JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D05312, doi:10.1029/2007JD008982, 2008
Effect of plume processes on aircraft impact P. F. Vohralik,1 L. K. Randeniya,1 I. C. Plumb,1 and S. L. Baughcum2 Received 17 May 2007; revised 17 September 2007; accepted 29 November 2007; published 13 March 2008.
 A versatile Gaussian plume model has been developed and used to investigate the
chemistry in expanding aircraft plumes for a wide range of conditions, including the plume expansion rate, the composition of the background atmosphere, and the total time of the plume integration. The dependence of plume processing on altitude, latitude and season has been investigated in order to generate plume parameterizations for use in global models. Two different parameterizations have been compared. The results of the two parameterizations have been incorporated into a global model to assess the importance of plume processing on calculated aircraft impact. In contrast to a previous plume study, which found reductions of 20–35% in aircraft-induced NOx at cruise altitude and 10– 12% smaller column ozone changes at northern midlatitudes when plume effects were incorporated, results from the present study suggest that plume processing has only a small effect on the calculated aircraft impact on ozone at subsonic cruise altitudes. Both plume parameterizations gave small changes in ozone perturbations, suggesting that differences between previous modeling studies are not due primarily to the different parameterizations used in those studies. Citation: Vohralik, P. F., L. K. Randeniya, I. C. Plumb, and S. L. Baughcum (2008), Effect of plume processes on aircraft impact, J. Geophys. Res., 113, D05312, doi:10.1029/2007JD008982.
1. Introduction  In recent years, considerable attention has been devoted to assessing the effects of subsonic aircraft at cruise altitude on climate [Thompson et al., 1996; Friedl, 1997; Brasseur et al., 1998; Penner et al., 1999; Sausen et al., 2005; Gauss et al., 2006]. In addition to direct radiative forcing by emissions of CO2, aircraft NOx (NO + NO2) emissions result in ozone production in the upper troposphere, where climatic impacts are greater than for groundlevel emissions. Emissions of aerosols, soot and water can also affect climate by formation of persistent contrails or through changes in cloud cover. Proposed albedo enhancement schemes to reduce global warming [Crutzen, 2006] may also require better understanding of dispersal processes and chemical transformations in plumes in the upper troposphere/lower stratosphere.  Given that aircraft NOx emissions have a relatively short atmospheric lifetime and other sources of NOx, both man-made and nonanthropogenic, need to be considered, effects of aircraft NOx emissions on the atmosphere are assessed using global chemical transport models. These models are grid point models, where the spatial resolution is generally determined by computational constraints. Aircraft emissions are of necessity averaged over grid cell volumes in such global models.
1 Materials Science and Engineering, Commonwealth Scientific and Industrial Research Organisation, Lindfield, New South Wales, Australia. 2 Boeing Company, Seattle, Washington, USA.
Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JD008982
 In the atmosphere, aircraft emissions are initially largely confined to the aircraft trailing vortices, with transverse dimensions of the order of meters. Turbulent mixing then results in expansion of the aircraft exhaust plumes to horizontal dimensions typical of three-dimensional chemical transport model grid cells (100– 500 km) on timescales of the order of a day. Because atmospheric chemistry is known to be highly nonlinear, it would be expected that the calculated chemical composition of the model grid cells could be significantly different if the evolution of the plume had been followed, rather than simply diluting the aircraft emissions into the grid cell.  Plume processes are inherently subgrid-scale in multidimensional global models, so they need to be studied using off-line models with dimensions of the order of plume dimensions and the effects of plume processes parameterized for inclusion in multidimensional models. Several studies have been made of plume processes [Danilin et al., 1994; Meijer et al., 1997; Petry et al., 1998; Moulik and Milford, 1999; Kraabøl and Stordal, 2000; Karol et al., 2000; Kraabøl et al., 2000b; Esler, 2003; Meilinger et al., 2005] and different parameterizations have been developed. Kraabøl et al.  obtained reductions of 15– 18% in calculated ozone changes at cruise altitude due to subsonic aircraft emissions in a 3-D model study when plume processes were included. Meijer et al.  reported similar percent reductions in ozone changes due to aircraft when they included plume processes in their 3-D model study. That study, however, did not include O3 generated during the plume expansion. When this was included, the effect of plume processes was to change the calculated ozone increase from aircraft by 0% to 5% in January and by +5% to 10% in July [Meijer, 2001]. There is thus
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considerable uncertainty in the importance of plume processes for aircraft assessment studies.  In order to address these issues and to quantify the effects of plume processes, a Gaussian plume model was used in the present study to investigate the chemistry of expanding aircraft plumes for a wide range of conditions. Plume processes are described using two different parameterizations: emission conversion factors [Kraabøl et al., 2002] and relative emission changes [Petry et al., 1998]. The sensitivity of the results to the plume expansion rate, the composition of the background atmosphere and the total time of the plume integration was considered. These studies allow insights to be gained about the processes which are important for determining the conversion of NOx to other nitrogen-containing compounds in the plume and on the production of ozone. Finally, the implications of these results for global model studies of aircraft impact are discussed. In particular, the contribution of plume processes to aircraft-related ozone change is estimated using a 2-D chemical transport model for the parameterizations of Kraabøl et al.  and Petry et al. .
plume than would be the case if the emissions were diluted into the global model grid cell. A greater fraction of the initial NOx would therefore be expected to remain as NOx after, say, 24 h for the case of an aircraft plume.  In a global assessment model, the emissions from all aircraft trajectories within each model grid cell over a given period of time are averaged and represented as a time-varying emission rate for each emitted species. What is required from a plume parameterization is a modification to the emissions (or a set of effective emissions), which takes into account the chemistry in the expanding plume. There are two schools of thought on how this should be done.  The first approach [Kraabøl et al., 2000a; Meijer, 2001] uses the plume model to calculate the chemical composition of the plume after it has expanded to dimensions corresponding roughly to a global model grid cell. Emission conversion factors (ECFs) are defined for each species X emitted or produced in the plume: ECFX ðt Þ ¼
Xðt Þ Xa ðt Þ NOyðt Þ NOya ðt Þ
2. Parameterizations of Plume Processes  Given the high emission rates of NOx from aircraft engines (relative to background production rates), the chemistry in the plume is dominated initially by high concentrations of NO, particularly toward the axis of the plume. This high NO results in strong suppression of HO2 by the reaction HO2 þ NO ! OH þ NO2
and other peroxy radicals via CH3 O2 þ NO ! CH3 O þ NO2
with analogous reactions for other organic precursors. There is an anticorrelation between NO and HO2 concentrations in the plume, which results in a lowering of the production efficiency for ozone, relative to what would be the case if the emissions were diluted into a global model grid cell. Given that NO2 also peaks on the axis of the plume, there is also an anticorrelation between HO2 and NO2, resulting in less efficient production of HO2NO2 via HO2 þ NO2 þ M ! HO2 NO2 þ M
than would be the case for emissions added directly to a global model grid cell. Similar considerations apply for the formation of peroxy nitrates, such as methyl-peroxy nitrate: CH3 O2 þ NO2 þ M ! CH3 O2 NO2 þ M
CH3 CðOÞO2 þ NO2 þ M ! CH3 CðOÞO2 NO2 þ M
 As a result, there is less efficient conversion of NOx to other nitrogen-containing compounds in the
where X and Xa are the total and ambient (i.e., background) amounts of X integrated over the cross section of the plume and NOy and NOya are the corresponding amounts of total odd nitrogen (NOy = NOx + HNO3 + HO2NO2 + CH 3O2NO2 + PAN + 2N 2O5 + other odd-nitrogen compounds). That is, the emission conversion factor is the ratio of the excess amount of species X above background to the amount of NOy above background. Because NOy is chemically conserved, the amount of NOy above background is constant, and D(NOx) = D(NOy) = NOy(t) NOya(t) represents the total odd nitrogen emitted by the aircraft as NOx. The sum of the ECFs for all NOy species is unity. However, because O3 is produced in the plume, there is also an effective emission of O3. Given that NOx will reduce over the time of the plume integration, this approach results in lower emission of NOx in the global model than would be obtained if the full aircraft NOx emission was used. However, there is an emission of O3 included which will tend to counter the effect of a lower NOx emission in a global model.  The second approach [Petry et al., 1998] compares the composition of the plume after it has expanded to the dimensions of a global model grid cell with a calculation in which the aircraft emissions (per km) are diluted at time of emission into a cross-sectional area corresponding to the global model grid cell. This ‘‘instantaneous dispersion’’ (ID) calculation is taken to represent a global model grid cell without plume corrections. The difference between these two calculations, which represents the effects of nonlinearities in the chemistry discussed above, is used to calculate a set of effective emission indices to use in the global model. For all species X emitted or produced in the plume, corrections d(X) are calculated such that, when the corrections are used to modify the original emissions in the ID calculation, the results of the ID calculation are made to agree with the plume integration. The relative emission change for X, expressed as a percentage of the total
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NOx emission D(NOx) in the absence of any added corrections, is then defined by drel ðXÞ ¼ 100
dðXÞ : DðNOxÞ
 In this expression, the units used for d(X) and D(NOx) must be the same, but whether one chooses mixing ratios, concentrations, or moles, makes no difference. Conversely, when using relative emission changes drel(X) to ‘‘correct’’ a global model calculation for plume effects, equation (7) can be used to redistribute the original NOx emission, D(NOx), as required. Finally, the relative emission changes can be used to define effective emission indices, EIeff(X), for each species X. In the case of NOx, this becomes EIeff ðNOxÞ ¼
d rel ðNOxÞ EI ðNOxÞ; 100
while for other species for which adjustments are made, the effective emission index corresponding to the relative emission change is given by EIeff ðXÞ ¼
mX d rel ðXÞ EI ðNOxÞ mNO2 100
where EI(NOx) is the emission index for nitrogen oxides, expressed in g of equivalent NO2 per kg of fuel, mX is the molar mass of species X (g/mol), and EIeff(X) is expressed in g-X/kg-fuel.  These two approaches for including the effects of plume processes in multidimensional models are fundamentally quite different, and there has been little discussion in the literature as to their relative merits. In the present study, both emission conversion factors and relative emission changes have been calculated and their sensitivities to emission parameters, plume expansion rates, the background atmosphere, latitude, altitude and season have been determined. In addition, a 2-D chemical transport model has been used to estimate the importance of plume effects for global model results using both of these parameterizations.
3. Model Description 3.1. Plume Model 3.1.1. Plume Dynamics  The exhaust plume behind an aircraft is considered to evolve in three regimes: the jet, vortex and dispersion regimes [Ka¨rcher, 1999; Kraabøl et al., 2000b]. These three regions are characterized by different mixing processes. Mixing processes in the atmosphere are not truly diffusive in nature, and the timescales for mixing are scale-dependent [Richardson, 1926; Davis et al., 1994; Lovejoy et al., 2001; Tuck et al., 2003; Lovejoy et al., 2004]. However, both observational data [Schumann et al., 1995] and fluid dynamical simulations [Durbeck and Gerz, 1995] have shown that is possible to represent the dispersion of aircraft exhaust plumes using Gaussian plumes with turbulent eddy diffusion coefficients which are consistent with both in situ
measurements and with calculations. The Gaussian profile is a central assumption of the present work, an assumption which has been made in most studies of the chemical evolution of aircraft plumes [Karol et al., 1997; Meijer et al., 1997; Petry et al., 1998; Kraabøl et al., 2000b]. However, it must be kept in mind that this is an approximation to the complex three-dimensional fluid dynamics, which requires large eddy simulation methods for its accurate description [Durbeck and Gerz, 1995; Ehret and Oertel, 1998; Gerz et al., 1998; Chlond, 1998; Lewellen and Lewellen, 2001a, 2001b].  The integration of the exhaust plume in the present studies begins at the start of the vortex regime, with dilution factors and chemical transformations which occur in the jet regime being taken from previous modeling studies of the jet regime [Ka¨rcher, 1995; Ka¨rcher et al., 1996]. During the vortex regime, the exhaust gases are efficiently trapped by the two trailing vortices. In this regime, which is still dominated by aircraft-induced turbulence, the assumption is made that the aircraft wakes can be replaced by a single Gaussian plume of circular cross section [Kraabøl et al., 2000b].  The vortex structures break down approximately 2 min downstream of the aircraft and thereafter, in the dispersion regime, mixing is dominated by turbulent mixing processes in the background atmosphere. The diameter of the plume at the end of the vortex phase is determined from near-field plume measurements [Kraabøl et al., 1999]. Because atmospheric horizontal mixing is much more rapid than vertical mixing, the plume cross section changes from circular to elliptical in the dispersion phase. However, the Gaussian approximation is still used to describe the horizontal and vertical radial profiles of the plume at any given time. Unless noted otherwise, dimensions of the expanding Gaussian plume were calculated using the parameters given in Appendix A (Table A1), which are representative of a 747 aircraft, using the formulation developed by Konopka  to calculate the horizontal and vertical standard deviations of the plume (sh and sv) from the diffusion coefficients (Dh, Dv and Ds) in the dispersion regime. The formulation developed by Konopka  was subsequently used by Schumann et al. , Durbeck and Gerz , Petry et al.  and Kraabøl et al. .  The first version of the plume model developed in the present work was based on the method of Kraabøl et al. [1999, 2000b]. Initial tests of the plume model focused on attempting to reproduce the results of the summer case described by Kraabøl et al. [1999, 2000b]. Although there were some differences, the overall agreement between the two models was reasonable, and it was concluded that the methodology of Kraabøl et al. had been implemented correctly. Further tests of model performance were then made, including testing the sensitivity of the results to the number of annuli in the plume. Results for conversion of NOx to products after 24 h of integration showed a dependence on the number of annuli used in the calculation. The percentage of the initial NOx remaining after 24 h of integration continued to increase with the total number of annuli, with no real sign of convergence as the number of annuli was increased.
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 Examination of the radial profiles after 24 h of integration revealed that species were highly peaked on the axis of the plume (i.e., non-Gaussian). These results (see section S1.1 of auxiliary material for details) reveal a flaw with this approach to modeling aircraft plumes.1 A central assumption in the model is that the radial profiles are Gaussian. The dimensions of the plume are derived from expressions based on analytical solutions of the diffusion equation for a Gaussian profile [Konopka, 1995]. It is the turbulent mixing which results in the expansion of the plume and the dimensions of the plume depend on the magnitudes of the horizontal and vertical diffusion coefficients. The expanding Gaussian plume approximation thus inherently takes into account entrainment of the surrounding background air and diffusion in the plume. It is therefore inappropriate to further account for these processes explicitly. By so doing, entrainment of the surrounding air further dilutes the concentrations of species in the plume and results in a more strongly peaked radial profile.  A solution to this difficulty was proposed by Melo et al. , based on earlier work by Freiberg . This approach has been used by Meijer and coworkers [Meijer et al., 1996, 1997; Meijer, 2001] for studies of aircraft plumes. In this approach, diffusion between the annuli and entrainment into the plume occur at rates appropriate to a Gaussian distribution. If chemical reactions in the plume result in departures from a Gaussian profile, then the interchange between layers will still be that appropriate for a Gaussian distribution and the radial distribution will relax toward a Gaussian.  Testing of the modified plume model revealed that the radial distributions of species such as NO were indeed close to Gaussian at the end of a 24-h integration. Simulation of the Kraabøl et al.  summer case with the modified model produced total plume conversion of NOx and product distributions of NOy species in broad agreement with results with the previous version of the model when the latter was run with 4 annuli. Furthermore, using the scheme of Melo et al. , conversion of NOx was found to be essentially independent of the total number of annuli N used over the range 4 N 16. The results of these tests suggest that the Melo et al.  scheme had been implemented correctly. Unless otherwise noted, the results discussed in the remainder of this paper were obtained using the Melo et al.  scheme with N = 8 to represent the expanding Gaussian plume. 3.1.2. Plume Chemistry, Emissions, and Background Atmosphere  The calculations reported in the present work used a comprehensive tropospheric/stratospheric reaction set, including reactions on background aerosols and aerosols resulting from aircraft emissions into the expanding plume (see Appendix B for further details). Where possible, rate coefficients were taken from the JPL00 recommendations [Sander et al., 2000]. The effect of using JPL97 [DeMore et al., 1997], JPL02 [Sander et al., 2003] and JPL06 [Sander et al., 2006] chemistry is discussed in section S2 of the auxiliary material. For a given plume simulation, a 5-d box model integration is carried out to establish a self-consistent 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2007JD008982.
diurnally varying solution for the background atmosphere. At the specified emission time, aircraft emissions are added to the plume (at the start of the vortex regime) and the chemistry occurring in the expanding plume is integrated forward for the required time. Emission conversion factors and relative emission changes are then calculated.  For sensitivity studies of the type discussed in this work, it is desirable to have a primary base case throughout. Because of the availability of measurements from the SONEX campaign and the importance of the North Atlantic Flight Corridor for air traffic, a latitude of 50°N on 1 November has been chosen for the location and time of the year for the base case. The composition of the background atmosphere for this base case is that for the background case in the work by Jaegle et al. [2000, Table 2]. This is typical of approximately 50% of the air masses sampled during the SONEX mission and is given in Appendix A (Table A2). Most of the mixing ratios in Table A2 are taken from Jaegle et al. [2000, Table 2]. The value for n-C4H10 is from Jaegle et al. . Values for C2H4, C3H6, CH3CHO and PPN are estimates based on data from the Pacific Exploratory Missions (PEM-Tropics and PEMWest) [Hoell et al., 1997, 1999; Raper et al., 1999].  The mixing ratios given in Table A2 are used to initialize the background spin-up at local noon and the box model is integrated for 5 d in order to obtain a selfconsistent diurnally varying representation of the background atmosphere. During this 5-d background spin-up: O3 and HNO3 are fixed; members of NOt (NO + NO2 + NO3 + 2N2O5 + HO2NO2) are rescaled at noon so that NOx (NO + NO2) is the same as specified in the background climatology; and NO2 is reset at every time step to maintain the specified value of NOt using NO2 = NOt(initial) NO NO3 2N2O5 HO2NO2. These adjustments are made to obtain a background atmosphere as consistent as possible with the specified O3, NOx and HNO3 values. Similar adjustments were made by Jaegle et al. [2000, 2001] for their SONEX box model studies. As a result of these adjustments, it is possible that NO, NO2, N 2O5 and HO2NO2 noon values at the end of the background spinup will differ from the specified initial values, although the NOx, HNO3, NOt and O3 values will be the same. In order to avoid any discontinuities during the plume integration, these adjustments are applied only during the background spin-up.  The other nonradical compounds in Table A2 encompass a broad range of chemical lifetimes. Some are long-lived (CH4, CO, H2), some change relatively slowly over 24 h (PAN, acetone, CH3COOH, C3H8, n-C4H10), and others are relatively short-lived (C2H4, C3H6), although the lifetimes can change considerably with latitude, altitude and season. While the hydrocarbons have no significant chemical sources, other compounds have both sources and sinks (acetone, PAN, H2O2, CH3CHO) and, given sufficient time, may reach a steady state concentration. These issues are discussed for the SONEX campaign by Jaegle et al. [2000, 2001]. In the present study, mixing ratios of species not included in the NOy adjustment were initialized at the start of the 5-d background spin-up using the values in Table A2 (or other specified values), and were not reset during the calculation. While this may be a reasonable approximation for moderately long-lived compounds, or those which tend
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toward a steady state concentration, short-lived species will have their mixing ratios reduced considerably before the plume integration starts. The alternative is to reset some or all of the mixing ratios at every noon, approximating sporadic convective updrafts, or to fix them at all times throughout the simulation. However, this may not be appropriate for compounds approaching steady state, or for cases where the initial concentrations are inconsistent with each other or with the local photochemical state (e.g., forcing a short-lived hydrocarbon to a value which is inconsistent with plausible atmospheric transport rates). Ideally, one would consider each case separately to decide how best to constrain the calculations, but given the number of cases considered, this was not feasible in the present work. Finally, given that we are interested in chemical transformations of aircraft emissions occurring in the plume, it is not possible to reset any species of interest after the emissions have been added.  After the 5-d spin-up, the background integration is continued until the specified emission time of day, at which point the emissions are added to the plume at the start of the vortex regime. For the base case scenario used in this work, aircraft emissions are determined using the parameters in Table A3 (Appendix A) and are assumed to have a Gaussian radial distribution. The composition of the aircraft hydrocarbon emissions is taken from Spicer et al. [1994, Table 3] for a CFM-56 engine using JP-5 fuel at 30% thrust, with unquantified hydrocarbon species represented as n-C4H10. Aerosol emissions are included using the scheme of Ka¨rcher , as discussed in Appendix B.  Although many of the parametric studies used the base case background composition as the starting point, other background atmospheres were considered. The sensitivity of plume processes to air masses of different origin was explored using the six different air mass types characterized by Jaegle et al. [2000, Table 2], which includes the background air mass used for the base case. Other calculations considered the latitude and altitude sensitivity of plume processes. Finally, midlatitude plume correction factors were determined for inclusion in global model studies of plume effects. For these studies, the composition of the background atmosphere was estimated using data from a number of sources. Temperatures were based on zonal mean 17-year-average NCEP values (for 1979 through 1997, as obtained from W.J. Randel at NCAR); ozone was based on the climatology developed by Logan and McPeters  for Models and Measurements II; water vapor was based on the climatology developed by Oort ; other compounds were estimated using data from the SONEX, POLINAT and PEM campaigns [Hoell et al., 1997, 1999; Raper et al., 1999; Singh et al., 1999; Jaegle et al., 2000; Thompson et al., 2000]. Data from these missions can be obtained from a number of data archives including: the Community Data Portal (CDP) at NCAR (https://cdp.ucar.edu/), NASA’s Earth Science Project Office (ESPO) database (http://espoarchive.nasa.gov/archive/arcs/ .index.html) and NASA’s Global Tropospheric Experiment (GTE) archive (http://eosweb.larc.nasa.gov/PRODOCS/gte/ table_gte.html). Given the sparseness of much of the available data, some interpolation, extrapolation and guesswork was required. Finally, for some species, values from
the CSIRO 2-D chemical transport model [Randeniya et al., 2002] were used to augment the data available from other sources. 3.1.3. Determination of Plume Parameterizations  As part of a plume simulation, it is necessary to solve both for the different regions of the plume and for the background atmosphere. Emission conversion factors (including NOx conversion and O3 production) can then be calculated directly by differencing the amount of a given species in the plume with the amount in an equivalent volume of the background atmosphere. The amount of conversion will clearly depend on the total time used for the plume integration.  In order to calculate relative emission changes, an additional box was included in the plume calculation to simulate the case where aircraft emissions are diluted instantaneously into a specified volume (the instantaneous dilution, or ID case of Petry et al. ). Differences between the plume calculation and the ID calculation were then used to calculate the corrections required to the emissions in the ID case to produce the same total amount of NOx, O3 and other NOy species as those from the plume calculation at a specified time in the simulation.  Petry et al.  used an iterative minimization technique to determine the corrections to the emissions. In the present work, a matrix-based method was used to determine the corrections. An outline of the method follows. First, we define a Jacobian matrix J relating the change in the final concentration of species i in the ID grid box at the matching time, Ci,final, to a change in species j at the time of emission, Cj,initial, such that Jij ¼
 This is implemented by including additional instantaneous dispersion boxes in the calculation to determine the Jacobian terms numerically. One additional ID box is included for each species for which emission corrections are to be determined (O 3, NOx, HNO 3 , HO 2 NO 2 , CH3O2NO2 and PAN) and a small additional emission for just one of the species is made in each box. Differences at the end of the simulation are then divided by the magnitude of the additional emission to determine the Jacobian terms. In the case of NOx, the perturbation is implemented as a change in the NOx emission index, so that emissions for both NO and NO2 will increase by the same percentage. An estimate of the required corrections can then be obtained by solving Jx = b, where b is the difference between the plume and ID solutions and x is the amount by which the emissions need to be changed to obtain agreement. The relative emission changes follow from x. If an improved estimate of the relative emission changes is required, an additional ID calculation can be performed, in which these estimated corrections are applied to the emissions for the ID calculation before calculating the Jacobian terms. In practice, however, relative emission changes from the first iteration usually produce good agreement between the plume calculation and the corrected ID calculation, reflecting the essentially uncoupled response to small perturbations in the initial emissions into the ID grid box.
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Table 1. Lower Boundary Conditions for Key Nonmethane Hydrocarbons Species
Mixing Ratio, pmol mol1
C2H4 C2H6 C3H6 C3H8 n-C4H10 CH2O CH3CHO CH3OOH ACETONE CH3OH C2H5OH
200 2000 50 800 200 1000 100 300 1000 500 100
 It is essential that the corrections applied to the emissions in the ID grid box neither create nor destroy odd nitrogen, but rather redistribute the total emissions between the subset of nitrogen-containing species used in the matching process. Although the corrections predicted using the above matrix solution produce agreement between the plume and ID calculations at the matching time (for the species used in the matching), they may not conserve odd nitrogen. Most of the calculations reported in the present work included O3, NOx, HNO3, HO2NO2, CH3O2NO2 and PAN in the fitting procedure, and it was found that the predicted corrections using these species required relatively small adjustments to conserve odd nitrogen ( 0.06% of initial NOx for the base case given by Tables A1 –A3). When PAN and CH3O2NO2 were omitted from the matrix solution, however, the adjustments to conserve odd nitrogen were more significant ( 1.5% of initial NOx for the base case). Unless noted otherwise, corrections added to the ID grid cell in the present work were adjusted to conserve odd nitrogen, with the adjustments applied equally to HNO3 and HO2NO2.  One further additional box was included in the model to allow a single region plume calculation of the type performed by Petry et al. . This allows a comparison to be made between single and multiregion calculations and also allows more direct comparison with the results of Petry et al. . The single plume calculation uses a timevarying cross section determined by a = 2.63 smajor and b = 2.63 sminor (from Meijer [2001, equation (4.16)], with N = 8). It also uses the same algorithm for entrainment of background air as the multiregion Melo et al.  model (with N = 8). 3.2. Global Model  An estimate of the importance of plume processes for aircraft assessment studies was obtained using the CSIRO 2-D chemical transport model [Randeniya et al., 2002]. This was done by comparing aircraft impact calculations with and without the inclusion of plume processes. While it is acknowledged that 3-D models are required for a more thorough assessment of the effects of subsonic aircraft, the present 2-D study allows a first-order estimate to be made of the importance of plume processes on the calculated aircraft impact. 3.2.1. CSIRO 2-D CTM  The 2-D calculations used a latitude grid with a 5° interval and a log-pressure altitude grid (z = 16 log10(1000/p))
extending from the ground to 80 km with a 1 km spacing when solving for the diurnally averaged zonal mean mixing ratios. The complete diurnal cycle was evaluated at all grid points every 10 d, and the diurnally averaged rate coefficients obtained from these integrations were used to determine the chemical evolution of the diurnally averaged concentrations. The model uses an implicit solver for the chemical solution which has been optimized for use on a vector machine (NEC-SX6) using the grid cell blocking and sparse-matrix techniques developed by Jacobson and Turco . The chemical solver is not family based, but explicitly includes the interactions between the species determined by the reaction set used. The zonal mean meridional circulation (i.e., the residual circulation) is determined from radiative heating rates calculated using the CCM3 Column Radiation Model Version crm-2.1 – crm3.6 [Kiehl et al., 1996] and rainfall-based latent heating rates. Atmospheric transport and mixing is evaluated using a 6 h time step for the longer-lived atmospheric compounds and the following groupings: Ox (O + O1D + O3), NOx (N + NO + NO2), Cly (total inorganic chlorine) and Bry (total inorganic bromine). 3.2.2. Conditions Used for Global Model Calculations  The calculations were for a projected 2015 atmosphere, with aircraft emissions and mixing ratios of key atmospheric compounds based on IPCC Scenario D from Penner et al.  (annual emission of 1.27 Tg N, see their Tables 4-8 and 4-10). The 2-D model runs included the same species and rate coefficients as used for the plume calculations (Appendix A), which includes a detailed representation of the gas phase chemistry of the troposphere. In addition to the mixing ratios specified by Penner et al. [1999, Table 4-8], nonmethane hydrocarbons were fixed at the ground using values specified in Table 1. The values given in Table 1 are estimated annual average values for northern midlatitudes based on data from Hauglustaine et al. , Kotamarthi et al. , Spivakovsky et al.  and Poisson et al. . PAN, PPN, PBN, CH3O2NO2 and other organic nitrates included a zero-flux boundary, which is equivalent to their concentrations at the ground being determined by the balance between chemical production and loss, rainout, surface deposition and atmospheric transport from adjacent grid cells. For short-lived species such as acetone whose concentrations in the upper troposphere are strongly influenced by convection [Jacob et al., 2002], the present study will underestimate their concentrations at cruise altitude. This, in turn, will mean that background OH concentrations in the 2-D model may be underestimated in the present study. Differences between observed and modeled HOx values have been noted by others [Jaegle et al., 2000] but have not been investigated in the present study.  Aircraft emissions are included for NOx, H2O, CO and hydrocarbons (as CH4). The emission data for a given model grid cell represent the time-averaged total emission rate into that grid cell. When including plume effects, the emissions are modified using either emission conversion factors or relative emission changes to account for differences between the subgrid-scale chemistry of the expanding plume and the chemistry occurring in the 2-D model grid cell (see sections 2 and 3.1.3). Several simplifying assumptions were made in determining the plume parameteriza-
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Table 2. Integration Times Used in Other Plume Studies Integration Time, h
Meijer et al. 
concentrations in plume within 10% of ambient time for plume area to reach area of mesoscale model grid box (5 107 m2)
Petry et al. 
36 14 – 36 15
Moulik and Milford  Karol et al.  Kraabøl et al. [2000b]
Variable, with a limit of 48 h
Kraabøl et al. [2000b]
tions. The plume parameters were derived for a single aircraft type (747) using fixed dynamical variables. In particular, the size of the expanding Gaussian plume and the aircraft emissions were determined by the parameters in Tables A1 and A3, respectively. Plume calculations were carried out at northern midlatitudes (40°N) for four times of the year (15 January, 15 April, 15 July and 15 October) and four altitudes (8 km, 10 km, 12 km and 14 km). These altitudes are based on US Standard Atmosphere geopotential heights and correspond to pressures of 365.5 hPa, 264.9 hPa, 193.9 hPa and 141.6 hPa, respectively. The equivalent 2-D model log-pressure altitudes are 6.99 km, 9.23 km, 11.40 km and 13.58 km, using z = 16 log10(1000/p). For each month and altitude, plume simulations were done at six emission times (midnight, 0400, 0800, noon, 1600 and 2000 local time (LT)), and the corresponding relative emission changes and emission conversion factors were averaged over the emission time and then interpolated onto the 2-D model log-pressure levels. In all cases, the expanding plume was integrated for 24 h, and the cross-sectional area of the ‘‘instantaneous dispersion’’ grid cell used when calculating the relative emission changes was 1 108 m2. The resulting northern midlatitude diurnally averaged relative emission changes and emission conversion factors are given in section S5 of the auxiliary material, together with the background atmosphere climatologies used for the plume runs. Note that the background atmosphere climatologies used for the plume calculations are based, where possible, on available observations, as discussed in section 3.1.2, so that the mixing ratios used to initialize the background spinup for the plume calculations were representative of current conditions. Finally, when including plume processes in the 2-D model, the plume correction factors determined at 40°N were used to modify the emissions at all northern latitudes. For this reason, the discussion of the results focuses on the results at northern midlatitudes.
4. Results and Discussions 4.1. Plume Studies  The following studies investigate the sensitivity of the NOx conversion in the plume and the associated relative emission changes to a range of parameters. These include dynamical parameters which determine plume expansion rates, the composition of the background atmosphere, the composition and magnitude of the aircraft emissions (in-
based on plume lifetime horizontal plume dimension comparable to horizontal resolution of NILU 3-D CTM based on time when differences between rates in plume and background atmosphere become small horizontal plume dimension comparable to horizontal resolution of OSLO-CTM2 3-D CTM, or emissions homogeneously mixed with surrounding air
cluding different aircraft types), and the location, time of day and time of year of the emissions. Results are presented for both emission conversion factors and relative emission changes (expressed as percentages). Section 4.2 considers the application of these results to global models. 4.1.1. Plume Integration Times and Grid Cell Dimensions  When calculating emission conversion factors, it is necessary to specify the length of the plume integration. For the calculation of relative emission changes, both the length of the plume integration and the cross-sectional area used for the instantaneous dispersion calculation must be specified. Several approaches have been used in the literature for specifying these parameters. As summarized in Table 2, plume integrations times between 14 and 48 h have been used for aircraft plume studies.  Some authors have used the time taken for the plume to expand to dimensions comparable to those used in 3-D CTMs as the basis for the integration time. However, as noted above, the arbitrary choice of the point at which the Gaussian radial distribution is truncated in order to calculate the plume area means that this can be at best a rough guide. Similarly, the choice of concentrations being within 10% of background is somewhat arbitrary. In the present work, a fixed integration time of 24 h has been chosen. It should be kept in mind, however, that emission conversion factors and, to a smaller extent, relative emission changes, continue to change for integration times beyond 24 h. Most of the calculations reported in this study were done using the base case dynamical variables given in Table A1. For this scenario, smajor = 41.6 km after 24 h, corresponding to a horizontal plume dimension of approximately 250 km (assuming a plume width of 6smajor, as used by Kraabøl et al. ).  Choice of an area for the ID calculation presents similar problems. While it might be argued that this area should match the area of the plume at the matching time, the fact that there is not a unique definition of the plume area means that this can at best be a rough guide. A study has been made of the sensitivity of calculated relative emission changes to the volume used for the ID calculation for the base case scenario (Tables A1– A3). The results of this study are summarized in Table 3.  For the base case, the cross-sectional area of the plume (defined by the outside of the outermost ring of an eightregion Melo et al.  plume) is 8.5 107 m2 at 24 h.
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Table 3. Calculated Relative Emission Changes (Expressed as Percentages) for Different Instantaneous Dispersion CrossSectional Areasa Area for ID Calculation, m2 5 1 2 5 1 2 5
10 107 107 107 108 108 108
O3 83.9 119.9 140.5 153.9 158.6 161.0 162.4
NOx HNO3 HO2NO2 CH3O2NO2 1.50 2.44 2.99 3.36 3.49 3.56 3.60
0.56 0.92 1.13 1.28 1.33 1.35 1.37
0.90 1.61 2.04 2.32 2.42 2.47 2.50
1.11 1.68 2.02 2.25 2.33 2.37 2.39
PAN 0.06 0.09 0.11 0.12 0.12 0.12 0.13
Results are for the base case and 0800 LT emissions.
On this basis, an area of 1 108 m2 has been chosen for the area for the ID cell, but it can be seen from Table 3 that the values calculated for the relative emission changes depend on this parameter, increasing slightly as the area is increased beyond 1 108 m2.  The reason for the dependence on the volume of the ID grid cell is that the standard aircraft emissions for a 747 cause an increase of approximately 3.5% in the initial mixing ratio of NO in the ID grid cell above its background value for an area of 1 108 m2. This increase in NO will result in a similar suppression of HO2 and other peroxy radicals, which will in turn affect calculated concentrations for species such as HO2NO2 and CH3O2NO2 in the ID cell. The smaller the ID grid cell volume, the greater the perturbations to NO and the greater the nonlinearities in the chemistry in the ID calculation.  Petry et al.  also investigated the dependence of relative emission changes on the horizontal baseline of the box used for the ID calculation. They considered values ranging from 10 to 300 km. Assuming that the vertical dimension remained constant at 1 km, this corresponds to an area range of 1 107 m2 to 3 108 m2. They found that the relative emission change for NO rose initially, passed through a maximum, and then was approximately constant beyond about 200 km (2 108 m2). For most of the calculations in their paper, Petry et al.  used an area of 5 107 m2. 4.1.2. Dependence on Dynamical Variables  Dynamical variables affect the plume chemistry primarily through determining the cross-sectional area of the plume as a function of time. The smaller the plume cross-sectional area, the greater the nonlinearities there are in the chemistry. The evolution of the plume area can be changed either by changing the diffusion coefficients or by changing the wind shear. Wind shear results in stretching of the plume along its major axis, but little change in the dimension along the minor axis. For example, changing the wind shear from 0.001 s1 to 0.01 s1 results in an increase in the minor axis of the plume of less than 5%, but an order of magnitude increase in the major axis. Wind shear is therefore a convenient way of investigating the effect of dynamical variables on plume chemistry, but is not fundamentally different to changing diffusion coefficients. In the present work, a range of wind shears from 0 to 0.01 s1 has been investigated. This range results in a range of final cross-sectional areas of the plume at 24 h from 5.6 106 m2 to 1.7 108 m2, or approximately a factor of 30.
 Table 4 shows emission conversion factors at 24 h for NOy species, expressed as percentages of the total NOy emission, for the base case scenario (Tables A1– A3). The final row in Table 4 shows results for the ID calculation, using an area of 1 108 m2. As can be seen in Table 4, all conversions approach the ID case as the wind shear is increased. This is to be expected, because increasing the wind shear results in more rapid dilution of the plume.  Relative emission changes for the NOy species and for ozone are shown in Figure 1. The relative emission changes tend toward zero as the wind shear is increased, as would be expected if the emission conversion factors approach the ID values. The trend is not monotonic in the case of HNO3, just as it was not monotonic for emission conversion factors. The diagonal terms Jii in the Jacobian matrix (equation (10)) are generally the largest, but the existence of significant off-diagonal terms means that there is not in general a simple relationship between emission conversion factors and relative emission changes. This is discussed further in section 4.1.5.  Although it would be possible to vary other dynamical variables (for example, horizontal or vertical diffusion coefficients), the effects of any such changes would be analogous to those caused by changes to the wind shear. Namely, the more rapidly the plume expands, the closer the chemistry in the plume is to the ID case and the smaller the magnitudes of the relative emission changes. 4.1.3. Dependence on Composition of Background Atmosphere  Calculations were performed to determine the effect of composition of the background atmosphere on plume processing. The air masses considered are those identified in the SONEX campaign [Jaegle et al., 2000] and important differences between the different air masses are summarized in Table 5. For this sensitivity study, base case parameters were used for plume dynamics and aircraft emissions (Tables A1 and A3), but the mixing ratios used to initialize the 5-d background spin-up were taken from Jaegle et al. [2000, Table 2]. For these comparisons, initial NO2 mixing ratios were obtained from the NO and NOx values given by Jaegle et al. [2000, Table 2] using NO2 = NOx-NO. In order to highlight differences due to the background composition, the calculations used the base case temperature (227 K) and pressure (287 hPa). Calculations were done for 1 November using a range of emission times.  Some of the more important features which should be noted in Table 5 are the high O3 for the stratospheric influence case, the high NOx for the continental convection case and the high aerosol surface area for the cirrus cloud Table 4. Emission Conversion Factors for NOy Species (Expressed as Percentages of Initial NOy Emitted) as Functions of Wind Shear for Base Case Scenario Wind Final Plume Shear, s1 Area, m2 NOx HNO3 N2O5 HO2NO2 CH3O2NO2 PAN
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0 0.001 0.002 0.005 0.010 ID
5.56 1.75 3.42 8.52 1.71 1.00
106 107 107 107 108 108
77.12 76.86 76.31 75.31 74.67 73.79
17.44 17.42 17.59 17.47 17.22 15.87
3.04 3.07 2.90 2.84 2.83 2.80
1.26 1.43 1.72 2.32 2.80 4.08
0.94 1.01 1.24 1.75 2.13 3.00
0.08 0.08 0.10 0.14 0.17 0.26
VOHRALIK ET AL.: PLUME EFFECTS ON AIRCRAFT IMPACT
routes for NOx: the daytime, which is dominated by reactions of NO2 with OH and HO2: OH þ NO2 þ M ! HNO3 þ M
HO2 þ NO2 þ M ! HO2 NO2 þ M
and the nighttime, which is dominated by conversion to N2O5 and ultimately to HNO3 via heterogeneous chemistry: ð13Þ
NO3 þ NO2 þ M ! N2 O5 þ M
Figure 1. Effective relative emission changes as functions of wind shear for the base case.
case. Table 5 includes noon values for HOx (OH + HO2) calculated by the present model during the background spinup. For some of the air masses, the model values differ considerably from the observed SONEX values. Differences between observed and modeled HO2 values have been discussed by Jaegle et al.  for the SONEX air masses, and are not explored in the present study.  Figure 2a shows emission conversion factors for NOx in the plume after 24 h for the different air masses. There are clearly significant differences in the fractions of NOx remaining for the different air masses. The continental convection air mass has the smallest conversion of NOx to products, while the stratospheric influence air mass has the largest.  Another notable feature of Figure 2a is the comparatively small variation in the amount of NOx remaining with time of day of the emissions. Other authors have reported larger variations [Karol et al., 2000; Kraabøl et al., 2000a; Meijer, 2001]. The reason for this can be understood by reference to Figure 3. This diagram shows the fraction of the initial NOy remaining as NOx as a function of time after emission for different emission times for the background atmosphere. For all times other than 24 h after emission, there are much larger differences between values of NOx for different emission times. This is because there are two main conversion
NO2 þ O3 ! NO3 þ O2
N2 O5 þ H2 O ! 2HNO3
 As can be seen in Figure 3 (noting that the horizontal axis shows the time after emissions were added), conversion is more rapid during the day. As long as a 24-h integration is used, the same total lengths of daytime are seen for all emission times, and similarly for nighttime. However, if a period other than 24 h is used, then different emission times will mean that the plumes are subjected to differing amounts of day and night, so different conversions will result. The small differences at 24 h are the consequence of nonlinearities in the chemistry discussed earlier.  The differences in conversion of NOx shown in Figure 2a can be explained in terms of differences in NOx, HOx and O3 in the background atmospheres. For the air of stratospheric origin, the higher O3 content means greater conversion to N2O5 at night, which more than compensates for the comparatively low HOx in this air mass. For the continental convection air mass, the high background NOx results in suppression of HOx and other peroxy radicals, so that formation of HO2NO2, CH3O2NO2 and PAN are all reduced.  The case for HO2NO2 is shown in Figure 2c. Conversion to HO2NO2 is a much stronger function of the emission time than was the case for NOx. This is because conversion to HO2NO2 is controlled by daytime HO2 concentrations (via reaction (12)), which are very sensitive to suppression by high NOx levels in the early plume. For emissions at night, there will be significant expansion of the plume before conversion of NOx to HO2NO2 occurs, so that the conversion to HO2NO2 integrated over 24 h will be less
Table 5. Important Characteristics of Different Air Masses Identified in the SONEX Campaign (Based on Jaegle et al. )a Parameter
Acronym used Temperature, K Pressure, hPa H2O, mmol mol1 O3, nmol mol1 NOx, pmol mol1 HOx (SONEX observation), pmol mol1 HOx (present study), pmol mol1 Aerosol surface area, mm2 cm3
BG 227 287 120 55 93 2.3 3.8 7.8
SI 223 239 42 149 135 1.3 1.8 8.1
TM 225 261 195 33 60 4.8 4.8 4.4
MM 231 303 208 47 68 2.8 4.8 10
CN 223 262 128 55 593 1.2 0.98 11.4
CR 231 287 388 50 83 2.8 5.2 27.8
For HOx (OH + HO2), noon values calculated in the present study are also given (see text for details).
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Figure 2. Emission conversion factors for (a) NOx, (b) HNO3 and (c) HO2NO2 24 h after emission as functions of emission time for different air masses (BG, background; SI, stratospheric influence; TM, tropical marine convection; MM, midlatitude marine convection; CN, continental convection; and CR, cirrus cloud). affected by daytime suppression of HO2 in the early plume, resulting in greater conversion to HO2NO2.  Comparison of the dependences on emission time for conversion to HO2NO2 (Figure 2c) with conversion to HNO3, shown in Figure 2b, gives some insight into the chemistry. For air masses in which HNO3 is formed predominantly via heterogeneous chemistry, the conversion peaks for emissions in the early evening, whereas when reaction with OH is more important, the HNO3 conversion peaks for emissions in the morning. It can be seen in Figure 2b that the cirrus cloud, tropical marine and midlatitude marine air masses are dominated by daytime conversion via OH, while the stratospheric influence, background and continental convection air masses have large components from heterogeneous chemistry. In summer (not shown),
only the continental and stratospheric air masses display significant components of heterogeneous chemistry, while in winter, all air masses are influenced by heterogeneous chemistry.  Relative emission changes for NOx, HNO3 and HO2NO2 as functions of time of day for the different air masses are shown in Figure 4. An interesting observation is that, while air masses with low conversion of NOx to NOy generally have smaller relative emission changes than air masses with larger conversions of NOx, the ordering of air masses is quite different. In particular, the stratospheric influence air mass, which has the largest conversion of NOx to NOy, has comparatively small magnitudes of relative emission changes. This may be because formation of HNO3 in this air mass has a larger contribution from heterogeneous chemistry, and is therefore less subject to nonlinearities in the chemistry. It is worth noting, however, that if HNO3 formed on the surface of ice particles were to remain on the surface [Popp et al., 2004; Gao et al., 2006] and affect reactivity of the ice, then some nonlinearities in the heterogeneous chemistry might result. For all air masses, the relative emission changes for HO2NO2 have their minimum magnitude for emissions in the late afternoon, because emissions at this time of day undergo the greatest dilution before HOx-based conversion of NOx to HO2NO2 occurs. This is the time of day for emissions when maximum conversion of NOx to HO2NO2 occurs. 4.1.4. Dependence on Aircraft Emissions  Studies have been performed on the dependence of plume conversions and relative emission changes on aircraft emission parameters. For these studies, the base case background atmosphere and dynamical variables defined in Tables A1– A3 were used, and aircraft emission parameters were varied about the base case values, with emissions occurring at 0800 LT. The perturbations considered are summarized in Table 6. The final experiment is not an aircraft emission change, but allows the effects of changes in aircraft-emitted aerosols (experiment 6 of Table 6) to be compared with changes in background aerosols. Plume emission conversion factors for these sensitivity studies
Figure 3. Emission conversion factors for NOx as functions of time after emission for different emission times (as specified in the legend).
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Figure 4. Relative emission changes for (a) NOx, (b) HNO3 and (c) HO2NO2 as functions of emission time for different air masses (BG, background; SI, stratospheric influence; TM, tropical marine convection; MM, midlatitude marine convection; CN, continental convection; and CR, cirrus cloud). are shown in Table 7 and corresponding relative emission changes are given in Table 8.  Results for greater NOx emissions are as expected. Increasing EI(NOx) reduces formation of HO 2 NO 2 , CH3O2NO2 and PAN because of the greater suppression of HO2 in the plume and this results in reduced processing of NOx to NOy (i.e., larger fractions of NOx remaining). Correspondingly, the production of O3 in the plume (per emitted NOx) also decreases as EI(NOx) increases. Note that the total ozone generated in the plume in 24 h increases by about 75% as EI(NOx) changes from 8 kg(NO2 equiv)/ kg(fuel) to 20 kg(NO2 equiv)/kg(fuel), which corresponds to the decrease in the production rate of O3 per emitted NOx seen in Table 7. For the relative emission changes shown in Table 8, the decrease in NOx conversion to HO2NO2,
CH3O2NO2 and PAN, compared with the instantaneous dispersion calculation, results in even larger differences between the plume and ID results, leading to larger magnitudes for the relative emission changes for NOx, HO2NO2, CH3O2NO2 and PAN.  Increasing EI(HC) results in a significant increase in the conversion of NOx to NOy, with increases in HNO3, HO2NO2, CH3O2NO2 and PAN (the last approximately doubling). This is due to an increase in HOx within the plume. The magnitudes of the relative emission changes (Table 8) for O3, NOx, HO2NO2, CH3O2NO2 and PAN are all reduced (because HOx in the plume is less strongly suppressed), while the relative emission change for HNO3 is increased. The speciation of the hydrocarbon emissions has only a comparatively small effect on the plume conversion. PAN increases by more than a factor of 2 when the Pleijel et al.  hydrocarbon distribution is used, because of the larger fraction of CH3CHO emissions.  Varying the percentage of NOx emitted in the form of NO from 80% to 100% reduces NOx conversion slightly, with most of the reduction appearing as a reduction in HNO3. Other NOx conversion products are largely unaffected.  Increasing the fuel flow rate reduces NOx conversion in much the same way as increasing the EI(NOx). In the case of fuel flow, emissions of H2O, HCs, CO and NOx will all be affected, but it appears that the NOx variation is most important. The relative emission changes (Table 8) also change in much the same way as variations in NOx emissions alone (i.e., variations in EI(NOx)). This result is consistent with the findings for the EI(HC) changes. In that case, the variation in HC emissions was an order of magnitude, considerably larger than the variation in fuel flow (a factor of 2.4). As discussed for the EI(NOx) perturbation, the production of O3 in the plume (per emitted NOx) also decreases as the fuel flow rate increases. In this case, the total ozone generated in the plume in 24 h increases by about 70% as the fuel flow rate changes from 0.5 kg s1 engine1 to 1.2 kg s1 engine1, which corresponds to a decrease in the production rate of O3 per emitted NOx.  Increasing either the emitted or the background aerosols results in little change in the NOx conversion in the plume. Higher surface areas result in increased conversion of N2O5 to HNO3, but other products are largely unaffected.  Finally, calculations were done to quantify the dependence of plume processes on aircraft type. For this study, results for a four-engine widebody aircraft (747) and a two-engine narrowbody aircraft (737) have been compared. Calculations were done for 40°N on 1 October for emissions at 0800 LT at 10 km altitude. In this case, the composition of the background atmosphere was based on the climatology given in Table S4 (auxiliary material section S3), which is used in the following section to investigate the altitude dependence of plume effects. The most important characteristics of the two aircraft are given in Table 9. For the 747, the fuel flow and EI(NOx) values are representative values for a heavy aircraft on a 5000 nautical mile (9260 km) flight, halfway through the flight. Values for the 737 are representative values for a 540 nautical mile (999 km) flight. For both aircraft, the data are for a cruise altitude of 35000 feet (10.7 km).
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Table 6. Calculations to Investigate the Dependence of Plume Processing on Aircraft Emission Parameters Experiment Number 1 2 3 4 5 6 7
Additional Values Used
EI(NOx) (kg(NO2 equiv)/kg(fuel)) EI(HC) (kg(CH4 equiv)/kg(fuel)) hydrocarbon speciation (for EI(HC) = 4.0) emitted NOx as NO (%) fuel flow (kg s1 engine1) emitted aerosols: droplet number density (cm3), soot number density (cm3) background aerosol surface area (mm2 cm3)
12.2 0.4 Spicer et al.  90 0.8194 1 1012, 5 106
8.0, 20.0 4.0 Pleijel et al.  80,100 0.5, 1.2 1 1011, 1 1013, 5 105, 5 107
 For the 747, the dimensions of the plume at the start of the dispersion regime are as given for the base case (Table A1). For the 737, the dimensions of the plume at the start of the atmospheric dispersion regime were calculated relative to those for the 747 according to Meijer . The horizontal dimension was assumed to be proportional to wingspan, while the vertical dimension was assumed to be proportional to the maximum vertical displacement of the plume, hs [Meijer, 2001]: hs ¼
8W p3 rair NB2 v
where W is the mass of the aircraft (kg), rair is the air density (kg m3), N is the Brunt-Vaisala frequency (s1), B is the wingspan (m) and v the velocity (m s1). The plume area at the start of the dispersion regime is approximately a factor of 2.5 larger for the 747, but the total fuel flow is a factor of approximately 4.4 greater. Hence the total emissions (as determined by the fuel flow) per area of the plume are approximately 70% higher for the 747 at the start of the dispersion regime.  Emission conversion factors and relative emission changes are given in Table 10 for a 24- h plume integration. The conversion of NOx to NOy is slightly greater for the 737 than for the 747, but the magnitudes of the relative emission changes are all smaller. This is because of the lower emissions per unit area of the plume cross section in the case of the 737, which result in lower initial NOx in the plume and smaller suppression of peroxy species. Hence, for the 737, smaller upward corrections are needed for emissions of NOx and HNO3 and smaller downward corrections for HO2NO2, CH3O2NO2, PAN and O3. 4.1.5. Altitude Dependence  A study was made of the dependence of plume processes on the emission altitude over the range 8 – 14 km. Calculations were done for 1 October conditions at 40°N. The composition of the background atmosphere was based on values estimated for September-October-November (SON) at 40°N, based on available observations and 2-D model results, as discussed in section 3.1.2. The resulting mixing ratios, pressures and temperatures used to initialize the background atmosphere spin-up are given in Table S4 in auxiliary material section S3, together with values for the base case for comparison. In order to focus on changes caused by variations in the background with altitude, the dynamical variables and the aircraft emissions were kept at their base case values for this study.
 Figure 5 shows emission conversion factors as a function of altitude for NOx, for emissions at 4-h intervals throughout the day. Results for all compounds for an emission time of 0800 LT are shown in Figure 6. Emission conversion factors and relative emission changes for NOy species and for ozone as functions of altitude and time of day of emissions are available in the auxiliary material.  As can be seen in Figures 5 and 6, there is a marked decrease in conversion of NOx to NOy with increasing altitude. This is particularly pronounced below 12 km. At high altitudes, HNO3 and N2O5 become the only important products. This is because of the increasing importance of reactions (13) – (15), resulting from the increase in O3 with altitude. At lower altitudes, HO2NO2, CH3O2NO2 and PAN become significant, with HO2NO2 the largest product at 8 km. As the altitude is decreased, thermal decomposition, particularly for CH3O2NO2, becomes increasingly imporTable 7. Emission Conversion Factors (Expressed as Percentages of NOy Emissions) as Functions of Emission Parameters Parameter Value
HNO3 N2O5 HO2NO2 CH3O2NO2 PAN
8.0 12.2 20.0
Experiment 256.30 74.60 17.70 217.86 75.31 17.47 170.03 76.26 17.20
1 (EI(NOx)) 2.55 2.75 2.84 2.32 3.08 1.85
2.06 1.75 1.37
0.17 0.14 0.10
Experiment 2 (EI(HC)) 217.86 75.31 17.47 2.84 2.32 312.14 70.55 19.95 2.64 3.74
Experiment 3 (HC Speciation) 312.14 70.55 19.95 2.64 3.74 306.58 71.42 18.34 2.68 3.81
80 90 100
Experiment 4 226.32 75.06 17.76 217.86 75.31 17.47 75.57 75.57 17.18
(% NOx as NO) 2.83 2.31 2.84 2.32 2.85 2.33
1.74 1.75 1.75
0.14 0.14 0.14
0.5 0.8194 1.2
Experiment 255.46 74.80 17.60 217.86 75.31 17.47 185.11 75.81 17.41
5 (Fuel Flow) 2.50 2.71 2.84 2.32 3.02 2.01
2.05 1.75 1.49
0.16 0.14 0.12
0.1 1.0 10.0
Experiment 6 (Emitted Aerosols) 217.83 75.31 17.54 2.78 2.32 217.86 75.31 17.47 2.84 2.32 217.60 75.21 19.37 1.05 2.32
1.75 1.75 1.74
0.14 0.14 0.14
1.0 7.8 15.0
Experiment 7 (Background 215.40 75.21 16.60 3.92 217.86 75.31 17.47 2.84 217.30 75.33 18.79 1.52
1.72 1.75 1.74
0.14 0.14 0.14
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Aerosols) 2.24 2.32 2.32
VOHRALIK ET AL.: PLUME EFFECTS ON AIRCRAFT IMPACT
Table 8. Relative Emission Changes (Equation (7), Expressed as Percentages) as Functions of Aircraft Emission Parameters Parameter Value
HNO3 HO2NO2 CH3O2NO2
8.0 12.2 20.0
Experiment 1 (EI(NOx)) 122.8 2.47 1.38 1.96 158.6 3.49 1.33 2.42 204.6 4.92 1.07 2.96
1.83 2.33 2.95
0.10 0.12 0.15
Experiment 2 (EI(HC)) 158.6 3.49 1.33 2.42 118.7 0.13 4.20 2.04
Experiment 3 (HC Speciation) 118.7 0.13 4.20 2.04 114.7 0.95 2.64 1.89
80 90 100
Experiment 4 (% NOx 158.3 3.57 1.25 158.6 3.49 1.33 158.9 3.42 1.40
as NO) 2.42 2.42 2.42
2.32 2.33 2.33
0.12 0.12 0.12
0.5 0.8194 1.2
Experiment 120.2 2.55 158.6 3.49 191.6 4.37
Flow) 1.91 2.42 2.82
1.79 2.33 2.78
0.10 0.12 0.14
0.1 1.0 10.0
Experiment 6 (Emitted 158.6 3.50 1.33 158.6 3.49 1.33 158.6 3.49 1.24
Aerosols) 2.42 2.42 2.43
2.33 2.33 2.33
0.12 0.12 0.12
1.0 7.8 15.0
Experiment 7 (Background Aerosols) 158.6 3.50 1.24 2.34 2.32 158.6 3.49 1.33 2.42 2.33 157.9 3.48 1.31 2.40 2.32
0.12 0.12 0.12
5 (Fuel 1.21 1.33 1.31
tant. At 8 km, the lifetime of CH3O2NO2 to thermal decomposition is 1 – 2 h. This is why the conversion of NOx to CH3O2NO2 peaks at 10 km. In the case of ozone, the results highlight the increasing efficiency of conversion of NOx to O3 with decreasing altitude, as discussed by Ehhalt and Rohrer . At an altitude of 14 km, the amount of ozone produced in the plume during daylight hours is smaller in magnitude than both the NOx-driven ozone loss at dusk (converting NO ! NO2 ! NO3) and the corresponding ozone production at dawn (as NO2 and N2O5 repartition in favor of NO as the sun returns). Depending on the balance between these terms, together with the rapid ozone loss which occurs if emissions are added during the night (as the emitted NO reacts with ozone), the net ozone change resulting from the aircraft emissions over 24 h is Table 9. Aircraft Parameters for 747 and 737 Aircraft at Cruise Altitude Parameter
Mach number Take off weight, tonnes Wingspan, m Fuel flow, kg engine1 h1 EI(NOx) EI(CO) EI(HC) Plume horizontal std dev at start of dispersion regime, m Plume vertical standard deviation at start of dispersion regime, m
0.850 354 64.4 2480 10.7 1.0 0.40 120
0.745 55 28.9 1140 9.2 3.6 0.14 53.9
either slightly positive or slightly negative (see Table S6 of auxiliary material section S3).  Relative emission changes as functions of altitude are given in Table S7 of auxiliary material section S3. In broad terms, the trends in relative emission changes mirror those in the conversions shown in Table S6. Relative emission changes at high altitudes are small and increase with decreasing altitude, reflecting the increasing efficiency of conversion of NOx to O3 with decreasing altitude.  For daytime emissions at 8 km, the relative emission changes for CH3O2NO2 change sign and those for NOx do not vary smoothly with the time of emission. The reasons for this apparently anomalous behavior were investigated and found to be correlated with the short lifetime of CH3O2NO2 at this altitude. The temperature of 240.8 K at 8 km (Table S4 of auxiliary material section S3) results in a lifetime to thermal decomposition of CH3O2NO2 of approximately 1 h. In contrast, the temperature of 226.7 K at 10 km results in a lifetime for CH3O2NO2 of approximately 1 d. The short lifetime of CH3O2NO2 at 8 km means that changes to the concentration of CH3O2NO2 at the end of the integration are only weakly related to adjustments in CH3O2NO2 at the time of emission (which correspond to the relative emission changes added to the instantaneous dispersion calculation). As a result, adjustments made to CH3O2NO2 at the time of emission are repartitioned predominantly to other species during the integration. Mathematically, this situation manifests itself by the appearance of large nondiagonal elements in the Jacobian matrix. Table 11 shows the terms in the Jacobian matrix for an altitude of 8 km and an emission time of noon.  It can be seen from Table 11 that less than 4% of an adjustment to the initial CH3O2NO2 appears in the final CH3O2NO2. The remainder is converted to NOx (31.5%), HNO3 (24.1%) and HO2NO2 (36.6%). O3 also responds strongly to a change in CH3O2NO2 because CH3O2 is a major source of ozone. Jacobian diagonal terms for O3, HNO3 and PAN are all close to unity. At 10 km altitude for the same noon emission, the CH3O2NO2 diagonal term is greater than 0.5.  While a solution of the coupled set of equations for the relative emission changes is still obtained, with good agreement between the corrected ID calculation and the plume result at the matching time, it is not clear how appropriate it would be to use such emission conversion factors to account for plume effects in global model calculations. That is, while such large correction terms for NOx,
Table 10. Percentages of NOy Species 24 h After Emission and Relative Emission Changes for 747 and 737 Aircraft Emission Conversion Factor, % of Initial NOy Emission
Relative Emission Change, % of Initial NOy Emission
NOx HNO3 N2O5 HO2NO2 CH3O2NO2 PAN O3
61.21 25.69 2.28 5.74 4.34 0.42 504.07
60.46 26.68 0.33 7.02 5.32 0.54 621.60
5.09 3.74 4.66 3.98 0.26 229.74
1.88 1.95 2.03 1.70 0.12 98.38
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Figure 5. Emission conversion factors for NOx 24 h after emission as functions of altitude and emission time. HO2NO2 and CH3O2NO2 give good agreement between the plume and corrected ID calculations, they may amplify any differences between the conditions used for the ID calculation and those existing in the global model grid cell being considered, leading to a less than ideal plume correction. One could omit such problematic species from the matrix solution, but then a decision would need to be made on how to ensure conservation of emitted NOy after applying the relative emission changes. Another possibility would be to omit CH3O2NO2 from the Jacobian matrix, but rather than solving for the exact solution, use an iterative scheme to minimize the residuals for the remaining species, while simultaneously conserving the total emitted odd nitrogen, in the hope of obtaining reasonable agreement between the ID and plume calculations for the remaining species. This would be similar to the scheme used by Petry et al. . However, even if such agreement could be found in all cases, the appropriateness of the resulting relative emission changes when accounting for plume effects in global model calculations would need to be confirmed. This is an issue which requires further consideration. 4.1.6. Latitude Dependence  The dependence of plume processes on latitude was investigated at a fixed altitude of 10 km (p = 264.9 hPa). In order to minimize seasonal effects, the calculations were performed close to equinox (1 October). The composition of the background atmosphere was based on values estimated for September-October-November (SON) using available observations. The mixing ratios and temperatures used to initialize the background atmosphere spin-up are given in Table S5 (auxiliary material section S3), together with values for the base case for comparison. The latitude dependence of the aerosol surface area is based on values taken from the SAGE II satellite climatology for 1995, using the base case value of 7.8 mm2 cm3 at 40°N. In order to focus on changes caused by variations in the background with latitude, the dynamical variables and the aircraft emissions were kept at their base case values for this study.  Emission conversion factors for NOx as functions of latitude for a number of different emission times are plotted in Figure 7 and results for all compounds for an emission
time of 0800 LT are shown in Figure 8. Emission conversion factors as functions of latitude for NOy species and ozone for a number of different emission times are given in the auxiliary material (Table S8), and corresponding relative emission changes are also given in the auxiliary material (Table S9). Conversion of NOx to products peaks at the equator, together with the formation of HNO3. Formation of HO2NO2 peaks at 20°N, while formation of CH3O2NO2 peaks at 40°S.  The magnitudes of relative emission changes increase sharply in the tropics and are also large at 40°S. In the tropics at 10 km, temperatures are higher than at midlatitudes (235 K at the equator, compared with approximately 226 K at midlatitudes). The lifetime of CH3O2NO2 is only a few hours at 235 K, so it is possible that some of the larger relative emission changes seen in Table S9 are the result of difficulties similar to those discussed in section 4.1.5. On the other hand, the dominance of HOx chemistry in the conversion of NOx to NOy means that larger magnitudes of relative emission changes would be expected in the tropics. Further work is necessary to establish whether there are reliable criteria for detecting difficulties arising from problematic Jacobian terms and identifying the best way to deal with them. 4.1.7. Seasonal Dependence  The seasonal dependence of plume processing was studied using the base case conditions (Tables A1 – A3) for 1 July, 1 November and 1 January. Emission conversion factors for NOx, HNO3 and HO2NO2 for different emission times are shown in Figure 9. It is clear that there is a strong seasonal dependence, with greater conversion of NOx to NOy in summer. This is due mainly to higher HOx concentrations in summer. Examination of the dependence of the conversion to HNO3 on time of day (Figure 9b) reveals that, in summer, the conversion is greatest for emissions in the morning, while in autumn and winter, the conversion is greatest for emissions in the late afternoon. As discussed in section 4.1.3, this is due to the greater importance of heterogeneous chemistry for the formation of HNO3 in the nonsummer months. The longer nights and
Figure 6. Emission conversion factors for NOy species 24 h after emission as functions of altitude for an emission time of 0800 LT.
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Table 11. Jacobian Matrix J Defined by Equation (10) for 8 km Altitude and Noon Emissionsa O3 NOx HNO3 HO2NO2 CH3O2NO2 PAN
0.979 0.0003 0.0001 0.0001 0.0000 0.0000
0.138 0.313 0.265 0.360 0.033 0.036
0.405 0.024 0.961 0.012 0.002 0.001
7.150 0.328 0.146 0.463 0.035 0.020
13.220 0.315 0.241 0.366 0.037 0.031
0.183 0.010 0.003 0.005 0.001 0.980
a The value in (row i, column j) corresponds to Jij, relating a change in species j at the time of emission to a change in species i at the end of the instantaneous dispersion calculation.
lower photochemical activity mean that heterogeneous chemistry increases in importance relative to HOx chemistry in the conversion of NOx to HNO3.  Figure 10 shows the relative emission changes for NOx, HNO3 and HO2NO2, as functions of time of day and time of year of the emissions. The magnitudes of the relative emission changes are largest in summer in all cases. For HNO3, the time of day of the maximum is a strong function of season, reflecting changes in the relative importance of heterogeneous processes and HOx chemistry. For HO2NO2, the relative emission change always has a minimum magnitude close to sunset, as discussed in section 4.1.3. 4.2. Results of Global Model Calculations  An estimate of the importance of plume processes for aircraft assessment studies was obtained using the CSIRO 2-D chemical transport model [Randeniya et al., 2002]. This was done by comparing aircraft impact calculations with and without the inclusion of plume processes. While it is acknowledged that 3-D models are required for a more thorough assessment of the effects of subsonic aircraft, the present 2-D study allows a first-order estimate to be made of the importance of plume processes on the calculated aircraft impact.  As noted previously, two different parameterizations of plume processes have been discussed in the literature. The first uses emission conversion factors (as used by Meijer  and Kraabøl et al. ) and the second
Figure 7. Emission conversion factors for NOx 24 h after emission as functions of latitude and emission time.
Figure 8. Emission conversion factors for NOy species 24 h after emission as functions of latitude for an emission time of 0800 LT. uses relative emission changes (as discussed by Petry et al. , Karol et al. , Esler  and Meilinger et al. ). In the present study, both methods for including plume effects in global models are compared using the same plume and global models.  Figure 11 (top) shows the calculated ozone increase in Dobson units from subsonic aircraft without including any plume corrections. Percent difference contours (not shown) have a similar shape, with a maximum increase of +1.9%. For 40– 50°N, the percent change in the annual average ozone column due to subsonic aircraft is +1.1%.  The effect of including plume processes is shown in Figure 11 (middle and bottom). When plume effects are included using relative emission changes (Figure 11, middle), the ozone increase due to subsonic aircraft is smaller throughout the northern hemisphere. Using emission conversion factors (Figure 11, bottom), the effect of plume processes is almost zero at northern midlatitudes, with regions of reduced impact at lower latitudes and enhanced ozone production at higher northern latitudes. The reasons for this crossover are not clear, but may be related to the use of plume correction factors calculated at 40°N for all northern latitudes. These results can be quantified by considering changes to the annual average ozone column at northern midlatitudes (40 – 50°N). Inclusion of plume effects reduces the annual average northern midlatitude aircraft impact by 2.5% when using relative emission changes (i.e., from 1.1% to 1.073%). Correspondingly, when plume processes are parameterized using emission conversion factors, the annual average northern midlatitude aircraft impact on column ozone is increased by 0.4% (i.e., from 1.1% to 1.104%). Therefore, for the present study, the inclusion of plume processes makes only a small difference to the aircraft impact on total ozone at northern midlatitudes.  The results obtained in the present study can be compared with those reported by Kraabøl et al.  and Meijer . These studies both used 3-D CTMs to quantify the effect of plume processes on the impact of subsonic aircraft on ozone, using emission conversion
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with the differences in local ozone perturbations, the plume effects reported by Kraabøl et al.  for total ozone are also considerably larger in magnitude than those obtained in the present work.  Meijer  also calculated the effect of plume processes on the subsonic aircraft impact. In the North Atlantic Flight Corridor (NAFC), the ozone increase from subsonic aircraft was 0 – 5% smaller in January and, in July, changes to the aircraft impact on ozone were between 5% and +10%. These plume corrections are smaller than those reported by Kraabøl et al. , but are similar in magnitude to those obtained in the present work.  In summary, the plume effects calculated in the present work are comparable in magnitude to those reported by Meijer , but are considerably smaller than those obtained by Kraabøl et al. . Two different methods have been suggested for including plume effects in global models, using either emission conversion factors (as used by Meijer  and Kraabøl et al. ) or using relative emission changes. In the present study both of these parameterizations have been used. Although the two meth-
Figure 9. Emission conversion factors for (a) NOx, (b) HNO3 and (c) HO2NO2 24 h after emission as functions of time of year and emission time. factors to couple the plume model to the global model. Although the details of the plume models and the aircraft emission scenarios differ from those used in the present work, it is nevertheless instructive to compare the magnitudes of the plume effects.  Kraabøl et al.  report aircraft NOx increase which are 20– 35% smaller at northern midlatitudes and 250 hPa (9.6 km log-pressure altitude) when plume effects are included. Corresponding aircraft ozone increases are 15– 20% smaller. These plume-related changes are larger then those calculated in the present study at northern midlatitudes between 8 km and 11 km, namely: 17% reductions in aircraft NOx when using emission conversion factors, with changes to the ozone impact typically between 5% and +5%.  The ozone column increase from subsonic aircraft calculated by Kraabøl et al.  at northern midlatitudes is reduced by about 10 – 12% when plume effects are included (compare Kraabøl et al. [2002, Figures 7 and 10], or see Figure 11 for the 30– 60°N average). Consistent
Figure 10. Effective relative emission changes for (a) NOx, (b) HNO3 and (c) HO2NO2 as functions of time of year and emission time.
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ods predict different NOx increases from subsonic aircraft, the changes to the aircraft-induced ozone perturbation are both relatively small compared with the results of Kraabøl et al. .
5. Conclusions  The plume model developed in the present study has been used to determine the sensitivity of the conversion of NOx to NOy in the plume to a range of parameters, including dynamical properties of the atmosphere, composition of the background atmosphere, composition and magnitude of aircraft emissions and location, time of day and time of year of emissions. The major findings from these studies are summarized below, with suggestions for further studies where appropriate.  The effect of different dynamical properties of the atmosphere (section 4.1.2) was studied by varying the model wind shear over a wide range. While other dynamical variables could have been varied, these all have the effect of changing the rate of expansion of the plume, so varying the wind shear can be considered to be a surrogate for all dynamical variables. This study revealed that, as the plume expansion rate is increased, the emission conversion factors of all species approach those for the instantaneous dispersion calculation and relative emission changes of all species tend to zero. This experiment emphasizes the fundamental difference between the two techniques used to develop plume parameterizations for 3-D models. When using relative emission changes, the parameterized effective emission indices differ from the original emission indices only in so far as the plume calculation differs from the instantaneous dispersion calculation and, as expected, the magnitudes of these differences decrease toward zero as the plume expands more rapidly.  The effect of composition of the background atmosphere (section 4.1.3) was studied by comparing calculations using identical aircraft emissions and dynamical variables for different background air masses identified in the SONEX measurement campaign. This study revealed that conversion of NOx to NOy is a strong function of the composition of the background air mass, due mainly to differences in O3 and HOx in the air mass. HOx is responsible for conversion in the daytime, while ozone affects the nighttime conversion to N2O5 and, ultimately, HNO3 via heterogeneous chemistry. Ozone also contributes to HOx production and so affects both daytime and nighttime conversion rates but, because there are other sources of HOx, the effect on nighttime chemistry is greater. Because the nighttime chemistry is less subject to nonlinearities in the chemistry than daytime chemistry, the magnitudes of Figure 11. Absolute change in ozone column due to subsonic emissions in 2015 as a function of time of year and latitude, as calculated using the 2-D model. (top) Total ozone change (DU) without including plume processes. (middle) Additional ozone change (103 DU) when including plume corrections using the scheme based on relative emission changes. (bottom) Additional ozone change (103 DU) when including plume corrections using the scheme based on emission conversion factors. 17 of 21
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Table A1. Base Case Dynamical Variables Describing the Expanding Gaussian Plume, Based on Kraabøl et al. [2000a] and Durbek and Gertz a Parameter
Start of vortex regime (t1) Start of vortex breakup (t2) Start of dispersion regime (t3) Time for change in Dv (t4) Typical length of integration (t5) sv and sh at t1 sv and sh at t2 sh at t3 sv at t3 Horizontal diffusion coefficient Dh Vertical diffusion coefficient Dv (t3 < t t4) Vertical diffusion coefficient Dv (t4 < t t5) Skewed diffusion coefficient Ds Wind shear
0 120 180 13 24 6 20 120 50 16.7 0.7 0.15 0.5 (Dh Dv)0.5 0.005
s s s min h m m m m m2 s1 m2 s1 m2 s1 m2 s1 s1
sv and sh are the vertical and horizontal standard deviations of the expanding plume, and Dv and Dh are the diffusion coefficients used to calculate sv and sh in the atmospheric dispersion regime. Times are relative to the start of the vortex regime, which is where the plume integrations in the present study commence.
relative emission changes are smaller for those air masses influenced strongly by nighttime chemistry.  Studies of the effects of changes in NOx, hydrocarbon and aerosol emissions are reported in section 4.1.4. Increasing NOx emissions enhances nonlinearities in the chemistry, reduces the conversion of NOx to NOy and increases the magnitudes of relative emission changes for NOy species affected by nonlinearities in the chemistry. Increasing hydrocarbon emissions increases HOx production in the plume and increases conversion of NOx to NOy. While calculations were performed to quantify whether hydrocarbon speciation in the emissions is important, further experiments are required to establish whether the magnitude of emissions of aldehydes and other partial oxidation products play a major role. Increasing the number density of aerosols emitted by the aircraft increases the conversion of N2O5 to HNO3, but has little effect on overall NOx conversion or on relative emission changes.  A study was also performed of the effect of different aircraft on plume conversion processes. Emissions for 747 and 737 aircraft were considered. Little difference was found for the overall conversion of NOx to NOy between the two aircraft, but the magnitudes of relative emission changes were found to be larger for the 747, largely because the emissions per unit area of the plume are larger for the 747. However, because of the opposing effects of negative relative emission changes for O3 and positive values for NOx, it is not possible to predict whether the final changes to ozone in a 3-D model will be greater for one aircraft than the other.  Conversion of NOx to NOy was found to be a strong function of altitude (section 4.1.5), with the conversion decreasing with increasing altitude. At high altitudes, N2O5 and HNO3 are the only important NOy products, but at low altitudes, HO2NO2, CH3O2NO2 and PAN are also significant products. The case of CH3O2NO2 is interesting because it becomes short-lived with respect to thermal decomposition at the lowest altitudes considered. As a result, the emission changes required to produce agreement
between the plume and instantaneous dispersion calculations at the end of the integration become decoupled from concentration changes at the end of the calculation. For these conditions, the relative emission changes calculated by the model may be meaningless. This appears to be an important limitation of the effective emission index approach which has not been reported previously. It maybe possible to omit short-lived species from the fitting process, but careful attention would need to be given to developing appropriate criteria for when species were to be omitted and to ensuring mass conservation. Further work is required to resolve these issues.  Conversion of NOx to NOy was also found to be a strong function of latitude (section 4.1.6) for near-equinox conditions, with conversions largest in the tropics. HOx chemistry plays an increasingly important role at low latitudes and the magnitudes of relative emission changes are also in general largest for low latitudes reflecting this trend. It must be stressed, however, that the climatological data set for the composition of the background atmosphere is sparse and there are large uncertainties in the mixing ratios of many species. A more meaningful investigation of the latitude dependence would require a much more complete climatology.  There is a strong seasonal dependence of the conversion of NOx to NOy (section 4.1.7), with much larger conversions in summer than in winter. This is due mainly to higher HOx concentrations in summer. The longer nights and lower HOx concentrations in winter mean that hetero-
Table A2. Composition of Background Atmosphere for Base Case Quantity
Pressure Geopotential height Temperature Potential temperature H2 H2O H2O2 OH HO2 NO NO2 HNO3 HO2NO2 O3 CO CH4 C2H6 C3H8 n-C4H10 C2H4 C3H6 CH2O CH3CHO CH3OOH HCOOH CH3COOH CH3OH Acetone PAN PPN Background aerosols
287 9.4 227 324 511 120 78 0.08 2.2 56 30 120 60 55 90 1761 670 79 26 2 2 50 60 25 37 27 380 510 64 1 7.8
mbar km K K nmol mol1 mmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 nmol mol1 nmol mol1 nmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 pmol mol1 mm2 cm3
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Table A3. Base Case Aircraft Emission Parameters Parameter
Aircraft type Aircraft speed Fuel flow per engine EI(H2O) EI(CO2) EI(SO2) EI(CO) EI(NOx) EI(HC) % of NOx as NO % of NO converted to HONO % of NO2 converted to HNO3 OH at engine exit Dilution in jet regime (for OH) % of OH converted to H2O2 % of HC as CH4 % of HC as C2H6 % of HC as C3H8 % of HC as n-C4H10 % of HC as CH2O % of HC as CH3CHO % of HC as acetone % of HC as CHOCHO % of HC as CH3COCHO Aerosols generated in plume
747 247 0.8194 1230 3160 1.0 1.0 12.2 0.4 90 1.5 4.3 9.0 0.01 3.0 33.65 1.16 0.19 14.8 44.7 0.87 3.09 1.19 0.19 as Ka¨rcher 
Units m s1 kg s1 g (kg fuel)1 g (kg fuel)1 g (kg fuel)1 g (kg fuel)1 g (kg fuel)1 g (kg fuel)1
geneous chemistry increases in importance relative to HOx chemistry in the conversion of NOx to HNO3.  Finally, a 2-D chemical transport model was used to estimate the effect of plume processes on the calculated aircraft impact. Calculations were done using both of the plume parameterizations which have been proposed in the literature, namely, emission conversion factors and relative emission changes. Although the two methods predict significantly different NOx increases from subsonic aircraft, the changes to the aircraft-induced ozone perturbation are both relatively small. As far as the aircraft impact on ozone
is concerned, the plume effects calculated in the present work are comparable in magnitude to those reported by Meijer , but are considerably smaller than those obtained by Kraabøl et al. .
Appendix A: Parameters for Base Case Plume Model Calculations  Key parameters used to define the base case simulation for the present study are given in Tables A1 – A3. Further discussion of these parameters is given in the body of the paper.
Appendix B: Reaction Scheme  Previous studies using the CSIRO 2-D model [Randeniya et al., 2002, and references therein] used a reaction set developed primarily for stratospheric modeling which included comprehensive reaction schemes for Ox, HOx, NOx, ClOx and BrOx chemistry, including heterogeneous chemistry, but only included methane hydrocarbon chemistry. For the plume model studies and the 2-D calculations discussed in the present work, the reaction scheme was expanded to include: C2 and C3 alkanes and their oxidation products, C4 and higher alkanes as n-butane, C2H4 and its oxidation products and C3 and higher alkenes as C3H6. The expanded reaction set includes 437 reactions, of which 79 are photolysis reactions. There are 127 species (see Table B1), excluding O2 and N2, which are maintained at fixed mixing ratios. Isoprene and terpenes are not included, because of their short tropospheric lifetimes, and alkynes and aromatics are also omitted (because they have not been included in most other modeling studies of the upper troposphere). Lumping techniques (for example, use of generic species such as RO2 or use of fractional stoichiometries as shorthand for multiple reaction pathways) are not used. Rate coefficients are taken from JPL00 [Sander et al.,
Table B1. Chemical Species Used in the Present Worka Descriptor Fixed species Source gases Oxygen species Hydrogen species Nitrogen species
Chlorine species Bromine species Fluorine species Hydrocarbon species
Species O2, N2 N2O, CH4, H2O, H2, CO, CFCl3, CF2Cl2, CFC-113, CCl4, HCFC-22, HCFC-141b, CH3CCl3, CH3Cl, CF3Br, CF2ClBr, CH3Br O, O(1D), O3 H, OH, HO2, H2O2 N, NO, NO2, NO3, HONO, HNO3, HO2NO2, N2O5, ClONO2, BrONO2, CH3O2NO2, PAN, PPN, PBN, CH3ONO2, C2H5ONO2, C2H5O2NO2, nC3H7ONO2, nC3H7O2NO2, iC3H7ONO2, iC3H7O2NO2, nC4H9ONO2, nC4H9O2NO2, sC4H9ONO2, sC4H9O2NO2 Cl, Cl2, BrCl, ClO, ClOO, OClO, Cl2O2, HOCl, HCl Br, BrO, HOBr, HBr HF, CF2O, CClFO CH3, CH3O2, CH3O, HCO, C2H5O2, C2H5O, CH3CO3, nC3H7O2, C2H5CO3, iC3H7O2, CH3COCH2O2, nC4H9O2, C3H7CO3, sC4H9O2, CH3COCCH3HO2, CH3COCOCH2O2, HOCH2CH2O, CH2OOA, CH2OOB, CH2OO, HOC2H5CHO, CH2O, CH3OOH, C2H6, C3H8, nC4H10, C2H4, C3H6, CH3CHO, C2H5CHO, ACETONE, C3H7CHO, MEK, C2H5OOH, nC3H7OOH, iC3H7OOH, nC4H9OOH, sC4H9OOH, CH3OH, C2H5OH, nC3H7OH, iC3H7OH, nC4H9OH, sC4H9OH, CH3CO3H, CH3COOH, C2H5CO3H, C2H5COOH, CH3COCH2OOH, CH3COCHO, CH3COCH2OH, C3H7CO3H, C3H7COOH, CH3COCCH3HOOH, CH3COCOCH3, CH3COCCH3HOH, CH3COCOCH3O2, CH3COCOCH2OH, CH3COCOCHO, HOC2H4O2H, HOCH2CHO, HOC2H4O2, HOC3H6O2
Species are arranged for ease of readability only. CH2OOA and CH2OOB are Criegee intermediates.
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2000], IUPAC-1999 [Atkinson et al., 1999], IUPAC-2000 [Atkinson et al., 2000], Muller and Brasseur , Poisson et al.  or the Master Chemical Mechanism, version 2.0 (http://mcm.leeds.ac.uk/MCM/). Most photolysis rates and/or cross sections are taken from JPL00 or IUPAC-1999.  Heterogeneous chemistry on background sulphate aerosols was included in the plume and 2-D models using specified surface areas (for the plume runs) or the SA0 climatology for 2-D runs [see Penner et al., 1999]. The 2D calculations also included enhanced surface areas under conditions where the background sulphate aerosols took up substantial amounts of and H2O and/or HNO3, using the formulation of Carslaw et al.  to determine the enhanced surface areas on the basis of equilibrium ternary solution properties. For the plume calculations, a constant background surface area was used, together with enhanced surface areas resulting from aircraft emissions based on the treatment of Ka¨rcher , with the following parameter values [see Ka¨rcher, 1997]: nd0 = 1012 cm3, ns0 = 5 106 cm3, rd0 = 0.5 nm, rs0 = 20 nm, vd = 7.5 103 cm s1, t0 = 0.5 s and s0 = 3 m. Following Ka¨rcher  (see Appendix A), the mixing parameter a can be related to the plume dimensions using ln smajor ðt Þsminor ðt Þ ln s20 aðt Þ ¼ lnðtÞ lnðt0 Þ
 In the present work, the total aerosol surface area (background + volatile droplet + soot) was treated as sulphate aerosol when calculating heterogeneous reaction rates.
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S. L. Baughcum, Boeing Company, Seattle, WA 98124, USA. I. C. Plumb, L. K. Randeniya, and P. F. Vohralik, Materials Science and Engineering, Commonwealth Scientific and Industrial Research Organisation, P.O. Box 218, Lindfield, NSW 2070, Australia. ([email protected]
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