Estimating Chemical Errors in Large-scale Simulations of Aircraft Emissions

Calculations of a relatively comprehensive chemical reaction mecha­ nism applied to individual parcels of aircraft emissions under upper tropo­ spheric conditions show that over a typical residence time of air in the up­ per troposphere, each aircraft-emitted NOx molecule produces about 2-3 molecules of 03 per day as long as the reactive NOY remains in the upper troposphere. In the upper tropospheric environment characterized by low ambient turbulence and appreciable vertical wind shear, aircraft plumes grow slowly during initial stages, and take several days to diffuse to a size comparable to the grid volume used by global-scale Eulerian models. By assuming aircraft emissions are immediately diluted into a larger grid cell volume, larger-scale models will overestimate the calculated 03 production by 20 to 30 % . This overestimate depends on the vertical diffusion efficiency, vertical wind shear, and NO concentrations in the ambient environment. x This overestimate can be compensated for in larger scale models by reducing the reaction coefficient of the NO+ H02 reaction by less than 3% under typical upper tropospheric conditions. (


INTRODUCTION
With the increased demand for aircraft transportation, pollution resulting from aircraft emissions has been identified as a potential problem to ambient environment.Aircraft emis sions include oxides of nitrogen (NO,• or NO + N02), nonmethane hydrocarbons (NMHC), carbon monoxide (CO), and particles.Globally, over half of the subsonic aircraft emissions are released at flight altitudes between 9 to 13 km, where aircraft spend most of their air time (Baughcum 1997).At these altitudes, both tropospheric and stratospheric conditions are with chemistry was used by Kraab�l et al. (1996) to calculate the chemical conversion ofNO x and the time evolution of 0 3 while the aircraft plume was mixing with the ambient air.Aircraft plumes in this multi-layer model were assumed to be in a Gaussian distribution, and the initial concentrations of the emitted chemical species were distributed uniformly within each con centric layer of the model.Diffusion occurs between these multiple layers and with the ambi ent air, which is the outermost layer.By applying this multi-layer plume model, Kraabol et al. concluded that aircraft plumes expand rapidly during the first few minutes after being emitted when aircraft-generated turbulence is present.They indicated that ab out 6-7% of the emitted NO x were converted to other nitrogen species during th e first 4 hours, and ozone increased up to 0.8 ppb ne¥ the core of the aircraft plume.Hayman and Markiewicz (1996) also used a multi-layer plume model to calculate 0 3 production due to aircraft em issions of NO x and NMHC in a two-day simulation.They found that aircraft NMHC emissions have a negligible effect on 0 3 in the upper troposphere, while aircraft NO x emissions have far more important effects .Applying a plume scale model to estimate the chemical conversion of aircraft emitted species, Petry et al. (1998) studied the effects of inhomogeneity of aircraft emissions in larger volumes of air and found that the impacts on 0 3 can be appreciably overestimated in meso-and large scale model calculations.
In this plume-scale study, a plume growth and chemistry model is developed to evaluate the chemical evolution of a parcel of aircraft-emitted NO , as the contrail slowly dilutes into the background air.In most global or mesoscale Eulerian model studies of the chemical im pacts of aircraft emissions, the emissions are immediately diluted throughout each model grid box where emissions are occurring, and the chemical effects of the ar tificially diluted emis sions are evaluated .In the real atmosphere, however, the initial aircraft plumes are small com pared to global or mesoscale model grid volumes .Under typical conditions, it takes up to several days or more for the emissions from individual aircraft plumes to be dispersed to the resolvable size ranges of large-scale models.The chemistry of this expanding plume is not necessarily the same as that of a plume instantly diluted to the volume of a global or mesoscale model grid cell.The purpose of this plume scale study, therefore, is to evaluate and quantify the er rors in calculated 0 3 impacts generated by artificially diluting plumes of aircraft NO x to large-scale sizes.
In this study, a crude model which instantly dilutes aircraft emissions over a larger air volume is compared with a more realistic model where aircraft NO x are added to a small contrail that slowly grows and diffuses to fill the same larger air volume.The overestimates of calculated aircraft impacts due to instant dilution of aircraft emissions under typical atmo spheric conditions are quantified.An adjustment method which reduces the 0 3 formation rate calculated by the crude model is proposed as a method to alleviate this error in larger-scale atmospheric models .

PLUME CHEMISTRY MODEL
To estimate the errors that are inherent in most global-scale or mesoscale simulations of aircraft emissions, two models of aircraft emissions into the upper troposphere are developed and compared, as shown schematically in Fig. 1.The first more accurate and realistic model simulates aircraft plumes slowly expanding with time in a larger-scale volume of air in the upper troposphere.The second more simplified model assumes that aircraft NO emissions are x immediately diluted throughout the same larger-scale air volume.For both models, the largerscale air volume over which aircraft impacts are being evaluated corresponds to the grid vol umes used by global-scale atmospheric models in the upper troposphere.The two plume mod els use the same meteorology and background initial concentrations of chemicals, and are integrated forward in time.Ozone perturbations calculated by both models are compared.
Both models are essentially "Lagrangian" in nature and explicitly simulate the chemical evolution of a unit length of aircraft contrail within a larger volume of air.These Lagrangian box models essentially follow the unit cross-sections of aircraft plumes as they are carried by the mean winds around the earth.The mean wind in the large-scale air volume is defined to be zero, but the vertical shear of the wind speed perpendicular to the plume axes deforms the individual aircraft plumes within the air volume as time progresses.

Growing Plume Model
In the growing plume model, several aircraft contrails have been assumed to transverse through an air volume where aircraft impacts are considered (Fig. 2).  is constant, the solution to this equation is a Gaussian-like function (Konopka 1995): where the emission rate Q is defined as the mass of pollutants emitted per meter of contrail.
The horizontal (ax), shear axis (a,) and vertical ( a z ) standard deviations are given by: TA O, Vol. 12, No. 1, March 2001 where the a xo and a zo are the initial horizontal and vertical standard deviations, respectively, and t is time after emission.
For this growing plume model study, the model grid volume is subdivided into two chemical regions: the aircraft plume region, which increases in size with time as shown in Fig. 3, and the ambient environment.Pollutants in the aircraft plume region are confined to the volume of the growing Gaussian-like plume described using Eqs.(1 -4), in which pollutants are assumed to be uniformly mixed as shown in Fig. 4. According to Equation (1), the distribution of plume concentrations is Gaussian in shape, where higher concentrations of pollutants are in the core of aircraft contrails and the concentrations decrease with distance from the core.Thus there is no obvious physical boundary to the region impacted by the aircraft emissions.However, one can reasonably approximate the plume boundaries by assuming that aircraft-emitted pollut ants are confined within a certain inner portion of the Gaussian plume, where the plume boundary is chosen so as to minimize the discrepancies between a well-mixed plume occupying a dis tinct Gaussian envelope and the exact smoothly-varying Gaussian distribution described above.The cross sectional area of the plume containing aircraft emissions is defined to be A=d.21;r1a2a2-a4 (5) which increases with time as the standard deviations ( (5) expand.The 1.21 factor arises from the conversion of a smooth-varying Gaussian to the best-fitting well-mixed concentration profile.
As the aircraft plumes grow inside the larger air volume, the initially high concentrations of pollutants are diluted with ambient air.For calculating the concentration tendency ((JC/ (Ji) of reactive species inside the growing plume, the chemical production and loss of the reactive species are first calculated in both the ambient air containing no aircraft emissions and the ul u2 --;,.

85
aircraft plumes initially containing higher mixing ratios of aircraft emitted compounds.Then, additional concentration tendencies due to entrainment of the ambient air are added to the concentration tendencies in aircraft plumes.The chemistry equations for this entraining plume and the ambient air in the growing plume model thus can be described as follows: where CP and C, are concentrations of chemical species in the entraining plumes and ambient environment; Vis plume volume, and dV! dt is the time rate change of the plume volume.The P and L terms on the right hand side of Eqs.(6) and (7) represent chemical production and loss, respectively.The third term on the right hand side of Eq. (6) represents the dilution and en trainment of ambient chemical constituents into the growing aircraft plume.The concentra tions of the reactive chemicals in the growing aircraft plume, therefore, change with time due to chemical production and loss, as well as due to plume growth and mixing with ambient air.
Since the combined model simulates the chemistry of a unit length of an aircraft plume, the plume volume is the area per meter of contrail length.Thus, plume area A and plume volume V are used equivalently in evaluating the plume growth rate.
For comparing species concentration at any time with the instantly diluted plume case, the average concentration c over the entire model consists of the volume-weighted average of the concentrations inside the entraining aircraft plume and the concentrations in the ambient air.

C=C P v+Ce(l-v),
where v is the plume volume fraction relative to the larger model grid volume.When the entraining aircraft plume grows to the model grid volume, the plume volume fraction v reaches 100%, and the aircraft emissions are essentially well mixed into the larger volume of air con sidered for estimating aircraft impacts: At this time, the averaged concentrations of pollutants in the growing plume model equal the concentrations of the entraining aircraft plume.

Instantly Diluted Plume Model
Global and many regional models of aircraft emissions implicitly assume that aircraft emissions are immediately diluted throughout the entire volume of the model grid cell where emissions are occurring.In the upper troposphere, horizontal model resolution is typically greater than 200x200 km 2 , and vertical resolution is 1-4 km.Here we mimic the behavior of these larger-scale models by adding aircraft emissions uniformly at the initial time as shown schematically in Fig. 1 b.Chemical tendencies due to production and loss only are calculated for this diluted environment and are compared with the chemical tendency averaged from the growing plume model.

METEOROLOGICAL, CHEMICAL AND INITIAL PLUME CONDITIONS
In order to estimate the errors of calculated aircraft impacts due to instantaneously spreading emissions over a wide area initially, the two plume models described above are integrated forward in time, and the calculations of the two models are compared.Table 1 lists the meteo rological conditions used for this comparison.These conditions are representative of the upper troposphere at aircraft cruising altitudes.In both plume models, there are 14 aircraft plumes inside the larger grid volume.This plume density represents a typical plume density within the larger-scale air volume considered in the study for conditions typical of a polluted flight corri dor in the eastern U. S. According to NASA emission inventories (Metwally 1995;Baughcum 1996), NOx emission rates are about 146 ppt/day averaged over a global-size model grid vol ume in the northeast U. S. flight corridor.Typical aircraft emit 0.1-0.2kg NO x per kilometer traveled (Petry et al. 1998), and for typical wind speeds at flight altitudes, the NO emission x rate of 146 ppt/day represents about 14 transients during the time it takes air within a typical GCM grid to be replaced by advection.
If the NO, emitted per kilometer travel is homogeneously diluted to the initial aircraft plume volume defined in Table 1, the NO, concentration in the initial aircraft plume of the growing plume model is approximately 10 ppb, which is consistent with previous plume-scale modeling studies of aircraft impacts (Danilin et al. 1994;Konopka 1996).If the same amount of NO x emissions is instantly diluted to the larger scale volume instead of to the initial aircraft plume volume, the initial NO, perturbation is 13.3 ppt.As listed in Table 1, the air volume over which aircraft impacts are calculated in this study has a size of 200 km in the horizontal by 2 km in the vertical.The initial 14 aircraft plumes of 50 x 200 m 2 in cross section occupy about 0.13% of the larger air volume.
Since this study considers the impacts of aircraft plumes under typical flight corridor conditions, the density of the aircraft emissions is the major concern regardless of the size of the larger air volume considered.If a smaller averaging air volume is considered, fewer air craft plumes will be present in the averaging volume corresponding to the same emission density, and the time for these fewer aircraft plumes to expand to the size of the smaller air  volume will be the same.Thus, as long as the air volume over which impacts are being aver aged is considerably greater than the initial volume of the emitted aircraft contrails, the fol lowing results are invariant to the air volume considered.
Aircraft emissions include several chemicals, but only NOx emissions are considered here.Both plume models assume that the initial NOx emissions are 96% NO and 4% N02 (Petry et al. 1 998).Aircraft emissions of CO and hydrocarbon are small and have little impact on the upper tropospheric chemistry (Beck et al. 1990;Hayman and Markiewicz 1996).
The initial chemical conditions for the ambient environment in both plume models are listed in Table 2. Ambient chemical concentrations represent an approximate chemical steady state where chemical production and loss for most intermediate and longer-lived constituents are approximately balanced.These ambient chemical concentrations are typical in the upper troposphere according to numerous measurements (Aikin et al. 1987;Ray et al. 1992;Murphy et al. 1993;Weinheimer et al. 1994;Liu et al. 1996;Schultz et al. 1999).
Both models integrate the Stockwell chemical mechanism (Stockwell et al. 1990) forward in time.The gas phase chemistry contains 157 reactions among 63 species, including 42 organics.21 photolysis rate coefficients are derived from a radiative transfer model and are a function of time, latitude and altitude.Diurnally varying photolysis rates typical of springtime, upper tro posphere 40°N conditions are used.

RESULTS
The following results compare the 03 perturbations due to aircraft emissions calculated by the instantly diluted plume and the more realistic growing plume cases.The 0 3 perturba tions are averaged over simulation times corresponding to the approximate residence time of 03 and reactive NO Y (NO, N02, HN03, Np5, and PAN) in the midlatitude upper troposphere.The residence time of 0 3 in the upper troposphere is mainly determined by chemical reactions and convective transport, and the residence time due to both processes varies with season.0 3 is chemically destroyed by photolysis in the presence of water vapor, and by reaction with H02 and HO.The chemical lifetime of 0 3 in the midlatitude upper troposphere is estimated to be approximately 40 days in summer and 300 days in winter (Schultz et al. 1999;Liu et al. 1987).The 03 lifetime due to convective transport is determined by the magnitude of the convective mass flux, which replaces the air in the upper troposphere with lower troposphere air.According to Costen et al. (1988) and Lin et al. (1996), the average convective mass flux into the atmospheric layer between 100 hPa and 350 hPa in midlatitudes is approximately 15 hPa/day in summer and 8 hPa/day in winter.Therefore 03 lifetime in the midlatitude upper troposphere resulting from convective mixing is about 17 days in summer and 32 days in winter.Combining the lifetimes due to chemical reactions and convective transport, the 03 lifetime probably varies between approximately 12 days in summer and up to 30 days in win ter in the midlatitude upper troposphere.This is only a rough estimate of the 0 3 lifetime in the midlatitude upper troposphere, as the actual 03 lifetime varies with time and location.Resi dence time of reactive NO Y in the upper troposphere is probably shorter than 03 lifetime since HN0 3 is efficiently scavenged by precipitation forming in the upper troposphere.Estimates of scavenging lifetimes in the upper troposphere are highly uncertain and variable, but time scales for removal are probably in the range of 1-10 days.In the following studies, a 12-day simula tion time is used.The volume fraction of the growing aircraft plume, which increases with time until it occupies the entire averaging volume, is also plotted in Fig. 6. Figure 6 shows that it takes about three days for the 14 aircraft plumes to grow to the size of the air volume in which aircraft impacts are being estimated.This is faster than the time for an individual plume to grow to the size of this grid volume ( 10 days) due to the greater number of plumes occupying a proportionally larger volume together as discussed in Section 2. 1.The simulation for the two plume models starts at 9 AM local time.Fig. 6 shows that there is slightly more 03 calculated in the air containing additional aircraft NO emissions (Case 1, 2 and 4) than in the ambient air conditions are close to a longer-term photochemical balance consistent with many upper tro pospheric observations.With aircraft emissions immediately mixed to the ambient air, Case 1 shows that 0 3 concentrations increase by about 0.5 ppb several days after emissions.In the entraining growing plume (Case 2) where 10 ppb of initial NO , are added, the 0 3 concentra tion peaks after several hours as the added NO x dramatically increases 0 3 concentrations.The peak 0 3 reoccurs around 3 PM local time within the first three days until aircraft plumes grow to the size of the large scale model grid volume.As the aircraft plumes grow, ambient air with lower 0 3 and NO , concentrations mixes into the plumes, lowering 0 3 concentrations, espe cially at night when no 0 3 is photochemically produced.As NO , is converted to other nitrogen species, 03 concentrations in the entraining growing and instantly diluted plumes decrease slightly during the final several days of the simulation.During each day of the simulation, 0 3 concentrations vary slightly with a diurnal cycle.The concentration of 0 3 reaches a maximum in the afternoon each day as a result of photochemical production.The volume-weighted aver age of the growing plume model (C:!se 4) shows 0 3 concentrations close to ambient 0 3 con centrations in the beginning of the integration when the size of the entraining aircraft plumes is small.As the relative size of the growing plumes increases, the average 0 3 concentration over the larger grid volume containing the entraining growing plume is nudged to the 0 3 concentra tions in the entraining growing plume itself.After about three days when the entraining plumes occupy the entire averaging volume, the averaged 0 3 concentration equals the 0 3 concentra tion in the entraining plumes.Comparing Case 4 with Case 1, Figure 6 shows that Case 4 calculates higher 0 3 concentrations than the more realistic growing plume at all times during the simulation.Thus, this case study shows that assu mi ng instant dilution of aircraft emissions into a larger air volume typical of a global-scale model grid induces an overestimate in the calculated 0 3 perturbations.
Figure 7 shows the time evolution of calculated NO , of the four cases from the two plume models corresponding to Fig. 6.As shown in Fig. 7, NO , concentrations in the ambient air (Case 3) remain at an approximate steady state 38 ppt throughout the simulation.In the in stantly diluted plume (Case 1), Figure 7 shows that NO , concentrations rapidly decrease dur ing the first two or three days from initially about 51 ppt to below 40 ppt as the emitted NO , are converted to other NO Y species.By the end of the third day, the NO , concentrations in Case 1 reach an approximate steady state and concentrations only change slightly with time.Case 2 shows the NO , concentrations in the entraining growing plume where aircraft-NO , are emitted decreasing from 10 ppb initially to about 38 ppt within the first three days.In addition to the conversion of emitted NO , , the rapid decrease of NO , concentrations in the entraining grow ing plume results from the dilution of the aircraft plumes with ambient air.After three days, the growing plumes have spread over the entire larger air volume, and the NO , concentrations thus equals the NO , concentrations in the averaged growing plume during the remaining simu lation period.Case 4 shows that the averaged NO , concentrations (volume weighted-average of Cases 2 and 3) in the growing plume model are slightly larger than in the instantly diluted model during the first one or two days, but the differences essentially disappear during the last 8-10 days.The slightly larger concentration of NO , in the growing plume model can be attrib uted to slower NO x conversion in the initially small aircraft plumes before they expand to a certain size.

Overestimate of 03 Impacts due to Assuming Instant Dilution of Aircraft Emissions
To quantify the overestimated 03 impacts due to assuming instant dilution of aircraft emissions, it is convenient to define the 0 3 molecules generated per molecule of aircraft-NO , Li03 emitted ( LiN O ), which is often referred to as the "ozone production efficiency" (OPE).
x O PE = (0 3 concentration in either of the plume cases -03 concentration in the ambient air) NO x concentration added to air volume Figure 8 shows 03 production per aircraft-NO, emitted in the averaged growing plume (Case 4 in Fig. 6) and in the instantly diluted plume (Case 1 in Fig. 6).The OPE increases with time after emissions in both plume cases.In the averaged growing plume, the increase of OPE in the first day is small, with only about two additional molecules of 03 generated per mol ecule of NO , emitted.In contrast, the instantly diluted plume calculates a rapid increase of up to about 10 ppb 0 3 per ppb NO x emitted during the first day.In both plume simulations, the number of 03 molecules generated per molecule of NO, emitted increases throughout the 12day simulation, after which 26-35 ppb 03 is generated per ppb NOx added to the upper troposphere.Therefore according to either model, 03 is continuously produced in the upper troposphere as additional NO, are added.Over a wide range of environmental chemical conditions, each additional ppb of NOx added to the upper troposphere induces an averaged net increase in 03 production of 2-3 ppb per day as long as the additional NO Y resides in the The different ozone production efficiency calculated by the two models shows that there is an appreciable overestimate of calculated 03 production if NO , emissions are instantly di luted throughout a larger averaging volume.Furthermore, most of the difference in net ozone production occurs while the plumes are relatively small -i.e., during the first day or so follow ing emissions.Then the overestimate of 03 production per NO x emitted remains constant at around 8-9 ppb 03 per ppb NO x at all times after the emissions are more or less uniformly mixed within the large-scale averaging volume.Under the conditions considered here, after 12 days 0 3 impacts are overestimated by 30% if emissions are added uniformly throughout grid volumes of air typical of the grid cells used by larger-scale chemical models of the atmosphere.
The overestimates of 03 production by assuming instant dilution of aircraft emissions result from the fact that the 03 formation rate is non-linearly related to NO x concentrations.
Higher NO x concentrations in small initial aircraft plumes do not necessarily generate more 03 formation and may even decrease 0 3 formation.Figure 9 shows an example of the instanta neous ozone formation rates due to chemical processes at local noon as a function of ambient NO concentrations.In the calculation of the formation rates shown in Fig. 9, the other main x species concentrations that are used are shown in Table 2. Figure 9 shows that the 0 3 forma- tion rate increases with ambient NO concentrations when NO concentrations are low and x x that 0 3 formation occurs most rapidly when NO , concentrations are between 0.1 to I ppb.

When ambient NO
, concentrations are greater than 1 ppb, the 03 formation rate decreases with During the first day when the aircraft plumes are small, assuming instant dilution of air craft emissions can create an appreciable overestimate of 03 formation due to this nonlinear relationship.After the first day, aircraft plumes become diluted with ambient air, and the production rate of 03 inside both plume models converges.However, the overestimated 0 3 production calculated during the first day is preserved and the absolute error is almost insensi tive with time no matter how long the simulation period is after the first day or two following significant dilution.

Sensitivity of Overestimate of OPE to Ambient Parameters
The overestimate of 03 production per NOx emitted due to the assumption of instant dilu tion of aircraft emissions is a function of several environmental and model parameters.For  1, unless otherwise indicated.
Figure 10 shows the ozone production efficiency in the averaged growing plume, the instantly diluted plume, and the errors generated due to instant dilution of aircraft emissions after 12 days as a function of the vertical diffusion coefficient.The dotted lines in the middle of each figure (Figs. 10 to 13) mark the standard atmospheric conditions we chose for the base case studies and are the same conditions shown in Tables 1 and 2. As noted in Fig. 8, the error in OPE grows rapidly during the first day or two and then slowly levels off to an approxi mately constant value afterwards.Therefore, the errors generated at the end of the simulation period shown in Fig. 10 and in later figures are not sensitive to the simulation time.Figure 10 shows that in the instantly diluted plume, the calculated ozone production efficiency remains Figure 11 shows the net effective error of calculated ozone production efficiency as a function of vertical wind shear.When the vertical wind shear is extremely small, 0 3 produc tion is overestimated by about 15 03 molecules per aircraft-NO, emitted, whereas with strong wind shear conditions there is almost no overestimate because of rapid shear-induced mixing.
The error is almost insensitive to wind shear under extremely low wind shear conditions as the overestimated 03 production per NOx remains about 15 03 molecules per aircraft-emitted NO, Under typical atmospheric conditions, absolute vertical wind shear ranges from 10-3 to 10 2 s•1, while the component of shear perpendicular to the plume axis can be much smaller, and thus the overestimated 0 3 production can be larger than the typical conditions shown in Fig. 8.  Figure 12 presents the overestimate of ozone production efficiency generated by assum ing instant mixing of aircraft emissions as a function of ambient NO, concentrations, while maintaining ambient NO , NO and 03 concentrations at an approximate chemical steady state.also decreases.When ambient NO, is about 10 ppt, about 18 more 03 molecules are calculated in the instantly diluted plume for each aircraft-NOx emitted.If ambient NOx approaches 110 ppt, only about 2 more 0 3 molecules are calculated in the instantly diluted plume for each aircraft-NO, emitted.Hence, there is a greater absolute error of calculated 0 3 production in low NO, environments than in high NO.environments, although the relative error is always about 30% under any ambient NO condition.
x Ambient 0 3 concentrations will also influence 03 production and thus the error inherent in calculated 03 perturbations by assuming instant dilution of emitted NOx.In the above NOx sensitivity study, ambient NO,, NO Y , and 03 concentrations are all changed in an approxi mately photochemical consistent manner.In order to estimate the calculated 03 production due to any change in ambient 03 concentrations alone, the concentration of 0 3 is changed in this sensitivity study, while the ambient NO , NO and other species remain the same as in the x y base case.
Figure 13 shows the calculated 03 production efficiency in both plume models as a func tion of ambient 03 concentrations.It can be seen that the 03 production per NOx emitted decreases with ambient 03 concentrations in both plume models.More than 40 molecules of 0 3 are calculated per molecule of NO, added according to the instantly diluted plume model when ambient 03 is less than 100 ppb.If ambient 03 is greater than 300 ppb, the 03 production per NO, decreases by nearly a factor of two.In the more realistic growing plume model, 03 production is about 25 % less than that calculated from the instant dilution model, over all 03 concentration ranges.The changes of 0 3 production per NO, with ambient 03 concentrations are smaller than the changes with ambient NO x concentrations according to both plume models.Figure 12 shows that the 03 production per NOx emitted can vary by a factor of 8 in both plume models due to changing ambient NO,, NO Y and 03 from low to high concentrations.This sensitivity study shows that changing the ambient 03 concentrations alone within the same ranges only accounts for a factor of 2 of these changes.The overestimated 03 production resulting from these smaller changes of 03 production is also smaller.Figure 13 shows that the error of calculated 03 perturbation remains at 6 -10 molecules of 0 3 per added molecule of added NO, over a wide range of 0 3 concentrations.

COMPENSATING FOR SUB-GRID SCALE CHEMICAL INHOMOGENEITIES IN LARGE-SCALE MODELS
The results presented in the previous section demonstrate that under typical conditions, appreciable overestimates (about 30%) can be made in calculating aircraft impacts on 0 3 if subgrid-scale NOx concentrations distributions are not accounted for.Downwind of major flight corridors, aircraft plumes take up to several days to diffuse slowly to the size of air volumes typical of larger-scale Eulerian models used to assess aircraft impacts.If these air craft emissions are assumed to be instantly diffused throughout a large air volume, ozone production will be overestimated due to the nonlinear relationship between ozone production and NO, concentrations.Thus, the implicit instant dilution of aircraft-NO, over grid volumes of global-scale GCMs probably leads to appreciable overestimates in calculated 03 impacts.ate or destroy 03, but their reaction rates during the daytime are considerably slower than Reactions (8) to (10).Thus, in a first order approximation, the net 03 formation rate may be written as: (1 1) where J8 is the photolysis rate constant of Reaction (8) and K10 is the rate coefficient of Reac tion (10).If the 03 formed through Reactions (8) to (9) is balanced by the 03 destroyed by (10), no net 03 is formed, and dO/dt is approximately zero.However, a small fraction of NO may react with H02 or other organic radicals to generate N02: The OH produced by Reaction (12) reacts with VOCs, methane and CO and regenerates H02• Therefore, in the presence of CH4, CO, and VOCs, N02 can be regenerated by Reaction (12) without consuming 03, thereby producing net 0 3 • Hence, as noted by Thompson (1984), the net 03 formation rate is largely determined by the speed of Reaction ( 12).When the reac tion rate of NO with H02 is large , more 03 is formed .The net 03 formation rate can be simpli fied as: ( 1 3) where K12 is the reaction coefficient for Reaction (12).Other reactions of organic hydroxyl radicals also convert NO to N02 and therefore influence 03 formation, but these reactions are only significant when hydrocarbon concentrations are relatively high.In the upper troposphere where the concentrations of hydrocarbon are smaller than in the lower troposphere, the reac tions of NO with organic hydroxyl radicals are not typically important relative to Reaction (12).
Since the 03 formation rate is proportional to the reaction coefficient K12, the method suggests here for lowering 03 formation in a diluted plume is to reduce the reaction rate coef ficient K1 2 • By reducing the reaction rate of this single equation, the "effective" ozone forma tion rate in the diluted plume can be adjusted to match the 03 generated in the growing plume .

Empirical Reduction of Reaction Coefficient K12
To reduce the 0 3 formation in a model where aircraft NOx emissions are unrealistically uniformly dispersed, the reaction coefficient of Reaction ( 12) is reduced to slow ozone formation.
By multiplying K12 by a reduction factor, 03 production in the instantly diluted plume model can be adjusted so as to minimize the differences between 03 production calculated using the more realistic growing plume model and ozone formation calculated in a uniformly dispersed NO, environment.The optimum reduction factor can be chosen by first calculating the 03 production difference between the two plume model s over the 12-day period: are the 03 concentrations in the instantly diluted plume and the growing plume at each time step during the 12-day period.
To select the optimum reduction factor during the 12-day period, K12 in the instantly diluted plume model is reduced in order to yield minimum differences with the more accu rately calculated 0 3 concentrations in the growing plume model during the simulation period.The optimum reduction factor will be a function of integration time as the 03 production difference between the two plume models varies with time.In this study, the integration time will be the approximate residence time of 03 in the upper troposphere which, as discussed in Section 4, is normally about 12 days.

Result of Reducing Reaction Coefficient (12)
Figure 14 shows the base case OPE as shown in Fig. 8, although additional calculations are performed using the instantly mixed model with different downward adjustments of the H02 +N O reaction coefficient (K1).It is evident that the 0 3 productions per NO x emitted calculated using the instantly diluted plume model are larger than the 03 productions per NOx emitted calculated by the growing plume model during the simulation period.If the 03 produc tions per NOx emitted in the instantly diluted plume are adjusted to match the first day value in the averaged growing plume, then K12 should be multiplied by a factor, /, of 0.877.Figure 14 shows that 03 productions are appreciably suppressed in this case, and 0 3 concentrations can be reduced to fall below ambient concentrations even when NO is added.The behavior re- of only 1.7% is needed to adjust the 03 productions in the instantly diluted plume, so the results match the 03 production in the growing plume on the last day.
Figure 15 shows the differences (Eq.14) in 03 production between the two plume models over the simulation period as a function of the adjustment factor.Although adjustment factors of 0.877 and 0.983 reduce 0 3 productions in the instantly diluted plume and match the values in the growing plume on the first and last days, Figure 15 indicates that the 03 error due to instant dilution does not reach the minimum.After summing the difference of 03 productions over the simulation period, Figure 15 shows that the optimum adjustment factor of about 0. 9778 yields the smallest differences between the "adj usted" instantly diluted plume model and the more realistic growing plume model.
Figure 14 shows that by multiplying K12 by an optimal 0.9778, 03 production per NO x emitted calculated by the instantly diluted model agrees much better with the more accurate growing plume model.In this iterative manner, the optimum factor under different atmospheric and model parameters condition can be estimated.

Effect of Adjustment on Other Constituent Concentrations
When adjusting the reaction coefficient to account for subgrid chemical effects, it is pos sible that concentration of other species will be perturbed in undesirable manners.Figure 16 shows the NO , concentrations in the instantly diluted plume and the adjusted instantly diluted plume compared to the concentrations in the more accurate averaged growing plume.Clearly, NO x concentrations in the growing plume and the instantly diluted plume decrease with time as NO are converted to other reactive nitrogen species, and the NO in the instantly diluted HO is a very important oxidant in the troposphere and its concentration is also affected by Reaction (12).Reducing the reaction coefficient (12) should decrease the chemical production of HO, thereby decreasing the concentration of OH.However, reactions of other constituents, such as 03, N02, HCHO, and CO are also involved in HO production and loss, and these species are either directly or indirectly affected by Reaction (12) and can feedback to the HO concentration.Figure 17 shows that HO concentrations are slightly reduced in the instantly diluted plume after K12 is reduced.In Fig. 17, the large change in HO in the beginning of the both plume model simulations is due to adding aircraft NO.emissions, which perturbs the background HO concentrations.Based on these comparisons and additional comparisons within other constituent concentrations (not shown), it is concluded that a minor adjustment of K 12 induces negligible changes in other species concentrations, but 03 perturbations calculated with the adjusted chemical reactions are closer to more accurate growing plume calculations.

CONCLUSIONS
A Lagrangian plume chemistry model has been used to estimate the potentially signifi cant errors of calculated aircraft impacts that are inherent in larger-scale simulations of aircraft chemical impacts.Realistic aircraft plumes grow slowly in the initial few hours to day after emission, and the emitted aircraft pollutants remain confined to relatively small plume vol- In this study, a simple adjustment method was suggested to reduce the error in calculating 03 production in large-scale models of aircraft emissions.Since to a first order approximation the net 03 formation rate is regulated by the NO + H02 reaction, the 03 formation rate can be reduced by adjusting the reaction coefficient of the NO + H02 reaction .Applying this method avoids the complexity of dividing a model grid cell into several sub grids (Sillman et al. 1990a(Sillman et al. , 1990b) ) or more expensively increasing Eulerian model resolution to higher levels.This ad justment effe ctively reduces 03 formation rates in a chemically reasonable manner rather than simply removing 03 whenever aircraft NO, emissions are occurring as suggested by Petry et Fujung Ts ai & Chris J. Wa lcek 105 al. (1998).By reducing this key reaction rate, calculated 03 formation rates are reduced and the 03 concentrations calculated by instantly diluting the NO, emissions are empirically nudged to the more realistic 03 concentrations calculated using an explicit simulation of the chemistry of the plume and the ambient environment.In the typical upper tropospheric conditions con sidered in this study, less than 3% adjustments for the reaction coefficient appreciably lowers calculated 03 production and results in more realistic calculated 0 3 perturbations.
The overestimated 0 3 production due to instant dilution of aircraft emissions into a larger scale air volume is a function of ambient conditions.Under larger vertical diffusion coefficients, wind shear, ambient NO, and 03 concentrations, the overestimated 0 3 production is smaller.
The optimum adjustment factor that reduces this error will also vary.Further studies are needed to find the appropriate adjustment factor under different ambient conditions encountered in the upper troposphere.
It is acknowledged that the actual distributions of aircraft plumes applied to regional or global scale models are complex and the calculated 0 3 perturbations due to aircraft emissions vary with location and time.Therefore, it is almost impossible to adjust the 03 production at each location and time.For practical applications of the method proposed here to global-scale modeling, one could adjust the rate coefficient in a specified sub-domain where aircraft NOx plumes are known to be present, such as in the actual NOx emissions region or the zonal are as downwind of these emission regions.Once a spatial area of adjustment is defined, the mean shear conditions there can be used to calculate the reaction adjustment factor as suggested above.

Fig. 1 .
Fig. 1.Schematic diagram of the two plume models of a flight corridor through which several aircraft have traversed.(a) The growing plume model, which shows aircraft plumes slowly growing with time inside a large scale model grid cell.(b) The instantly diluted plume, in which the air craft emissions are immediately diluted throughout the model grid cell after they are emitted.
Fig. 2. Schematic diagram of aircraft contrails transversing through a model grid box lo cated in the upper troposphere.

Fig. 3 .
Fig. 3. Plume cross section initially and at time t, with ul,u2, and u3 represent ing the horizontal winds perpendicular to the plume cross section.

Fig. 4 .
Fig. 4. Schematic diagram of Gaussian-like plume and the assumed uniform plume in this study.
growth rate.The vertical and horizontal diffusion coefficients in the upper troposphere were estimated by Schumann et al. (1995) based on aircraft turbulence measurements.They found that upper tropospheric air contains little turbulent mixing.The turbulent diffusion coefficients they inferred from vertical velocity variance and a model of stable Brunt-Vaisala oscillations is about 0.05 m2 s-1• Using another inferential approach de rived from direct measurements of turbulent dissipation rates, they inferred essentially no turbulent diffusion as the calculated diffusion coefficients are in the molecular diffusion range.Other measurements have shown that the upper troposphere, where aircraft pollutants are emitted, generally has high static stability, and thus vertical motions are small and mixing is much slower in the vertical than in the horizontal (Pearson et al. 1983; N astrom and Gage 1985; Nastrom et al. 1987).The typical vertical wind shear in the upper troposphere is about 4xl0•3 s•1 according to the mean wind profiles of the atmosphere and observations compiled by Schumann et al. (1995).

Fig. 5 .x
Fig. 5. Aircraft plume growth rate as a function of days after emissions.Al A0 is the size of the plume cross section relative to the initial size .The diffusion coefficients and vertical wind shear used in this study are K,=0.05m2/s, (Jul :iz;:::; 4xI0-3 s•1 and K ==10 m2/s.u TableI.Meteorological conditions and aircraft plume parameters for two plume models.Plume initial horizontal disp ersion (crxo)Plume initial vertical dispersion (cr 20)Vertical diffusion coefficient (K2) Horizontal diffusion coefficient (Kx)Plume number in the box grid Simulation

4. 1
Time Evolution of 03 and NO x in Both Plume Models

Figure 6
Figure 6 compares the time evolution of the 03 concentrations in the two plume models for 12-days following emission.In Fig. 6, 0 3 concentration curves of four cases are shown: Case 1-the 0 3 concentration calculated assuming aircraft emissions are instantly diluted through out the averaging volume; Case 2-the 03 concentration in the actual growing plume into which aircraft-NOx are emitted; Case 3-the 03 concentration in the ambient environment surrounding the aircraft plumes (no aircraft emissions); and Case 4-the volume-weighted average of chemically distinct subregions of the growing plume model (i.e., the average of Cases 2 and 3).The volume fraction of the growing aircraft plume, which increases with time until it occupies the entire averaging volume, is also plotted in Fig.6.Figure6shows that it takes about three days for the 14 aircraft plumes to grow to the size of the air volume in which aircraft impacts are being estimated.This is faster than the time for an individual plume to grow to the size of this grid volume ( 10 days) due to the greater number of plumes occupying a proportionally larger volume together as discussed in Section 2. 1.The simulation for the two plume models starts at 9 AM local time.Fig.6shows that there is slightly more 03 calculated in the air containing additional aircraft NO emissions (Case 1, 2 and 4) than in the ambient air

•(Fig. 6 .
Fig. 6.Time evolution of the calculated 03 from the two plume model studies.

Fig. 7 .
Fig. 7. Time evolution of the calculated NOx from the two plume model studies.

Fig. 8 .
Fig. 8. Time evolution of 03 molecules generated per aircraft-emitted NO x in the base case study.
Fig. 9. Instantaneous 03 for mation rates after one-hour integration in the upper tropo sphere as a function of ambient NO x concentrations.

example, 0 3
productions will vary in both plume models when the ambient NO, concentra tions are different.The vertical diffusion coefficient and the vertical wind shear in the ambient air govern the growth rate of the aircraft plumes, and thus induce different 0 3 formation within the growing plume.Under these different ambient conditions, assuming instant dilution within a larger air volume can produce different overestimates of 03 production.In the following studies, the overestimate due to assuming instant dilution of aircraft emissions is calculated over a wide range of vertical wind shears, vertical diffusion coefficients, ambient NO, concentrations, and ambient 0 3 concentrations .In each sensitivity study, only one factor is changed, while the other factors are set to values listed in Table unchanged with vertical diffusion coefficient, while in the averaged growing plume the value increases with vertical diffusion coefficient, and thus the overestimate of ozone production efficiency decreases with increasing vertical diffusion coefficient.When vertical diffusion coefficient decreases to within the molecular diffusion range (10-5 to 10 4 m2/s), about 20 more 03 molecules are calculated by the instantly diluted plume model than by the growing plume model for each NO emitted.This represents about a 100% error.When vertical diffusion x coefficients are in the range of large turbulent diffusion, the overestimate of ozone production efficiency due to assuming aircraft emissions are instantly diluted to the ambient air is only about 2 ppb 0 3 per ppb NOx, a relatively small error of only 5%.Aircraft plumes are more rapidly mixed into the larger air volume in high diffusing conditions .Under these conditions, the calculated ozone production efficiency from the growing plume case is closer to the ozone production efficiency calculated assuming instant mixing.While large upper tropospheric turbulence is relatively rare, under typical upper tropospheric conditions, vertical diffusion coefficients are probably in the range of molecular to small turbulent diffusion (l0-4-1 o-1m2s-1), with the overestimate of ozone production efficiency at about 8 ppb 0 3 per ppb NOx as shown in the base case study.This corresponds to about a 30% error.

Fig.
Fig. JO.03 molecules generated per molecule of aircraft-emitted NO, calculated from the two plume models as a function of upper tropospheric vertical diffusion coefficient, K .z

xFig. 14 .
Fig. 14. 110 / /1NO x calculated from the two plume models and the instantly diluted plume model with reaction coefficient K12 adjusted by constant/

Fig. 16 .
Fig. 15.Difference in 0 3 pro duction between the two plume models over a 12-day period as a function of the adjustment factor.

Fig. 17 .
Fig. 17.Concentration of HO calculated from the two original plume models and the instantly diluted plume model with reaction coefficient K12 ad justed by f = 0.9778.umes where emitted NOx concentrations are high, and little 03 is produced.Under shear and turbulent conditions typical of the upper troposphere, it takes several days for aircraft plumes to diffuse to a size comparable to the grid volume used by global-scale Eulerian models.By assuming aircraft emissions are immediately diluted into a grid cell air volume, larger-scale models will overestimate the calculated 03 production resulting from aircraft NO , emissions by about 30%.Over a typical residence time of air in the upper troposphere, the plume scale model suggests that on average, each aircraft emitted NO, molecule induces the production of about 2-3 molecules of 03 per day as long as the reactive NO Y remains in the upper troposphere.During the first one or two days following emissions, instantly mixing aircraft NO emissions x over volumes of air typically used by global-scale atmospheric chemistry models leads to an overestimate of about 8 -9 molecules of 03 produces per aircraft NO , emitted .This overesti mated increment of ozone formation remains constant for all times after the first few days.

Table 2 .
Initial steady state chemical concentrations (ppb or ppbC) for major species.