On the Nonlinearity of the Tropospheric Ozone Production

The relationship of photochemical ozone production versus photochemical loss of an ozone precursor, that is, either NO,, or nonmethane hydrocarbons (NMHCs), is studied by using a box model with particular emphasis on the nonlinearity problem of the relationship with respect to the concentration of the precursor. Model calculations indicate that the composition of NMHCs, the ratio of NMHCs to NO,`, and the background concentrations of natural hydrocarbons, CO, and CH 4 all play important roles in determining the nonlinearity of 0 3 production with respect to the loss of NO,,. In addition, influences on the nonlinearity due to radical loss via reactions of HO e with RO e, exchanges between PAN and NO 2, and inclusion of nighttime NO,, loss processes are also investigated. Mechanisms that contribute to the nonlinearity are discussed. The nonlinear property of 0 3 production versus loss of hydrocarbons and CO is different from that of NO,,. When the sum of CO and all hydrocarbons, including CH,•, natural NMHCs, and anthropogenic NMHCs, is used as the reference 0 3 precursor, the nonlinearity is much less pronounced for ambient conditions usually found in rural air.


INTRODUCTION
In the troposphere the solar UV radiation does not have enough energy to dissociate 0 2 directly and produce 0 3 . The existence of a high concentration of 0 3 in the urban atmosphere prompted Leighton [1961] to suggest that peroxy radicals, such as HO 2 and RO 2 (where R denotes organic radicals), might lead to the oxidation of NO to NO 2, resulting in the production of 0 3 following the photodissociation of NO 2.
The peroxy radicals are produced mostly during the oxidation of hydrocarbons. Photochemical processes involved in 0 3 production from oxidation of NMHCs are very complex [Seinfeld, 1986;Finlayson-Pitts and Pitts, 1986]. To facilitate later discussion, a highly simplified scheme is shown,  The reactivity of a composition is defined as the reaction rate constant weighted by the percentage of each component in carbon number. Read 2.59(-13) as 2.59 x 10 -13. Whitten et al., 1980, Leone andSeinfeld, 1985]. For this study we chose three NMHC compositions: (1) the rural composition observed at Niwot Ridge, Colorado ; (2) the composition of a representative anthropogenic emission used by a regional acid deposition model [Acid Deposition Modeling Project (ADMP), 1987]; and (3) the so-called "default EKMA" composition [Dodge, 1977a, b]. For simplicity, we will refer to these three NMHC compositions as Niwot, ADMP, and EKMA, respectively, in the text that follows. The components of each composition are listed in Table 1. It should be pointed out that our intention here is not to reproduce the ADMP and EKMA reaction schemes. The purpose is to have a diversified representation of NMHC mixtures in order to study the dependence of the nonlinearity on the NMHC composition. For simplicity, we have made the following adjustments on the ADMP composition. They are as follows: (1) dimethylbutane and xylene are treated as butane and toluene, respectively, and (2) butene is omitted. A comparison between 0 3 calculated from our model with the adjusted ADMP composition and that calculated from the regional acid deposition model with the original ADMP composition is made. In these calculations the model starts at 0500 LT, with initial conditions of 30 parts per billion by volume ( NMHCs that are proportional to the space between isopleths, rather than the absolute value of the isopleth. Therefore differences in absolute 0 3 values will not affect significantly the outcome of our study. In addition to these investigations, effects on the nonlinearity of 03 production due to combination reactions of HO2 with RO2 and the formation of peroxyacetyl nitrate (PAN) are studied. Since nighttime chemistry of NO,• is recognized to be important to the NO,• loss, hence the 0 3 production, possible effects of the inclusion of nighttime chemistry on the nonlinearity are also discussed.

NONLINEARITY AND THE HYDROCARBON COMPOSITION
In the troposphere the competition of (2) and (3), with the loss of odd nitrogen, determines how much 0 3 is formed per NO x consumed. Therefore it is crucial to understand the budgets of odd hydrogen and NO x. The major NO x loss during the daytime is

OH + NO 2 + M-• HNO 3 + M (lO)
In the presence of NMHCs, NO x can also be converted into inactive forms, such as PAN, that do not produce O 3 directly.

CH3COO 2 + NO 2 + M--• PAN + M (11)
At room temperature the reverse reaction is efficient enough that PAN and NO 2 tend to be in equilibrium. PAN may serve as a temporary storage and a carrier of NOx into the more remote troposphere [Crutzen, 1979;Singh et al., 1985]. In addition, NO x may be lost at nighttime as a result of reactions involving NO 3 and N20 5 [Ehhalt and Drummond, 1982;Platt et al., 1984;Noxon, 1983]. On the other hand, the reaction scheme (1)-(5) implies that in the absence of competing reactions, at least two 0 3 molecules are formed following each reaction of OH with NMHC. Photochemical sinks for odd hydrogen include (10) and recombination reactions of HO2 and RO2 radicals HO 2 + HO 2--•H202 + 02 HO 2 + RO 2--} ROOH + 0 2 followed by the reaction of OH with the peroxide. The preceding discussion indicates that interplay of the catalytic cycle and the radical loss reactions determines the production of 0 3 with respect to the loss of its precursors. Because of the variation of the relative importance of the catalytic cycle versus the termination reactions that result in losses of precursors and odd hydrogen, the production of 0 3 is not a linear function of the concentrations of its precursors. Liu et al. [1987] discussed the finding that the total 0 3 production in a region could be estimated from the total NO x emission flux E within the region. This can be done by using a formula S = EP/(LENOx] ) where P and L[NOx] are the production of 0 3 and the loss of NO x, respectively. It is clear that a large uncertainty would result in the estimated total 0 3 production if the value of P/(L[NOx]) varies widely in the region of interest. Both the 0 3 production and the NO x loss vary with the level of NO x and the composition and abundances of the other 0 3 precursors, such as hydrocarbons. Liu et al. [1987] found that variations in the 0 3 production and the NO x loss are often similar and therefore cancel each other. This reduces substantially the uncertainty in the estimated total regional 0 3 production. However, significant nonlinearity still exists.
In the preceding formula, NO x is chosen as the reference precursor. This choice has two advantages' (1) The loss of NO,, on a regional scale is roughly equal to the emission flux, a result of the short photochemical lifetime of NO x. (2) NO x is the rate-limiting 0 3 precursor in relatively clean air [Fishman et al., 1979' Logan et al., 1981. Later, we will also discuss results from model calculations in which NMHCs are assumed to be the reference 0 3 precursor. The quantity P/(L[NOx] ) can be considered to represent the amount of 0 3 produced for each NO x molecule emitted, because in steady state the NO x loss equals the NO x emissions. We will call the quantity 0 3 production efficiency.
It is important to note that the definition of absolute 0 3 production and loss terms is not unique. It depends on how so-called "odd oxygen" is defined [Liu, 1977' Fishman et al., 1979' Levy et al., 1985. On the other hand, the definition for net production of 0 3 (i.e., photochemical production minus loss) is unique. Quantities calculated by using net production of 0 3 are relatively easy to reproduce by other groups. In addition, the net production can be directly compared to the divergence of 0 3 flux due to transport. In the following, the absolute 0 3 production will be used only on one occasion, to calculate the 0 3 production efficiency for the purpose of comparing results from this work with the results of Liu et al. [1987]. In the rest of the study, the net 0 3 production will be used exclusively.
The nonlinearity of the ozone production efficiency obtained by Liu et al. [1987] (i.e., the Niwot case) is reproduced in profile A of Figure 2, using their definition of ozone production. It has essentially the same values as those of Liu et al. [1987]. Profiles B and C are the corresponding values for the ADMP composition and the EKMA composition, respectively. In these calcula,tions the model is run for 5 days at first. During the 5-day period, 0 3 is fixed at 40 ppbv, while NO x is fixed at its specified levels (0.1 --• 100 ppbv). The ratio of anthropogenic NMHCs to NO x is taken as 23.4 ppbc/ppbv, the same value used by Liu et al. [1987]. This ratio is about a factor of 5 higher than the ratio in the emissions of anthropogenic NMHCs and NO x. The higher ratio is expected for a rural site like Niwot Ridge as a result of the fact that NO x is removed faster photochemically than most NMHCs. The levels of H20 and CH 4 are fixed at 60% of relative humidity and 1600 ppbv of mixing ratio, respectively. The mixing ratio of CO is scaled to NO,, similarly to Liu et al. [1987]. This scaling gives 283 ppbv of CO at NO x = 0.5 ppbv and 615 ppbv of CO at NO,, = 10 ppbv. We assume that natural hydrocarbons can be represented by isoprene and fix its value at a level of 0.1 ppbv. Nonzero initial values of the secondary hydrocarbons are specified only for formaldehyde and acetaidehyde. Their values are shown in Table 1

NO x (ppbv)
Same as Figure 2, except for concentration of OH. 40øN on July 21 to represent the average summer solar insolation. The overhead ozone column density is fixed at 313 Dobson units and the ground albedo is assumed to be 10%.
From 0500 LT on the sixth day, the 0 3 mixing ratio is allowed to vary with time. All the results are taken from the sixth day. Since an approximate steady diurnal cycle is obtained from the first 5-day run, we omit the exchanges between PAN and NO 2 in calculating diurnally integrated production and loss for NO,` and 0 3. This will be discussed in more detail later. Figure 2 shows that the nonlinearity of the 0 3 production efficiency decreases with the reactivity of anthropogenic NMHCs when the efficiency is defined by using absolute 0 3 production. For example, at 0.1 ppbv of NO,`, the differences in the 0 3 production efficiency among the three cases are within 20%. In contrast, at 100 ppbv of NOx, the ozone production efficiency for the EKMA case is about 4 times that of the Niwot case. This is  Figure 3a and Figure 3b, respectively. It is clear that higher reactivity of NMHCs leads to a higher concentration of HO 2 + RO2, which tends to enhance the 0 3 production. The increase in HO 2 4-RO 2 reduces the nonlinearity by enhancing 0 3 production at high concentrations of NO,` and NMHCs. The nonlinearity is reduced even further by the decrease of NO,` loss due to reduced concentrations of OH.

cals (HO 2 4-RO2), as shown in
When the net 0 3 production is used to calculate the 0 3 production efficiency, the results shown in Figure 4 are obtained. For the Niwot and ADMP compositions, the difference in the nonlinearity between Figure 4 and Figure 2 is small in the NO,` range from 0.4 to 10 ppbv. Below 0.4 ppbv of NO,,, the 0 3 loss significantly suppresses the 0 3 production efficiency, because the 0 3 loss is almost independent of NO,`, while 0 3 production is roughly proportional to NO,` [Fishman et al., 1979;Liu et al., 1983]. In fact, the ozone production efficiency becomes negative at NO,, levels lower than 80 parts per trillion by volume (pptv) as the 0 3 loss becomes greater than 0 3 production. When the NO,, level is greater than 10 ppbv, the 0 3 production efficiency is also significantly affected by the inclusion of the 0 3 loss, especially for the EKMA composition, in which a significant loss of 0 3 occurs as a result of its reactions with propene. For the EKMA composition, at 100 ppbv of NO,,, which corresponds to 585 ppbc of propene, the 0 3 production efficiency is a factor of 30 smaller with the 0 3 loss included than that without the 0 3 loss. Because of the large reduction of 0 3 production efficiency at high NO,, levels as the 0 3 loss is included, the overall nonlinearity is enhanced for all three hydrocarbons compositions. For the EKMA case the ratio of 0 3 production efficiency at 1 ppbv NO,, to that at 100 ppbv NO,` is greater than 40 in Figure Table 2 for the three NMHC compositions. One can see that at low NO,` levels (e.g., below 1 ppbv), increase of the NMHC reactivity enhances the 0 3 production efficiency presses its production efficiency. This is similar to the results shown in Figure 4. Therefore there is a stronger nonlinearity of the 0 3 production efficiency at high NMHCs/NO x ratios. We also calculated the variation of the 0 3 production efficiency with respect to various NMHCs/NO x ratios for the Niwot and EKMA compositions. The results showed patterns similar to the ADMP case.
When levels of atmospheric NMHCs are low, the 0 3 production efficiency depends on levels of CO, CH 4 and natural hydrocarbons. Consequently, the nonlinearity will depend on the levels of those species. Figure 6 shows results from four model runs for the ADMP composition. Curve A shows a baseline run with standard ADMP composition (i.e., curve D in Figure 5); curve B, a run with isoprene removed; curve C, a run with isoprene and CH4 removed; and curve D, run with isoprene, CH4 and CO removed. As expected, the 0 3 production efficiency decreases when isoprene, CH4, and CO are through both increased 0 3 production and decreased NO x loss. On the other hand, at higher NO x levels increase of the reactivity reduces the 0 3 production efficiency because of increased 0 3 loss, mostly due to the 0 3 reaction with alkenes.

The dependence of the nonlinearity on the ratio of NMHCs
to NO x is studied by varying the ratio over a wide range in the model calculations. 0 3 production efficiencies for seven cases, corresponding to ratios of 0. 3, 1, 4, 23.4, 50, 100, and 300, respectively, are plotted in Figure 5 for the ADMP composition. This range of the ratio more than covers the values found in rural and urban atmospheres, according to a survey by Stockwell et al. [1988]. The degree of nonlinearity remains large for all cases. It is seen that below 10 ppbv of NO x, the 03 production efficiency increases with the ratio of NMHCs to NO x. The increase of the efficiency is due to the combined effect of smaller OH concentration and greater HO2 + RO2 concentration. However, when NO x is above 10 ppbv, a tendency for the efficiency to decrease with the ratio becomes apparent. This is because the higher ratio leads to greater 0 3 loss through its reaction with alkenes and, consequently, sup-

Production and loss are given in units of cm -3 s-l; production efficiency is given in units of molecules of ozone produced per NOx molecule consumed; concentration is given in units of cm-3; NMHC is scaled to NOx by 23.4) Read 1.89(11) as 1.89 x l0 TM
As stated earlier, in our calculations conversions between PAN and NO 2 are omitted because the diurnally integrated conversion rates are nearly equal and cancel each other in most cases. It is important to check the accuracy of this assumption. In Table 3 Figure 1 and is the approach traditionally adopted by the EKMA control strategy. Figure 8 illustrates the 0 3 production efficiencies plotted against initial NO,, for the Niwot, the ADMP, and the EKMA compositions. Here initial NHMCs are scaled to the initial NO,, with a factor of 23.4, as before. In these calculations, NO x and NMHCs are computed by assuming no emission sources and therefore decrease with time. The profiles in Figure 8 should be compared to those of Figure 4. The degree of nonlinearity of Figure 8 is substantially smaller than that in Figure 4. This is expected because the 0 3 production efficiency is a value integrated over a day and thus represents an averaged quantity. Since photochemical lifetimes of reactive hydrocarbons and NO,, are short compared to a day, the 0 3 production efficiency for certain initial NO,, and NMHC levels represents a value averaged over a wide range of NO,, and NMHC concentrations. For example, in the case of the ADMP composition, an initial 100 ppbv of NO,, at 0500 LT will result in 42 ppbv of NO,,, 39 ppbv of HNO3, and 19 ppbv of PAN at noon. In addition, there is another factor involved in reducing the nonlinearity of 0 3 production efficiency, that is, the changing NMHCs to NO,, ratio. Our model calculations indicated that the ratio generally increases with time in the initial value mode. Therefore the value of 0 3 production efficiency is also averaged over a range of NMHCs to NO,• ratios. These two averaging procedures suppress the nonlinearity of 0 3 production efficiency.

EFFECTS OF UNCERTAINTY IN PHOTOCHEMISTRY
There are significant gaps and uncertainties in our understanding and treatment of the photochemistry. It is not practical to quantify all of the uncertainty factors of the nonlinearity of 03 production efficiency. In the following, however, we will examine the effects on the nonlinearity due to two major uncertainties in the photochemistry, namely, combination reactions of RO 2 with HO 2 and the nighttime sink of NO,,.
In our model runs the combination reactions of RO 2 with HO 2 are included. These reactions have significant impact on abundances of HO 2 and RO 2 radicals and hence the 0 3 production efficiency. However, reaction rates and products formed in these reactions are still quite uncertain at the present time. In the model, we adopt a value of 7.7 x 10-x4 x exp (1300/T)cm 3 s -1 for the HO2 reaction with CH302, as recommended by the Jet Propulsion Laboratory rDeMore et al., 1985], and a value of 3 x 10-12 cm 3 s-1 for reactions of HO 2 with all other higher RO2, as recommended by Atkinson and Lloyd [1984]. As for the products of the reactions, we take CH3OOH as the surrogate. To examine the effect of these combination reactions on the nonlinearity of 0 3 production, we ran the model without the combination reactions of HO 2 and RO 2. Model results corresponding to the ADMP composition case are presented in Table 3. One can see that exclusion of HO 2 reactions with RO 2 increases peroxy radical concentrations, especially at low NO.• levels. At these levels the combination reactions compete with reactions of peroxy radicals and NO in converting the radicals [Carter et al., 1979].
As for the 0 3 production efficiency, the value is increased at NO.• levels below 1 ppbv when the combination reactions are removed. For example, the efficiency is increased by 58% at NO.• = 0.1 ppbv. On the other hand, when NO,, is above 10 ppbv, the efficiency is only slightly changed. This pattern is also valid for the Niwot and EKMA cases. In summary, the role played by the combination reactions of HO 2 with RO 2 in a photochemical system is to reduce the overall nonlinearity of 0 3 production efficiency, mainly through suppressing the efficiency at NO,• levels below 1 ppbv.
Another uncertainty in the chemistry that may significantly affect the 0 3 production efficiency is the nighttime chemistry of NO,•. During the night, NO 2 is converted to NO 3 and N20 5 through reactions  However, measurements of NO 3 at night indicate that there are additional reactions involving NO 3 or N205 that may lead to a significant loss of NO x [Platt et al., 1984;Noxon, 1983], that is, where X and Y are as yet unspecified reactants. The possible candidates for X and Y may include propene, acetaldehyde, aerosols, clouds, and dew droplets [Ehhalt and Drummond, 1982;Platt et al., 1984]. Obviously, inclusion of the nighttime sink will increase the NO,` loss. At the same time, the 0 3 destruction would also be enhanced through (12) and (13).
Consequently, the overall efficiency of 0 3 production would decrease. At the present time the rate and the reaction products are not well understood. We can estimate the effect by assuming NO 3 formed in (12) is totally lost during the night.   Table 4. The negative efficiency at NO x = 100 ppbv for the EKMA case, when the nighttime NO•, loss is included, indicates that 0 3 loss exceeds 0 3 production as result of the inclusion of (12) as O3 loss. If we choose the ratio of O3 production efficiency at NO• = 1 ppbv to that at NO• = 10 ppbv as a measure of the overall nonlinearity of the 03 production efficiency, the overall nonlinearity is raised from 2.20 to 5.02, from 2.03 to 5.10, and from 2.06 to 6.12, for the three NMHC compositions, respectively. It should be noted that the effect would double ifN2Os, instead of NO3, is assumed to be removed totally.
As mentioned earlier, an interesting question is the degree of nonlinearity of 0 3 production efficiency when NMHCs, instead of NO•, are used as the reference precursor. To investigate the problem, we present three profiles in Figure 10 for the Niwot, ADMP, and EKMA compositions, respectively. They are 0 3 production efficiencies calculated by using the sum of photochemical losses of CO, CH,,, and NMHCs, rather than the loss of NO,`. The nighttime loss of NO 3 is included in these calculations. We continue to use NOx as the coordinate in Figure 10. It is obvious that the same nonlinearity will remain if NO• is replaced by NMHCs as the horizontal coordinate, since they are scaled by a constant ratio. The new 03 production efficiency is essentially linear in the range of NOx value between 0.3 and 15 ppbv that is commonly found in rural air [Fehsenfeld et al., 1988]. One can see that the efficiency varies between 0.5 and 2 in this NO,, range. Particularly for the two more realistic atmospheric NMHC compositions on a regional scale (Niwot and ADMP), the efficiency is confined to between 1 and 2. In other words, one to two 0 3 molecules are produced for every molecule of CO or hydrocarbons that is oxidized. It appears that we may avoid the nonlinear problem in estimating regional 0 3 budget by using CO and hydrocarbons as the reference precursor. However, while the nonlinearity problem is alleviated in this situation, one can no longer assume that loss rates of CO and hydro-carbons are the same as their emission fluxes within the region where NO• is between 0.3 and 15 ppbv. Because of their long photochemical lifetimes, substantial amounts of CO, CH 4, and other hydrocarbons emitted within the region will be transported and oxidized outside the region where the NOx level is substantially below 0.3 ppbv and the nonlinearity is much greater.
Although the major objective of this study is to investigate the chemistry aspect of the nonlinearity of the 0 3 production efficiency, it is clear that transport processes also play an important role. For example, transport processes tend to dilute secondary hydrocarbons and 0 3 to values significantly lower than those calculated by our model. The net effect is to reduce the nonlinearity. By using a box model the effect of transport has been neglected in this study. A transport process that has a direct impact on the nighttime sink of NOx is the formation of a shallow nocturnal inversion layer near the surface. In such a situation the exchange between the surface layer and the air aloft is inefficient. As a result, there usually is not enough 0 3 in the surface layer to react with NO and NO 2 to form NO3, especially at high NOx levels. Therefore the high degree of nonlinearity shown in Figure 9 should be regarded as an upper limit. In this context we note that transport processes do not always reduce the degree of nonlinearity. For instance, transport of PAN, formaldehyde, and other similar secondary compounds from urban centers to rural areas will increase the nonlinearity by shifting ozone production from the former area to the latter. Obviously, a realistic study of the nonlinearity can best be accomplished by using a threedimensional model with realistic transport parameterizations and emission sources.

IMPLICATIONS FOR OZONE BUDGET AND DISTRIBUTION
The existence of various degrees of nonlinearity relative to NO.• and NMHCs has several important implications for the budget and distribution of ozone and therefore its control strategy. An obvious implication can be readily seen from Figure 4 or 9. It shows that for a constant area-integrated NO•, emission flux, a concentrated emission source produces significantly less total ozone than a diffused emission source, except for NO•, levels less than 0.3 ppbv. This means that atmospheric transport processes play an important role in increasing the ozone production efficiency because the transport processes tend to diffuse concentrated sources . To evaluate accurately the budget and distribution of ozone, models with realistic transport processes are needed.

This usually implies sophisticated three-dimensional models.
On the other hand, if one's objective is to estimate an integrated regional ozone budget to within a factor of 3, a relatively simple approach can be adopted . For example, to estimate the total ozone production in the eastern United States, our results show that knowledge of the average concentrations of NO x, CO, and hydrocarbons and the emission rate of NO x is probably enough. These parameters can then be used in the formula S = EP(L[NO•]), given earlier, to estimate the total ozone production. This is possible because the degree of nonlinearity in rural air is small enough to allow the ozone efficiency to be represented by an average value.
An interesting phenomenon of ozone distribution in the eastern United States is that rural ozone levels observed in the summer are either comparable to or frequently even higher than values of urban areas. This is surprising, because the levels of ozone precursors in urban atmosphere are usually an order of magnitude or more greater than those of rural air.

For instance, NO• mixing ratios in rural air in industrialized
countries usually lie in the range between 0.2 and 20 ppbv [Fehsenfeld et al., 1988], while the values of urban areas range from tens to hundreds of ppbv •e.g., U.S. Environmental Protection Agency (EPA), 1983]. We believe that the nonlinearity shown in this study is a major factor that contributes to this phenomenon. This can be demonstrated by the following example.
For simplicity, we assume that the NO•, level is 5 ppbv in rural air and 50 ppbv over an urban area. In addition, we assume that the ratio of NMHCs to NO• is 23.4 for the former and 2 for the latter. Adopting the ADMP hydrocarbon composition, from the profiles in Figures 4 and 5 the ozone production efficiency can be seen to be 14 in the rural air and 2 in the urban air. This compensates, to a large degree, for the factor of 10 disparity in the NO•, concentrations of the two areas.
It is clear that the nonlinarity will have important impacts on the control strategy for urban as well as rural oxidants. The factors that affect the degree of nonlinearity have to be considered in formulating an effective control strategy.

CONCLUSIONS
In this paper we have shown the dependence of the nonlinearity of the O 3 production efficiency, defined as net O 3 production divided by NO•, loss, on various parameters. These include the NMHCs composition, the ratio of NMHCs to NO x, and the background abundance of natural hydrocarbons, CO and CH4. Generally, the overall nonlinearity increases with both the reactivity of the hydrocarbon mixture and the ratio of NMHCs to NO•. The increase of the nonlinearity is due (1) to enhancement of O 3 production through increased RO 2 and HO 2, (2) to reduction of NOx loss through decreased OH at lower NO x levels; and (3) to increase in O 3 destruction, that is attributed mainly to reactions of O 3 with alkenes, at higher NO x levels. The background natural hydrocarbons, (20 and CH• play a very important role in generating the nonlinearity. When (20, (2H 4, and natural hydrocarbons are absent and NMHCs are scaled to NO•, the O 3 production efficiency varies almost linearly with NOx in most situations. In addition to these findings, our model study also reveals the effects of combination reactions of peroxy radicals (HO 2 and R O2) on the nonlinearity of 0 3 production efficiency in the photochemical system. The radical combination reactions generally reduce the nonlinearity by substantially suppressing 0 3 production efficiency at low NOx levels.
When nighttime NO,• loss is included in the model calculation, 0 3 production efficiency drops substantially for all levels of NO,•. The drop is due to increased loss of both NOx and 0 3. The overall nonlinearity of the 0 3 production efficiency is increased by a factor more than 2 because of a relatively greater effect at higher NOx.
The nonlinear property also exists if this 0 3 production efficiency is defined as net 0 3 production, divided by total loss of CO, CH•, and NMHCs. In this case the 0 3 production efficiency becomes almost linear in a NO,• range from 0.3 to 15 ppbv that is usually found in rural air [Fehsenfeld et al., 1988]. However, the smaller nonlinearity of the new 0 3 production efficiency in this NO x range will not reduce the complexity in estimating regional 0 3 budget, because the losses of CO, CH4, and some NMHCs can not be approximated by their regional emission fluxes as a result of their long photochemical lifetimes.
The nonlinearity has several important implications for the budget and distribution of ozone. It shows that for a constant area-integrated NO x emission flux, a concentrated emission source produces significantly less total ozone than a diffused source, except at very low NOx levels. This may be the major factor that contributes to the observed phenomenon in the eastern United States that rural ozone levels are comparable to values in urban areas. The nonlinearity also implies that atmospheric transport processes tend to increase the ozone production by diffusing concentrated NO• sources.
By using a box model the present study is limited to examining the nonlinearity arising from photochemical processes. Moreover, many of the model calculations made were not realistic, because transport processes were omitted. It would be very valuable if this problem could be studied with a threedimensional model that includes realistic parameterizations for transport processes.