Article pubs.acs.org/est
Global Sensitivity Analysis of the Regional Atmospheric Chemical Mechanism: An Application of Random Sampling-High Dimensional Model Representation to Urban Oxidation Chemistry Shuang Chen,†,* William H. Brune,† Oluwayemisi O. Oluwole,‡ Charles E. Kolb,‡ Fred Bacon,‡ Genyuan Li,§ and Hersch Rabitz§ †
Department of Meteorology, Pennsylvania State University, 503 Walker Building, University Park, Pennsylvania 16802, United States Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821, United States § Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States ‡
S Supporting Information *
ABSTRACT: Chemical mechanisms play a crucial part for the air quality modeling and pollution control decision-making. Parameters in a chemical mechanism have uncertainties, leading to the uncertainties of model predictions. A recently developed global sensitivity analysis (SA) method based on Random Sampling-High Dimensional Model Representation (RS-HDMR) was applied to the Regional Atmospheric Chemical Mechanism (RACM) within a zero-dimensional photochemical model to highlight the main uncertainty sources of atmospheric hydroxyl (OH) and hydroperoxyl (HO2) radicals. This global SA approach can be applied as a routine in zero-dimensional photochemical modeling to comprehensively assess model uncertainty and sensitivity under different conditions. It also highlights the parameters to which the model is most sensitive during periods when the model/measurement OH and HO2 discrepancies are greatest. Uncertainties in 584 model parameters were assigned for measured constituents used to constrain the model, for photolysis and kinetic rate coefficients, and for product yields of the reactions. With simulations performed for the hourly field data of two typical days, modeled and measured OH and HO2 generally agree better for polluted conditions than for cleaner conditions, except during morning rush hour. Sensitivity analysis shows that the modeled OH and HO2 depend most critically on the reactions of xylenes and isoprene with OH, NO2 with OH, NO with HO2, and internal alkenes with O3 and suggests that model/ measurement discrepancies in OH and HO2 would benefit from a closer examination of these reactions.
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(e.g., refs 2 and 3), Direct Decoupled Method (DDM),4,5 Highorder DDM (HDDM),6,7 and Multiple Linear Regression (MLR).8,9 There are generally two types of SA methods, called local and global SA methods. Local SA methods are performed at a given point in the input space and reflect the importance order of inputs in a small region around the chosen point. Outside of this small region, the importance order may be different. In contrast, global SA methods cover a larger region of the input space and reflect the average importance order of inputs over the whole desired region. However, published applications of global SA for photochemical models are limited since the computational cost of global SA increases greatly with the number of model inputs n. For instance, the computational cost of traditional Sobol’s indices10 or Fourier Amplitude Sensitivity Test11 methods is ∼n × N, where sample size N is usually in the range of hundreds to thousands.12 Hence there is
INTRODUCTION The atmospheric processes causing air pollution are complex and contain a large number of chemical reactions. Gas-phase chemical mechanisms describe these complex atmospheric reactions mathematically and hence are essential for air quality modeling. However, model predictions may be subject to large uncertainties resulting from uncertainties in the inputs, including the parameters of a chemical mechanism. Hence analyzing the model sensitivity to the uncertainties of the chemical mechanism and input parameters is necessary to assess confidence in photochemical model predictions. The main goal of such sensitivity analysis (SA) is usually to study how the uncertainties in a model output can be apportioned to different sources of uncertainties in the model inputs1 and then to find the subset of parameters that contribute most to the model uncertainty. Thus, SA results provide guidance for further studies of the parameters and chemical mechanisms that are most important for improving air quality model performance. Chemical mechanisms have been evaluated in previous studies using a variety of SA methods such as Finite Difference © 2012 American Chemical Society
Received: Revised: Accepted: Published: 11162
April 19, 2012 September 10, 2012 September 10, 2012 September 10, 2012 dx.doi.org/10.1021/es301565w | Environ. Sci. Technol. 2012, 46, 11162−11170
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a need for global SA methods that can be efficiently applied for photochemical models with hundreds or more parameters. Global SA methods based on High Dimensional Model Representation (HDMR)13,14 have been developed for complex model systems. Recently a practical extension of the HDMR method, Random Sampling-High Dimensional Model Representation (RS-HDMR),15,16 provides an approach to determine input−output relationships with only one set of N random samples, greatly reducing the computational cost. The RSHDMR has been demonstrated to be efficient for sensitivity studies of several model systems with up to hundreds of inputs.17−21 For a model with a great number of inputs (e.g., n > 50), a prescreening method such as the Morris Method,22 which provides qualitative sensitivity measures at low computational cost of several times of (n + 1), can be applied to exclude the noninfluential inputs in advance (e.g., refs 17,19, and 23). Additional advantages of this approach include the ability to capture nonlinear relationships of the chemical kinetics and to explore the interactions among the inputs. This work presents an application of the RS-HDMR method to study the sensitivity of the Regional Atmospheric Chemical Mechanism (RACM)24 within a zero-dimensional photochemical model with respect to hundreds of model parameters under real atmospheric conditions. The goal of this work is to develop a methodological approach to conduct global SA for a photochemical model constrained by observational field data and to examine the temporal variation of the model sensitivity resulting from the variations of the model constraints, which differ from the previous sensitivity studies with several predetermined initial conditions. This paper describes the SA methods and then applies them to constrained steady-state modeling of hydroxyl (OH) and hydroperoxyl (HO2) for urban conditions. A brief description of the photochemical model and the uncertainty assignments for model parameters is presented. Then the sensitivity analysis results are compared and discussed for two urban cases, one polluted and one clean.
The sensitivity indices can be defined through normalizing the eq 2 by the total variance as:
i
(3)
Sij + ... + S12...n
1≤i 0.98) and HO2 (R > 0.97), indicating that the variation of model results are only due to the uncertainties of influential inputs. In addition, the results of [Y]noninf are almost constant, indicating that varying the values of noninfluential parameters within their uncertainties has little effect on the model results. These comparisons consistently confirm that both SA methods using only the first-order analysis are effective tools to identify the key model inputs for this modeling system. If all influential model inputs are correctly prescreened, then the RS-HDMR results must be the same with and without applying the MM. For most cases, the sensitivity results with different threshold values of MM followed by RS-HDMR are very consistent (see SI Table S5 for the noon case example). Even applying a relatively large threshold value, 10% of the
the model system boundaries are different. The original uncertainty factors were doubled and halved for the rate coefficients for which the panel evaluations are not available. As expected, the relative uncertainties of HOx increase with the increase of undetermined uncertainties for selected reaction rate coefficients (SI Table S4). For example, the uncertainty of OH is reduced from 15% to 12% with reduced rate coefficient uncertainties and increases to 24% with increased rate coefficient uncertainties. Although mostly the same sets of the most influential input parameters are identified, their individual contributions have different ranks (Figure 1). Reducing the estimated uncertainty ranges enhances the contributions from some influential inputs, particularly the rate coefficients of some inorganic reactions. This is because organic reactions are less uncertain in this case, compared to their previous assignments. On the other hand, doubling the uncertainty factors brings the ∑Si down to only 0.90 and 0.88 for OH and HO2, respectively. The Si of the 15 most influential inputs generally decreases, but three inputs become more important. As indicated by the different means of the simulations (e.g., average value of OH decrease to 0.41 pptv from 0.47 pptv, SI Table S4), larger uncertainty factors can shift the distribution of model results due to the greater deviations from the original values of model parameters. Therefore it is necessary to systematically examine the impact of uncertainty estimates for inputs on model uncertainty and sensitivity. The Morris Method was also applied for the noon base case to compute model sensitivity. The average elementary effects μ* calculated from the different sets of r and M agree well with one another (SI Figure S1, correlation coefficients R > 0.98). This result confirms that, through the optimization process, a small sample size (e.g., r = 4 out of M = 50) is able to generate the same results produced with a large sample size (e.g., r = 50). The comparison of μ* of MM with Si of RS-HDMR also shows a good correlation with R of 0.80−0.93, especially when larger r is applied. To compare with the RS-HDMR sensitivity measures (N = 28 500) at comparable sample sizes, only the sensitivity measures of MM from r = 50 and M = 50 (N=(n+1)r = 29 250) were used hereafter. A pairwise comparison of μi* 11165
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Figure 2. Diurnal variations of modeled and observed OH and HO2 on the polluted day and clean day. Errorbars denote the 2σ uncertainties associated with the measurements and modeling results. Observed HO2 was corrected by considering the interference of RO2 from alkenes and aromatics,36−38 which was simulated in the model.
Figure 3. The diurnal variations of model sensitivity to the significant model parameters (Si > 0.03) for OH and HO2 on the typical polluted and clean days. See SI Table S6 for the full list of the significant model parameters.
largest μ*, the importance rank and sensitivity amounts of the most influential inputs (Si > 0.02) are consistent with the results from RS-HDMR only, although the number of influential inputs identified by MM is greatly reduced to around 50 and less. The only exception is for one of the nighttime cases (SI Table S5), in which one input is not identified as influential by the prescreening method and is excluded for the following RSHDMR analysis even though its contribution is significant with Si of 0.05. For all cases except this nighttime case, ∑Si is larger than 0.90, indicating the overall contribution from the individual inputs and insignificant contribution from the interactions among inputs. For the case with ∑Si < 0.90, it seems that the higher-order contributions might be important so that the second-order sensitivity Sij should be computed by a
combination of MM and RS-HDMR. A threshold of 10% of μ*max has been verified to retain a much smaller number of the influential inputs and generate first-order sensitivity results comparable to using the RS-HDMR only. Applying the SA Approach for Urban Data. The SA approach was applied for hourly data of a polluted day (September 4, 2006) and a clean day (September 17, 2006). For both days (Figure 2), the uncertainties are lower (∼20% at 1σ) around midnight, higher (∼35% or larger) during the early morning and reach the lowest values (∼15%) in the afternoon. Uncertainties on the clean day are generally lower than the uncertainties on the polluted day. As expected, the relative uncertainties of OH and HO2 follow the same patterns throughout the day since their values are related to each other. 11166
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number of the significant inputs reduces to only 4−9, suggesting that the model uncertainty is mainly resulted from the uncertainties in a small number of model parameters. The significant inputs are generally associated with rate coefficients of inorganic reactions (up to 39%, mainly photolysis of HONO and reactions of OH+NO2 and HO2+NO due to their important roles as an OH source, sink and cycling between OH and HO2, respectively); reactions of VOCs with OH (up to 42%), and RO2 with NO (up to 30%) and HO2 (up to 14%) during the day, which initiate radical propagation, convert HO2 to OH and terminate HO2, respectively; and reactions of alkenes with O3 at night (up to 69%), which are the primary sources of nighttime HOx. In the morning, the largest contributions are from the yields of aromatic−OH adduct and RO2 formed from the reactions of xylenes + OH (31% and 20%, respectively) and from rate coefficient of NO2 + OH (12% and 9%) for the polluted and clean days, respectively. For the afternoon, the most important parameters are rate coefficients of HO2+NO (11%) and isoprene+OH (10%) on the polluted day and the rate coefficient of ISOP (isoprene peroxy radicals)+NO and its HO2 yield (12−30%) on the clean day. During the nighttime, rate coefficient of OLI(internal alkenes)+OH contributes 22− 39% and 52% to the model uncertainty on polluted and clean days, respectively, while the constrained amount of monoterpenes can also contribute up to 46% for the polluted day. As expected, the model parameters that have great impact on modeled HOx are very influential for ozone production prediction30 since their chemical pathways are correlated. One unresolved source of urban HOx is the suspected photosensitized heterogeneous production of HONO on the surfaces of aerosol particles, buildings, and the ground.39 The vertical daytime boundary layer HONO concentration profiles initially measured in German urban areas,40 and more recently in Houston,41 have revealed HONO levels significantly elevated above those attributable to known gas phase photochemical sources, but have failed to distinguish between those sources. Since the mechanism producing excess HONO is not well characterized, it is not well represented in current photochemical mechanisms. For this work, measured gas phase HONO concentrations are input to the model with a specified ±10% uncertainty. Interestingly, HONO concentration contribute insignificantly to OH uncertainty (Si = 0.01−0.02), while HONO photolysis rate is one of the most significant contributors (Si ∼ 0.08). Impact of Uncertainty Estimates of Inputs on SA Results. The global SA method configures the input-output relations based on the ranges of input values. In this model, uncertainties of some inputs have not been determined by either the measurements or the panel evaluations so their ranges were estimated (SI Table S1). Their impact on model uncertainty and sensitivity was evaluated using a Monte Carlo approach. These estimated uncertainties were varied using 10 multiplying factors that were randomly and independently drawn from 0.2 to 2 with an interval of 0.2. In this way, 10 more simulations were run to obtain 10 more possible sensitivity results and then were compared to the original simulation. A larger number of the multiplying factors (e.g., 100) was not practical due to the high computational cost for the Monte Carlo simulations. This evaluation approach was applied for the data on the two typical days for every three-hour interval where the model uncertainty and sensitivity varied greatly, as indicated above.
The modeled and measured HOx on these two days were also compared (Figure 2). General model-measurement agreement is only observed for the polluted day during daytime within their 2σ uncertainties. There are a couple of possible reasons causing the significant model-measurement discrepancies. One is that the real values of some influential model parameters deviate greatly from their current uncertainty ranges so that the model uncertainty is even larger. The other is either a model structural error or a measurement error or both. In fact, it is now known that the TRAMP OH measurement likely had interference due to ozone and alkenes. For a 2009 study at the same location as TRAMP, a second method for determining OH showed that OH was actually 0.7 and 0.5 of the measurement during the day and the night, respectively.36,37 This same correction may apply to the TRAMP OH results, although the correction is not made here. In addition, the HO2 measurement included a contribution from organic peroxyl radicals (RO2) produced from alkenes and aromatics.36,38 The measured HO2 values shown in Figure 2 have been corrected for this contribution by using the modeled RO2 values and measured detection sensitivities for a representative subset of these RO2 species.36 This correction reduces the HO2 values by average 25%. For both OH and HO2, these corrections tended to bring the measured and modeled values into better agreement, but discrepancies remain (Figure 2). These discrepancies do not affect the sensitivity results presented here, but they do motivate the need for this sensitivity analysis. Further investigation into the discrepancies between measured and modeled OH and HO2 are aided by the determination of the influential model parameters. About one-half of the cases on the polluted day and three cases on the clean day have ∑Si of 0.86−0.90 (Figure 3), suggesting that the higher-order sensitivity might be important. For these cases, the prescreening method followed by the RSHDMR method was applied to investigate the second-order sensitivity Sij. The MM suggests that the number of influential model inputs (ninf) ranges from 19 to 58. Then Sij of pairs among these influential inputs were computed by RS-HDMR. However, the values of Sij of these cases are all very small (0.03), called significant inputs, are summarized in Figure 3. The model sensitivity of OH and HO2 are very similar, sharing ∼20 significant inputs in common. Only 17−27 parameters were identified as significant for both days. At each hour, the 11167
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determining the model results and hence the model-measurement discrepancies. The application of this approach for field data obtained on two typical days under urban environment demonstrates that model uncertainty and sensitivity can vary significantly with different initial conditions, exhibiting diurnal and daily patterns. Thus, it can be misleading to apply the model uncertainty and sensitivity analysis for the atmospheric conditions at any one time to the conditions at all other times. This global SA approach can be routinely applied to evaluate sensitivities and uncertainties in photochemical models, providing valuable guidance for model application as well as laboratory and field studies designed to better constrain influential model inputs.
The uncertainty of these additional runs spans a larger range on the polluted day than on the clean day, especially for the morning rush hour (SI Figure S4). For instance, at 0600 CST, OH uncertainty ranges 25−43% under polluted conditions (originally 32%) and ranges 26−30% under clean conditions (originally 27%). As discussed above, most of the estimated uncertainties are associated with organic reactions. For the morning rush hour VOC-limited condition,42 reactions VOCs + OH are very important in determining modeled levels of HOx. Therefore, the model uncertainty is more sensitive to the uncertainties associated with these reactions in the morning. For nighttime, the model results are more sensitive to the amount of some alkenes on the polluted day (Si = 0.16−0.47) than on the clean day (Si < 0.05). Thus changing the uncertainty for these alkenes amounts could lead to larger variation of nighttime model uncertainty for polluted conditions. Depending on the assigned uncertainty estimates of inputs, the uncertainties of HOx roughly fluctuate within a factor of 1.4 and 1.1 with respect to the original model uncertainties during nighttime, 1.6 and 1.3 in the morning, and 1.3 and 1.4 in the afternoon under polluted and clean conditions, respectively. The RS-HDMR was rerun to produce 10 more estimated first-order sensitivity coefficients (denoted by Si′). The normalized sensitivity coefficients Si′/Si, where Si is the sensitivity calculated from original simulation, is plotted as a function of Si in SI Figure S5a,b to reflect the spread of the sensitivity results. The average values of Si′/Si for each bin are very close to 1. Their relative uncertainties were estimated for each bin with the width of Si = 0.10: for OH sensitivity, the uncertainty is 81%, 52%, 57%, 40%, and 8% (±1σ) with the increase of Si from 0.01 to 0.50; for HO2 sensitivity, the uncertainty is 84%, 42%, 69%, 42%, 46%, and 9% with the increase of Si from 0.01 to 0.60. In general, the uncertainty of Si’/Si tends to decrease with increasing Si, especially when Si is greater than 0.30. This makes sense because, for the model inputs with smaller sensitivities (e.g., 0.01−0.10), a small change in Si (say, 0.05) leads to a large deviation to the original value, especially for Si less than 0.05. In addition, the model inputs with larger sensitivities generally have better uncertainty estimates. For instance, of the 10 model parameters with Si > 0.10 for OH on the polluted day, seven parameters are kinetic rate coefficients that have the uncertainties evaluated in the literature. Since the uncertainty ranges of these important parameters are well evaluated, changing the uncertainty ranges of other parameters does not vary the model sensitivity greatly, especially for the more influential parameters. In addition, the total contribution from the 15 most important model parameters identified originally was calculated for the additional simulations (see SI Figure S5c,d for the results of noon cases on the two days). These key parameters contribute 60−80% together to the model uncertainties for all additional simulations, indicating that they are identified as the major uncertainty sources. Relatively consistent total contribution of these parameters confirms that the same set of key model parameters are generally identified with different uncertainty estimates of inputs. Our study of quantifying the uncertainty sources of modeled HOx shows how an efficient global SA method can be applied for SA of chemical mechanisms, which are highly nonlinear. As indicated by the sensitivity results, the parameters associated with the reactions of xylenes and isoprene with OH, NO2 with OH, NO with HO2, and internal alkenes with O3 are critical in
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ASSOCIATED CONTENT
* Supporting Information S
Details on the uncertainty assignments of model parameters and comparison of sensitivity results for testing the SA approach. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +1-814-863-8752; fax: +1-814-865-3663; e-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank all participants in the TRAMP field campaign for sharing the data to make the model calculations possible. We gratefully acknowledge helpful discussions provided by A. M. Thompson, G. S. Young, and T. Wagener. This study was supported by the NSF grant 0706821.
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