Evaluation of NO₂ predictions by the plume volume molar ratio method (PVMRM) and ozone limiting method (OLM) in AERMOD using new field observations

Abstract

The U.S. Environmental Protection Agency (EPA) plume volume molar ratio method (PVMRM) and the ozone limiting method (OLM) are in the AERMOD model to predict the 1-hr average NO₂/NOx concentration ratio. These ratios are multiplied by the AERMOD predicted NOx concentration to predict the 1-hr average NO₂ concentration. This paper first briefly reviews PVMRM and OLM and points out some scientific parameterizations that could be improved (such as specification of relative dispersion coefficients) and then discusses an evaluation of the PVMRM and OLM methods as implemented in AERMOD using a new data set. While AERMOD has undergone many model evaluation studies in its default mode, PVMRM and OLM are nondefault options, and to date only three NO₂ field data sets have been used in their evaluations. Here AERMOD/PVMRM and AERMOD/OLM codes are evaluated with a new data set from a northern Alaskan village with a small power plant. Hourly pollutant concentrations (NO, NO_2, ozone) as well as meteorological variables were measured at a single monitor 500 m from the plant. Power plant operating parameters and emissions were calculated based on hourly operator logs. Hourly observations covering 1 yr were considered, but the evaluations only used hours when the wind was in a 60° sector including the monitor and when concentrations were above a threshold. PVMRM is found to have little bias in predictions of the C(NO₂)/C(NOx) ratio, which mostly ranged from 0.2 to 0.4 at this site. OLM overpredicted the ratio. AERMOD overpredicts the maximum NOx concentration but has an underprediction bias for lower concentrations. AERMOD/PVMRM overpredicts the maximum C(NO₂) by about 50%, while AERMOD/OLM overpredicts by a factor of 2. For 381 hours evaluated, there is a relative mean bias in C(NO₂) predictions of near zero for AERMOD/PVMRM, while the relative mean bias reflects a factor of 2 overprediction for AERMOD/OLM.

Implications: This study was initiated because the new stringent 1-hr NO₂ NAAQS has prompted modelers to more widely use the PVMRM and OLM methods for conversion of NOx to NO₂ in the AERMOD regulatory model. To date these methods have been evaluated with a limited number of data sets. This study identified a new data set of ambient pollutant and meteorological monitoring near an isolated power plant in Wainwright, Alaska. To supplement the existing evaluations, this new data were used to evaluate PVMRM and OLM. This new data set has been and will be made available to other scientists for future investigations.

Introduction

The plume volume molar ratio method (PVMRM) (Hanrahan, 1999a) and ozone limiting method (OLM) (Cole and Summerhays, 1979) are used in the U.S. Environmental Protection Agency (EPA) AERMOD model (U.S. EPA, 2004a) to predict the 1-hr average NO₂/NOx concentration ratio in plumes within a few kilometers of the source. These ratios are multiplied by the AERMOD predicted NOx concentration to predict the 1-hr average NO₂ concentration.

The increased interest in plume NOx chemistry occurred after the U.S. EPA promulgated a new short-term (1-hr) National Ambient Air Quality Standard (NAAQS) for nitrogen dioxide (NO₂) in January 2010. Demonstrations of compliance with this 1-hr NO₂ standard require consideration of the role of ozone in the ambient air in converting nitrogen oxide (NO) emissions to NO₂. PVMRM and OLM are options in AERMOD for calculating the NO₂/NOx concentration ratio in a plume.

The PVMRM technique was originally developed by Hanrahan (1999a) to calculate the ratio of NO₂ to NOx concentrations downwind from single and multiple sources of NOx. It was coded as a postprocessor to the Industrial Source Complex (ISC) model (U.S. EPA, 1995), which calculated NOx concentrations as if NOx were a nonreacting tracer. Hanrahan (1999b) presented results of evaluations of the ISC/PVMRM model using three field data sets: the Netherlands aircraft-based observations (Arellano et al., 1990; Bange et al. 1991), the Empire Abo, New Mexico, gas plant with multiple sources and two ground-level monitors, and the Pala'au, Hawaii, power plant with a single monitor. It was concluded that “These performance evaluations show that PVMRM can realistically predict the NO₂/NOx fraction at close-in receptors yet still provide conservative estimates so that air quality standards can be protected” (Hanrahan, 1999b, p. 1332). The method was thought to offer a practical alternative to the use of simpler methods to estimate the conversion of NOx to NO₂, namely, the ambient ratio method (ARM) (U.S. EPA, 2011) and the ozone limiting method (OLM).

PVMRM and OLM make use only of the reactions involving ozone, NO, and NO₂, and do not include photolysis, reactive hydrocarbons, or other nitrogen compounds. They also assume instantaneous reactions.

AERMOD is the U.S. EPA replacement for the ISC model as the recommended guideline model for New Source Review and other regulatory applications. The U.S. EPA (2004a) implemented the PVMRM technique into the AERMOD model as a series of internal subroutines rather than as the stand-alone postprocessor used in ISC applications. However, a few changes were made to the scientific components and assumptions in PVMRM when incorporating PVMRM into AERMOD.

MACTEC (2004, 2005) carried out sensitivity analyses and an evaluation of the AERMOD/PVMRM model, focusing on the annual NAAQS for NO₂, and updated and augmented the three field databases originally used by Hanrahan (1999b) in order to carry out these evaluations. More recently, the U.S. EPA (2011) has reevaluated AERMOD/PVMRM with the Pala'au and Empire Abo field data bases focusing on the new 1-hr NO₂ NAAQS.

In order to instill more confidence in an evaluation of a model or model options, as many field data sets as possible should be used so that a multitude of conditions, source data, and so on can be included. Thus, the literature was reviewed to determine whether any additional NO₂ field data exist beyond those previously mentioned. A new field data set must be sufficiently complete to allow a comprehensive model evaluation. Ideally, the new field data set should include observations of nitrogen dioxide (NO₂), oxides of nitrogen (NOx), and ozone (O₃) from several monitors, as well as emission inventories and meteorological observations. One such ambient monitoring field database was identified in Wainwright, Alaska. PVMRM and OLM predictions of the NO₂/NOx concentration ratio, AERMOD/PVMRM and AERMOD/OLM predictions of NO₂ concentrations, and AERMOD predictions of NOx concentrations were evaluated with the Wainwright data set. The full project report (Hendrick et. al., 2012) is available and the data set can be provided upon request.

Overview of the Scientific Assumptions of PVMRM and OLM

The basic concept and the chemistry equations in PVMRM and OLM are fairly simple. In PVMRM, the assumption is made that the production of NO₂ from the reaction of NO (in an effluent plume) with ambient ozone is proportional to the amount of ambient ozone that is entrained into the plume as it is advected downwind (Hanrahan, 1999a). The conversion of NO to NO₂ at a downwind distance x from the source is determined by the ratio of the number of moles of ambient ozone that have been entrained into a plume segment at downwind distance x to the number of moles of NOx in the same segment that have been emitted from the source. The calculated initial NO₂/NOx ratio is then added to the in-stack ratio of NO₂ to NOx in the emissions (user input) to determine the final PVMRM ratio used to compute NO₂ concentrations. This approach is conservative in that the initial fraction of NO₂ in the plume is double counted since the NOx emissions are not adjusted for the fraction of NOx that converted to NO₂ prior to leaving the stack before PVMRM calculates the moles of NOx emitted. The predicted NO₂ concentration (C(NO₂)) at the receptor location equals the AERMOD-predicted NOx concentration (C(NOx)) at that receptor multiplied by the PVMRM-predicted ratio of C(NO₂)/C(NOx) in the plume at that downwind distance x.

In OLM, the AERMOD-estimated NOx concentration at a receptor location is compared with the ambient ozone (O₃) concentration to determine which is the limiting factor to NO₂ formation (Cole and Summerhays, 1979). If, at the specific receptor location, the ambient concentration of O₃ is greater than the AERMOD-predicted plume concentration of NOx, then total conversion of all emitted NOx to NO₂ is assumed. Otherwise, the formation of NO₂ is assumed to be limited by the available O₃.

OLM and PVMRM both incorporate the same chemical equation (NO + O₃ → NO₂ + O₂) and both use the AERMOD dispersion model to estimate NOx concentrations. The main difference is that PVMRM theory calculates the NO₂/NOx ratio for a given downwind distance, x, and applies it to all receptors across the plume at that distance (even on the edge where concentrations of NOx may be much lower than in the center of the plume), whereas OLM theory calculates the NO₂/NOx ratio as a function of the maximum NOx concentration. In AERMOD, this is applied at every receptor location, which can produce overestimations of NO₂ due to lower NOx concentrations at the edge of the plume.

An empirical restriction to the maximum allowed ratio C(NO₂)/C(NOx), called the ambient equilibrium ratio, is assumed in PVMRM and OLM in AERMOD. This simplifying assumption limits, at large distances downwind, the conversion of NO to NO₂ to 90%, or other user input value. This value accounts for the fact that, with sunlight and/or in the presence of reactive hydrocarbons, there are reverse reactions, such as those due to NO₂ photolysis, which occur to break down the NO₂. These reverse reactions are not directly treated in these methods.

In both PVMRM and OLM, it is assumed that a good measurement of the ambient ozone concentration is available and is unaffected by any local NOx plumes. If the ozone monitor is in the NOx plume, then part of the ozone will have been used in the reaction with NO and the resulting ozone observation will be less than that in the ambient air outside of the plume. Therefore, it is best to observe the ozone concentration at a location upwind of the NOx sources.

As stated earlier, PVMRM was originally developed for ISC and the scientific rationale is well explained (Hanrahan, 1999a). However, because AERMOD has some different scientific approaches to plume modeling than ISC, modifications were made to PVMRM (U.S. EPA, 2004a), as summarized in the following.

Relative versus continuous dispersion coefficients. The dispersion models ISC and AERMOD are calculating hourly averaged continuous dispersion coefficients (σ_y and σ_z). ISC uses Pasquill–Gifford (P-G) stability classes to define the continuous dispersion coefficients. AERMOD uses Monin–Obukov similarity formulas to calculate σ_y and σ_z as a function of the friction velocity (u*), the convective scaling velocity (w*), the mixing depth (z_i), and the Monin–Obukhov length (L). However, as Hanrahan (1999a) points out, relative dispersion coefficients σ_yr and σ_zr should be used because the chemical reactions in PVMRM are assumed to be instantaneous. Fundamental texts (e.g., Pasquill, 1974) stress that at any downwind distance or time of travel, the continuous σ_y and σ_z must be equal to or greater than the relative σ_yr and σ_zr . Hanrahan (1999a) did not use a separate formula for relative dispersion coefficients. Instead, he parameterized the relative diffusion effect for ISC by assuming that σ_y and σ_z equaled σ_yr and σ_zr for P-G stability classes C, D, E, and F (slightly unstable, neutral, and stable conditions), and that for P-G stability classes A and B (unstable), σ_yr and σ_zr equaled the σ_y and σ_z for P-G stability class C. This system, which satisfies Pasquill's (1974) constraints, was modified for AERMOD, where σ_yr and σ_zr values were independently calculated using a relative dispersion theory developed by Weil (1998) for unstable conditions. But the unstable relative dispersion coefficient formula was used for stable conditions, also. Furthermore, there is no check to satisfy Pasquill's (1974) conditions and make sure that the PVMRM relative dispersion coefficients did not exceed the AERMOD continuous dispersion coefficients. A topic for future study is to develop a set of relative and continuous plume dispersion coefficients that satisfy Pasquill's (1974) conditions and follow the basic results in his plots (e.g., the ratio σ_zr/σ_z starts out less than 1 (about ¼ or ½) at x = 0, and gradually approaches unity at large distances).

Size of plume assumed to determine the amount of entrained ozone. It is assumed in PVMRM that the flux of moles of NOx in the plume (due to primary stack emissions) reacts instantaneously with the flux of moles of entrained ambient ozone. At any downwind distance, x, the plume is characterized by continuous and relative σ_y and σ_z. The flux of entrained ozone is assumed to be the product of the wind speed, the ambient ozone concentration, and the “instantaneous plume cross sectional area.” Note that in PVMRM, the ozone concentration is assumed constant across the plume segment at the value of the ambient air ozone concentration. However, the NOx concentration distribution has a Gaussian shape with standard deviation σ_y in the lateral dimension and σ_z in the vertical dimension. In Hanrahan's (1999a) original PVMRM description, the effective plume “radius” (semi-major or semi-minor axis of an ellipse) for calculating the plume cross-sectional area for estimating the ozone flux in the plume was assumed to be n_zσ_y in the horizontal and n_zσ_z in the vertical, with n_z assumed to equal 1.28. This is a reasonable choice for matching the Gaussian distribution of NOx to the constant distribution of O₃ in the plume flux calculations. But MACTEC (2004, 2005) modified PVMRM for use in AERMOD by increasing n_z to 4. This large increase may result in too much ozone being assumed to mix into the plume and react with the NO that was emitted from the stack, thus producing too much NO₂.

Initial downwash. Many sources of NOx emissions are vented to the atmosphere through relatively small stacks near buildings and are therefore subject to downwash. Hanrahan (1999a) accounted for the downwash or the initial plume spread in the original PVMRM through the assumption of an initial plume σ_zr of 15 m, thus effectively assuming a generic small stack and a medium-sized building. But for use in AERMOD, MACTEC (2004, 2005) assumed that the initial plume σ_zr was 5 m, or a factor of 3 less. The reasoning is that the new relative dispersion coefficients (Weil, 1998) used in AERMOD were expected to be smaller than the continuous plume dispersion coefficients used in ISC and assumed by Hanrahan (1999a) in the development of PVMRM. But as described earlier, this may not be the case. Clearly, in future improvements, it would be helpful to develop a method to estimate the initial plume σ_zr based on existing building downwash models, such as PRIME (Schulman, et. al., 2000) used in AERMOD.

Evaluation of PVMRM and OLM using the Wainwright Data

Three field data sets were used in the development of the PVMRM model as used in ISC and in AERMOD (Hanrahan, 1999b). It is desirable to evaluate PVMRM and OLM using an independent field data set. Ideally, the data should be from a research-grade comprehensive plume NO₂ field study. However, no new independent research-grade data set of this type could be found. Consequently, a search for an industrial site with adequate routine monitoring of NO₂, NOx, and ozone, along with on-site meteorological observations and a reasonable knowledge of the emissions, was conducted. Data were available from a small power plant site with short stacks in Wainwright, Alaska. There is an ambient monitoring station (operated by an offshore drilling company) nearby (approximately 500 m).

The left side of Figure 1 shows the area around the village of Wainwright, Alaska. The power plant, the ambient monitoring location, and the Wainwright Airport National Weather Service (NWS) Automated Surface Observing Station (ASOS) site are noted. The Arctic Ocean is to the west of Wainwright and there is an inlet to the southeast. As seen in the photographs on the right side of Figure 1, the power plant has five diesel generators, each vented through its own stack (three Caterpillar model 3508 engines with a rated design capacity [output] of 450 kW each and two Caterpillar model 3512 engines with a rated design capacity of 950 kW each).

Figure 1. (a) Village of Wainwright, Alaska. (b) Side and end views of power plant building, showing stack locations. The building is approximately 75 ft long by 48 ft wide by 30 ft 8 inches tall at the peak. Stacks 1, 2, and 3 have a stack top height of 30 ft 7 inches, and stacks 4 and 5 have a stack top height of 29 ft 7 inches.

The stack heights are about the same as the building height. The single monitoring station, located about 500 m to the east-southeast of the plant, observes NO₂, NO, NOx, and ozone concentrations, as well as meteorological variables such as wind speed, wind direction, temperature, and solar radiation. The NWS ASOS meteorological data were used for hours when wind speed and direction were not available from the ambient monitoring site.

An evaluation of the PVMRM and OLM modules in AERMOD (version 11103) was carried out using hourly averaged observations from an ambient monitoring station 500 m from the Wainwright power plant site. Model performance was evaluated for the AERMOD-predicted C(NOx), the PVMRM and OLM-predicted ratio of C(NO₂)/C(NOx), and the AERMOD/PVMRM and AERMOD/OLM predicted C(NO₂).

The results of the AERMOD C(NO₂) evaluations depend not only on the PVMRM or OLM modules (which only predict the ratio C(NO₂)/C(NOx)) but also on the many other modules in AERMOD (e.g., plume rise, downwash, lateral and vertical dispersion, low wind parameterizations, etc.). These other modules were not evaluated.

The model evaluation data set consisted of 12½ months of the hourly averaged observations at Wainwright. Since the plume is likely to impact the monitoring station only when the wind direction is blowing towards the sector containing the monitor, the evaluation took place only for those hours when the wind direction was in that 60° sector. Additionally, the evaluations could be carried out only when the required source input data and monitoring data were valid (e.g., nonmissing meteorological and observed concentration data, nonzero emissions data, etc.). This resulted in 594 hr of data for the 60° sector. Table 1 presents a summary of the ambient air quality measurements and relevant meteorological conditions for the 594 hr that were modeled. The monitored ozone concentrations ranged from 0 to 43 ppb, the monitored NOx concentrations ranged from 0 to 151 ppb, and the monitored NO₂ concentrations ranged from 0 to 32 ppb. The ambient monitoring station used a ThermoElectron model 42i NO-NO₂-NOx analyzer, which has a lower detectable limit of 0.4 ppb. A review of the capabilities of the monitoring equipment suggested that the smallest nonzero reported NO₂ concentration value, 1 ppb, in the Wainwright data set was above the detection threshold and therefore a valid measurement. The average wind speed modeled was 4.7 m/sec and the air temperatures ranged from –27.3 °F to 61.3 °F for the hours modeled. The relative humidity was between 40 and 100%.

Table 1. Summary of hourly averaged ambient pollutant and meteorological observations in Wainwright, Alaska, for hours used in evaluations

	Oxides of nitrogen (NOx) (μg/m^3)	Nitrogen dioxide (NO2) (μg/m^3)	Ozone (μg/m^3)	Wind speed (m/s)	Temperature (F)	Relative humidity (percent)
Number of hours	594	594	594	594	594	508
Max	283.9	60.2	84.4	9.6	61.3	100
Min	0.000	0.000	0.000	0.4	−27.3	40
Mean	22.6	7.5	43.2	4.7	20.4	82.7
Std dev	41.4	11.3	17.7	2.0	25.2	9.7

Note that since the emissions are in mass units, the AERMOD predictions of concentrations use mass units (e.g., μg/m³). Since the concentration observations are in ppb, when converting a threshold value we use the following general conversion relation for NO₂: 1 ppb = 1.88 μg/m³. For the conversion of hourly monitoring data, the exact number used in the conversion was dependent on the temperature and pressure measured for that hour.

Model inputs

The physical stack parameters for units 1 through 5 that were input to AERMOD are listed in the top portion of Table 2. It is important to note that no stack test data exist for these engines, and it is assumed that actual emissions are representative of Caterpillar engine performance specifications. The Wainwright hourly operator logs indicated which engines were running each hour and their output in kilowatts. Based on these actual operating conditions for each hour stack NOx mass emissions, exit volume flow rate and exit temperature were estimated by interpolation from Caterpillar (2008a, 2008b) maximum design capacity data. The ranges of each operational hourly source parameter are presented in the bottom portion of Table 2. There is no specific indication in the manufacturer's published information regarding a mean bias or an uncertainty range in the use of their data. It is difficult to quantify the uncertainty, as there are many contributing factors. Operation at colder temperatures (i.e. the Wainwright site) may reduce combustion temperature and decrease NOx emissions. Use of a lighter grade fuel (i.e. number 1 fuel oil instead of number 2 fuel oil) may also reduce the combustion temperature and by extension decrease the NOx emissions. Equipment condition plays a role as well; for example, older equipment may run less efficiently and have higher NOx emissions.

Table 2. Stack locations and parameters for the Wainwright power plant

Unit	UTM E(m)	UTM N (km)	Base elevation (m)	Stack height (m)	Stack diameter (m)
Unit 1	462247.5	7837899.0	11.5	9.32	0.23
Unit 2	462247.1	7837899.4	11.5	9.32	0.23
Unit 3	462246.5	7837899.9	11.5	9.32	0.23
Unit 4	462263.0	7837887.5	11.5	9.02	0.31
Unit 5	462262.2	7837888.0	11.5	9.02	0.31
Range of assumed hourly source parameters for the individual engines
Exhaust gas temperature (°F)		490–880
Exhaust gas flow rate (CFM)		1022–5070
NOx emission rate (lb/hr)		4–28

The initial C(NO₂)/C(NOx) ratio at the stack exit was assumed to be 0.20 based on the value recommended for diesel internal combustion engines (San Joaquin Valley Air Pollution Control District, 2010). As mentioned earlier, the C(NO₂)/C(NOx) ambient equilibrium ratio (i.e., the maximum allowed ratio) was set to 0.9. This is the U.S. EPA recommended default value and is based on the initial justification of this value by Hanrahan (1999a, p. 1329), who states: “PVMRM limits this conversion to 90% for annual calculations. Equilibrium is reached when the forward reaction (NO + O₃ → NO₂ + O₂) rate equals the reverse reaction (NO₂ + uv → NO + O) rate.” The “reverse reaction rate” is the result of photolysis.

The U.S. EPA Building Profile Input Program (BPIP-Prime) (Schulman et al., 2000) was run for all the stacks and the major buildings in the vicinity of the power plant to create the building parameter inputs to AERMOD. In addition to the power plant building (height = 9.35 m), the adjacent L-shaped shop building (height = 10.67 m) and two storage tanks (height = 7.32 m) west of the power plant building were included. Although the power plant roof is gently sloped, the model runs assumed a flat-topped building with a height equal to that of the roof crest, which follows U.S. EPA standard recommended procedure. For each stack, and depending on the wind direction, the power plant and the shop buildings were found to be the dominant structures for downwash.

The AERMOD preprocessor codes and tools that were used are AERMET, AERMINUTE, and AERMAP. The surface meteorological data were combined in AERMET with concurrent upper air observations from the closest upper air site (Barrow, Alaska), which were obtained through the National Climatic Data Center. The AERMINUTE tool has been used to process the NWS 1-min wind data that were incorporated into the AERMET processing as backup wind speed and direction data. The AERSURFACE tool is typically used to estimate the surface characteristics in the modeling domain that are used as inputs to AERMET. However, the data required for this tool are limited in Alaska and are unavailable for the Wainwright area. Therefore, the land use values were assigned manually. Between 218° and 37° (clockwise), “water” characteristics were used (see Figure 1a, which shows the orientation of the coastline). Between 37° and 218° (clockwise) the “desert shrubland” surface characteristics values were used (U.S. EPA, 2004b). AERMAP processes terrain elevation data and generates receptor information for input to AERMOD.

Results

Two sets of AERMOD runs have been used for primary analysis and evaluations with the Wainwright data set. The first employs the PVMRM option, and the second employs the OLM option. Results are presented in the following for C(NOx) predictions by AERMOD, for C(NO₂) predictions by AERMOD/PVMRM and AERMOD/OLM, and for C(NO₂)/C(NOx) ratio predictions by PVMRM and OLM.

Quantitative performance measures for NOx and NO₂ concentrations. C(NOx) is directly predicted by AERMOD independent of the PVMRM or OLM modules. NOx is treated as a tracer (i.e., no chemical reactions). Figure 2 is a Q-Q plot for C(NOx), where an average background concentration of 2 μg/m³ was added to the predicted NOx concentrations. For regulatory modeling purposes, predicting the maximum concentration is important regardless of whether the impact matches the observation in time and space. Therefore, a Q-Q plot presents the predicted and observed data as ranked from highest to lowest, unpaired. A Q-Q plot shows how well the model predicts the range of observations. The point with the single highest observed hourly NOx concentration is seen to be overpredicted by about 50%. But for the lower 98% of the range in Figure 2, the model underpredicts, with the amount of the underprediction increasing to almost an order of magnitude at smaller and smaller concentrations until the predictions are so small that the values become dominated by the background concentration.

Figure 2. Q-Q plot of ranked observed and predicted AERMOD NOx concentrations, for 594 hr. A background of 1 ppb (about 2 μg/m³) has been added to the predicted NOx in this plot.

Figure 3 presents a Q-Q plot of the unpaired ranked observed and predicted concentrations (including a background of 2 μg/m³) for NO₂ concentrations using AERMOD with PVMRM, OLM, and full conversion (i.e., NO₂ = NOx). The NO₂ concentration predictions are strongly influenced by the AERMOD NOx concentration predictions. The relative differences between OLM and PVMRM are consistent with the results reported in the following for the C(NO₂)/C(NOx) ratio.

Figure 3. Q-Q plot of ranked observed and predicted NO₂ concentrations by AERMOD/OLM and AERMOD/PVMRM. A background concentration of 1 ppb (about 2 μg/m³) was added to the predicted concentrations in this plot.

It is also seen in Figure 3 that the AERMOD/OLM model curve follows the “full conversion” curve at lower concentrations, when the ambient ozone concentration is sufficient to convert most of the C(NOx) predicted at the monitor location to C(NO₂). The AERMOD/OLM curve then deviates below the “full conversion” curve, approaching the AERMOD/PVMRM curve at higher concentrations, when the predicted NOx concentration at the monitor location is sufficiently high that OLM accounts for the fact that there is not enough ambient ozone to react with all of the C(NOx) at that location.

A similar shape of the AERMOD/PVMRM Q-Q curve for C(NO₂) was also found by the U.S. EPA (MACTEC, 2004, 2005) for the Empire Abo site in New Mexico, where the stack heights and monitor distances were similar to those at Wainwright.

Table 3 presents the top 10 concentration rankings paired by observed C(NO₂). This pairing was analyzed to see whether there was any correlation between the observed C(NO₂) and observed C(NOx), and whether this correlation is apparent in the modeling. No distinct correlation can be found in the top 10 paired observations and modeled results. The differences between the observed and predicted values for the 99 hr where the predicted and observed NOx concentration exceeded 10 ppb are separated into three ranges (i.e., underpredicts by more than 50%, predictions are within ±50%, and overpredicts by more than 50%.). The distribution of the percentage of the hours evaluated that fall in each range is presented in Table 4. The distribution of C(NO₂) predictions with AERMOD/PVMRM is found to be similar to the AERMOD C(NOx) distribution. The AERMOD/OLM C(NO₂) distribution does not mimic the AERMOD C(NOx) distribution, as it is weighted toward overprediction.

Table 3. Top 10 rankings (by observed NO₂) for observed and AERMOD-predicted hourly-averaged NOx and NO₂ concentration (paired), with a background of 2 μg/m³ added to the AERMOD predictions

	Observed	AERMOD		Observed		AERMOD/OLM		AERMOD/PVMRM
Rank	NOx (μg/m^3)	NOx (μg/m^3)	Percent difference	NO2 (μg/m^3)	Ozone (μg/m^3) for NO2 hour	NO2 (μg/m^3)	Percent difference	NO2 (μg/m^3)	Percent difference
1	289.94	98.36	−66%	65.69	28.36	83.66	27%	44.43	−32%
2	297.72	28.31	−90%	57.70	31.31	27.48	−52%	12.98	−77%
3	78.56	107.27	37%	56.12	32.79	85.44	52%	29.23	−48%
4	199.69	201.20	1%	54.46	49.73	117.37	116%	83.36	53%
5	244.64	94.22	−61%	53.08	38.53	84.71	60%	40.02	−25%
6	208.01	22.24	−89%	51.47	31.33	22.02	−57%	9.93	−81%
7	232.81	30.26	−87%	50.71	38.48	29.23	−42%	13.84	−73%
8	233.04	84.85	−64%	50.56	36.71	52.78	4%	28.89	−43%
9	152.64	47.54	−69%	47.97	40.96	44.78	−7%	21.34	−56%
10	190.06	21.14	−89%	45.80	40.62	21.03	−54%	10.25	−78%

Table 4. Distribution of observed and AERMOD-predicted hourly-averaged NOx and NO₂ concentration (paired), with a background of 2 μg/m³ added to the AERMOD predictions

Observed versus predicted NOx		Observed versus predicted (AERMOD/OLM) NO2		Observed versus predicted (AERMOD/PVMRM) NO2
<−50%	16%	<−50%	3%	<−50%	15%
−50 to 50%	55%	−50 to 50%	23%	−50–50%	51%
>50%	29%	>50%	74%	>50%	34%

Performance measures were calculated for AERMOD/PVMRM and AERMOD/OLM predictions of hourly NO₂ concentrations. The BOOT quantitative model evaluation software (Chang and Hanna, 2004, 2005) calculates a set of five standard performance measures: the fractional bias (FB), the geometric mean bias (MG), the normalized mean square error (NMSE), the geometric variance (VG), and the fraction of predictions within a factor of two of observations (FAC2). The 95% confidence limits of the performance measures can be calculated by BOOT. Furthermore, the software allowed calculation of whether the performance measures for one model are significantly different from those for another, and whether the mean bias measure (FB or MG) for a single model was significantly different from that for a perfect model (i.e., FB = 0.0 and MG = 1.0).

The performance measures used in the BOOT software are defined next, where C is the concentration. Subscripts p and o refer to predicted and observed, and the overbar represents an average over the set of hours being evaluated.

Fractional mean bias:

1

Normalized mean square error:

2

Geometric mean:

3

Geometric variance:

4

FAC2 is the fraction of data that satisfy

5

There were 381 hours when the observed C(NO₂) ≥ 1 ppb (about 2 μg/m³) and the predicted C(NO₂) was greater than or equal to the minimum threshold (0.000005 μg/m³, or about 0.000003 ppb) for AERMOD. The BOOT evaluations include comparisons paired in time and space. A background concentration of 2 μg/m³ (slightly larger than 1 ppb) is added to the AERMOD predictions before carrying out the performance evaluations. The results of the NO₂ concentration evaluations are listed in Table 5.

Table 5. Statistical performance measures for hourly averaged NO₂ concentrations (in μg/m³), for 381 hr when observed concentration of NO₂ ≥ 1 ppb (about 2 μg/m³) and predicted concentration of NO₂ > AERMOD minimum threshold (0.000005 μg/m³), with a background of 2 μg/m³ added to all modeled concentrations

	Observed	AERMOD/OLM	AERMOD/PVMRM
Highest NO2 (μg/m^3) (unpaired)	72.5	158.3	130.5
2^nd highest (unpaired)	65.7	142.2	112.0
Mean	12.9	21.5	12.7
Sigma	14.0	31.1	21.1
FB (perfect is 0.0)		−0.50	0.01 *
MG (perfect is 1.0)		0.94 **	1.35
NMSE (perfect is 0.0)		3.60	3.09
VG (perfect is 1.0)		6.48	4.92
FAC2 (perfect is 1.0)		0.402	0.470
Note. Number of hours with observed and both model predicted C's at background = 69, or 69/381 = 0.181 of the 381 hours.
*Not significantly different from 0.0 (for perfect model) at 95% confidence level.
**Not significantly different from 1.0 (for perfect model) at 95% confidence level.

Table 5 shows that the AERMOD/PVMRM mean predicted C(NO₂) is within 2% of the mean observed value (12.7 vs. 12.9 μg/m³). Thus, the fractional bias (FB) is quite small. However, focusing just on the unpaired highest (maximum) C(NO₂) in the table, the prediction by AERMOD/PVMRM is about 58 μg/m³ (or 80%) larger than the observed value. The normalized mean square error (NMSE) is about 3.1 for AERMOD/PVMRM. This implies that the root mean square error (scatter) is about (3.1)^1/2 = 1.7 times the mean concentration. This is typical of most model evaluation exercises (Chang and Hanna, 2004). Another measure of the scatter, the fraction of predictions within a factor of two of the observations (FAC2), is 0.47, again typical of other model evaluation exercises.

There is an overprediction of the highest C(NO₂) by a factor of 1.80 by AERMOD/PVMRM. There is a factor of 2.18 overprediction of the highest C(NO₂) by AERMOD/OLM. Thus the maximum unpaired AERMOD/OLM-predicted C(NO₂) in Table 5 is 21% larger than that for AERMOD/PVMRM. The mean (average) predicted NO₂ concentration is 69% larger for AERMOD/OLM than for AERMOD/PVMRM. FAC2 is 0.40 for AERMOD/OLM, slightly less than that for AERMOD/PVMRM. But since about 18% of the 381 hours have both observed and predicted NO₂ concentrations near the 2 μg/m³ background, those small values are included as being within a factor of 2 and help to increase the FAC2 value.

Table 5 also includes the results of BOOT's significance tests in the notes under the main table. For example, the fractional bias, FB, for AERMOD/PVMRM predictions of NO₂ concentration is not significantly different from 0.0, at the 95% confidence level. All differences in performance measures between AERMOD/PVMRM and AERMOD/OLM are significantly different from zero, probably because of the relatively large number of data pairs (hours), 381. The 95% confidence range is proportional to 1/N^1/2, where N is the number of data pairs.

Comparison of observed to predicted C(NO₂)/C(NOx) ratio. In an attempt to distinguish between the dispersion versus conversion influence on the results, the C(NO₂)/C(NOx) ratios were compared. Although the C(NO₂)/C(NOx) ratio is computed by the PVMRM and OLM modules directly, it is not standard output. Ratios were calculated from the hourly C(NO₂) and C(NOx) output from AERMOD. For OLM, this computation makes use of the AERMOD computation of the NOx concentration at the location of interest. Comparing these predicted and observed ratios is the major test of how well the PVMRM and OLM modules are performing. Table 6 contains a listing of some statistical characteristics of the observed values of the C(NO₂)/C(NOx) ratio. Separate columns contain the number of data points (hours) in the group and the maximum, minimum, mean, and standard deviation of the ratios in that group. Hours of data are constrained to observed and modeled NOx concentration exceeding 10 ppb (≈ 18.8 μg/m³). The choice of a limit of 10 ppb is to increase the likelihood that the monitored concentrations are influenced by the plume from the Wainwright power plant. The same threshold is used for both observed and predicted concentrations so that the comparison is balanced. There are 99 points (hours) that satisfy this criterion. The mean value of the observed C(NO₂)/C(NOx) ratio is 0.301 and the overall maximum is 0.714.

Table 6. Summary of hourly averaged observed NO₂/NOx concentration ratios and ozone concentrations at Wainwright, for hours when both observed NOx and modeled NO₂ concentrations are ≥10 ppb (≈ 18.8 μg/m³)

	Observed NO2/NOx ratio	Predicted NO2/NOx ratio (AERMOD/OLM)	Predicted NO2/NOx ratio (AERMOD/PVMRM)	Ozone values (μg/m^3)
Number of data points (hr)	99	99	99	99
Max	0.714	0.900	0.465	82.237
Min	0.091	0.234	0.230	2.313
Mean	0.301	0.757	0.352	42.842
Std dev	0.087	0.182	0.056	18.127
GeoMean	0.290	0.729	0.347	38.054
GeoStdDev	1.329	1.350	1.181	1.743

The maximum observed C(NO₂)/C(NOx) ratio (0.714) occurred on November 21 2009, hr 15, when the measured ozone was 32.8 μg/m³ and the sensible heat flux was –0.4 W/m². It is found that the maximum observed concentrations of NOx and NO₂ and the maximum values of the observed ratio, C(NO₂)/C(NOx), occur in the October through March period when the boundary layer at Wainwright is more stable. Note that in the winter when the sun does not rise at the latitudes of Wainwright, the boundary layer can remain stable all afternoon. The background ozone concentration is higher during that period, too, though providing more opportunity for the NO to react with ozone to form NO₂.

Scatter plots of paired predictions and observations of the C(NO₂)/C(NOx) ratio for PVMRM and for OLM are presented in Figures 4 and 5, respectively. A point (i.e., an hour) is included in these plots only if both the observed and predicted concentrations are greater than or equal to 10 ppb (about 18.8 μg/m³).

Figure 4. Scatter plot of PVMRM-predicted and observed ratio of NO₂ to NOx concentrations, for observed and predicted NOx concentration exceeding 10 ppb (about 18.8 μg/m³). There are 99 points (hours) with 30 unstable and 69 stable. Different colors are used for unstable and stable hours and different symbols for different ranges of observed NOx concentration.

Figure 5. Scatter plot of OLM-predicted and observed ratio of NO₂ to NOx concentrations, for observed and predicted NOx concentration exceeding 10 ppb (about 18.8 μg/m³). There are 99 points (hours) with 30 unstable and 69 stable. Different colors are used for unstable and stable hours and different symbols for different ranges of observed NOx concentration.

In Figure 4, for PVMRM-predictions and for observations, the C(NO₂)/C(NOx) ratios are roughly evenly distributed with 72% of the points between 0.2 and 0.4. Note that the initial in-stack C(NO₂)/C(NOx) ratio has been assumed to be 0.20. Therefore, most of the time, there is minimal (less than 20%) conversion of NO to NO₂ in the Wainwright plume before it reaches the single monitor location. The distribution of points leads to the conclusion that PVMRM is slightly overpredicting the C(NO₂)/C(NOx) ratio (by about 0.1). PVMRM has a slight tendency to overpredict the smaller values of observed C(NO₂)/C(NOx) ratios and to underpredict the larger values, even though the model's mean bias is not large.

It was hoped that by differentiating the plotted data for unstable and stable hours and for four ranges of observed NOx concentration, differences could be seen in the scatter plot and reasons found for mean biases and scatter. But there are no obvious differences among these subsets of data in Figure 4. As mentioned during the discussion of Table 6, the largest observed C(NO₂)/C(NOx) ratios occur during stable conditions. These largest ratios were actually occurring during the day in the winter, when the sun is very low or below the horizon.

In Figure 5, for OLM, the predicted C(NO₂)/C(NOx) ratio is 0.9 about two-thirds of the time, and there is nearly always a significant overprediction of the C(NO₂)/C(NOx) ratio. The value of 0.9 is the maximum ratio allowed by the model and is indicating that OLM converts a maximum amount of NO to NO₂.

Sensitivity runs

The first sensitivity run was carried out using a tiered assumption for the sloped roof of the Wainwright Power Plant. The AERMOD-predicted maximum C(NOx), in the downwashed plume near the building, were a factor of 2 lower for the tiered roof than for the flat roof assumed in the base run. The factor of 2 difference illustrates the sensitivity that the downwash algorithms in AERMOD can have to model inputs, especially for stacks whose height is close to the building height.

A second AERMOD sensitivity run was made using the PVMRM algorithms, but using the Hanrahan (1999a) assumed value of 1.282 for n_z instead of the AERMOD/PVMRM value of 4. The n_z value of 4 used in the AERMOD code is coupled with assumptions of A = 1.0 (where A corresponds to the fraction of the area under the normal curve for the chosen n_z), and of a minimum σ_z value of 5 m. The AERMOD code was modified to reflect Hanrahan's (1999a) original values as described in his PVMRM model formulation paper (i.e., n_z = 1.282 with A = 0.8 and minimum σ_z = 15 m). The sensitivity runs with the Hanrahan original assumptions resulted in only minor differences in the predicted impacts for the Wainwright scenario (Hendrick et al., 2012).

A third sensitivity run was carried out where PVMRM and OLM were run with the ambient observed ozone concentration replaced by the sum of the observed ozone concentration and the observed NO₂ concentration at the monitor. The reasoning is that when the plume impacts the monitor, the observed ozone concentration is likely to be less than the actual ambient background ozone concentration because some of the ambient background ozone has been used to convert NO to NO₂ in the plume. This change in the input background concentration of ozone was found to have an insignificant effect on the predictions of the maximum overall NO₂ concentration for both AERMOD/PVMRM and AERMOD/OLM. However, the predictions of the mean C(NO₂) over the hours modeled showed a small increase (7.0% for AERMOD/PVMRM and 5.7% for AERMOD/OLM). The mean C(NO₂)/C(NOx) ratio for AERMOD/PVMRM increased by 5% and for AERMOD/OLM by 1.1%. This sensitivity run resulted in slightly more NO₂ being produced because more ozone is entrained into the plume.

Conclusion

The technical code review identified areas for future improvements in the implementation of PVMRM in AERMOD. An appropriate relative dispersion formula must be added to properly handle stable and neutral atmospheric conditions, and it should be confirmed that all dispersion coefficients satisfy Pasquill's conditions. It would be desirable to revert back to Hanrahan's original parameterization of the number of standard deviations from the centerline used to define the plume volume (n_z). A method to adjust the initial plume sigma based on existing building downwash algorithms should be implemented.

The implementation of OLM in AERMOD leads to overpredictions of conversion to NO₂. The comparison of the NOx predicted concentration to the ambient ozone concentration is made at each receptor, rather than at the maximum impact location (as specified in Cole and Summerhays, 1979). Lower predicted NOx concentrations will lead to higher NO₂/NOx ratios. Further investigation into the OLM implementation to assure that it closely follows the formulation of Cole and Summerhays is warranted.

The following general conclusions may be drawn from the preceding model evaluation results using the Wainwright data set:

1.	The OLM-predicted hourly averaged C(NO2)/C(NOx) ratios are nearly all larger than the observed ratios, with many OLM-predicted ratios at the maximum permitted value of 0.9. PVMRM has a slight tendency to overpredict the smaller values of observed C(NO2)/C(NOx) ratios and to underpredict the larger values, even though the model's mean bias is not large.
2.	It is found that the hourly NO2 concentrations predicted either by AERMOD/OLM or with AERMOD/PVMRM paired in time do not show any distinct correlation with observations. The model cannot match the highest observed values or the lowest observed values, or any specific hour concentration with any certainty paired in time and space. This is not necessarily due to the NO to NO2 conversion algorithms, but to the AERMOD model's prediction of NOx concentrations.
3.	Both AERMOD/PVMRM and AERMOD/OLM conservatively overpredict the high end hourly-averaged NO2 concentrations (irrespective of time) by about a factor of 2 (OLM by more), but this may be caused by AERMOD's overprediction of the high-end NOx concentrations. Although not a measure of true accuracy in the model algorithms, some conservatism is desired in regulatory modeling to protect human health and property, but overpredicting by more than a factor of 2 is overly conservative and is not considered a good simulation of reality.

This evaluation using the Wainwright data set is useful to supplement the limited number of data sets used by U.S. EPA to date to evaluate the PVMRM and OLM options in AERMOD for predicting 1-hr NO₂. It is recommended that further evaluations with additional data sets continue to be performed.

Acknowledgment

The authors express their gratitude to the American Petroleum Institute for sponsoring this study. We also thank the offshore drilling company and their consultant who provided the ambient monitoring data for the model evaluation study. The authors also thank the North Slope Borough Utilities: Power & Light Division for sharing the source information for the Wainwright Power Plant. The authors appreciate the discussions with Brian Lamb concerning ambient monitoring devices, and with Roger Brode of U.S. EPA/OAQPS regarding the AERMOD, PVMRM, and OLM codes and the issues regarding the model technical descriptions.