Quantitative assessment of parametric uncertainty in Northern Hemisphere PAH concentrations

Abstract

We quantitatively examine the relative importance of uncertainty in emissions and physicochemical properties (including reaction rate constants) to Northern Hemisphere (NH) and Arctic polycyclic aromatic hydrocarbon (PAH) concentrations, using a computationally-efficient numerical uncertainty technique applied to the global-scale chemical transport model GEOS-Chem. Using polynomial chaos (PC) methods, we propagate uncertainties in physicochemical properties and emissions for the PAHs benzo[a]pyrene, pyrene and phenanthrene to simulated spatially-resolved concentration uncertainties. We find that the leading contributors to parametric uncertainty in simulated concentrations are the black carbon-air partition coefficient and oxidation rate constant for benzo[a]pyrene, and the oxidation rate constants for phenanthrene and pyrene. NH geometric average concentrations are more sensitive to uncertainty in the atmospheric lifetime than to emissions rate. We use the PC expansions and measurement data to constrain parameter uncertainty distributions to observations. This narrows a priori parameter uncertainty distributions for phenanthrene and pyrene, and leads to higher values for OH oxidation rate constants and lower values for European PHE emission rates.

Graphical Abstract

INTRODUCTION

Polycyclic aromatic hydrocarbons (PAHs) are mutagenic and carcinogenic environmental contaminants¹. As persistent organic pollutants (POPs) that are transported through the atmosphere across national boundaries after emission, PAHs are regulated internationally by the Convention on Long-Range Trans-boundary Air Pollution (CLRTAP)². Despite regulatory efforts, PAHs continue to be transported via the atmosphere to the Arctic^3–6, far from source regions. In this study, we quantitatively examine the relative importance of emissions and physicochemical parametric uncertainty to Northern Hemispheric (NH) and Arctic PAH concentrations, using efficient numerical uncertainty techniques applied to the global-scale chemical transport model (CTM) GEOS-Chem.

The pathways by which PAHs reach the Arctic have been studied with numerical models of varying complexity^7–13. However, our understanding of these pathways is limited by substantial uncertainty associated with the physicochemical parameters (including reaction rate constants, partition coefficients and energies of phase change) that govern the atmospheric fate of PAHs. Some physicochemical parameters representing PAH behavior, such as oxidation rate constants and black carbon partition coefficients, are poorly constrained by measurements or several have not been measured directly^14–16. For some PAHs, e.g. phenanthrene (PHE; three ring), physicochemical parameters important to their atmospheric fate have been relatively more studied than for the larger PAHs like benzo[a]pyrene (BaP; five ring) and pyrene (PYR; four ring). Even for PHE, measurements of physicochemical parameters can differ by more than a factor of two¹⁵. Limited knowledge of emissions sources and associated uncertainty also contributes to uncertainty in atmospheric transport, as emissions factors for some processes (e.g. waste incineration, biomass burning) can vary by orders of magnitude¹⁷.

Model uncertainty has been studied for multimedia fate models of persistent organics^18–20. Multimedia model analyses have found that chemical properties have a larger influence on persistence and long-range transport potential than model parameters such as spatial scales, media heights/depths, and land and water surface fractions¹⁸. Detailed Monte Carlo analyses have been performed for multimedia models, finding that emissions and degradation constants were the most influential sources of uncertainty in DDT concentrations¹⁹ and that partition coefficients and reaction rate constants accounted for more than half of the uncertainty in mercury concentrations in air and the surface ocean²¹.

PAHs have been studied using finer-scale models at both the global and regional scales^{7,12,13,22,23}. Through comparison to spatially and temporally fine-scale measurements, these studies show that highly spatially resolved models can be useful in predicting the pattern of exposure to PAHs, an important factor for human health impacts. While multimedia models are computationally efficient and thus can quantitatively examine relative influences of parameters on uncertainty, they lack the spatial resolution and ability that CTMs possess to resolve the episodic nature of atmospheric transport.

Monte Carlo-type methods like those used for multimedia models¹⁹ can be prohibitively computationally expensive for more finely spatially resolved models, as they require on the order of thousands of samples for detailed analyses. Individual simulations run with complex atmospheric CTMs such as GEOS-Chem can require hours to days of computational time, leading to years for the full Monte Carlo analysis. Thus, first-order parameter sensitivity tests are often used to characterize uncertainty in spatially resolved models^12,23,24.

One previous study²⁴ reported quantitative estimates of the relative importance of physicochemical parameter uncertainty and emissions uncertainty in PCB153 and α-HCH simulations by the large-scale, spatially-resolved (15°×15°) BETR Research model using a first-order error propagation method. Though first-order error propagation methods are computationally cheaper than Monte Carlo analysis, they do not directly quantify the effect of parameter uncertainty interactions. Polynomial chaos (PC)-based methods can greatly reduce the computational cost of uncertainty propagation for CTMs compared to Monte Carlo methods, while approximating the resulting uncertainty distributions more closely than first-order methods by extending to higher order. Parametric uncertainty in complex chemical mechanisms has been quantified using PC methods in a number of applications^25–28. PC-based methods quantify the relative importance of each parameter, as well as account for their interactions in the model system, a significant advantage over traditional model parameter sensitivity tests. They also provide computational efficiency while retaining the spatial and temporal fidelity of CTMs.

We present here a first application of PC-based methods to a global atmospheric CTM of POPs. We use this analysis to quantify the contributions of emissions and physicochemical parameter uncertainty to NH- and Arctic-average concentrations of PHE, PYR, and BaP. We then combine the results of our PC analysis with measurements from long-term observation sites to constrain the values of these parameters.

METHODS

To quantify uncertainty in the GEOS-Chem PAH simulations, we compare simulated concentrations and associated uncertainties to measurements at non-urban sites, and use these measurements and their uncertainties in a Bayesian analysis to constrain the probability distributions of the physicochemical parameters. Throughout this work we will refer to model “parametric uncertainty”, which is the uncertainty in simulated concentrations resulting directly from the uncertainty in the model input parameters; i.e. physicochemical properties and emissions magnitudes.

GEOS-Chem Model

The simulations we assess in this study are carried out using the GEOS-Chem PAH chemical transport model¹². This model has been used in previous studies to simulate long-range atmospheric transport of PAHs and has allowed comparison to measurements where it has been able to resolve meteorologically-driven episodic high-concentration events¹². Evaluation of the model against measurements in both mid-latitudes and the Arctic, and traditional sensitivity tests have been conducted previously; we refer the reader to the referenced papers for a detailed assessment of model perfomance^12,13. Here, we briefly describe major features of the model, including meteorology, emissions, chemistry, and gas-particle partitioning. GEOS-Chem uses assimilated meteorology from the NASA Goddard Earth Observing System’s GEOS-5 dataset at a temporal resolution of 6 hours, a horizontal resolution of 0.5° × 0.667° re-gridded to 4°×5° for computational efficiency, and 47 levels vertically. The simulations for this study were run for the years 2006–2008. PAH emissions in the model come from the inventory of Zhang and Tao¹⁷, which represents annual emissions from the year 2004, is resolved on the national scale, and includes details for individual sectors and PAHs but is not time-resolved, meaning the emissions are not seasonally or annually varying. Emissions are discussed in more detail in following sections. Each model run begins with a “spin-up” period of one simulated year to negate the transient effects of initial conditions.

Upon emission, the model partitions PAHs between the gas and aerosol phases using a black carbon-air partition coefficient (K_BC) to represent partitioning to black carbon (BC) aerosol and an octanol-air partition coefficient (K_OA) to represent partitioning to organic carbon (OC). The overall gas-particle partitioning is governed by a dual OC absorption and BC adsorption model¹² based on the Dachs-Eisenreich²⁹ equation. Both OC and BC concentrations are prescribed as monthly averages in the PAH simulations, pre-calculated from full chemistry GEOS-Chem simulations^10,30 for computational efficiency. Gas-particle partitioning is recalculated at each chemistry time step of GEOS-Chem (60 min). The effect of using this coarse time resolution of prescribed particle concentrations was found to be small compared to the parametric uncertainties discussed below¹³.

Each of these partition coefficients’ temperature dependence is determined by an internal energy of phase change according to the van’t Hoff relationship. These internal energies are governed by enthalpies of phase change. The enthalpy of vaporization ΔH_vap is the uncertain parameter that determines the sensitivity of particle partitioning to changing temperature, while the enthalpy of solvation in liquid water ΔH_sol in combination with ΔH_vap determines that of wet deposition.

We simulate the oxidation of gas phase PAHs by reaction with hydroxyl radicals (OH). Monthly average OH concentrations are prescribed by a GEOS-Chem full chemistry simulation³¹ with a daily cycle overlaid on these monthly averages. PAH reaction with OH is represented by a second order reaction with reaction rate constant k_OH. On-particle oxidation by ozone is simulated using the parametrization of Kahan et al.³²

Both gas- and particle-phase PAHs undergo wet deposition in the simulations. Gas-phase PAH is scavenged by liquid water according to the air-water partitioning coefficient K_AW, which is temperature dependent according to ΔH_AW (a combination of ΔH_sol and ΔH_vap) following the van’t Hoff relationship. Dry deposition for gas-phase PAH is simulated according to Wang et al.³³, with lipophilic uptake scaled by the K_OA ¹². A complete evaluation of GEOS-Chem simulations of PAHs can be found in the original work by Friedman and Selin¹². The seven uncertain physicochemical parameters mentioned above are included in our analysis for each PAH.

Polynomial chaos

The PC-based estimator uses orthogonal polynomials to approximate GEOS-Chem model output as a function of model inputs. The polynomial expansion of the model output to be estimated takes the form

$$\eta (\xi )={\alpha }_0+\sum _{j=1}^d\sum _{k=1}^M{\alpha }_{j,k}{H}_j({\xi }_k)+\sum _{k=1}^{M-1}\sum _{l=k+1}^M{\beta }_{k,l}{H}_1({\xi }_k)H_1({\xi }_l)+\cdots +\mathit{Order}(d)$$ (1)

where the estimator η of degree d is a function of the polynomials H_j of order j, the M variables ξ_k representing model inputs, the expansion coefficients α_j,k and β_k,l, and higher order coefficients. The terms not shown in the equation are cross terms of degree greater than two, which include the product of up to d Hermite polynomials of different variables, analogous to the second order cross terms shown. In this study, we truncate the polynomial after third order. To obtain the expansion coefficients, one model run at a unique set of inputs is performed for each term in equation (1)³⁴. The set of inputs for the model runs for each degree’s terms are the values corresponding to the roots of the next degree’s polynomials. The outputs of these model runs and the corresponding sets of input values are used to set up a system of equations to solve for the expansion coefficients²⁷. Further description, along with validation, of the PC expansion can be found in the Supporting Information (section S4).

We use the polynomial estimator to directly infer properties of the uncertainty distribution of model output (in this case total (gas plus particulate phase) PAH mass concentration) without relying on Monte Carlo methods, which is accomplished using the analytical forms of the mean, variance and skewness from the polynomial coefficients²⁷. We also calculate the portion of the total output variance contributed by each input parameter using the expansion coefficients^27,28.

Physicochemical parameter uncertainties

We conduct an extensive review of the literature for experimentally determined values of each of seven uncertain physicochemical parameters for the three PAHs investigated in this study, and construct probability distributions based on the available data (summarized in Tables S1–S3). The distributions (Table 1 and discussed below), are for the parameters that most directly affect the simulated atmospheric fate and transport of the PAHs based on previously-conducted traditional model sensitivity testing¹². Model processes that are sources of uncertainty for all chemicals (including non-POPs) simulated by GEOS-Chem, such as advection and wet deposition schemes, are not the focus of this study.

Table 1.

Uncertainty of physicochemical properties in GEOS-Chem PAH simulations (means and standard deviations of normal distributions).

Parameter	Role	BaP Value (std.)	PYR Value (std.)	PHE Value (std.)
log10KBC-Water (unitless)	BC partition coefficient	8.8 (0.4)	7.5 (0.2)	6.85 (0.3)
log10KOA (unitless)	OC partition coefficient	11.27 (0.21)	8.78 (0.08)	7.58 (0.06)
ΔHvap (kJ/mol)	Enthalpy of vaporization	99.9 (7.4)	82.3 (3.9)	68.3 (8.9)
log10KAW (unitless)	Air-water partition coefficient	−4.42 (0.08)	−3.34 (0.07)	−2.81 (0.06)
ΔHsol (kJ/mol)	Enthalpy of solvation	37.9 (17.7)	37.9 (8.9)	34.5 (2.0)
kOH (cm3 molec−1 s−1) (log10 kOH for BaP and PYR)	Gas-phase oxidation rate constant	−9.88 (0.26) (log10 kOH)	−10.1 (0.35) (log10 kOH)	1.9×10−11 (0.4×10−11)
kO3 (10−7 s−1, at 50ppb O3)	On-particle oxidation rate constant	24.5 (3.5)	2.92 (1.21)	2.91 (0.92)

Partition coefficients (air-water: K_AW, black carbon-air: K_BC, octanol-air: K_OA)

Since the partition coefficients used in the model are experimentally determined and reported in log form, we estimate their uncertainty distributions as normal distributions of the log values, with the means and standard deviations derived from literature values (see SI for details and references).

K_BC, which describes the fraction of PAH found in the BC phase given an amount of BC particulate matter, is the combination of K_AW and the BC-water partition coefficient (K_BC-Water)³⁵,

$$log(K_{BC})=-log(K_{AW})+log(K_{BC-\mathit{Water}})$$ (2)

where K_BC-Water gives the ratio of concentrations of PAH in the BC particulate phase to dissolved PAH at equilibrium. Since K_BC itself is not an independent parameter due to its relationship to K_AW, we use the independent K_BC-Water instead as the uncertain parameter for this study.

Enthalpies of phase change (ΔH_vap and ΔH_sol)

We estimate the uncertainty distributions for the enthalpy of vaporization (ΔH_vap) and the enthalpy of solvation (ΔH_sol) for PHE, PYR and BaP as normal distributions with the means and standard deviations of a collection of literature values of ΔH_vap or ΔH_sol for each PAH (see SI for details and references).

On-particle ozone oxidation rate constant (k_O3)

For all three PAHs, we use the reported “A” and “B” kinetic parameter values and their uncertainties from Kahan et al.³² as model inputs. Across all atmospheric ozone concentrations, the B-parameter dominates the contribution to uncertainty in k_O3, so we neglect A-parameter uncertainty in our analysis.

OH oxidation rate constant (k_OH)

For PHE, we estimate the uncertainty distribution from three literature values and their associated uncertainties^14,36,37. The mean value of the normal uncertainty distribution is estimated by the uncertainty-weighted mean of these three values, and the standard deviation of the distribution is estimated by the standard deviation of the weighted mean.

While there is no literature value for BaP’s or PYR’s k_OH, values can be obtained from the Atmospheric Oxidation Program software AOPWIN, which uses an ionization potential-activity relationship³⁸,

$$ln(k_{OH})=-4.345-2.494(IP)$$ (3)

where k_OH has units of cm³ molec⁻¹ s⁻¹ and IP is the ionization potential in units of eV.

We use the mean and standard deviation of the National Institute of Standards and Technology collection of reported ionization potentials for BaP³⁹ to estimate a normal distribution that results in a log-normal distribution of IP-derived k_OH values. Similarly, for PYR we use the mean and standard deviation of the collection of reported PYR IPs⁴⁰ to estimate the uncertainty distribution for PYR’s k_OH.

Regional emissions uncertainties

Emissions uncertainty results from uncertainties in both emission activities (quantity of a given type of emitting process) and emission factors (PAH emission quantity per activity). The total PAH emission E due to a process i can be divided into those two elements:

$$E_i=A_i{F}_i$$ (4)

where A_i is the emissions activity of process i and F_i is the emission factor for that process. F_i can be uncertain to a much larger degree than A_i ¹⁷ because the conditions under which each emitting process is carried out in reality are highly varying but summarized by a single value. Measurements of F_i of the same process by different experimenters can yield orders of magnitude differences¹⁷. For example, F_i associated with diesel fuel in the transport sector will depend on such factors as the type of fuel burned, type of engine burning the fuel, and temperature and condition of the engine. PAH emissions processes with the largest uncertainties in F_i include primary aluminum production, use of traffic gasoline, diesel, and kerosene, industrial coal burning, and non-transport petroleum combustion¹⁷.

Given that there are distinct source contributions to PAH emissions and their uncertainties in different regions of the globe, we define discrete emissions regions, and calculate an a priori probability distribution for the total emissions of each region. We choose the regions of North America, Europe, South Asia, East Asia and Africa because of the large magnitude of emissions (South Asia, East Asia, Africa), and proximity to the Arctic (North America and Europe). We estimate the uncertainty distribution of total emissions of each region using Monte Carlo sampling over each country’s A_i and the F_i uncertainty distributions¹⁷ and assume that the spatial distribution of emissions within each region remains fixed. Regional emission distributions (Figures S1–S3) are then used as input parameters, along with physicochemical parameters, in the above-described PC analysis.

In-situ observations

We use observed annual average total (gas+particulate) BaP, PYR, and PHE concentrations from each of 10 sites monitored by the Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe (EMEP), Integrated Atmospheric Deposition Network (IADN), and Environment Canada (EC) observation networks in the Northern Hemisphere (NH) for comparison to model values. All observations were collected at land-based non-urban sites using high-volume air samplers. Particle-bound PAHs were collected on glass fibre filters, and volatile PAHs were adsorbed to polyurethane foam (PUF) plugs. Spatial coverage includes the Great Lakes, Northern Europe, and two Arctic sites. Site locations, concentrations and references are summarized in Table S4, and are the same sites used for model-measurement comparison by Friedman and Selin¹².

For site-by-site comparison to simulated concentrations, we calculate observational errors following Chen and Prinn⁴¹. The observational error for comparison to a model grid box accounts for statistical representativeness (accounting for some stations’ non-continuous sampling), analytical method precision error, site inter-calibration error, and spatial mismatch error (i.e. a single point’s representativeness of the whole grid-box). These errors (see Table S4) represent the variability in observed values that is impossible to capture with any model, and are thus separate from model uncertainty. These errors range from ±25% to a factor of 3, depending on the measurement site and the PAH in question.

Constraint of physicochemical parameters by observations

Using the annual average measurements outlined above, and PC-estimated concentrations based on annual average model output, we constrain the physicochemical parameter uncertainty distributions by Bayesian inference, combining information from observations and a priori parameter uncertainties. We compare 1) the PC polynomial-estimated concentration in the model grid box encompassing a measurement location for a given set of physicochemical and emissions parameter values to 2) the observed concentration at the same location. By mapping the predicted concentrations as a function of the uncertain parameters using the PC estimator, we define a weighted least-squares cost function of the form:

$$K{(\xi )}^2=\sum _{i=1}^N{\left(\frac{Y_i-{\eta }_i(\xi )}{{\sigma }_i}\right)}^2$$ (5)

where summation is over the N measurement locations, Y_i is the observed value at a particular site, η_i(ξ) is the polynomial estimate at parameter values ξ, and σ_i is the total “observation errors” from above at measurement site i.

With the least-squares comparison above, the likelihood function P(Y|ξ) is related to the cost function via

$$P(Y\mid \xi )\propto e^{-K{(\xi )}^2}.$$ (6)

This makes use of the PC estimators and the site measurements and their errors to estimate the likelihood of observing the concentrations Y as a function of the parameter values ξ.

To update the a priori uncertainty distributions, we use Bayes’ rule for the a posteriori distribution P(ξ|Y):

$$P(\xi \mid Y)\propto P(\xi )P(Y\mid \xi )$$ (7)

where P(ξ) is the prior uncertainty distribution. This results in a description of the relative probabilities of each physicochemical parameter value, given the available constraining measurements.

RESULTS

We calculate polynomial estimators as described above, and evaluate their predicted log-concentrations against independent full GEOS-Chem model runs. Over the parameter space covered by the physicochemical property uncertainty distributions, the polynomial estimator matches the validation data-set with r² greater than 0.99 (see Figure S4) for all three PAHs. We use the polynomial estimators to calculate model uncertainty distributions for NH and Arctic (above 66°N) surface concentration geometric averages for annual and Northern Hemisphere winter (DJF) and summer (JJA) periods for all three PAHs, attribute fractions of this uncertainty to individual model parameters, and constrain parameter uncertainty distributions using observation site data.

Comparison to measurements

Figure 1 shows a comparison of monthly average concentrations simulated using the PC-based estimator and associated parametric uncertainties to measured average concentrations and measurement uncertainties for non-urban sites for each PAH. The simulations capture the measurements within the ±2σ parametric uncertainty interval for all three PAHs, with PYR and BaP capturing the measurement means within the ±σ interval.

Figure 1.

Measured and simulated total (gas and particulate) concentrations at non-urban sites for PHE (top), PYR (middle), and BaP (bottom). The black lines are means across the measurements at all non-urban sites, and their error bars show the standard deviation of the mean for each month. The blue lines are the simulated means across the same sites, with the shaded regions marking the σ and 2σ intervals of the parametric uncertainty distributions for each month.

Simulated PHE concentrations show agreement with measurements during the winter-spring and summer-fall transitions, but measured means are higher than simulated during JJA and lower during DJF¹². In the summer, the measured mean falls within the ±σ bounds of the model, but during the winter months (Nov, Dec, Jan, Feb), the measured concentrations fall between the –σ and -2σ model values. This discrepancy could be due to unresolved seasonality of emissions, or secondary sources which are not represented in the simulations, but have been tested and discussed previously¹³. PYR simulated concentrations are lower than observed concentrations for all except the winter months. The observed values do, however, fall into the ±σ range of the model uncertainty distribution for all months. BaP simulated concentrations have the highest parametric uncertainty, and the observed concentrations fall into the ±σ range of the model for all months of the year, with the simulated seasonal cycle following the observed cycle closely.

Northern Hemisphere and Arctic model uncertainty in concentration

Figure S5 shows model parametric uncertainty distributions for BaP, PYR and PHE, for both NH and Arctic average concentrations, and for annual, winter, and summer temporal averages. Across all three PAHs, JJA average simulated concentrations are lower with higher uncertainty than DJF averages. PHE concentrations have the least parametric uncertainty, with a range (95% confidence interval) spanning approximately one order of magnitude for annual, summer, and winter averages. PYR and BaP parametric uncertainty ranges during the summer span more than two orders of magnitude, and close to an order of magnitude during the winter.

In the Arctic, parametric uncertainty is at its lowest for all three PAHs during the winter, when there is little to no sunlight to drive photochemical oxidation. Average concentrations of PAHs are highest during the winter, and lowest during the summer in the Arctic because of the presence of OH for oxidation, and this relative abundance of OH also drives the sensitivity of the PAH concentrations to oxidation rate constant uncertainty. The seasonal difference in the Arctic average PAH concentration is more pronounced than the NH average, with summer-winter differences for all three PAHs of more than three orders of magnitude.

Contributors to model parametric uncertainty

The important sources of model parametric uncertainty are substantially different between NH and Arctic average concentrations, and across the three PAHs. Table S5 shows the fractional contribution of leading parameters to the total resulting model parametric concentration uncertainty for PHE, PYR, and BaP. Figures S10–S20 show the spatial distributions of these contributions across the globe.

At the hemispheric scale, PHE concentration parametric uncertainty is driven year-round by uncertainty in the oxidation rate constant. Since PHE is mostly in the gas phase (90%–100% ¹²), uncertainty in its gas-phase lifetime is the most important contributor to parametric uncertainty in the NH average simulated concentrations. In the Arctic average, however, uncertainty in European emissions gains importance, contributing close to a third of the parametric uncertainty annually and 64% in the winter. The relative importance of emissions and reduced importance of oxidation rate constant uncertainty during Arctic winter is due to the lack of atmospheric OH radicals. During the summer, European emissions uncertainty remains a significant secondary contributor, but k_OH uncertainty makes up the largest fraction of the total for the model.

The contributors of PYR parametric concentration uncertainty follow a similar pattern to those of PHE. Because of the large uncertainty in the oxidation rate constant for PYR (see Table 1) and the fact that >50% of atmospheric PYR is in the gas phase¹², the parametric concentration uncertainty in the NH annual average is dominated by uncertainty in k_OH. Like for PHE, the second-most important contributor to parametric uncertainty is European emissions.

BaP has the most varied contributions of the three PAHs studied. For the NH annual average, uncertainty in K_BC-Water contributes 63% of the total uncertainty, with k_OH uncertainty contributing 30%, and the uncertainty in ΔH_vap, European, and North American emissions making up the other 7%. This behavior changes little between the winter and summer season.

In the Arctic, K_BC-Water is the leading source of parametric uncertainty for BaP. It contributes 55% annually, while k_OH contributes 35% and 6% is due to ΔH_vap. During the relatively photochemistry-free winter months, the contribution from k_OH drops to 3%, and the difference is made up by increases in the contributions of ΔH_vap (to 11%), and European emissions (to 29%). In the summer, the opposite occurs and k_OH uncertainty contributes 52% of the total.

Across all three PAHs, the contribution of physicochemical parameter uncertainty makes up more than 94% of the NH average parametric uncertainty. This is because a large fraction of the globe is far from emission sources, so wide spatial average concentrations are more sensitive to the uncertainty in the atmospheric lifetime than they are to emissions magnitude. In the case of PYR, parametric uncertainty in the atmospheric lifetime is almost entirely due to uncertainty in the oxidation rate because of the extremely high uncertainty in oxidation rate constant. For PHE, k_OH also contributes most to uncertainty because PHE is mostly found in the gas phase. In the case of BaP, the uncertainty in the atmospheric lifetime is due to both the highly uncertain gas phase oxidation rate, but also the amount of BaP found in the particulate phase, which is primarily controlled by BC partitioning. Because of its nature as a mostly particulate matter-bound PAH, BaP uncertainty has a larger contribution from the uncertainty in K_BC-Water and ΔH_vap, which together control partitioning to BC.

Closest to each emissions source region, uncertainty in that region’s emissions becomes most import, as removal during transport has not had time to take effect. Europe is the region with sources closest to the Arctic, and therefore European emissions uncertainty contributes more to simulated Arctic concentration uncertainty than other regional emissions. The emissions uncertainty contribution reaches a maximum during the winter, when concentrations of all three PAHs are highest due to lower loss rates, making it an important factor in the quantification of PAH transport to the Arctic.

Observation-constrained parameter distributions

We constrain the probability distributions of parameter values using the spatially distributed modeled and observed concentrations as described in the Methods section. Figure 2 shows the observation-derived likelihood distributions, and prior and posterior probability distributions of the two most important parameters for model uncertainty at the measurement sites. PHE’s and PYR’s leading parameters are constrained by the analysis, while BaP’s are effectively unconstrained.

Figure 2.

Constraint of parameter uncertainty distributions by measurement data. (a) PHE, (b) PYR, (c) BaP distributions for the two most important parameters each. Prior distributions (dashed lines), observation-based likelihoods (dot-dashed lines), and posterior distributions (solid lines) shown.

As shown in Figure 2(a), for PHE, the highest observation-constrained likelihood comes when k_OH is highest and the European regional emission rate is low. The result is that the posterior distributions for k_OH and E_Europe have maximums at higher and lower values, respectively. Figure 2(b) shows a similar constraining effect of the observations for PYR’s k_OH, which is shifted higher, while the E_Europe posterior distribution is narrowed around the same value as the prior distribution. Figure 2(c) shows that the measurement comparison added no constraints to the prior parameter distributions for BaP (neither confirming nor denying the assumed prior), due to the larger uncertainties in both its simulated and observed concentrations.

After constraint by the measurement data, we estimate new most likely values for PYR’s and PHE’s k_OH and rate of emission in Europe. The a priori best estimate of k_OH for PYR was 7×10⁻¹¹ cm⁻³s⁻¹, while the updated best estimate is 1×10⁻¹⁰ cm⁻³s⁻¹. The prior estimate of k_OH for PHE of 1.9×10⁻¹¹ cm⁻³s⁻¹ is updated to 2.3×10⁻¹¹ cm⁻³s⁻¹. We lower our best estimates of European emissions for PHE from 5.8 kt/yr to 4.1 kt/yr.

DISCUSSION

Through the uncertainty attribution described above, we identify the key parameters for which reducing uncertainty would improve our ability to model long-range transport of PAHs. For PHE and PYR, k_OH uncertainty has the largest impact on model results, while for BaP k_OH, K_BC-Water, and ΔH_vap all contribute to uncertainty in simulated concentrations. These results are similar to findings for multimedia models of other environmental toxics, which indicate that degradation rates and partition coefficients are the largest contributors to parametric uncertainty^19,21. Across all three PAHs, more precise experimental quantification of k_OH could greatly reduce parametric model uncertainty. In particular for PYR and BaP, the lack of experimental values of k_OH leads to an additional step in the propagation of uncertainty, as the value of k_OH used in the model is itself a parametrization. With reduced k_OH uncertainty, we would be better able to constrain PAH emissions using observations of concentrations, and we would improve our ability to use modeling to inform policy⁴².

We are able to quantitatively attribute simulated concentration uncertainty to individual model parameters while accounting for non-linear model responses in a computationally efficient manner. Because of the method’s relatively low number of required model runs, it could be applied to other spatially resolved environmental models for low-cost but detailed identification of leading contributors to parametric uncertainty. The detailed parametric uncertainty analysis that this method provides is an important aspect of environmental transport model simulations that is commonly unreported in the literature. This type of analysis should be carried out for other substances and models, as the conclusions from our simulations of PAHs specifically may not apply to other substances or models. This is evident in comparison to the first-order uncertainty analysis for BETR Research PCB153 simulations²⁴, which suggests that emissions uncertainties account for more than 90% of the simulated atmospheric concentration parametric uncertainty under current climate and emissions.

We constrain physicochemical and emissions parameters using measurements, with updated uncertainty distributions for k_OH and E_Europe for PHE and PYR. While this method represents a quantitative improvement over traditional model sensitivity tests, in which parameters are altered based on forward matches to observations, our approach also has important limitations. The constraint relies on the comparison of concentrations measured at a point to the average concentration within a GEOS-Chem grid-box. While we account for this through an estimate of representativeness error, spatial heterogeneities within the grid-box are not represented and could introduce an unquantified bias in the comparisons due to this mismatch of spatial resolutions. We do not optimize for the spatial distribution of emissions in this study, which precludes the ability to account for a local emission source that could be driving observed concentrations at a site. Our analysis also relies on the quantification of the emissions parameters and their uncertainty at the inventory’s national level, and any potential biases in these estimates would propagate to our results. For example, an underestimation of the uncertainty in biomass burning emissions factors in the inventory would propagate through the model to result in an underestimate of concentration uncertainty.

While we quantify the impact of uncertainties in regional emission magnitudes and physicochemical properties on simulated concentrations in detail, there are other sources of uncertainty in simulated concentrations. Emissions can vary substantially temporally, and on spatial scales finer than those considered here. These temporal and spatial resolution mismatches between the simulations and reality will have a more limited effect on large spatial and time averages than on shorter-term localised concentrations. Along with direct emissions, secondary emissions (revolatilization) from surface media can affect atmospheric PAH concentrations, and these secondary sources are not resolved in this work. The accuracy and time-resolution of prescribed concentrations of particulate matter and OH used in the model can also introduce uncertainty, but this uncertainty is significantly smaller than that due to their associated chemical parameters¹³. There is also non-parametric uncertainty associated with the particle partitioning scheme used, as deviations from measurements can be large, especially for smaller PAHs¹⁵ whose concentrations have lower sensitivity to particle partitioning. Theoretical issues have been identified with the parametrization of partition coefficients⁴³, which we have not accounted for here. Limitations of particle partitioning schemes for PAHs in GEOS-Chem have been investigated in detail previously²³. Considering these uncertainties, our results suggest that for BaP, further constraints on partitioning properties would improve our ability to capture long-range transport.

Chemical transport modeling is susceptible to a variety of sources of uncertainty that are not unique to the simulation of PAHs. Advection in the atmosphere is carried out on a large scale that is only representative of the actual advection in the atmosphere on a coarse scale. This advection is based on meteorological reanalysis fields that have their own uncertainty. Prescribed precipitation also contributes to uncertainty in wet deposition. However, many of these processes in GEOS-Chem are evaluated and constrained using simulations of other atmospheric constituents (e.g. carbon monoxide, ozone) for which measurement data are less uncertain and more widely available^44–46. The source of uncertainty most difficult to quantify is that which is associated with PAH-specific processes not represented by the model (e.g. on-particle oxidation reactions other than ozonation). A process that is not described by the model would not be represented in a parametric uncertainty analysis, and depending on the importance of the process could be a major source of unquantified uncertainty.

Based on model sensitivity (Figures S6–S9), the most effective locations for hypothetical future measurement sites that could be used to improve the constraint of the most important PAH physicochemical properties are far from sources and are generally in regions where wet deposition is relatively less important, particularly in the Southern Hemisphere. These locations, however, have very low PAH concentrations, below common quantification limits. The resulting measurement constraint paradox is that the locations that would best constrain physicochemical properties have concentrations that are the most difficult to measure. This means that greatly reducing model parametric uncertainty by observational constraint will require very low detection limits at long-term remote sites. Measuring these low concentrations is potentially achievable for the gas phase using passive air samplers, which accumulate greater contaminant mass over longer periods of time than traditional active samplers⁴².

The results we present give important insight into the parametric uncertainty distributions of simulated PAH concentrations and their relationship to specific inputs. Our analysis demonstrates that there is a need to reduce the large parametric uncertainties stemming from physicochemical property data for PAHs, and identifies the properties which contribute most to model parametric uncertainty. While our analysis shows that long-term measurement sites can be used to constrain physicochemical property values for PHE and PYR, highlighting the importance of such measurements of atmospheric PAHs, better experimental quantification of PAH properties would provide the greatest reductions in simulated concentration uncertainty. We identify quantitatively which physicochemical properties of PHE, PYR and BaP could be targeted experimentally to greatly reduce simulated concentration uncertainty.