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Instantaneous secondary organic aerosol yields and their comparison with overall aerosol yields for aromatic and biogenic hydrocarbons
ARTICLE IN PRESS
Atmospheric Environment 37 (2003) 5439–5444
Technical note
Instantaneous secondary organic aerosol yields and their comparison with overall aerosol yields for aromatic and biogenic hydrocarbons Weimin Jiang* National Research Council of Canada, 233, M2, 1200 Montreal Road, Ottawa, Ont., Canada K1A 0R6 Received 31 March 2003; accepted 4 September 2003
Abstract An instantaneous secondary organic aerosol yield (IAY) is a different quantity than an overall aerosol yield (OAY), both qualitatively and quantitatively. Starting from Odum’s OAY equation, this paper derives and presents a new equation for the calculation of IAY values. As examples, the two-product form of the equation is applied to 10 representative aromatic and biogenic reactive organic gas (ROG) experiments in the literature. Values of IAY and OAY corresponding to wide ranges of organic aerosol mass concentrations (M0 ) are calculated using the new IAY equation in this paper and the original Odum’s OAY equation. These IAY and OAY values are shown through aerosol yield curves, which are the plots of IAY or OAY versus M0 : Comparative analysis of the IAY and OAY curves shows that both IAY and OAY increase monotonically with M0 and they approach a common maximum value when M0 becomes very high. However, when M0 approaches zero, OAY also approaches zero but IAY approaches a fixed positive value for a given ROG. At any given M0 value, the value of IAY is always higher than that of OAY. The relative differences between IAY and OAY are especially significant under typical ambient and experimental M0 levels. IAY values can be orders of magnitude higher than OAY values and are much better representations of aerosol yields under these M0 levels. When it is used for secondary organic aerosols (SOA) estimation and modelling, the new IAY equation will significantly improve the underestimation of SOA formation caused by directly using the original OAY equation. More sophisticated SOA algorithms could also be developed based on the IAY equation presented here. Crown Copyright r 2003 Published by Elsevier Ltd. All rights reserved. Keywords: Aerosol yield; Secondary organic aerosols; Particulate matter; Reactive organic gas; Air quality modelling
1. Introduction Secondary organic aerosols (SOA) are formed in the atmosphere through the oxidation of reactive organic gases (ROGs) followed by condensation or gas/aerosol partitioning (Seinfeld and Pandis, 1998). To model the formation of SOA, a concept called aerosol yield (or SOA yield), loosely defined as the SOA mass formed per unit mass of ROG reacted, has been widely used. Early research was focused on estimating and deriving *Fax: +1-613-941-1571. E-mail address: [email protected] (W. Jiang).
constant SOA yields for ROGs of interest (Grosjean and Seinfeld, 1989; Pandis et al., 1992). In a new generation of studies on aerosol yields, Odum et al. (1996) demonstrated experimentally that instead of being constant, a SOA yield is a function of aerosol organic mass concentration. Based on the gas/ aerosol partitioning theory proposed by Pankow (1994), they derived a general equation that links an SOA yield with an aerosol organic mass concentration. Using smog chamber experimental data, they showed that the relationship between the aerosol yield and the organic mass concentration can be well described by assuming two condensable SOA products only. Based on this
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assumption, they simplified the equation to a twoproduct form and derived the associated equation parameters for m-xylene, 1,2,4-trimethylbenene, and apinene. Later, the two-product form of their equation was applied to other aromatic ROGs (Odum et al., 1997) and biogenic hydrocarbons (Hoffmann et al., 1997; Griffin et al., 1999). For simplicity, we call this aerosol yield equation Odum’s equation in this paper. The aerosol yield calculated by Odum’s equation is an overall secondary organic aerosol yield (OAY) from the beginning of an experiment to a certain level of accumulated organic mass concentration in particles. In atmospheric modelling studies, it is often required to know an instantaneous secondary organic aerosol yield (IAY) under a specific pre-existing aerosol organic mass concentration in order to estimate the incremental amount of SOA formed. At a glance, OAY and IAY may seem similar; however, they are fundamentally different quantities and their values can also differ dramatically. According to the author’s knowledge, there are no published formulas or equations available for the calculation of these important IAY values. Starting from Odum’s equation, this paper derives an equation for the IAY calculation. The equation is then simplified to its two-product form. As examples, the two-product form of the equation is applied to 10 representative aromatic and biogenic ROG experiments originally investigated in the literature. IAY and OAY values in wide ranges of organic aerosol mass concentrations are then calculated. They are shown and compared through aerosol yield curves, which are the plots of aerosol yields versus organic aerosol mass concentrations. To help, understand the impact of replacing the Odum’s OAY equation with the new IAY equation in an air quality model, the issue of applying the equations in SOA estimation and modelling is briefly discussed.
This is Odum’s OAY equation. Note ‘‘OAY’’ is used to replace ‘‘Y’’ in Odum et al. (1996) to show the real meaning of ‘‘aerosol yield’’ in the equation. In the equation, M0 is the concentration of all species in organic aerosol phase; ai and Kom;i are the mass-based stoichiometric coefficient and the partitioning coefficient of the ith condensable species CSi. OAY is defined as OAY ¼
DM0 ; DROG
where DROG and DM0 are the overall concentration changes of ROG and organic aerosol mass from the beginning of the reaction, respectively. Since the value of M0 is zero at the beginning of the reaction, we have DM0 ¼ M0 and OAY ¼
M0 : DROG
ð2Þ
In the equations above, if the units of all concentrations are mg m3, the unit of Kom;i is then m3 mg1. OAY and ai are dimensionless quantities. The stoichiometric coefficients in the chemical reaction above are massbased instead of mole-based to simplify the discussions. The two-product form of Eq. (1) is a1 Kom;1 a2 Kom;2 OAY ¼ M0 : ð3Þ þ 1 þ Kom;1 M0 1 þ Kom;2 M0 Graphically, an OAY calculated by Odum’s equation is the slope of a line connecting the origin and a point on an experimental M0 versus DROG curve. As an example, the slope of line 1 in Fig. 1(a) shows conceptually the OAY of m-xylene from the start of an experiment to the point where DROG has been consumed and M0 has been generated. 2.2. The new IAY equation
2. A new equation for IAY calculation 2.1. The original Odum’s OAY equation Considering a gas phase reaction between a ROG and an oxidant (OX) that generates a set of gaseous products (P1, P2, y) and a set of condensable organic species (CS1, CS2, y): ROG þ OX ¼ p1 P1 þ p2 P2 þ ? þ a1 CS1 þ a2 CS2 þ ?; the overall yield of SOA formed from the beginning of the reaction to a point where gas/aerosol partitioning equilibria for all condensable species have been achieved is (Odum et al., 1996) X ai Kom;i OAY ¼ M0 : ð1Þ 1 þ Kom;i M0 i
To model the evolution of SOA, we need to know the aerosol yields at given M0 values. Graphically, the aerosol yield at a specific M0 is the slope of the tangent line at the point (DROG, M0 ) on an experimental M0 versus DROG curve. This is represented, for example, by the slope of line 2 in Fig. 1(a). Since this slope is the rate of M0 change with respect to DROG at the given point only, we call it IAY to reflect its instantaneous nature in SOA evolution. Mathematically, IAY is the derivative of M0 with respect to DROG, i.e., IAY ¼
dM0 : dDROG
ð4Þ
A general equation for the calculation of IAY can be derived from Eq. (1) as follows.
ARTICLE IN PRESS W. Jiang / Atmospheric Environment 37 (2003) 5439–5444
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0.2
M0
100,000
0.16
10,000
IAY
Slope = OAY Slope = IAY
M0*
1,000 0.12
IAY-OAY × 100 OAY
100
0.08 10 0.04
1
1 IAY-OAY
0
∆ ROG
∆ ROG*
0
0.1 (a)
% Difference
Aerosol Yield
OAY
2
1
10
0.1
100 1,000 10,000 100,000
M0(µg m-3)
(b)
Fig. 1. Differences between OAY and IAY for the photo-oxidation of m-xylene: (a) conceptual differences; and (b) quantitative differences. Curves are drawn based on the two-product assumption and the parameters in Table 1.
Table 1 OAY and IAY equation parameters for some representative aromatic and biogenic ROGs ROG
a1
Kom;1 (m3 mg1)
a2
Kom;2 (m3 mg1)
a (m6 mg2)
b (m3 mg1)
c (m12 mg4)
d (m9 mg3)
e (m6 mg2)
m-xylenea 1,2,4-trimethylbenzenea p-diethylbenzenea a-pinenea a-pinene (O3)a b-pinenea b-pinene (O3)a D3-carenea D3-carene (O3)a Sabinene (O3)a
0.03 0.0324 0.083 0.038 0.125 0.130 0.026 0.054 0.128 0.037
0.032 0.053 0.093 0.171 0.088 0.044 0.195 0.043 0.337 0.819
0.167 0.166 0.22 0.326 0.102 0.406 0.485 0.517 0.068 0.239
0.0019 0.002 0.0010 0.004 0.0788 0.0049 0.0030 0.0042 0.0036 0.0001
1.198E05 2.103E05 2.818E05 2.490E04 1.574E03 1.156E04 2.989E04 1.031E04 2.378E04 2.260E05
1.277E03 2.049E03 7.939E03 7.802E03 1.904E02 7.709E03 6.525E03 4.493E03 4.338E02 3.033E02
7.282E10 2.229E09 2.621E09 1.703E07 1.092E05 2.492E08 1.749E07 1.862E08 2.885E07 1.851E09
1.553E07 4.344E07 1.477E06 1.067E05 2.640E04 3.324E06 7.634E06 1.623E06 1.053E04 4.968E06
3.132E05 9.168E05 7.181E04 1.116E03 1.601E03 2.614E04 9.930E04 1.090E04 1.454E02 2.482E02
a
Values of ai ; Kom,i , i ¼ 1; 2, are from Odum et al. (1996), Odum et al. (1997), and Griffin et al. (1999).
Combining Eqs. (1) and (2) and canceling a M0 from the combined equation, we get X ai Kom;i 1 ¼ : DROG 1 þ Kom;i M0 i Therefore P 2 ai Kom;i =ð1 þ Kom;i M0 Þ2 dDROG ¼ Pi 2 : dM0 ai Kom;i =ð1 þ Kom;i M0 Þ
IAY ¼
ðaM0 þ bÞ2 ; cM02 þ dM0 þ e
ð6Þ
where the parameters are functions of Kom;i and ai (i ¼ 1; 2Þ a ¼ ða1 þ a2 ÞKom;1 Kom;2 ; b ¼ a1 Kom;1 þ a2 Kom;2 ;
i
The needed IAY equation is then P 2 ai Kom;i =ð1 þ Kom;i M0 Þ dM0 ¼ Pi : IAY ¼ 2 2 dDROG i ai Kom;i =ð1 þ Kom;i M0 Þ
(a, b, c, d, e):
2 2 Kom;2 ; c ¼ ða1 þ a2 ÞKom;1
ð5Þ
The simplified two-product form of Eq. (5) contains the independent variable M0 and five parameters
d ¼ 2Kom;1 Kom;2 ða1 Kom;1 þ a2 Kom;2 Þ; 2 2 þ a2 Kom;2 : e ¼ a1 Kom;1
As examples, Table 1 lists values of the five new IAY parameters for 10 representative ROG experiments in
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behaviour of the IAY and OAY curves in a wider range of M0 values and the dramatic range of % differences between IAY and OAY values. Both IAY and OAY curves show monotonic increases of the aerosol yield with M0 : When M0 becomes very high, both IAY and OAY values approach a common limit value of a1 þ a2 as proved by the following:
the literature along with the original parameters in Odum’s OAY equation. ‘‘O3’’ in brackets indicate ROG reactions with O3 rather than photo-chemical reactions. The IAY Eq. (5) is directly derived from the OAY Eq. (1) without any other assumptions or approximations. Therefore, experimental data that satisfy Eqs. (1) and (3) also satisfy Eqs. (5) and (6), respectively.
ðaM0 þ bÞ2 a2 ¼ 2 M0 -N cM þ dM0 þ e c 0
lim IAY ¼ lim
M0 -N
3. Comparison of IAY and OAY values for the aromatic and biogenic ROGs
¼
IAY and OAY are not only conceptually different as shown in Fig. 1(a), their values can also be dramatically different. As an example, Fig. 1(b) shows quantitative differences of IAY and OAY values over a wide M0 range for the photo-oxidation of m-xylene described by the two-product forms of the IAY and OAY equations. For simplicity, we call the plots of IAY or OAY versus M0 aerosol yield curves. Log-scale is used for M0 and ‘‘% Difference’’ in Fig. 1(b) in order to show the
Aerosol Yield
0.20
M0 -N
0.40 α-pinene
p-diethylbenzene
0.30 0.20
0.12
0.20 0.08
0.10
0.10 0.00
0.00
0.00 0.25
Aerosol Yield
When M0 approaches zero, the OAY value approaches zero while the IAY value approaches a positive value of b2 =e; which can be easily derived from Eq. (6). Using the
0.04
β-pinene
α-pinene (O3)
0.20
β-pinene (O3)
0.40
0.40
0.20
0.20
0.00
0.00
0.00
0.60
0.20
0.15 0.10 0.05
∆3-carene
Aerosol Yield
a1 Kom;1 a2 Kom;2 þ M0 -N 1 þ Kom;1 M0 1 þ Kom;2 M0 a1 Kom;1 a2 Kom;2 þ ¼ a1 þ a2 : ¼ Kom;1 Kom;2
lim OAY ¼ lim M0
0.30 1,2,4-trimethylbenzene
0.16
2 2 ða1 þ a2 Þ2 Kom;1 Kom;2 ¼ a1 þ a2 ; 2 2 ða1 þ a2 ÞKom;1 Kom;2
0.40
0.20
0.10 ∆3-carene (O3)
0.16 0.12
0.06
0.08
0.04
0.04
0.02
0.00
0.00 0.1
1 10 100 1,000 M0 (µg m-3)
sabinene (O3)
0.08
0.00 0.1
IAY
1 10 100 1,000 M0 (µg m-3)
0.1
1 10 100 1,000 M0 (µg m-3)
OAY
Fig. 2. Comparison of IAY and OAY curves for the aromatic and biogenic ROGs (except m-xylene) listed in Table 1. The M0-axis is in log-scale and covers typical ambient and smog chamber M0 levels.
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b and e values for m-xylene in Table 1, we get IAY=0.052 at M0 ¼ 0: Fig. 1(b) shows that IAY is always higher than OAY at any given M0 level. The absolute difference between IAY and OAY is shown by the curve ‘‘IAY–OAY’’ using the scale on the left vertical axis. The relative difference (% Difference) is shown by the curve ‘‘(IAY– OAY)/OAY 100’’ using the log-scale on the right vertical axis. Note dramatic relative differences between IAY and OAY at low M0 levels. At typical ambient M0 levels of 1–10 mg m3, IAY values are 4135% to 470% higher than OAY values. In the m-xylene experiments by Odum et al. (1996) where the level of M0 is in the range 1.5–396 mg m3, the IAY values are 2775% to 76% higher than the corresponding OAY values. Fig. 2 shows more comparison of IAY and OAY curves for other ROGs listed in Table 1. The log-scale used on the horizontal axis covers typical ambient and smog chamber M0 levels. For simplicity, the difference curves seen in Fig. 1(b) are not shown. Similar comparison and analysis have also been applied to other ROGs investigated by Odum et al. (1996) and the follow-up studies. They are omitted here for brevity. Details on the analysis of other ROGs are available from the author.
4. Comments on using the IAY and OAY equations for SOA estimation and modelling To estimate or model SOA formation, it is often required to calculate the incremental increase of SOA mass caused by a certain amount of reacted ROG at certain pre-existing levels of M0 : Most aerosol yieldbased approaches conduct the estimation based on the following simplified equation: DSOA ¼ AY DROG;
ð7Þ
where DSOA is the incremental SOA increase, AY is an aerosol yield, and DROG is the reacted ROG that causes the formation of DSOA. The key here is to get an estimate of the aerosol yield. Some earlier studies used constant aerosol yield values in their modelling exercise (e.g., Bowman et al., 1995). More recently, the twoproduct form of Odum’s equation has been built into a state-of-the-art air quality model with the intention to improve the representation of SOA production (Binkowski and Roselle, 2003; Jiang and Roth, 2003). As discussed above, Odum’s equation generates OAY instead of the aerosol yields at M0 ; and the OAY values obtained from the equation are very low under typical ambient M0 levels. Therefore, using the OAY equation directly for aerosol yield calculations will cause significant underestimation of new SOA formation. Using the IAY equation presented in this paper will make the approach more scientifically defensible and
5443
M0
M0.2 M0.IAY
Slope = IAY
M0.OAY
Slope = OAY
M0.1
0
∆ROG1
∆ROG
∆ROG2
Fig. 3. Qualitative comparison of errors caused by using OAY and IAY equations in estimating new SOA formation.
improve the modelling results. Fig. 3 shows qualitatively the difference in errors caused by using the IAY and OAY equations in estimating new SOA formation. The curve in Fig. 3 is an assumed true M0 versus DROG relationship that we need to simulate. At the beginning of a time step, M0 ¼ M0;1 and DROG=DROG1. At the end of the time step, DROG changes to DROG2 and M0 should become M0;2 if we could simulate the system perfectly. Using the OAY Eq. (1) or (3) to calculate the aerosol yield and Eq. (7) to calculate the new SOA formed causes M0 ¼ M0;OAY : Using the IAY Eq. (5) or (6) similarly causes M0 ¼ M0;IAY : Although both estimations result in underestimation of M0 ; the error caused by using IAY, which is equal to M0;2 M0;IAY ; is much smaller than the error caused by using OAY, which is equal to M0;2 M0;OAY : The improvement to the modelling results by using the IAY equation is especially significant when a model is used in simulations under ambient conditions. As shown in Figs. 1(b) and 2, IAY values can be 100%, 1000%, or even 10,000% higher than OAY values under ambient M0 levels. Although the estimations of new M0 based on both OAY and IAY values are lower than true values according to Fig. 3, the errors of the IAY-based results can be orders of magnitude smaller than the errors of the OAY-based results. The results obtained by using the IAY equation can be improved further through more sophisticated mathematical manipulation using the IAY equation or its two-product form. An simple example would be to calculate an IAY value at M0;IAY in addition to the IAY
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at M0;1 in Fig. 3, and then use the average of the two IAY values as the aerosol yield in Eq. (7). An iterative process could also be built on this idea to minimise the error. This is a subject beyond the scope of this paper and will not be explored further here.
5. Conclusion and discussion Using Odum’s OAY equation as a starting point, this paper derived a new equation for calculation of IAY, which reflects the dependence of instantaneous aerosol yields on the concentrations of pre-existing organic species. The equation is then applied to some representative aromatic and biogenic ROG experiments in the literature. Although they may seem similar and they are both related to an organic aerosol concentration M0 ; IAY and OAY are fundamentally different quantities and need to be clearly distinguished. IAY is a function of a pre-existing organic aerosol concentration while OAY is a function of an accumulated organic aerosol concentration. Comparative analysis of the IAY and OAY curves shows that both IAY and OAY increase monotonically with M0 and they approach a common maximum value when M0 becomes very high. However, when M0 approaches zero, OAY also approaches zero but IAY approaches a fixed positive value for a given ROG. At any given M0 values, values of IAY are always higher than those of OAY. The relative difference between IAY and OAY is especially significant under typical ambient and experimental M0 levels. IAY values can be orders of magnitude higher than OAY values and are much better representations of aerosol yields under these M0 levels. Both qualitative analysis and quantitative comparisons demonstrate that using the new IAY equation will cause lower level of errors in SOA estimation than using the OAY equation. Although they are beyond the focus of this paper, more sophisticated SOA algorithms could be developed based on the IAY equation presented in this paper. As an extension of Odum’s equation, the IAY equation in this paper is subject to the same uncertainties as in the original Odum’s equation. An issue of interest is the reliability of the equations under typical lower levels of M0 in the atmosphere in comparison with the smog chamber. More theoretical, experimental, and/or modelling studies are needed to address this issue.
Acknowledgements ! I would like to thank my colleagues Eric Giroux, Dazhong Yin and Helmut Roth for their substantial technical assistance in preparing the manuscript and in verifying the mathematical derivation of the equations. The project is funded by the interdepartmental Program of Energy Research and Development in Canada and by the National Research Council of Canada.
References Binkowski, F.S., Roselle, S.J., 2003. Models-3 Community Multiscale Air Quality (CMAQ) model aerosol component, 1, Model description. Journal of Geophysical Research 108 (D6), 4183, doi:10.1029/2001JD001409. Bowman, F.M., Pilinis, C., Seinfeld, J.H., 1995. Ozone and aerosol productivity of reactive organics. Atmospheric Environment 29, 579–589. Griffin, R.J., Cocker III, D.R., Flagan, R.C., Seinfeld, J.H., 1999. Organic aerosol formation from the oxidation of biogenic hydrocarbons. Journal of Geophysical Research 104, 3555–3567. Grosjean, D., Seinfeld, J., 1989. Parameterization of the formation potential of secondary organic aerosols. Atmospheric Environment 23, 1733–1747. Hoffmann, T., Odum, J.R., Bowman, F., Collins, D., Klockow, D., Flagan, R.C., Seinfeld, J.H., 1997. Formation of organic aerosols from the oxidation of biogenic hydrocarbons. Journal of Atmospheric Chemistry 26, 189–222. Jiang, W., Roth, H., 2003. A detailed review and analysis of science, algorithms, and code in the aerosol components of Models-3/CMAQ I. Kinetic and thermodynamic processes in the AERO2 module. Report Number PET-1534-03S, institute for chemical process and environmental technology, National Research Council of Canada, Ottawa, Canada, 2003/03. Odum, J.R., Hoffmann, T., Bowman, F., Collins, D., Flagan, R.C., Seinfeld, J.H., 1996. Gas/particle partitioning and secondary organic aerosol yields. Environmental Science and Technology 30, 2580–2585. Odum, J.R., Jungkamp, T.P.W., Griffin, R.J., Forstner, H.J.L., Flagan, R.C., Seinfeld, J.H., 1997. Aromatics, reformulated gasoline, and atmospheric organic aerosol formation. Environmental Science and Technology 31, 1890–1897. Pandis, S.N., Harley, R.A., Cass, G.R., Seinfeld, J.H., 1992. Secondary organic aerosol formation and transport. Atmospheric Environment 26A, 2269–2282. Pankow, J.F., 1994. An absorption model of the gas/aerosol partitioning involved in the formation of secondary organic aerosol. Atmospheric Environment 28, 189–194. Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics. Wiley, New York.
Atmospheric Environment 37 (2003) 5439–5444
Technical note
Instantaneous secondary organic aerosol yields and their comparison with overall aerosol yields for aromatic and biogenic hydrocarbons Weimin Jiang* National Research Council of Canada, 233, M2, 1200 Montreal Road, Ottawa, Ont., Canada K1A 0R6 Received 31 March 2003; accepted 4 September 2003
Abstract An instantaneous secondary organic aerosol yield (IAY) is a different quantity than an overall aerosol yield (OAY), both qualitatively and quantitatively. Starting from Odum’s OAY equation, this paper derives and presents a new equation for the calculation of IAY values. As examples, the two-product form of the equation is applied to 10 representative aromatic and biogenic reactive organic gas (ROG) experiments in the literature. Values of IAY and OAY corresponding to wide ranges of organic aerosol mass concentrations (M0 ) are calculated using the new IAY equation in this paper and the original Odum’s OAY equation. These IAY and OAY values are shown through aerosol yield curves, which are the plots of IAY or OAY versus M0 : Comparative analysis of the IAY and OAY curves shows that both IAY and OAY increase monotonically with M0 and they approach a common maximum value when M0 becomes very high. However, when M0 approaches zero, OAY also approaches zero but IAY approaches a fixed positive value for a given ROG. At any given M0 value, the value of IAY is always higher than that of OAY. The relative differences between IAY and OAY are especially significant under typical ambient and experimental M0 levels. IAY values can be orders of magnitude higher than OAY values and are much better representations of aerosol yields under these M0 levels. When it is used for secondary organic aerosols (SOA) estimation and modelling, the new IAY equation will significantly improve the underestimation of SOA formation caused by directly using the original OAY equation. More sophisticated SOA algorithms could also be developed based on the IAY equation presented here. Crown Copyright r 2003 Published by Elsevier Ltd. All rights reserved. Keywords: Aerosol yield; Secondary organic aerosols; Particulate matter; Reactive organic gas; Air quality modelling
1. Introduction Secondary organic aerosols (SOA) are formed in the atmosphere through the oxidation of reactive organic gases (ROGs) followed by condensation or gas/aerosol partitioning (Seinfeld and Pandis, 1998). To model the formation of SOA, a concept called aerosol yield (or SOA yield), loosely defined as the SOA mass formed per unit mass of ROG reacted, has been widely used. Early research was focused on estimating and deriving *Fax: +1-613-941-1571. E-mail address: [email protected] (W. Jiang).
constant SOA yields for ROGs of interest (Grosjean and Seinfeld, 1989; Pandis et al., 1992). In a new generation of studies on aerosol yields, Odum et al. (1996) demonstrated experimentally that instead of being constant, a SOA yield is a function of aerosol organic mass concentration. Based on the gas/ aerosol partitioning theory proposed by Pankow (1994), they derived a general equation that links an SOA yield with an aerosol organic mass concentration. Using smog chamber experimental data, they showed that the relationship between the aerosol yield and the organic mass concentration can be well described by assuming two condensable SOA products only. Based on this
1352-2310/$ - see front matter Crown Copyright r 2003 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2003.09.018
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assumption, they simplified the equation to a twoproduct form and derived the associated equation parameters for m-xylene, 1,2,4-trimethylbenene, and apinene. Later, the two-product form of their equation was applied to other aromatic ROGs (Odum et al., 1997) and biogenic hydrocarbons (Hoffmann et al., 1997; Griffin et al., 1999). For simplicity, we call this aerosol yield equation Odum’s equation in this paper. The aerosol yield calculated by Odum’s equation is an overall secondary organic aerosol yield (OAY) from the beginning of an experiment to a certain level of accumulated organic mass concentration in particles. In atmospheric modelling studies, it is often required to know an instantaneous secondary organic aerosol yield (IAY) under a specific pre-existing aerosol organic mass concentration in order to estimate the incremental amount of SOA formed. At a glance, OAY and IAY may seem similar; however, they are fundamentally different quantities and their values can also differ dramatically. According to the author’s knowledge, there are no published formulas or equations available for the calculation of these important IAY values. Starting from Odum’s equation, this paper derives an equation for the IAY calculation. The equation is then simplified to its two-product form. As examples, the two-product form of the equation is applied to 10 representative aromatic and biogenic ROG experiments originally investigated in the literature. IAY and OAY values in wide ranges of organic aerosol mass concentrations are then calculated. They are shown and compared through aerosol yield curves, which are the plots of aerosol yields versus organic aerosol mass concentrations. To help, understand the impact of replacing the Odum’s OAY equation with the new IAY equation in an air quality model, the issue of applying the equations in SOA estimation and modelling is briefly discussed.
This is Odum’s OAY equation. Note ‘‘OAY’’ is used to replace ‘‘Y’’ in Odum et al. (1996) to show the real meaning of ‘‘aerosol yield’’ in the equation. In the equation, M0 is the concentration of all species in organic aerosol phase; ai and Kom;i are the mass-based stoichiometric coefficient and the partitioning coefficient of the ith condensable species CSi. OAY is defined as OAY ¼
DM0 ; DROG
where DROG and DM0 are the overall concentration changes of ROG and organic aerosol mass from the beginning of the reaction, respectively. Since the value of M0 is zero at the beginning of the reaction, we have DM0 ¼ M0 and OAY ¼
M0 : DROG
ð2Þ
In the equations above, if the units of all concentrations are mg m3, the unit of Kom;i is then m3 mg1. OAY and ai are dimensionless quantities. The stoichiometric coefficients in the chemical reaction above are massbased instead of mole-based to simplify the discussions. The two-product form of Eq. (1) is a1 Kom;1 a2 Kom;2 OAY ¼ M0 : ð3Þ þ 1 þ Kom;1 M0 1 þ Kom;2 M0 Graphically, an OAY calculated by Odum’s equation is the slope of a line connecting the origin and a point on an experimental M0 versus DROG curve. As an example, the slope of line 1 in Fig. 1(a) shows conceptually the OAY of m-xylene from the start of an experiment to the point where DROG has been consumed and M0 has been generated. 2.2. The new IAY equation
2. A new equation for IAY calculation 2.1. The original Odum’s OAY equation Considering a gas phase reaction between a ROG and an oxidant (OX) that generates a set of gaseous products (P1, P2, y) and a set of condensable organic species (CS1, CS2, y): ROG þ OX ¼ p1 P1 þ p2 P2 þ ? þ a1 CS1 þ a2 CS2 þ ?; the overall yield of SOA formed from the beginning of the reaction to a point where gas/aerosol partitioning equilibria for all condensable species have been achieved is (Odum et al., 1996) X ai Kom;i OAY ¼ M0 : ð1Þ 1 þ Kom;i M0 i
To model the evolution of SOA, we need to know the aerosol yields at given M0 values. Graphically, the aerosol yield at a specific M0 is the slope of the tangent line at the point (DROG, M0 ) on an experimental M0 versus DROG curve. This is represented, for example, by the slope of line 2 in Fig. 1(a). Since this slope is the rate of M0 change with respect to DROG at the given point only, we call it IAY to reflect its instantaneous nature in SOA evolution. Mathematically, IAY is the derivative of M0 with respect to DROG, i.e., IAY ¼
dM0 : dDROG
ð4Þ
A general equation for the calculation of IAY can be derived from Eq. (1) as follows.
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0.2
M0
100,000
0.16
10,000
IAY
Slope = OAY Slope = IAY
M0*
1,000 0.12
IAY-OAY × 100 OAY
100
0.08 10 0.04
1
1 IAY-OAY
0
∆ ROG
∆ ROG*
0
0.1 (a)
% Difference
Aerosol Yield
OAY
2
1
10
0.1
100 1,000 10,000 100,000
M0(µg m-3)
(b)
Fig. 1. Differences between OAY and IAY for the photo-oxidation of m-xylene: (a) conceptual differences; and (b) quantitative differences. Curves are drawn based on the two-product assumption and the parameters in Table 1.
Table 1 OAY and IAY equation parameters for some representative aromatic and biogenic ROGs ROG
a1
Kom;1 (m3 mg1)
a2
Kom;2 (m3 mg1)
a (m6 mg2)
b (m3 mg1)
c (m12 mg4)
d (m9 mg3)
e (m6 mg2)
m-xylenea 1,2,4-trimethylbenzenea p-diethylbenzenea a-pinenea a-pinene (O3)a b-pinenea b-pinene (O3)a D3-carenea D3-carene (O3)a Sabinene (O3)a
0.03 0.0324 0.083 0.038 0.125 0.130 0.026 0.054 0.128 0.037
0.032 0.053 0.093 0.171 0.088 0.044 0.195 0.043 0.337 0.819
0.167 0.166 0.22 0.326 0.102 0.406 0.485 0.517 0.068 0.239
0.0019 0.002 0.0010 0.004 0.0788 0.0049 0.0030 0.0042 0.0036 0.0001
1.198E05 2.103E05 2.818E05 2.490E04 1.574E03 1.156E04 2.989E04 1.031E04 2.378E04 2.260E05
1.277E03 2.049E03 7.939E03 7.802E03 1.904E02 7.709E03 6.525E03 4.493E03 4.338E02 3.033E02
7.282E10 2.229E09 2.621E09 1.703E07 1.092E05 2.492E08 1.749E07 1.862E08 2.885E07 1.851E09
1.553E07 4.344E07 1.477E06 1.067E05 2.640E04 3.324E06 7.634E06 1.623E06 1.053E04 4.968E06
3.132E05 9.168E05 7.181E04 1.116E03 1.601E03 2.614E04 9.930E04 1.090E04 1.454E02 2.482E02
a
Values of ai ; Kom,i , i ¼ 1; 2, are from Odum et al. (1996), Odum et al. (1997), and Griffin et al. (1999).
Combining Eqs. (1) and (2) and canceling a M0 from the combined equation, we get X ai Kom;i 1 ¼ : DROG 1 þ Kom;i M0 i Therefore P 2 ai Kom;i =ð1 þ Kom;i M0 Þ2 dDROG ¼ Pi 2 : dM0 ai Kom;i =ð1 þ Kom;i M0 Þ
IAY ¼
ðaM0 þ bÞ2 ; cM02 þ dM0 þ e
ð6Þ
where the parameters are functions of Kom;i and ai (i ¼ 1; 2Þ a ¼ ða1 þ a2 ÞKom;1 Kom;2 ; b ¼ a1 Kom;1 þ a2 Kom;2 ;
i
The needed IAY equation is then P 2 ai Kom;i =ð1 þ Kom;i M0 Þ dM0 ¼ Pi : IAY ¼ 2 2 dDROG i ai Kom;i =ð1 þ Kom;i M0 Þ
(a, b, c, d, e):
2 2 Kom;2 ; c ¼ ða1 þ a2 ÞKom;1
ð5Þ
The simplified two-product form of Eq. (5) contains the independent variable M0 and five parameters
d ¼ 2Kom;1 Kom;2 ða1 Kom;1 þ a2 Kom;2 Þ; 2 2 þ a2 Kom;2 : e ¼ a1 Kom;1
As examples, Table 1 lists values of the five new IAY parameters for 10 representative ROG experiments in
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behaviour of the IAY and OAY curves in a wider range of M0 values and the dramatic range of % differences between IAY and OAY values. Both IAY and OAY curves show monotonic increases of the aerosol yield with M0 : When M0 becomes very high, both IAY and OAY values approach a common limit value of a1 þ a2 as proved by the following:
the literature along with the original parameters in Odum’s OAY equation. ‘‘O3’’ in brackets indicate ROG reactions with O3 rather than photo-chemical reactions. The IAY Eq. (5) is directly derived from the OAY Eq. (1) without any other assumptions or approximations. Therefore, experimental data that satisfy Eqs. (1) and (3) also satisfy Eqs. (5) and (6), respectively.
ðaM0 þ bÞ2 a2 ¼ 2 M0 -N cM þ dM0 þ e c 0
lim IAY ¼ lim
M0 -N
3. Comparison of IAY and OAY values for the aromatic and biogenic ROGs
¼
IAY and OAY are not only conceptually different as shown in Fig. 1(a), their values can also be dramatically different. As an example, Fig. 1(b) shows quantitative differences of IAY and OAY values over a wide M0 range for the photo-oxidation of m-xylene described by the two-product forms of the IAY and OAY equations. For simplicity, we call the plots of IAY or OAY versus M0 aerosol yield curves. Log-scale is used for M0 and ‘‘% Difference’’ in Fig. 1(b) in order to show the
Aerosol Yield
0.20
M0 -N
0.40 α-pinene
p-diethylbenzene
0.30 0.20
0.12
0.20 0.08
0.10
0.10 0.00
0.00
0.00 0.25
Aerosol Yield
When M0 approaches zero, the OAY value approaches zero while the IAY value approaches a positive value of b2 =e; which can be easily derived from Eq. (6). Using the
0.04
β-pinene
α-pinene (O3)
0.20
β-pinene (O3)
0.40
0.40
0.20
0.20
0.00
0.00
0.00
0.60
0.20
0.15 0.10 0.05
∆3-carene
Aerosol Yield
a1 Kom;1 a2 Kom;2 þ M0 -N 1 þ Kom;1 M0 1 þ Kom;2 M0 a1 Kom;1 a2 Kom;2 þ ¼ a1 þ a2 : ¼ Kom;1 Kom;2
lim OAY ¼ lim M0
0.30 1,2,4-trimethylbenzene
0.16
2 2 ða1 þ a2 Þ2 Kom;1 Kom;2 ¼ a1 þ a2 ; 2 2 ða1 þ a2 ÞKom;1 Kom;2
0.40
0.20
0.10 ∆3-carene (O3)
0.16 0.12
0.06
0.08
0.04
0.04
0.02
0.00
0.00 0.1
1 10 100 1,000 M0 (µg m-3)
sabinene (O3)
0.08
0.00 0.1
IAY
1 10 100 1,000 M0 (µg m-3)
0.1
1 10 100 1,000 M0 (µg m-3)
OAY
Fig. 2. Comparison of IAY and OAY curves for the aromatic and biogenic ROGs (except m-xylene) listed in Table 1. The M0-axis is in log-scale and covers typical ambient and smog chamber M0 levels.
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b and e values for m-xylene in Table 1, we get IAY=0.052 at M0 ¼ 0: Fig. 1(b) shows that IAY is always higher than OAY at any given M0 level. The absolute difference between IAY and OAY is shown by the curve ‘‘IAY–OAY’’ using the scale on the left vertical axis. The relative difference (% Difference) is shown by the curve ‘‘(IAY– OAY)/OAY 100’’ using the log-scale on the right vertical axis. Note dramatic relative differences between IAY and OAY at low M0 levels. At typical ambient M0 levels of 1–10 mg m3, IAY values are 4135% to 470% higher than OAY values. In the m-xylene experiments by Odum et al. (1996) where the level of M0 is in the range 1.5–396 mg m3, the IAY values are 2775% to 76% higher than the corresponding OAY values. Fig. 2 shows more comparison of IAY and OAY curves for other ROGs listed in Table 1. The log-scale used on the horizontal axis covers typical ambient and smog chamber M0 levels. For simplicity, the difference curves seen in Fig. 1(b) are not shown. Similar comparison and analysis have also been applied to other ROGs investigated by Odum et al. (1996) and the follow-up studies. They are omitted here for brevity. Details on the analysis of other ROGs are available from the author.
4. Comments on using the IAY and OAY equations for SOA estimation and modelling To estimate or model SOA formation, it is often required to calculate the incremental increase of SOA mass caused by a certain amount of reacted ROG at certain pre-existing levels of M0 : Most aerosol yieldbased approaches conduct the estimation based on the following simplified equation: DSOA ¼ AY DROG;
ð7Þ
where DSOA is the incremental SOA increase, AY is an aerosol yield, and DROG is the reacted ROG that causes the formation of DSOA. The key here is to get an estimate of the aerosol yield. Some earlier studies used constant aerosol yield values in their modelling exercise (e.g., Bowman et al., 1995). More recently, the twoproduct form of Odum’s equation has been built into a state-of-the-art air quality model with the intention to improve the representation of SOA production (Binkowski and Roselle, 2003; Jiang and Roth, 2003). As discussed above, Odum’s equation generates OAY instead of the aerosol yields at M0 ; and the OAY values obtained from the equation are very low under typical ambient M0 levels. Therefore, using the OAY equation directly for aerosol yield calculations will cause significant underestimation of new SOA formation. Using the IAY equation presented in this paper will make the approach more scientifically defensible and
5443
M0
M0.2 M0.IAY
Slope = IAY
M0.OAY
Slope = OAY
M0.1
0
∆ROG1
∆ROG
∆ROG2
Fig. 3. Qualitative comparison of errors caused by using OAY and IAY equations in estimating new SOA formation.
improve the modelling results. Fig. 3 shows qualitatively the difference in errors caused by using the IAY and OAY equations in estimating new SOA formation. The curve in Fig. 3 is an assumed true M0 versus DROG relationship that we need to simulate. At the beginning of a time step, M0 ¼ M0;1 and DROG=DROG1. At the end of the time step, DROG changes to DROG2 and M0 should become M0;2 if we could simulate the system perfectly. Using the OAY Eq. (1) or (3) to calculate the aerosol yield and Eq. (7) to calculate the new SOA formed causes M0 ¼ M0;OAY : Using the IAY Eq. (5) or (6) similarly causes M0 ¼ M0;IAY : Although both estimations result in underestimation of M0 ; the error caused by using IAY, which is equal to M0;2 M0;IAY ; is much smaller than the error caused by using OAY, which is equal to M0;2 M0;OAY : The improvement to the modelling results by using the IAY equation is especially significant when a model is used in simulations under ambient conditions. As shown in Figs. 1(b) and 2, IAY values can be 100%, 1000%, or even 10,000% higher than OAY values under ambient M0 levels. Although the estimations of new M0 based on both OAY and IAY values are lower than true values according to Fig. 3, the errors of the IAY-based results can be orders of magnitude smaller than the errors of the OAY-based results. The results obtained by using the IAY equation can be improved further through more sophisticated mathematical manipulation using the IAY equation or its two-product form. An simple example would be to calculate an IAY value at M0;IAY in addition to the IAY
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W. Jiang / Atmospheric Environment 37 (2003) 5439–5444
at M0;1 in Fig. 3, and then use the average of the two IAY values as the aerosol yield in Eq. (7). An iterative process could also be built on this idea to minimise the error. This is a subject beyond the scope of this paper and will not be explored further here.
5. Conclusion and discussion Using Odum’s OAY equation as a starting point, this paper derived a new equation for calculation of IAY, which reflects the dependence of instantaneous aerosol yields on the concentrations of pre-existing organic species. The equation is then applied to some representative aromatic and biogenic ROG experiments in the literature. Although they may seem similar and they are both related to an organic aerosol concentration M0 ; IAY and OAY are fundamentally different quantities and need to be clearly distinguished. IAY is a function of a pre-existing organic aerosol concentration while OAY is a function of an accumulated organic aerosol concentration. Comparative analysis of the IAY and OAY curves shows that both IAY and OAY increase monotonically with M0 and they approach a common maximum value when M0 becomes very high. However, when M0 approaches zero, OAY also approaches zero but IAY approaches a fixed positive value for a given ROG. At any given M0 values, values of IAY are always higher than those of OAY. The relative difference between IAY and OAY is especially significant under typical ambient and experimental M0 levels. IAY values can be orders of magnitude higher than OAY values and are much better representations of aerosol yields under these M0 levels. Both qualitative analysis and quantitative comparisons demonstrate that using the new IAY equation will cause lower level of errors in SOA estimation than using the OAY equation. Although they are beyond the focus of this paper, more sophisticated SOA algorithms could be developed based on the IAY equation presented in this paper. As an extension of Odum’s equation, the IAY equation in this paper is subject to the same uncertainties as in the original Odum’s equation. An issue of interest is the reliability of the equations under typical lower levels of M0 in the atmosphere in comparison with the smog chamber. More theoretical, experimental, and/or modelling studies are needed to address this issue.
Acknowledgements ! I would like to thank my colleagues Eric Giroux, Dazhong Yin and Helmut Roth for their substantial technical assistance in preparing the manuscript and in verifying the mathematical derivation of the equations. The project is funded by the interdepartmental Program of Energy Research and Development in Canada and by the National Research Council of Canada.
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