Probability analyses of combining background concentrations with model-predicted concentrations

Abstract

In order to calculate total concentrations for comparison to ambient air quality standards, monitored background concentrations are often combined with model predicted concentrations. Models have low skill in predicting the locations or time series of observed concentrations. Further, adding fixed points on the probability distributions of monitored and predicted concentrations is very conservative and not mathematically correct. Simply adding the 99th percentile predicted to the 99th percentile background will not yield the 99th percentile of the combined distributions. Instead, an appropriate distribution can be created by calculating all possible pairwise combinations of the 1-hr daily maximum observed background and daily maximum predicted concentration, from which a 99th percentile total value can be obtained. This paper reviews some techniques commonly used for determining background concentrations and combining modeled and background concentrations. The paper proposes an approach to determine the joint probabilities of occurrence of modeled and background concentrations. The pairwise combinations approach yields a more realistic prediction of total concentrations than the U.S. Environmental Protection Agency's (EPA) guidance approach and agrees with the probabilistic form of the National Ambient Air Quality Standards.

Implications: EPA's current approaches to determining background concentrations for compliance modeling purposes often lead to “double counting” of background concentrations and actual plume impacts and thus lead to overpredictions of total impacts. Further, the current Tier 1 approach of simply adding the top ends of the background and model predicted concentrations (e.g., adding the 99th percentiles of these distributions together) results in design value concentrations at probabilities in excess of the form of the National Ambient Air Quality Standards.

Introduction

For modeling compliance demonstration purposes, background concentrations are appropriately time-averaged concentrations of the pollutant(s) of concern, which are not attributable to the source(s) being modeled. Background concentrations for near field modeling are generally considered to be spatially uniform over the entire modeling receptor array, but may vary temporally. The modeled inventory of sources is used to account for spatial gradients in the concentration field.

The “Guideline on Air Quality Models” (the Guideline; U.S. Environmental Protection Agency [EPA], 2005) recommends determining background concentrations for short-term averaging periods by finding concentrations “at monitors not impacted by the source in question” and directs modelers to exclude “monitoring sites inside a 90° sector downwind of source” when defining which monitors to use in background calculations. When using meteorological observations to define the downwind sector, monitored plume impacts from the modeled source may occur outside the downwind sector, and thus these impacts are “double counted” as background and as part of the modeled source impact. This effect becomes especially critical for 1-hr averaging periods when selecting the 98th or 99th percentile of the monitored concentrations as the background for compliance demonstrations with the 1-hr National Ambient Air Quality Standards (NAAQS).

Further, in order to move away from unstable “highest second-high” extreme value- and “expected exceedance”-based NAAQS, for which observed and modeled design concentrations may vary dramatically from year to year and result in nonattainment area misclassifications, the Clean Air Scientific Advisory Committee (CASAC), advisors to the U.S. Environmental Protection Agency (EPA) Administrator, recommended probabilistically based NAAQS. For example, the 1-hr average sulfur dioxide (SO₂) NAAQS was promulgated as the 3-yr average of the 99th percentile of maximum daily concentrations. With these more stringent NAAQS, background concentrations determined following current modeling guidance often become the dominant portion of the total design value concentration (model predicted plus monitoring background). As a “first-tier” approach to demonstrate compliance with the 1-hr average sulfur dioxide (SO₂) NAAQS, the EPA recommended adding the model-predicted (Pre) 99th percentile 1-hr daily maximum design concentration to the 3-yr average of the monitoring design value background (Bkg) concentrations (i.e., the 99th percentile of the maximum hourly daily monitored concentrations) over a 3-yr period (Page, 2011). It is not mathematically correct to simply add probability distributions; that is, the 99th percentile Pre plus the 99th percentile Bkg does not equal the 99th percentile of the combined total concentrations.

As an alternative to the single value background approaches above, the EPA also suggested (Page, 2011)

calculating temporally varying background monitored concentrations by hour of day and season (excluding periods when the source in question is expected to impact the monitored concentration) … this same methodology is applicable to SO₂ designations modeling based on use of the 99^th percentile by hour of day and season for background concentration excluding periods when the dominant source(s) are influencing the monitored concentration (i.e., 99^th percentile, or 4^th highest, concentrations for hour 1 for January or winter, 99^th percentile concentrations for hour 2 for January or winter, etc.). Recent updates included in AERMOD allow for the inclusion of temporally varying background concentrations in the design value calculation in combination with modeling results.

In the hourly/seasonal approach, the Pre is added to the 99th percentile of the Bkg for each hour of the day in each season and the total 99th percentile maximum daily 1-hr concentration is determined from this distribution. Inherent in this approach is the assumption that the model is capable of predicting concentrations on an hour-by-hour basis; otherwise, it makes little sense to combine hour of the day predicted and hour of the day observed concentrations. Each of these techniques inappropriately adds Pre and Bkg probability distributions to determine the total concentration distribution.

Background

Evaluation studies indicate that air quality dispersion models have low skill in predicting the location or time of occurrence of ambient concentrations resulting from point source (stack) emissions:

•	“Existing plume models are generally unable to predict air quality impacts for a specific event. Uncertainties associated with the magnitude and location of plume impacts are as large as the predicted or observed values” (Bowne et al., 1983, p. 7–3).
•	“The large discrepancies between observed and predicted concentration values for the same event are not simply a consequence of uncertainty about the location of plume impacts. For the dense tracer sampling array, large discrepancies were found for the magnitude of the concentration, independent of location” (Bowne, et al., 1985, p. 7–4).
•	“The models exhibited little skill in predicting the magnitude or location of plume impact for a given event” (Murray and Bowne, 1988, p. 5–7).

For this study, the Kincaid Power Station sulfur hexafluoride (SF₆) tracer and sulfur dioxide (SO₂) model evaluation databases collected by the Electric Power Research Institute (EPRI) (Atmospheric Transport and Diffusion Data Archive, 2013), and EPA Support Center for Regulatory Atmospheric Modeling (Technology Transfer Network Support Center for Regulatory Atmospheric Modeling, 2013) were used, together with the AERMOD (version 12345) modeling system (Technology Transfer Network, 2013), to illustrate model performance characteristics and possible background treatments. The Kincaid tracer database consists of 348 hr of tracer concentration data collected by approximately 200 samplers over three intensive field campaigns to distances of 50 km from the release stack (see Figure 1 for an example tracer array deployment). The Kincaid SO₂ database contains 6,024 hr of observed concentrations (covering two spring and summer periods: April 3, 1980 to August 31, 1980, and March 10, 1981 to June 17, 1981) from 28 monitoring stations deployed 2 to 20 km from the isolated plant (see Figure 2). There are no nearby significant emissions sources of either SF₆ or SO₂ and the terrain in the modeling domain is very flat so there are effectively no complications regarding either other sources contributing to the observed concentrations or for terrain induced plume steering. For this study, the SO₂ data were treated as a continuous data set rather than as two separate modeling years. The SF₆ data were evaluated for each hour using unit emissions and thus treated as unitized ambient concentrations, Chi/Q (χ/Q), in units of seconds/meter³ × 10⁻⁹.

Figure 1. Example tracer array.

Figure 2. Location of Kincaid Power Station and 28 SO₂ monitor locations.

Similar to the model performance evaluation performed for the EPA (EPA, 2003), AERMOD (12345) was used to predict concentrations from plant emissions using hourly emission data and concurrent meteorological data.

SO₂ modeling was conducted to investigate the ability of AERMOD to match the observed concentrations on the monitoring network. The SO₂ modeling employed National Weather Service data from Springfield, IL, typical of modeling approaches used to support ambient air quality impact studies for permitting purposes and consistent with the Guideline. The meteorological data were processed using AERSURFACE (08009) and AERMET (12345) to be consistent with current modeling practice. Figure 3 shows the 1-hr average observed and predicted SO₂ concentrations at the Kincaid monitoring sites fully paired in space and time. AERMOD demonstrates little prediction skill (correlation coefficient r ² = 0.02) in matching the location and time of the observed concentrations. In fact, the highest predicted and observed concentrations are asymptotic along the axes, showing the model predicts high concentrations when the observed values are close to zero and the high observed concentrations occur when the model is predicting close to zero. Appropriately for this isolated site, no background concentrations have been added to the predicted concentrations shown in Figure 3. As demonstrated by others (EPA, 2003) and shown here, AERMOD does do reasonably well predicting the magnitude of the peak hourly concentration values, but frequently the modeled location of the plume based on input wind direction is misaligned with the observed plume direction. This misalignment has serious implications for the Guideline's recommended technique of identifying monitors that are not being impacted by the plume.

Figure 3. Observed vs. AERMOD predicted hourly SO₂ concentrations fully paired in time and space.

In Figure 4, the maximum hourly concentration observed at any monitoring station is plotted against the maximum predicted at any monitoring station, paired in time. Again, the model demonstrates little prediction skill (correlation coefficient r ² = 0.08) in matching the time of the observed concentrations. Thus, background addition techniques that rely on the ability of AERMOD to predict either the locations or the times (hour of the day) of concentration events are inherently unreliable for determining the combined total impact.

Figure 4. Maximum observed vs. maximum AERMOD predicted hourly SO₂ concentrations paired in time only.

EPA-Recommended Background Approaches

90-Degree downwind sector

The Guideline recommends determining background concentrations for short-term averaging periods by finding concentrations “at monitors not impacted by the source in question” and directs modelers to exclude “monitoring sites inside a 90° sector downwind of source” when defining which monitors to use in background calculations. Table 1 presents the results of applying this guidance for both SF₆ tracer and SO₂ using the hourly wind direction data available from the National Weather Service office at Abraham Lincoln Capital Airport in Springfield, IL (approximately 30 km from the Kincaid station), and onsite observations at the 10- and 100-m level of a research-grade instrumented meteorological tower. Note that observations during hours for which calm conditions were reported have not been included in these statistics, since wind directions were not available for these hours. Analogous to the form of the 1-hr SO₂ standard, the 99th percentile of the maximum hourly observed SF₆ χ/Q (m³/s × 10⁻⁹) and SO₂ concentration (μg/m³) are reported (third column) for all observed concentrations, as well as the 99th percentile of the maximum hourly observed χ/Q and concentration only for monitors outside of the 90-degree wind sector (fourth column), which following EPA guidance (Page, 2011) would be used as background. For the tracer the expected background concentration is zero since the global SF₆ background was less than the lower detection limit of the instruments used for the study. The SO₂ background is also expected to be very low since the Kincaid station is isolated from other significant SO₂ emission sources. Comparing the third and fourth columns, the 99th percentile of the hourly maximum observed tracer χ/Q and SO₂ concentrations outside the downwind sector are substantial fractions of the overall hourly maximum 99th percentile observed, with the 99th percentile out-of-sector hourly background tracer χ/Q and SO₂ concentrations ranging from 47 to 76% of the 99th percentile of the maxima of all observed hourly χ/Q and concentrations. Note that Figures 1 and 2 show the 90-degree wind sector based on National Weather Service data for the hour producing the 99th percentile outside the sector tracer χ/Q and SO₂ concentration, respectively. For both cases, the actual plume location was outside the indicated “downwind sector.”

Table 1. Summary of tracer and SO₂ observed outside 90° downwind sector

	Basis:	Maximum per hour			Average per hour			Minimum per hour
Pollutant	Wind direction	99th Percentile observed (10^−9 s/m³)	99th Percentile outside sector (10^−9 s/m³)	Percent hours outside sector >10% hourly max	99th Percentile observed (10^−9 s/m³)	99th Percentile outside sector (10^−9 s/m³)	Percent hours outside sector >10% hourly max	99th Percentile observed (10^−9 s/m³)	99th Percentile outside sector (10^−9 s/m³)	Average observed (10^−9 s/m³)
SF6	National Weather Service	247.2	188.0	60.3%	29.1	23.9	6.5%	0.00	0.00	0.00
	100 m Onsite	247.2	147.3	53.1%	29.1	16.5	3.9%	0.00	0.00	0.00
	10 m Onsite	247.2	116.3	55.7%	29.1	13.0	3.9%	0.00	0.00	0.00
	Basis:	Maximum per hour			Average per hour			Minimum per hour
Pollutant	Wind direction	99th Percentile observed (μg/m³)	99th Percentile outside sector (μg/m³)	Percent hours outside sector >10% hourly max	99th Percentile observed (μg/m³)	99th Percentile outside sector (μg/m³)	Percent hours outside sector >10% hourly max	99th Percentile observed (μg/m³)	99th Percentile outside sector (μg/m³)	Average observed (μg/m³)
SO2	National Weather Service	504.6	366.1	90.8%	77.2	65.9	59.9%	0.00	2.62	0.02
	100 m Onsite	507.3	300.7	90.1%	79.5	57.2	57.8%	0.00	2.62	0.02
	10 m Onsite	507.3	287.6	91.3%	79.5	58.0	58.6%	0.00	0.00	0.02

For both SF₆ and SO₂, the percentages of hours where the observed χ/Q or concentration outside of the nominal 90-degree downwind sector exceeds 10% of the maximum observed χ/Q or concentration during that hour are also reported (fifth column). Ideally, no hours would show plume contribution outside of the nominal 90-degree downwind sector, but this analysis shows that the plume frequently has significant contribution outside of the downwind sector.

The Guideline is somewhat unclear regarding data handling for out of sector monitored concentrations: “Concentrations for meteorological conditions of concern, at monitors not impacted by the source in question, should be averaged for each separate averaging time to determine the average background value” (EPA, 2005). It is unclear whether this applies to spatial as well as temporal averaging. For this reason, the sixth and seventh columns present the 99th percentile χ/Qs and concentrations based on the average of all receptors and for only receptors outside the nominal downwind sector for the hour. The eighth column presents the percent of hours when the concentration outside the 90-degree nominal downwind sector exceeds 10% of the maximum observed concentration for the hour. These statistics are very dependent on the network design, as seen by comparing the results for the 200 tracer array monitors versus the 28 SO₂ monitors. The tracer monitors have far more measured zero χ/Q values than the SO₂ monitors have zero measured concentrations, and thus the hourly spatial average is much lower for the tracer monitors. The “average per hour” columns have been included for completeness, but the authors see little value to such results. The authors recommend that the EPA clarify the intent of the above quoted language in the Guideline.

Finally, Table 1 shows the 99th percentile minimum concentrations observed over all observations and the 99th percentile observed over concentrations outside the 90-degree nominal downwind sector (columns 9 and 10, respectively). The temporal average of the minimum hourly tracer χ/Q and SO₂ concentrations observed on the networks is shown in column 11. The expected background χ/Q for the tracer is zero, and since the site is isolated, the expected background for SO₂ is near zero. The minimum observed values at all monitors are much closer to the expected background and more reliable indications of true background than the values outside of the downwind sector. If there are multiple monitors available the authors recommend using the minimum observed hour-by-hour concentrations observed on all representative monitors within the airshed or modeling domain as the appropriate background concentration. If multiple-hour (e.g., 24-hr average) or annual background concentrations are needed, these should be calculated as the appropriate average of the hourly minimum concentrations observed on the monitoring network.

It is important to keep in mind that most air quality monitors are located near significant emission sources to monitor concentration “hot spots” and thus tend to report concentrations that are higher than the regional concentrations. This siting makes many air quality monitoring stations inherently conservative for the purpose of determining area-wide background. If only a single monitor is available, efforts must be made to ensure that monitored contributions from sources in the modeling inventory are not included in the determination of background. This will entail monitoring data analysis and professional judgment.

Treating monitor observed concentrations

For the purposes of simulating a typical regulatory modeling exercise, AERMOD was rerun for SO₂ with a Cartesian receptor array (50 m spacing out to 1.5 km, 100 m spacing out to 2.5 km, 250 m spacing out to 4 km, 500 m spacing out to 10 km, and 1 km spacing out to 25 km, for a total of 9,561 receptors) using National Weather Service data. The observed background SO₂ concentrations were taken from the monitors lying outside the 90° downwind sector. Both the predicted and observed data sets were processed to find the maximum daily 1-hr average concentrations. In addition, the hourly/seasonal 99th percentile background concentrations were tabulated. Table 2 presents the hourly/seasonal background data. Recall that the evaluation database was collected over two summer and spring seasons, so no background or predicted data are available for the autumn or winter seasons.

Table 2. Monitored hourly/seasonal SO₂ background concentrations (μg/m³)

	Season*
Hour of day	Spring (March April May)	Summer (June July August)
1	159	52
2	165	52
3	118	47
4	144	173
5	170	60
6	146	73
7	178	115
8	183	183
9	562	437
10	397	455
11	492	782
12	523	638
13	648	463
14	763	356
15	437	361
16	293	295
17	413	275
18	290	175
19	238	201
20	225	230
21	214	128
22	227	81
23	175	60
24	152	126
*Monitors did not collect winter and autumn data.

The resulting predicted (Pre) and monitored background (Bkg) data sets were then processed using the background techniques recommended by the EPA (Page, 2011):

•	Adding the modeled 99th percentile of the maximum daily 1-hr AERMOD predictions (871 μg/m3) and the “monitored design value concentration” (99th percentile of the maximum daily 1-hr observed concentrations, 1116 μg/m3) results in a total predicted concentration of 1987 μg/m3.
•	Adding the 99th percentile of the hourly/seasonal background with the hourly predicted concentrations to determine the 99th percentile of the daily maximum 1-hr total concentration results in a predicted design value of 1511 μg/m3.

Recall that the actual regional background at this site is expected to be near zero.

Alternatively, the daily maximum of the hourly minimum observed concentrations anywhere on the monitoring network (rather than the EPA approach of using the monitored 1-hr daily maximum concentrations outside of the downwind sector) can be used to build the distribution of background concentrations. Using the daily 1-hr maximum of the minimum hourly observed concentration on the monitoring network results in a combined 99th percentile concentration of 879 μg/m³ (871 μg/m³ predicted plus 8 μg/m³ background).

Each of these approaches produces different estimates of the total predicted 99th percentile concentration, but in each case relies on inappropriately adding concentrations from the frequency distributions to calculate the total 99th percentile concentration. Further, the hourly/seasonal approach inherently assumes that the models are capable of correctly predicting hourly concentrations paired in time, when in fact the models have little skill matching concentrations paired in time. A method for appropriately combining model predicted and monitored background concentrations is described next.

Combining Concentration Frequency Distributions

To demonstrate compliance with the 1-hr SO₂ NAAQS, modelers must find the combinations of the predicted concentration (Pre) probability distribution and the monitored background concentration (Bkg) probability distribution that result in the total concentration distribution at the 99th percentile level, or equivalently at the marginal probability level of 0.01. For discrete data sets of 1-hr daily maximum observed Bkg and daily maximum Pre, the distributions can be established by creating all possible pairwise combinations of these quantities. This was done by finding the 1-hr daily maximum Bkg and adding to this all the 1-hr daily maximum Pre for the modeling period, receptor by receptor.

For this example there were 242 days with at least 18 hr of observed Bkg (the minimum required by the EPA to determine a valid Bkg) and 251 days in the modeling period of record. To generate the pairwise combinations for a receptor, the 242 1-hr daily maximum Bkg were found and the 251 daily maximum Pre values were added to each daily maximum Bkg, for a total of 60,742 possible combinations of Bkg and Pre per receptor for each of the 9,561 receptors modeled. For each receptor, the 99th percentile concentration of the pairwise combinations was determined and the overall highest 99th percentile pairwise combination concentration from all receptors was reported. This process was conducted both with Bkg determined using the EPA 90-degree sector approach which resulted in a 99th percentile total concentration of 1397 μg/m³ and Bkg determined using the daily 1-hr maximum of the minimum observed hour-by-hour concentrations observed on all representative monitors as recommended earlier, which resulted in a 99th percentile total concentration of 871 μg/m³. It is worth noting that this approach remains conservative because it adds together the 1-hr daily maximum Bkg and Pre, which may occur at different hours of the day. In reality, the 1-hr daily maximum Bkg and Pre are likely to occur at different hours (recall that models generally have low skill at matching the time of occurrence of observed concentrations), and combining Bkg and Pre to determine the total concentration in this manner is likely to be both unrealistic and conservative.

Summary

Downwind sectors as determined by meteorological data sets and the AERMET meteorological processor often do not correctly encompass the ground-level plume from elevated sources. As such, using the downwind sector approach to identify monitoring locations not impacted by a source's plume is unreliable and leads to significant “double counting” of plume impacts and monitored concentrations. Error attributable to the downwind sector approach, especially as applied at the top end of the frequency distribution, leads to overestimating the design value concentrations.

Air quality models have little skill in predicting either the locations or the times of peak observed concentrations, and techniques that rely on predicting either the location or time of occurrence of concentrations, such as hourly/seasonal background calculations, are limited by the model's skill. Simply adding like probabilities of predicted and background concentrations (e.g., the concentration at the 99th percentile of each distribution) does not yield the same probability of the combined distributions and in fact yields a concentration representative of a substantially higher point on the frequency distribution. Table 3 presents a summary of the total predicted concentrations (background plus the model predicted) as described earlier for the Kincaid SO₂ data set and AERMOD using:

Table 3. Summary of total design value concentrations (predicted+background) for the Kincaid SO₂ data set

Background technique	Total concentrations (μg/m^3)
99th Percentile observed max daily 1-hr outside 90-degree sector	1987
Hourly/seasonal	1511
99th Percentile observed max daily minimum 1-hr (anywhere in monitoring network)	879
99th Percentile pairwise combinations with observed max daily 1-hr outside 90-degree sector	1397
99th Percentile pairwise combinations with observed max daily minimum 1-hr (anywhere in monitoring network)	871

•	The EPA guidance approaches with the 99th percentile observed outside the nominal downwind sector and 99th percentile predicted.
•	The hourly/seasonal approach.
•	The 99th percentile background determined using the minimum observed concentrations on the network plus the 99th percentile predicted concentrations.
•	The 99th percentile pairwise combination using the background concentrations for monitors outside the nominal downwind sector added to the predicted concentrations.
•	The 99th percentile pairwise combination using the minimum background concentrations added to the predicted concentrations (author recommended approach).

Recommendations

In conclusion, the authors recommend that regulatory agencies review the modeling compliance procedures presently established relating to the inclusion of background concentrations in the design value. If there are several monitors in the modeling region, background concentration distributions should be determined from the lowest reported representative concentration observation on the monitoring network within the airshed under consideration. If only a single monitor is available, efforts must be made to ensure that monitored contributions from sources in the modeling inventory are not included in the determination of background; this will entail monitoring data analysis and professional judgment.

Simply adding the 99th percentile of the daily hourly maximum predicted and background concentrations, while a straightforward Tier 1 approach for demonstrating compliance, is very conservative. The authors recommend inclusion of a Tier 2 background approach using the minimum representative hourly concentrations on the monitoring network to determine background concentration and pairwise combinations to determine the 99th percentile of the combined background plus predicted concentrations. Note that since this approach still employs the maximum daily observed and predicted hourly concentrations (unpaired in time), it remains a conservative approach for estimating the total concentrations.

The regulatory agencies should provide the air quality modeling community with a definitive procedure whereby the modeled probabilistic concentrations are added to a representative probabilistic background concentration to ensure compliance at the appropriate concentration level (e.g., the 99th percentile for the 1-hr SO₂ NAAQS). Current modeling guidance places an undue burden on emission sources by going beyond the intent of the promulgated NAAQS.