state reaction cross sections and for rate constants.

A quasiclassical trajectory study of the F+HH⇄FH+H reaction

A detailed forward and reverse quasiclassical trajectory computation for the FHH reaction is presented. An adiabatic analysis of the results shows that to a large extent the differences between HF(v=3) and HF(v=2) product distributions are due to the existence of an exit channel adiabatic barrier for the v=3 state. A sideways peak in the angular distribution for HF(v=2, j) is found in the reverse quasiclassical computation. Total cross sections computed from reverse quasiclassical trajectories are in good agreement with the quantal lin reactive infinite order sudden approximation. We conclude that many of the discrepancies between forward quasiclassical results and quantal computations are not due to quantal resonances but rather to the large boxing of vibrational states.

Quasiclassical trajectory (and variational transition state theory) study of the rates and temperature-dependent activation energies of the reactions Mu+H2 (completely thermal) and H, D, and Mu+H2 (v=0, j=2)

We report forward and backward quasiclassical trajectory calculations of the rate constant for the reaction Mu+H2→MuH+H at 444–2400 K. The accuracy of the calculations is assessed by comparison to variational transition state theory, both with and without tunneling contributions, and to experiment. We find the backward trajectory calculations are more accurate, as would be expected since the dynamical bottleneck occurs towards the products in the Mu+H2 reaction. Both the reverse trajectory calculations and the variational transition state theory calculations including tunneling agree with the experimental rate constants within a factor of about 2, which is considered very good agreement. We also report trajectory calculations and variational transition state theory calculations for the temperature-dependent activation energy, which increases by about 4 kcal/mol over the temperature range studied. To aid in the interpretation of this temperature dependence and that found in previous studies for H+H2 and D+H2, we also report temperature-dependent activation energies for the three state-selected rate constants H(D,Mu)+H2(v=0, j=2) →H2(HD,HMu)+H.

On self-consistent and stochastic treatments of V—T energy transfer in collinear atom-diatom collisions

The use of stochastic reduction approximations in studies of vibrational energy transfer in collinear atom plus diatomic molecule (harmonic oscillator) collisions is investigated. We begin by deriving exact coupled Liouville equations for the time evolution of vibrational and translational degrees of freedom in these collisions. Neglect of terms involving T—V correlation leads directly to the well known self-consistent approximations (SCA), and with further simplification to impulsive approximations. A self-consistent stochastic (SCS) method is then introduced, and it is found to provide an intermediate level of approximation between SCA and impulsive. For the simple hamiltonian considered, the SCS approximation leads to closed form expressions for the translational equations of motion. A special partitioning of translation and vibration first developed by Rosen is then introduced via two canonical transformations and is shown to lead to an improved description of translation—vibration correlations. Application of the SCS approximation within the framework of this partitioning leads to an energy conserving closed form trajectory which reduces to the refined impulse approximation of Matahan in the appropriate limit. Consideration of collision ensembles corresponding to both forward and reverse trajectories leads to a velocity symmetrized method analogous to that used in the ITFITS method. Numerical applications of the refined SCS method to He + H 2 and (N 2) + N 2 indicates that this method is more accurate than ITFITS (with only a small increase in complexity) in predicting low order moments of the energy transfer, at least at low collision energies ( E T/ñω < 3–4). Transition probabilities for single quantum jump transitions are also accurately predicted at these energies (in comparing with exact quantum results) but probabilities of multiple quantum jump transitions, and of single quantum jump transitions at high collision energies are often less quantitative, primarily due to inaccuracies in the treatment of vibrational motion by master equation methods.

Exact quantum, quasiclassical, and semiclassical reaction probabilities for the collinear F+H2 → FH+H reaction

Exact quantum, quasiclassical, and semiclassical reaction probabilities and rate constants for the collinear reaction F+H2 → FH+H are presented and compared. The exact quantum results indicate a large degree of population inversion of the FH product with PR02 and PR03 being the dominant reaction probabilities. The energy dependence of these two probabilities at low translational energies are quite different. PR02 shows an effective threshold of 0.005 eV which can largely be interpreted as resulting from tunneling through a vibrationally adiabatic barrier. PR03 has a much larger effective threshold (0.045 eV) apparently resulting from dynamical effects. Quasiclassical probabilities for the collinear F+H2 reaction were calculated by both the forward (initial conditions chosen for reagent F+H2) and reverse (initial conditions for product H+FH) trajectory methods. The results of both calculations correctly indicate that PR03 and PR02 should be the dominant reaction probabilities. However, the threshold behavior of the quasiclassical forward PR03 disagrees strongly with the corresponding exact quantum threshold energy dependence. By contrast, there is good agreement between the reversed trajectory results and the exact quantum ones. The uniform semiclassical results also agree well with the corresponding exact quantum ones indicating that the quasiclassical reverse and the semiclassical methods are preferable to the quasiclassical forward method for this reaction. The important differences between the threshold behavior of the exact quantum and quasiclassical forward reaction probabilities are manifested in the corresponding rate constants primarily as large differences in their activation energies. Additional exact quantum results at higher total energies indicate that threshold effects are no longer important for reactions with vibrationally excited H2. Resonances play an important role in certain reaction probabilities primarily at higher relative translational energies.

Violation of microscopic reversibility and the use of reverse quais-classical trajectories for calculating reaction cross sections

In order to calculate the transition probabilities (or cross sections) for reactive collisions, such as A + BC(ν, j)→ AB(ν′, j) + C, using the quasi-classical trajectory method, one quantizes the internal energy of the reagents and in addition adopts some algorithm for calculating the internal quantum numbers of the products. A serious consequence of this procedure is that the quasi-classical results do not obey microscopic reversibility. It is shown that for the collinear F + H 2(ν = 0) → FH(ν = 2, 3)+ H reaction (and its D 2 counterpart), the quasi-classical trajectory probabilities for the reverse reaction not only differ substantially from the forward ones but in general are in much better agreement with accurate quantum calculations. A similar situation was found for the collinear H + H 2(0) → H 2(1) + H reaction. We suggest that in doing quasi-classical calculations, the reverse of the process of interest should also be considered. Comparison of forward and reverse quasi-classical collinear calculations with accurate collinear quantum results could give an indication of whether forward or reverse calculations should be used for the three-dimensional case.