ozone-precursor relationships: a modeling study of semiempirical relationships

Environ. Sci. Technol. 1993, 27, 2213-2219

Ozone-Precursor Relationships: A Modeling Study of Semiempirical Relationships

Tal Y. Chang’ and Sara J. Rudy

Research Laboratory, Ford Motor Company, P.O. Box 2053, Oearborn, Michigan 48121

The functional relationships of maximum ozone levels to non-methane organic gases (NMOG) and NO, concentrations (and emissions), which are relevant to urban ozone issues, have been investigated using data generated by a single-cell trajectory model as well as outdoor smog chamber data. A general relationship is shown to exist, a t least approximately, for outdoor smog chamber simulations with initial precursors and for air masses which have initial input and continuous emissions of precursors and are diluted. When diurnally varying sunlight intensity and temperature are fixed, the relationship expresses maximum ozone concentrations as a product of the square root of effective NO, concentrations (initial input and continuous emissions) and a function of effective NMOGI NO, ratios (R). The function of R can be approximated as a simple function involving an exponential function. The present model holds for the entire domain of effective precursor concentrations and for NMOG mixtures as well as single NMOG species. The present model (with a temperature-dependent function) represents outdoor smog chamber data reasonably well. The temperature dependence of maximum ozone levels is shown to be larger for outdoor smog chamber data than predicted by current photochemical models.

Introduction

The functional relationships, observed or theoretically derived, between urban ozone and its precursors, non- methane organic gases (NMOG) and nitrogen oxides (NO, = NO + NOz), have been reviewed in criteria documents (1). Air-quality simulation models (AQSM) represent the most fundamental approach to relating precursor emissions to ozone air quality. However, there are still significant uncertainties in results obtained from AQSM because of the difficulties in representing atmospheric processes accurately as well as large uncertainties in the AQSM input data. Another approach to the ozone- precursor relationship is to derive semiempirical models based on ambient and smog chamber data. These semiempirical models could supplement results based on AQSM and could provide useful insight into the ozone- precursor relationship relevant to ozone control strategies.

There have been several attempts to derive semiempirical models based on ambient data (ref 2, and references cited therein). However, the variability of ozone is generally dominated by meteorological variables, partic- ularly temperature. Consequently, it is difficult to discern the relationship of ozone to NMOG and NO,. Furthermore, available ambient NMOG data are very limited.

Many attempts have been made to correlate the maximum ozone concentration attained in smog chamber experiments with initial concentrations of NMOG and NO, and other experimental parameters such as light intensity and temperature (ref 3, and references cited therein). On the basis of smog chamber studies of the

0013-936X/93/0927-2213$04.00/0 0 1993 American Chemical Society

olefin-NO, system, Akimoto et al. ( 4 ) have proposed that the following relationship holds in the NMOG-excess region

(0,) = a(03)ps (1) where (03) is the maximum ozone concentration reached, (03)ps is the photostationary ozone concentration in the absence of NMOG, and a is the proportionality constant. The same relationship has been suggested to hold in smog chamber studies of sampled ambient air (5 ) . Shen et al. (6), on the basis of flow reactor studies of the cyclohexene- NO2 system, have proposed the following relationship

(0,) = [kl(N0,)11/2F(R) (2) where k l is the photolysis rate constant of NOz, (NO,) is the initial concentration of NO,, R is the initial NMOGI NO, ratio and F(R) represents a function of R only. Since ( 0 3 ) p s is proportional to [kl(N0,)11/2 when (NO,) is not too low (20.01 ppm) (4 ) , eq 1 is a special case of eq 2 where F(R) becomes constant. Sakamaki et al. (3) performed computer simulations using a detailed chemical mechanism for the propene-NO, system which reproduced their smog chamber experimental results a t relatively high initial concentrations of propene and NO, and showed that eq 2 holds for the propene-NO, system. Kinosian (7) used empirical kinetic modeling approach (EKMA) diagrams to show that maximum ozone is approximately a linear function of the geometric mean of the precursor concentrations within limited ranges of NMOG and NO, concentrations and their ratios, and he also examined data from smog chamber studies to confirm the ozone-precursor relationship.

During the 1987 Southern California Air Quality Study (SCAQS) (8), extensive outdoor smog chamber experiments were performed on Los Angeles air by the General Motors Research Laboratories. Kelly and Gunst (9) have shown that, in irradiations of identical NMOG/NO, mixtures, ozone maximum concentrations are strongly dependent on the average temperature, and that, from multiple linear regression modeling, temperature and initial NMOG and NO, concentrations are sufficient to represent ozone maximum concentrations. They derived an empirical model

(0,) = 0.129 + (N0,)(2.8 - 6.8/R) + 0.019(7,, - 21.1) (3)

where concentrations are in ppm, R is the initial NMOGI NO, ratio (ppm C/ppm), TaVis the run-average temperature in OC, and 21.1 OC is the average of the daily run-average temperatures. It is noted that eq 3 relates (03) to a function of (NO,) and R similar to eq 2.

Based on an extensive smog chamber study, Johnson (10, 11) has proposed an empirical model called the integrated empirical rate (IER) model, which is separately applicable to the light-limited regime and the NO,-limited

Environ. Scl. Technoi., Voi. 27, No. 10, 1993 2213

regime. During the light-limited regime

(4) where (Ox), is the concentration of oxidant (smog produced), defined by (0x)t = ( 0 3 ) t - (0310 + (NO10 - (NO),; (Ox),, (03)t, and (NO), denote concentrations at time t; (O& and (NO10 represent the initial concentration of O3 and NO, respectively; E is a parameter; and T is temperature in K. A,, is the rate coefficient for the oxidant formation defined by a function of NMOG concentrations

A,, = xai(NMOGi) where ai is the activity coefficient for oxidant formation by NMOGi (which is an individual NMOG species or a mixture), and (NMOGi) is the initial concentration of NMOGi. During the NO,-limited regime, Johnson showed maximum (Ox) to be linearly related to initial NO, concentration

(0x1 = @(NO,) (6) where @ is the NO, stoichiometric coefficient. The rate coefficient A,, and stoichiometric coefficient p are measurable quantities by smog chamber experiments; consequently, Johnson’s IER model could be very useful for understanding characteristics of urban oxidants. However, no model has been derived for the intermediate regime, which is important for urban oxidant formation.

In this paper, a general, but simple ozone-precursor relationship similar to eq 2 is investigated using data generated by a simple air-quality model. It is shown that the relationship holds approximately under wide ranges of environmental conditions. The SCAQS outdoor smog chamber data (9) are also examined to determine the applicability of the simple ozone-precursor relationship.

Relationships Based on Air-Quality Model Simulations

Since experimental data bases for deriving semiempirical relationships are generally limited, relationships will be derived first based on data generated by a single-cell trajectory model, the ozone isopleth plotting package with optional mechanism (OZIPM) (12). Utility and limitations of AQSM ranging from the simplest trajectory model to three-dimensional Eulerian models have been described in criteria documents (I). The single-cell trajectory model is based on an extreme approximation of real air parcels, i.e., the integrity of well-mixed air parcels. Effects of wind sheer and horizontal diffusion are assumed to be insig- nificant because of relatively homogeneous horizontal distributions of emission sources and pollutant concentrations, and pollutants are assumed to be well-mixed within the daytime mixing layer. These assumptions are not always acceptable; however, for days conducive to ozone formation, these assumptions may be quite rea- sonable for many urban areas. In the present paper, it is assumed that the single-cell trajectory model is appropriate for studying the main features of ozone-precursor relationships relevant to urban-center precursor emissions and downwind ozone concentrations.

Two chemical mechanisms are used: CBM4.1, which is the carbon-bond mechanism IV (13) modified as shown in Milford et al. (14); and the Lurmann-Carter-Coyner (LCC) mechanism (15). In this work, air-quality simulations are carried out using CBM4.1 unless specified explicitly. Typical simulation conditions are chosen (16).

Sunlight intensity is diurnally varying under clear sky conditions. Ambient NMOG compositions are chosen to be United States “urban averagen derived by Jeffries et al. (1 7). Two dilution scenarios are chosen: low dilution (the mixing height rising from 300 to 600 m) and high dilution (the mixing height rising from 300 to 1500 m). Ozone-precursor relationships are investigated for three different situations: (A) case with initial precursors only and no dilution; (B) case with initial precursors, continuous emissions, and no dilution; and (C) case with initial precursors, continuous emissions, and dilution. For all cases, the total amount of precursor input (i.e., the sum of initial precursors and the total emissions) is chosen to be equivalent, unless specified explicitly.

(A) Case with Initial Precursors Only. This case simulates smog chamber experiments with initial input of precursors, but with no emissions (no additional input of precursors) and no dilution. Using the OZIPM, a data base of maximum ozone concentrations as a function of initial NMOG and NO, concentrations is generated for initial concentration ranges: (NMOG) = 0-2.0 ppm C and (NO,) = 0-0.2 ppm. This initial concentration domain is used for air-quality simulations, unless specified explicitly. Data points are uniformly distributed in the initial concentration domain of precursors. With this data base, functional forms similar to eq 2 have been searched, emphasizing simplicity in the functional form. After a number of trials, the following functional form was chosen

(7) Parameters c, y, a, and b are determined by a nonlinear least-square method using a nonlinear function minimi- zation routine (18). Parameter c is used to account for aloft polluted air being entrained. Since there is no dilution in this case, parameter c is not used, and the following relationship is obtained

(0,) = 1.17(N0,)1~2(1.0 - e~p[-0.00147R~.~~)] (8) with correlation coefficient, R2 = 0.997, for data and predictions of (03) . When the initial concentration domain of (NMOG) = 0-1.0 ppm C and (NO,) = 0-0.1 ppm is chosen, the following relationship is obtained

(0,) = 1.14(N0,)1~2(1.0 - exp[-0.00502R3~’3)l (9) with correlation coefficient, R2 = 0.997. Equation 9 is close to eq 8. Thus, the change of initial concentration domain does not greatly change the values of the model parameters. In order to consider a single NMOG species, the ethene-NO, system is evaluated and the following relationship is obtained

(0,) = 2.06(N0,)’/2(1.0 - ex~[-O.O372R~.~~)I (10) with correlation coefficient, R2 = 0.989.

In Figure 1, (03)/(N0,)l/2 vs R (corresponding to eq 8) is plotted along with data points generated with OZIPM- CBM4.1. Agreement is good in general. At large R, eq 10 for the ethene-NO, system tends to slightly underestimate the maximum ozone concentrations, while eqs 8 and 9 for the urban NMOG/NO, system tend to slightly overesti- mate maximum ozone concentrations as seen from Figure 1. This is due to NO, sinks provided by some NMOG species, i.e., the urban NMOG mixture contains species which provide NO, sinks, such as aromatics, while ethene does not provide NO, sinks. At large R (NMOG-rich regime), eqs 8-10 show that (03) is independent of NMOG

(0,) = c + y(N0,)1/2[l- exp(-aRb)l

2214 Envlron. Scl. Technol., Vol. 27, No. 10, 1993

t

0.4

0.2

0 0 5 10 16 20 26 30 36 40

NMOQINO, (ppmClppm)

Flgure 1. Plot of eq 8 (solid line) as (03)/(NOx)1’2 vs R (NMOG/NO, ratlo) along with data points (squares) based on OZIPM-CBM4.1 for the case with initial precursors only.

0.08 0.24 0.40 , , 0.2

0.18 , I

I f ,

0.14

0 1 2

0.08 ;

0.04 1 0.02 v v - r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - - - - 0.16

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 1.8 2

NMOG (ppmC)

Flgure 2. Ozone isopleths (solid line) generated by eq 8 and ozone Isopleths (dashed line) generated by interpolatlng data points of OZIPM- CBM4.1 for the case with initial precursors only.

concentrations; consequently, if NO,-sink effects by NMOG species are important, an additional term is needed to describe such effects. In Figure 2, ozone isopleths generated by eq 8 are shown along with isopleths generated by interpolating data points from OZIF’M-CBM4.1. Agree- ment is good in general.

Figure 1 along with eqs 8-10 shows that a general relationship satisfying eq 2 exists, a t least approximately, for NMOG/NO, irradiation in outdoor chamber experiments. The existence of such a relationship in indoor experiments has been shown for the cyclohexene-NO, system by Shen et al. (6) and for the propene-NO, system by Sakamaki et al. (3) . Furthermore, a simple function taking the form of eq 7 can represent ozone-precursor relationships quite accurately for the full domain of initial precursor concentrations. The simple functional form properly represents NO,-inhibition effects (i-e., decreasing NO, concentrations increase ozone concentrations) in the NO,-rich or low R zone (upper-left part of Figure 2) and asymptotes in the NO,-limited (NMOG-rich) or large R zone (lower-right part of Figure 2). At large R, eq 8 overestimates ozone levels somewhat. There is a ridge or knee region between NO,-rich and NMOG-rich regions in Figure 2. The ridge isopleth curves given by eq 8 are a little more sharply bent than those obtained by interpolating data points from OZIPM-CBM4.1.

Equation 3 is perhaps the simplest possible form to represent the NO,-inhibition effect. However, eq 3 is not

applicable when R becomes small because (03) becomes negative. On the other hand, eq 7 is applicable to the entire domain except for one boundary at R = 0 or (NMOG) = 0; however, this boundary is not important for urban ozone problems.

In the region of large R, eq 3 indicates that maximum ozone concentration is linearly related to initial NO, concentration, Since eq 6, Johnson’s relationship in the NO,-limited regime, can be written in the form

(11) where f is the fraction of NO in NO,, eq 6 also indicates that maximum ozone concentration is linearly related to initial NO, concentration. It is, however, recognized from photochemical modeling studies that ozone production efficiency per NO, molecule is a complex function of NMOG and NO, concentrations and their ratio, and ozone production efficiency increases as NO, concentration decreases (19). Furthermore, smog chamber studies show that ozone concentration in the NO,-limited regime is linearly related to (N0,)1/2 for a wide range of NO, concentrations (4). Thus, eq 7 is applicable to a wide range of NO, concentrations in the large R regime and represents nonlinear dependence of ( 0 3 ) on (NO,) properly. Johnson (10) derived P = 4.1 f 0.4 based on smog chamber experiments on ambient Sydney suburban hydrocarbons with (NO,) = 0.04-0.15 ppm. Equation 8 at large R is consistent with Johnson’s relationship (eq 11) in the NO,- limited regime for (NO,) = 0.1-0.15 ppm, although NMOG compositions used for the present study are different from those used by Johnson. However, eq 8 at large R deviates significantly from Johnson’s linear expression (eq 11) when (NO,) < 0.1 ppm.

The coefficient y in eq 7 may be used as a NMOG reactivity scale for NMOG species and mixtures in terms of ozone formation potential as suggested by Akimoto et al. (4) . It is noted that this reactivity scale can be measured directly by smog chamber experiments. The present modeling calculations show that the reactivity (value of y) of “urban average” NMOG is approximately half of the reactivity of ethene (see eqs 8-10).

(B) Case with Initial Concentrations and Emis- sions. OZIPM is run to generate a data base for the case with initial concentrations of NMOG and NO,, and emissions, but without dilution. The effective, initial concentrations, which represent the sums of initial concentrations of precursors and total emissions converted into equivalent, initial concentrations, are chosen to be the same as the case with initial concentrations only (case A). This implies that initial precursor concentrations in case B are half of those in case A for the emission schedule chosen here. The nonlinear regression results in the following relationship

(0,) = 1.16(N0,)1’2[1 - exp(-0.00101R3~76)l (12) with correlation coefficient, R2 = 0.998. In eq 12, (NO,) is the effective, initial concentration of NO, and R is the effective, initial NMOG/NO, ratio. Values of parameters in eq 12 are close to those in eq 8. A plot of (03)/(N0,)1/2 vs R corresponding to eq 12 (not shown here) is very close to Figure 1: Thus, even with substantial emissions added (case B), the ozone-precursor relationship does not change significantly compared to case A with initial concentrations only.

(0,) = (P - n(N0,)

Envlron. Scl. Technol., Vol. 27, No. 10, 1993 2215

0.5 I I

0.1

" ~~~ ~~

0 5 10 15 20 25 30 35 40 NMOG/NO, (ppmC/ppm)

Flgure 3. Plot of eq 14 (solld line) as [(Oa) - c]/(NO,)"* vs R (NMOGI NO, ratio) along with data points (squares) based on OZIPM-CBM4.1 for the case with initial precursors, emissions, and high dilution.

(C) Case with Initial Concentrations, Emissions, and Dilution. OZIPM is run to generate a data base for the case with initial concentrations, emissions, and atmospheric dilution. The effective, initial concentrations of precursors are chosen to be equivalent to the case with initial concentrations only (case A). NMOG entrained from the aloft layer are included in representing effective, initial ratios, R. For this case, a constant parameter c in eq 7 is retained to represent entrained 0 3 as the mixing layer increases. Low and high dilution scenarios are considered. For the low dilution case, the nonlinear regression results in the following relationship

(0,) = 0.0122 + 0.758(N0,)1/2[1 - e~p(-0.00311R~.~~)] (13)

with correlation coefficient, R2 = 0.995. For the high dilution case, the following relationship is obtained

(0,) = 0.0193 + 0.447(N0,)'/2[1 - e~p(-0.0460R'.~~)] (14)

with correlation coefficient, R2 = 0.982. When the LCC mechanism is used to generate the data base, the following relationship is obtained for the high dilution case

(0,) = 0.0251 + 0.459(N0,)1/2[1 - e~p(-0.0441R'.~~)I (15)

with correlation coefficient, R2 = 0.988. Equations 14 and 15 are plotted as [(Od - cI / (NO,)~/~

vsR along with data points generated by OZIPM in Figures 3 and 4, respectively. Equations 13-15 have been derived excluding OZIPM-simulation data points a t boundaries of no initial concentrations and no emissions of NMOG and/or NO,. Equations 13-15 give lower values of maximum ozone concentrations at these boundaries (not shown in Figures 3 and 4) than those from the OZIPM model; however, these boundaries are not important for urban ozone issues. Figures 3 and 4 show that a relationship approximately satisfying eq 2 exists for an air mass which is diluted and receives emissions and entrained pollutants from the aloft layer.

In Figure 5, ozone isopleths generated by eq 14 are shown for the case based on CBM4.1 and the high dilution scenario along with ozone isopleths generated by interpolating data points from OZIPM-CBM4.1. Agreement

I (0, - 0.0251) / NO,'" = 0.459(1 - e4)OUIR ''72)/

"0 5 10 15 20 25 30 35 40 NMOG/NO, (ppmC/ppm)

Figure 4. Plot of eq 15 (solid line) as [(03) - c]/(NO,)'/~ vs R (NMOG/ NO, ratio) along with data points (squares) based on OZIPM-LCC mechanism for the case with initial precursors, emissions, and high dilution.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 1.8 2 NMOG (ppmC)

Figure 5. Ozone isopleths (solid line) generated by eq 14 and ozone isopleths (dashed line) generated by interpolating data points of OZIPM- CBM4.1 for the case with initial precursors, emissions, and hlgh dilution.

between the ozone isopleths is fairly good. For the low dilution scenario (eq 131, agreement is much better. It is noted that parameter a determines the strength of the NO,-inhibition effect (or slope of upper-left ozone isopleth curves). Larger values of parameter a give weaker NO,- inhibition effects, that is, slopes of the upper-left isopleth curves are larger. As dilution increases, NO,-inhibition effects get weaker (see values of parameter a in eqs 8,13, and 14, and Figures 2 and 5). Parameters a and b appear to be anticorrelated.

Johnson (10) has proposed that ozone concentrations in an air mass which is being diluted can be estimated by introducing linear dilution factors to smog chamber results with no dilution. To consider this proposition, effects of dilutions are examined here. If dilution factors are introduced in eq 8 [Le., (NO,) in eq 8 is replaced by (N0,)/2 and (N0,)/5 for low and high dilution cases, respectively], the following expressions are obtained

(13a) (0,) = 0.827(N0,)1/2[1 - e~p(-O.O0147R~~'~)1 for the low dilution case and

(0,) = 0.523(N0,)112[1 - e~p(-0.00147R~.~~)] (14a) for the high dilution case. Alternatively, if effective, initial NO, concentrations in eqs 13 and 14 are replaced by effective, final concentrations [i.e., (NO,) = 2(NO,)f and (NO,) = 5(NO,)f are introduced into eqs 13 and 14,

2216 Envlron. Scl. Technol., Vol. 27, No. 10, 1993

respectively], eqs 13 and 14 in the large R regime are

(0,) = 0.0122 + 1.07(N0,)f/2

(0,) = 0.0193 + 1.00(N0,)f/2 (14b) for the high dilution case. It is interesting to note that values of y in eqs 13a and 14a are fairly close to those in eqs 13 and 14, respectively, and values of y in eqs 13b and 14b are fairly close to those in eq 8 (differences are 9% and 17%, respectively). In deriving eqs 13 and 14, pollutants (0, and NMOG) are entrained from the aloft layer. For air-quality simulations without the aloft pollutants, the value of y for the high dilution case is derived to be 0.44 compared to 0.45 in eq 14. Thus, values of y do not vary greatly with or without entrained pollutants for the simulation conditions considered here. These results show that, a t large R or NOJimited regime, dilution may be approximately accounted for by introducing a dilution factor to smog chamber results. However, dilution does change parameters a and b in eq 7 significantly; consequently, an introduction of a dilution factor appears to be not sufficient a t intermediate values of R.

(13b) for the low dilution case and

0.2

Relationships Based on Smog Chamber Data

The SCAQS's captive air irradiation study on Los Angeles air (9) has produced an extensive outdoor smog chamber data base, which is suitable for deriving ozone- precursor relationships. This data base is used to evaluate the applicability of relationships derived in the previous section. As pointed out earlier, Kelly and Gunst (9) derived an empirical model (eq 3) based on this data.

In the captive air irradiation experiments, each NMOG/ NO, mixture was prepared by filling a bag with morning ambient air. To extend ranges of initial precursor concentrations and their ratios, ambient air was diluted by clean air for some experiments and NMOG and/or NO, were added for some other experiments. The NO,-spike gas was NO in N2, and the ambient NMOG surrogate- spike gas was a mixture of butane, toluene, and propene with the proportions of 71:21:8 in ppm C. In addition to measurements of NMOG, NO,, and 03, other variables such as ultraviolet flux and ambient and chamber temperatures were measured. In-chamber temperatures were not measured continuously. Kelly and Gunst (9) showed that temperature and initial NMOG and NO, concentrations are sufficient to represent ozone maximum concentrations. The captive air irradiation study produced 234 runs which have all the required data: 0 3 , NMOG, NO,, and run-average temperature. Out of the 234 runs, there were 55 repeat runs, leaving 179 runs in the no- repeat data base. In the present paper, the no-repeat data base of 179 runs is used in order to give each ambient mixture an equal weighting. The repeat runs were averaged to derive the no-repeat data base.

In order to include the temperature effect, eq 7 is changed to the following functional form

(0,) = c + y(N0,)1/2[1 - exp(-aR*)l exp[-d(l/T - UTav)] (16)

where c, y, a , b and d are parameters to be determined by the non-linear regression described earlier. Parameter c is added to represent the smog chamber wall effects in

-

(0, - o.ooa) I NO,'^ I e-(lfl.*m = I .W(I - ea-'=

. I r - 1


0.08 0.18 0.24 032 0.40

, 1 I !

1

0.2

0.18

0.24

0.18

0 0 2 0 4 0.6 0.0 1 1.2 1.4 1.6 1 8 2 NMOG (ppmC)

Flgure 7. Ozone isopleths (solid lines) generated by eq 17 and ozone isopleths (dashed lines) generated by eq 3 at the average value of daily run-average temperatures.

other hand, the temperature effect from the OZIPM- CBM4.1 with no emissions and no dilution indicates that maximum ozone levels increase approximately 2-4 % per "C except for the very low R regime where model results are very uncertain. Thus, the temperature effect on maximum ozone levels in smog chamber experiments is greater than the temperature effect indicated by the photochemical model. It is not known whether the difference between temperature effects resulting from smog chamber experiments and photochemical models is due to chamber surface effects and/or errors in chemical mechanisms. It is also noted that the temperature effect given by eq 17 is very similar to the temperature effect on the ozone formation rate during the light-limited regime derived from outdoor smog chamber experiments with ambient urban air by Johnson (10). Johnson derived parameter E = 4700/K in eq 4 for ambient urban air, which is compared to parameter d = 4550/K in eq 17.

Conclusions and Discussions

The functional relationships between maximum ozone levels and precursor (NMOG and NO,) concentrations (and emissions), which are relevant to urban ozone issues, have been investigated using data generated by a single- cell trajectory model, OZIPM, and SCAQS's outdoor smog chamber data (9). Based on model-generated data bases, a general relationship is shown to exist for outdoor smog chamber simulations with initial precursors, and for air masses which have initial input and continuous emissions of precursors and are diluted. When diurnally varying sun-light intensity and temperature are fixed, the relationship expresses maximum ozone concentrations as a product of the square root of effective, initial NO, concentrations and a function of effective, initial NMOG/ NO, ratios (R). Previously, such relationships have been shown to exist in the case of indoor experiments of NMOG- NO, mixtures (3, 6). The function of effective R can be approximated as a simple function involving an exponential function (see eq 7). The present model (eq 7) holds for the entire domain of precursor concentrations. The model with a temperature-dependent function (eq 16) has also been applied to the SCAQS outdoor smog chamber data (9). It is shown that the model represents the outdoor smog chamber experiments reasonably. The present model involves nonlinear parameters; consequently, the nonlinear least-square method, which is much more

complex than the linear least square method, is needed to determine the optimum values of parameters.

The present model is simple, yet is applicable to the entire domain of effective precursor concentrations, and may be applicable approximately to any urban air mass. The parameter y (eqs 7 and 16) is a measurable quantity by smog chamber experiments, and it may be used as a maximum NMOG reactivity scale in the sense of maximum ozone-forming potential as suggested by Akimoto et al. ( 4 ) . Parameters a and b (see eqs 7 and 16) appear to be anticorrelated. Parameter a determines the strength of NO,-inhibition effects (slope of upper-left ozone isopleth curves), and a smaller value of parameter a implies a stronger NO,-inhibition effect. A t large R (or NMOG- rich regime), the present model gives ozone isopleths which are horizontal. The present model does not take into account NO, sinks by some NMOG species, such as aromatics, a t large R. When NO,-sink effects by NMOG species are important, an additional term is needed to describe such effects. There is a ridge or knee region between NO,-rich and NMOG-rich regions in an ozone isopleth diagram. The ridge lines given by the present model are somewhat more sharply bent than those obtained by interpolating points of the OZIPM data base. The model, with a temperature-dependent function (eq 161, represents outdoor smog chamber data reasonably well. The present analysis shows that the temperature effect on ozone concentrations based on smog chamber data is larger than that indicated by current chemical mechanisms as pointed out by Kelly and Gunst (9).

Although an extensive effort has been made to develop and evaluate chemical mechanisms for use in AQSMs, there still remains a number of significant uncertainties in chemical mechanisms such as mechanisms of aromatic and biogenic NMOG species. There is another critical uncertainty in current chemical mechanisms at low NMOG and NO, concentrations and low NMOG/NO, ratios, since current models have been evaluated using smog chamber data a t high reactant concentrations and relatively high NMOG/NO, ratios. There has been some difficulty in simulating smog chamber experiments at low NMOG/ NO, ratios using current chemical mechanisms. For example, Hess et al. (20) have shown that CBM4 under- predicts ozone concentrations at low NMOG/NO, ratios ( R < 5) compared to those from smog chamber experiments. If this is proven to be the case by additional studies, correct chemical mechanisms will result in higher ozone formation at low R and will reduce NO,-inhibition effects. That is, slopes of upper-left curves in ozone isopleth diagrams will be increased, and the value of parameter a in eq 7 will be increased. Reducing uncertainties in chemical mechanisms is essential for credible evaluations of NMOG and NO, control strategies in order to reduce urban ozone levels.

The present study has shown that simple relationships between urban-center NMOG/NO, emissions and downwind ozone concentrations may approximately hold under a wide range of conditions. The existence of such general relationships should be useful for designing experimental studies of ozone-precursor relationships and for analyzing experimental and modeling data. The present study, however, is based on one-day, simple trajectory modeling and one-day outdoor smog chamber data. High ozone levels are often observed during multiday episodes. Since three-dimensional Eulerian photochemical dispersion

2218 Environ. Scl. Technol., Vol. 27, No. 10, 1993

models can approximate real atmospheric processes in- cluding multiday episodes much better than the simple trajectory model, it would be interesting to examine the existence of simple relationships, such as eq 7, based on results of three-dimensional Eulerian models. If such relationships are shown to hold for air masses in general by further studies based on more extensive smog chamber data and more accurate modeling results, such simple relationships could be used for preliminary impact analyses of precursor controls on ozone levels before detailed, complex modeling analyses are performed.

Acknowledgments

The authors thank Dr. N. A. Kelly of General Motors Research Laboratories for providing the SCAQS’s outdoor smog chamber data and for helpful discussions.

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(5) Sakamaki, F.; Akimoto, H.; Hoshino, M.; Inoue, G.; Okuda,

(6) Shen, C. H.; Springer, G. S.; Stedman, D. H. Environ. Sci.

(7) Kinosian, J. R. Environ. Sei. Technol. 1982, 16, 880-883. (8) Lawson, D. R. J. Air Waste Manage. Assoc. 1990,40,156-

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Received for review February 16, 1993. Revised manuscript received June 25, 1993. Accepted June 28, 1993.’

* Abstract published in Advance ACS Abstracts, August 15,1993.


ozone-precursor relationships: a modeling study of semiempirical relationships

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