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An extended approach to calculate the ozone relative

response factors used in the attainment demonstration

for the National Ambient Air Quality Standards

Sarika Kulkarnia, Ajith P. Kaduwelaab, Jeremy C. Aviseac, John A. DaMassaa & Daniel Chaua

a

 Air Quality Planning and Science Division, Air Resources Board, California Environmental

Protection Agency, Sacramento, CA, USA

b

 Air Quality Research Center, University of California, Davis, CA, USA

c

 Department of Civil and Environmental Engineering, Washington State University, Pullman,

WA, USA

Published online: 16 Sep 2014.

To cite this article: Sarika Kulkarni, Ajith P. Kaduwela, Jeremy C. Avise, John A. DaMassa & Daniel Chau (2014) An

extended approach to calculate the ozone relative response factors used in the attainment demonstration for the

National Ambient Air Quality Standards, Journal of the Air & Waste Management Association, 64:10, 1204-1213, DOI:

10.1080/10962247.2014.936984

To link to this article: http://dx.doi.org/10.1080/10962247.2014.936984

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TECHNICAL PAPER

An extended approach to calculate the ozone relative response factors

used in the attainment demonstration for the National Ambient Air

Quality Standards

Sarika Kulkarni,1,⁄ Ajith P. Kaduwela,1,2Jeremy C. Avise,1,3John A. DaMassa,1

and Daniel Chau1

1

Air Quality Planning and Science Division, Air Resources Board, California Environmental Protection Agency, Sacramento, CA, USA

2

Air Quality Research Center, University of California, Davis, CA, USA

3Department of Civil and Environmental Engineering, Washington State University, Pullman, WA, USA

⁄Please address correspondence to: Sarika Kulkarni, Air Quality Planning and Science Division, Air Resources Board, California Environmental

Protection Agency, 1001 I Street, Sacramento, CA 95814, USA; e-mail: skulkarn@arb.ca.gov

With the promulgation of the National Ambient Air Quality Standards (NAAQS or standard) for 8-hr ozone (O3), the

U.S. Environmental Protection Agency (EPA) issued modeling guidance that advocated the use of results from photochemical air

quality models in a relative sense. In doing so, the EPA provided guidance on how to calculate relative response factors (RRFs) that

can project current design value (DV) mixing ratios into the future for the purpose of determining the attainment status with respect

to the O3 standard. The RRFs recommended by the EPA represent the average response of the photochemical model over a broad

range of O3 mixing ratios above a specified cutoff threshold. However, it is known that O3 response to emission reductions of limiting

precursors (i.e., NOx and/or VOC) is greater on days with higher O3 mixing ratios compared to days with lower mixing ratios. In this

study, we present a segmented RRF concept termed band-RRF, which takes into account the different model responses at different O3

mixing ratios. The new band-RRF concept is demonstrated in the San Joaquin Valley (SJV) region of California for the 1-hr and 8-hr

O3 standards. The 1-hr O3 analysis is relevant to work done in support of the SJV O3 State Implementation Plan (SIP) submitted to

the EPA in 2013. The 8-hr example for the future year of 2019 is presented for illustrative purposes only. Further work will be

conducted with attainment deadline of 2032 as part of upcoming SIPs for the 0.075 parts per million (ppm) 8-hr O3 standard. The

applicability of the band-RRF concept to the particulate matter (PM2.5) standards is also discussed.

Implications: Results of photochemical models are used in regulatory applications in a relative sense using relative response

factors (RRFs), which represent the impacts of emissions reductions over a wide range of ozone (O3

) values. It is possible to extend

the concept of RRFs to account for the fact that higher O3 mixing ratios (both 1-hr and 8-hr) respond more to emissions controls of

limiting precursors than do lower O3 mixing ratios. We demonstrate this extended concept, termed band-RRF, for the 1-hr and 8-hr

O3 National Ambient Air Quality Standard (NAAQS or standard) in the San Joaquin Valley of California. This extension can also be

made applicable to the 24-hr PM2.5 and annual PM2.5 standards.

Introduction

In 1979, the U.S. Environmental Protection Agency (EPA)

promulgated a National Ambient Air Quality Standard (NAAQS

or standard) of 0.12 ppm for 1-hr ozone (O3). Here, we also use

the alternate form of 124 ppb for this standard. Although the EPA

revoked the 1-hr O3 standard and has since adopted a more

health-protective 8-hr O3 standard of 0.075 ppm (or 75 ppb),

subsequent litigation led to the reinstatement of portions of the

implementation requirements under the revoked 1-hr O3 standard. Because the San Joaquin Valley (SJV) region of California

did not attain the 1-hr O3 standard by the attainment deadline of

2010, a new State Implementation Plan (SIP) was prepared by

the California Air Resources Board (CARB) and the San Joaquin

Valley Air Pollution Control District (SJVAPCD), which was

submitted to the EPA in 2013. The modeling protocol that

describes the modeling process for this new SIP can be found

elsewhere (CARB, 2013).

EPA advocated the use of modeling results in a relative sense,

using relative response factors (RRFs), in the attainment demonstration of a given standard. It is important to note that the current

RRF concept was developed by the EPA for the 8-hr O3 and

PM2.5 standards (EPA, 2007) and there is no comparable concept

for the 1-hr O3 standard. Described here is an improved procedure that can be used to develop RRFs for both 1-hr and 8-hr O3

.

We describe the development and application of this procedure

in the context of modeling conducted in support of the 2013 SJV

1-hr O3 SIP. We then describe its applicability to 8-hr O3. It is

1204

Journal of the Air & Waste Management Association, 64(10):1204–1213, 2014. Copyright © 2014 A&WMA. ISSN: 1096-2247 print

DOI: 10.1080/10962247.2014.936984 Submitted October 31, 2013; final version submitted May 29, 2014; accepted June 16, 2014.

Downloaded by [Ajith P. Kaduwela] at 14:39 19 September 2014 
important to note that this application for 8-hr O3 (with a future

year of 2019) is not associated with SIPs for the 75 ppb standard

since SIP work is still under development with an attainment

date in 2032. The applicability of this method to the 24-hr PM2.5

and annual PM2.5 standards is discussed in later sections. More

detailed descriptions of the development of RRFs for PM2.5

standards will be presented in the future after we conduct photochemical modeling to support the preparation of those SIPs.

A rigorous demonstration of attainment with respect to the

standard for O3 involves the projection of a reference year design

value (DV) mixing ratio into the future (EPA, 2007). The DV for

the 1-hr O3 standard is the fourth highest 1-hr O3 mixing ratio

measured at a given monitor during 3 consecutive calendar

years, while the 8-hr O3 DV is the average of the annual fourth

highest 8-hr O3 mixing ratio over a consecutive 3-year period.

This projection of this DV to the future is generally based on

three grid-based photochemical air quality simulations. The first

simulation, known as the base year or model performance simulation, involves simulating the measured O3 mixing ratios for a

recent year to evaluate the performance of the modeling system.

The emissions inventory used for the base year simulation is dayspecific to the extent possible for evaluating model performance.

The second simulation, known as the reference year simulation,

is often conducted with less day specificity in the inventory.

The EPA modeling guidance (EPA, 2007) defines “base case”

as the base year used for model performance evaluation, and

“baseline” as the reference year used in the DV calculation and

the starting point for emissions projections. The base and the

reference years need not be the same, but they can be. The third

simulation involves repeating the reference year simulation for a

future year, where the meteorology is held constant but the

inventory has been forecasted to the future year. In the work

presented here, both the base and reference years are 2007 and

the future year is 2019. Here, we also used the same inventory for

both the base and reference years since the day specificities in the

5-month base year and reference year inventories were very

comparable. Thus, for the rest of this document, the terms base

year and reference year are interchangeable. However, we keep

both terms to acknowledge the fact that they can represent

different years/inventories in other applications.

As mentioned earlier, the EPA modeling guidance (EPA,

2007) for the 8-hr O3 standard recommends using photochemical air quality models in a relative sense to project the reference

year DV into the future for a given monitoring location. This is

accomplished by multiplying the reference year DV by an RRF

specific to that location (EPA, 2007). In the calculation of the

RRF, first the reference year model predictions above a predetermined threshold are averaged for a given monitor. Then the

future predicted values for the same calendar days included in

the reference year average are used to form the future year

average. The ratio of the future year average to the reference

year average is the RRF. A numerical example of this procedure

is presented in the EPA modeling guidance (EPA, 2007).

Since all days in the reference year above a predetermined O3

threshold level are used to calculate a single RRF for a given

monitor, this RRF is representative of a broad range of O3 values

in the reference and future years. However, as our previous

modeling experience shows and the EPA modeling guidance

(EPA, 2007) demonstrates, in general, the higher the referenceyear O3 mixing ratios, the larger is the response to emissions

reductions of limiting precursors. A recent EPA memorandum

(EPA, 2012) also documents the enhanced response to emissions

reductions at higher O3 values.

The phenomenon of enhanced response of higher O3 mixing

ratios to emissions controls is also supported by observed trends

in 1-hr and 8-hr daily maximum O3. As a part of the health-based

review process of the State Ambient Air Quality Standards for

O3, the California Air Resources Board (CARB) reported the

historic (1980–2002) trends in annual percentiles of daily maximum 1-hr and 8-hr O3

in the South Coast air basin (CARB,

2005). The 40th to 90th percentiles in increments of 10 and the

maximum O3 mixing ratios were calculated as 3-year averages

from the annual distribution of the basin’s daily maximum. The

CARB (2005) report (see Figure 10-1 in that work) showed a

consistent downward trend in the observed 1-hr O3 for the

maximum and different percentile levels, but the highest values

showed the largest decrease (e.g., the relative percent reductions

between the first [1981] and last [2001] year of the time series

[i.e., Figure 10-1 of CARB, 2005] in annual daily maximum 1-hr

O3

, and the 90th, 80th, 70th, 60th, 50th, and 40th percentiles of

1-hr O3 mixing ratios are ~57, 54, 50, 46, 41, 34, and 29%

respectively). Similar behavior is also seen in observed 8-hr O3

trends (Figure 10-2 of CARB, 2005).

The EPA modeling guidance (EPA, 2007) suggests that this

enhanced response of higher O3 values to emission reductions

may be suggestive of O3 being more “controllable” at those

levels. In other words, the contribution of local and regional

sources to formation of O3 is relatively larger on days with

elevated O3 levels, when compared to the low-/medium-range

O3 values. In addition, high O3 days can also occur due to

stagnation caused by high pressure systems. The higher temperatures can result in increased chemical reaction rates and

enhanced emissions of highly reactive biogenic volatile organic

compounds. This could lead to enhanced ozone production

efficiency (OPE) (Zhou et al., 2014) on high O3 days. It should

be possible to further clarify the underlying causes for this trend

with retrospective studies linking the enforced emission control

strategies with the observed values.

The current form of the RRF concept does not allow for this

enhanced response to emissions controls at the high end of the

simulated/measured O3 distribution and uses a single RRF value

to represent a broad range of O3 values in the reference and

future years. For this reason, we use the term “single-RRF” when

we refer to the current form. Due to its representation of a broad

range of O3 values, single-RRFs indeed represent an average

response and could be too conservative in some cases. To better

represent the enhanced response of higher O3 mixing ratios to

emissions controls, we have developed a segmented RRF

method termed “band-RRF,” which is a logical extension to the

single-RRF method. The details of this method are provided in

Kulkarni et al. / Journal of the Air & Waste Management Association 64 (2014) 1204–1213 1205

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the following sections for application to both the 1-hr and 8-hr

O3 NAAQS in the SJV region of California. We discuss other

advantages of this new method in later sections.

The Modeling System

We first describe the modeling system that produced the

simulated O3 mixing ratios used to calculate the RRFs. The

Weather Research and Forecasting (WRF; Skamarock et al.,

2005) model was used to generate the meteorological fields for

the 5-month simulation period of May through September 2007

(CARB, 2013). The initial and boundary conditions (IC/BCs) for

WRF were prepared based on National Centers for

Environmental Prediction (NCEP) Eta 212 grid (40 km) model

output that is archived at the National Center for Atmospheric

Research (NCAR). Initial conditions for WRF were updated at

6-hr intervals for the 36-, 12-, and 4-km grids. In addition,

surface and upper air synoptic observations obtained from

NCEP were also used to further refine the IC/BCs. The WRF

model was nudged toward observed meteorological conditions

by using the analysis nudging option of the Four Dimensional

Data Assimilation (FDDA) for the 36-km grid only. The physics

options used for WRF include the WSM 6-class graupel microphysics scheme, the Monin–Obukhov surface layer scheme, the

unified Noah land-surface model, the YSU planetary boundary

layer scheme, the Kain–Fritsch (new Eta) cumulus scheme for

the 36- and 12-km domains, the RRTM long-wave radiation

scheme, and the Dudhia short-wave radiation scheme. There

were 31 vertical model layers telescoping from the surface to

50 mb.

Two sets of emissions inventories were prepared by CARB in

consultation with the local air districts. The reference year inventory was prepared with emissions developed specifically for each

day of the simulation period for sources such as motor vehicles,

biogenics, wildfires, prescribed fires, agricultural burning, road

dust, and ocean-going vessels. Since the same meteorology was

used for both the reference year and the future year, the same dayspecificity was included in the 2019 reference inventory as well.

For model performance evaluation, a fully day-specific base year

inventory is the most appropriate. However, in practice, it is very

difficult to make an inventory fully day-specific for a long simulation period. Therefore, the only difference between the reference

and base year inventories was the inclusion of day-specific agricultural burning and wildfires in the base year inventory. The

reference year inventory had a more average representation of

the agricultural burning and wildfires.

Since the difference between the two inventories was not

significant, the same 2007 base year inventory was used as the

2007 reference year inventory. An emission forecast was developed for the future year of 2019. The anthropogenic emissions

forecasts for 2019 were based on forecasted economic conditions, population growth, and implemented/planned emission

controls. Biogenic emissions were generated using the

MEGAN model version 2.04 with California-specific emission

factor and plant functional type data (CARB, 2013). Biogenic

emissions were kept constant between 2007 and 2019 because

future inputs such as land use/land cover are highly uncertain.

Detailed descriptions of the emission inventory preparation

including temporal and spatial distributions as well as chemical

speciation can be found elsewhere (CARB, 2013). The future

2019 total anthropogenic emissions of NOx and VOC were

approximately 55% and 20% lower when compared to the corresponding base year 2007 totals.

The CMAQ model version 4.7.1 (Foley et al., 2010) was used

to simulate O3 formation in the SJV region of California. The

following options were used: the SAPRC99 gas-phase chemical

mechanism (Carter, 2000) with the EBI solver, the aero5 aerosol

module, the unmodified piecewise parabolic method for horizontal and vertical advection, and the eddy diffusivity algorithm

for vertical diffusion. Figure 1 shows the CMAQ modeling

domains that were used in this work. The larger domain covering

all of California has a grid size of 12 km and was used to provide

boundary conditions for the smaller domain, which covers central California with a finer grid size of 4 km. The 31 vertical

layers in the WRF simulation were mapped onto 15 vertical

layers in CMAQ that extended telescopically from the surface

to 50 mb, with the majority of layers falling within the planetary

boundary layer. The boundary conditions for the larger 12-km

domain were extracted from the global atmospheric chemical

transport model for ozone and related chemical tracers

(MOZART; Emmons et al., 2010; CARB, 2013).

To assess the model prediction skills in simulating O3 values, a

model performance analysis was carried out for the 2007 base

case by including simulated O3 values above a 60-ppb threshold

and using statistical metrics recommended by the EPA for 1-hr O3

(EPA, 1991). These metrics are peak (unpaired) prediction accuracy (15–20%), overall bias (5–15%), and gross error statistics

(30–35%). The acceptable ranges indicated in the parentheses are

approximate and were recommended by Tesche at al. (1990).

Detailed model performance statistics are presented in the

Supplemental Materials. In general, the fraction of days from the

model that meets the performance criteria for 1-hr O3 is highest in

the lower elevation regions of the central (~58%) and southern

(~56%) SJV. In the northern region and above 3000 ft in the SJV,

the number of days meeting model performance criteria was

generally lower (~13 and 36%, respectively) due to the lower O3

mixing ratios and fewer monitoring stations in those areas. The 8-

hr O3 model performance statistics show similar behavior and are

consistent with the corresponding1-hr O3 statistics (Table S1 in

Supplemental Materials).

Calculation of the Reference Year 1-Hour

O3 DVs

A key quantity that needs to be calculated a priori based on

observations is the reference year 1-hr O3 DV. This DV is then

projected to a future year using RRFs. The form of the 1-hr O3

standard has evolved over the years,and the current form requires

that the expected number of days per calendar year with daily

maximum 1-hr O3 mixing ratio exceeding 124 ppb must be less

than or equal to 1 per year over a 3-year period. If every day is

monitored at a given location, then during a 3-year period the

fourth highest daily maximum 1-hr O3 mixing ratio becomes the

DV for that location. If there are missing data in the observational record, then one can use the method advocated by Curran

1206 Kulkarni et al. / Journal of the Air & Waste Management Association 64 (2014) 1204–1213

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and Cox (1979), which assumes the same exceedance rate of the

measured days for the unmeasured days.

In California, all major locations are monitored daily.

Therefore, the fourth highest daily maximum 1-hr O3 mixing

ratio during a 3-year period is a very good representation of the

DV. This methodology also allows for data incompleteness (i.e.,

missing data in the observational record) by allowing the data

analyst to select the third (or even the second) highest daily

maximum 1-hr O3 mixing ratio as the DV if the data completeness criteria are not met. For these reasons, we use that form of

the DV in this study. The 2007 1-hr O3 DVs, calculated over the

period of 2005–2007, for representative sites (see Figure 1 for

location of sites) in the SJV region are shown in the second

column of Table 1. The 2007 1-hr O3 DVs for the SJV monitoring sites exhibit a large variability with the highest and lowest

values seen at the Edison (135 ppb) and Madera (95 ppb and not

shown in Table 1) sites respectively.

Methodology to Calculate the RRFs

The calculation of single-RRFs for the 8-hr O3 standard is

described in the EPA modeling guidance (EPA, 2007), and is

summarized briefly here. First, the 8-hr daily maximum O3

mixing ratios for both reference and future years are computed

using the simulated 1-hr O3 mixing ratios. Then, for each day

and each monitor, the highest “nearby” (i.e., in a grid cell within

a 15-km radius of the monitor) 8-hr daily maximum O3 mixing

ratio is selected from the reference and future year simulations.

The mean 8-hr daily maximum O3 mixing ratios from future and

reference year simulations are computed for each nearby grid

cell of a monitoring site.

A subset of reference year days with simulated 8-hr daily

maximum O3 above a predetermined threshold are selected

next and the mixing ratios are averaged separately for the reference and future year for those days. This threshold is monitor

specific and is determined using the following procedure outlined in the EPA modeling guidance (EPA, 2007). For the previous 84-ppb 8-hr O3 standard, the starting threshold is set to 84

ppb and an RRF is calculated if there are at least 10 simulated

days above the threshold (i.e., 84 ppb). However, if the number

of simulated days above the threshold is less than 10, this threshold is lowered to 70 ppb (i.e., the absolute minimum threshold)

until 10 days become available. In the event of having less than

10 days above 70 ppb, all the available days above 70 ppb are

used for calculating the RRF provided there are at least 5 days. If

a monitor does not have at least a minimum of 5 days above 70

ppb, then an RRF is not calculated for that monitor (EPA, 2007).

The single-RRF is then computed as the ratio of the average

future year and reference year 8-hr daily maximum O3 mixing

ratios. The EPA modeling guidance (EPA, 2007) provides a

numerical example on pages 27–28.

The EPA modeling guidance (EPA, 2007) requires that the

model performance criteria be met to evaluate prediction skills of

the base year simulation and to build confidence in projecting

the future values. However, the model performance statistics are

not explicitly considered in the 8-hr O3 single-RRF calculations,

which are typically based on reference and future year simulations (Hogrefe et al., 2008). In the current application, we

Figure 1. The ozone monitoring stations in the San Joaquin Valley (SJV) region of California. SJVAPCD stands for the San Joaquin Valley Air Pollution Control

District. The outer box of the left panel is the California statewide 12-km modeling domain. The gray shaded and black line contours denote the gradients in topography

(km), while the thick black lines show the boundaries of the SJV subregions used in model performance analysis (see Supplemental Materials for further details on

model performance). Simulations for this study were conducted using the inner modeling domain at 4 km resolution that covers the entire Central Valley of California.

The insert on the right shows a zoomed-in view of the site locations that were used for model performance evaluation. Table 1 lists only a subset of these sites (the 10

highest 1-hr and 8-hr O3 DVs for the year 2007).

Kulkarni et al. / Journal of the Air & Waste Management Association 64 (2014) 1204–1213 1207

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followed the RRF procedure outlined in the EPA modeling

guidance (EPA, 2007) but have imposed an additional constraint

that only the reference year simulated values that are within

20% of the corresponding observed values be used in the

single-RRF calculation. This criterion attempts to exclude simulated data for some days that have less than ideal model performance and also impacts the band-RRF calculations as discussed

in later sections.

1-Hour O3 RRF calculation methodology

Single-RRF. It is important to note that there is no RRF concept for 1-hr O3 since the RRF concept was developed by the

EPA for the 8-hr O3 and PM2.5 standards (EPA, 2007). In this

study, the calculation of single-RRFs for the 1-hr O3 standard

follows the procedure described in the EPA modeling guidance

(EPA, 2007) to calculate single-RRFs for the 8-hr O3 standard

with one notable exception of including the reference year

simulated values that are within 20% of the corresponding

observed values.

The choice of the absolute minimum threshold for the 1-hr O3

daily maximum value, which is used to select modeled reference

year days as input to the RRF calculation, is subject to scientific

judgment. The EPA modeling guidance (EPA, 2007) recommends using 70 ppb as the absolute minimum threshold for the

84 ppb 8-hr O3 standard. An equivalent minimum threshold for

the 124 ppb1-hr O3 standard would be approximately 100 ppb.

However, it must be noted that the 1-hr O3 daily maximum

values represent real values in the atmosphere and exhibit relatively larger variability than the 8-hr O3 daily maximum values

(which are average values). Thus, in the 1-hr O3 RRF calculations, it may not be appropriate to use the equivalent minimum

threshold for 1-hr O3 daily maximum that is calculated based on

the minimum threshold used for the 8-hr O3 daily maximum

values.

To evaluate the impact of the choice of minimum threshold

value on the 1-hr O3 single-RRF values, a series of RRF calculations was performed using fixed minimum thresholds ranging

from 60 ppb to 100 ppb in 10-ppb increments. The two factors

considered in selecting a suitable threshold were (1) encompassing the broad range of 2007 DVs exhibited by the SJV monitoring sites and (2) availability of a minimum number of 5 days to

form a stable single-RRF (EPA, 2007). Based on the criteria

already described, we chose 90 ppb as the minimum threshold

for 1-hr O3 single-RRF calculations. This choice depends on the

nature of the O3 problem in a given geographical location and

should be reevaluated accordingly for applications outside of the

SJV region of California.

We applied the procedure outlined in the EPA modeling guidance (EPA, 2007) to determine the number of days and the

minimum threshold and subsequently calculate the single-RRF

at each monitor in the SJV region for the 124 ppb 1-hr O3

standard. The reference year (i.e., 2007) 1-hr O3 DVs were then

multiplied by the 1-hr O3 single-RRFs to determine the future 1-hr

O3 DVs, which are shown in the third column of Table 1.

Band-RRF. We now describe the procedure to calculate 1-hr

Table 1.

band-RRFs. We begin with the same data set used in the

The 2007 and 2019 O3 DVs for representative monitoring sites in the San Joaquin Valley of California; listed here are the top 10 2007 DV sites for both 1-hr and 8-hr O3

1-hr O3 8-hr O3

Monitoring station

DV (ppb)

ambient

(2005

–2007)

a

DV (ppb)

single

(2007

–2019)

b

DV (ppb)

band

(2007

–2019)

b Monitoring station

DV (ppb)

ambient

(2005

–2007)

a

DV (ppb)

single

(2007

–2019)

b

DV (ppb)

band

(2007

–2019)

b

Edison 135 111.9 108.1 Arvin 107 88.8 85.5Arvin 131 105.5 103.1 Sequoia and King Canyon 103 86.2 84.7Fresno 1st street 130 105.3 98.1 Edison 99 83.2 81.0

Clovis 125 100.9 96.1 Fresno 1st street 98 81.6 78.3

Fresno Sierra Skypark 124 100.9 92.1 Bakersfield 97 81.3 79.0

Parlier 121 95.4 92.6 Fresno Sierra Skypark 95 79.1 76.1

Sequoia and King

Canyon

118 98.7 94.8 Sequoia National Park 95 81.0 81.6

Bakersfield 117 96.8 94.5 Visalia N. Church Street 95 80.4 78.7

Sequoia National Park 113 94.9 92.1 Clovis 93 77.1 75.0Visalia N. Church Street 112 88.6 87.8 Parlier 93 76.7 74.3Oildale 112 93.3 92.0 Oildale 91 74.5 73.1

Notes:

aThe three year period included in the ambient design value calculations.

bThe base year 2007 and future year 2019 used for air quality model simulations used in this study.

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calculation of single-RRFs that includes reference year simulated 1-hr O3 mixing ratios falling within 20% of the corresponding measured values. We then bin the reference year data

into regular 5-ppb bands from 60 to 120 ppb. The selection of the

width of the bands (5 ppb in this case) is subject to scientific

judgment. If the bands are too wide, there will not be enough

points for performing a linear regression to represent missing

bands, which is described in the later sections. If the bands are

too narrow, then the RRFs within each band will be based on

very few days. We found 5 ppb to be a reasonable balance

between these two extremes in this application.

It should be noted that in each bin the lower limit values are

included but not the upper limit (e.g., bin 60–65 ppb includes

values greater than or equal to 60 but less than 65). Even though

it is important to spread high values (considering their enhanced

response to emission reductions) into more bands, all values

greater than or equal to 120 ppb were segregated into a single

band due to the small number of simulated high values 120

ppb. Within each band, an RRF was calculated as a ratio of

average future year mixing ratios to average reference year mixing ratios.

The calculation of band-RRFs is illustrated in Figure 2. The

top left panel of Figure 2 shows the daily maximum 1-hr O3 timeseries plot for the Edison monitoring site located in the southern

SJV region (see Figure 1). Edison had the highest reference year

(i.e., 2007) DVof 135 ppb (based on measurements made during

2005–2007) in the SJV region. The agreement between the

observations (solid black circles) and the simulation was satisfactory (~54% of the simulated days meet the model performance criteria outlined earlier in the modeling system section)

for the highest value simulated within a 15-km radius of the

monitor (solid black line).

The top right panel of Figure 2 shows the band-RRF values

(y-axis) for each band (x-axis). The decrease in band-RRF

values with increasing band number illustrates that the model

is more responsive to emissions controls at higher O3 values. For

comparison, the single-RRF for this site is shown as a black

dashed line. For some sites, the RRF values for certain bands

(especially at the high end) may be missing because the model

did not simulate mixing ratios within that band.

To represent the missing bands, we performed a linear regression of available RRFs starting from the 60 ppb bin and only

when at least three bands with simulated 1-hr O3 mixing ratio

 90 ppb were available (solid black line). We chose this criterion

to prevent the lower less responsive bands from dominating the

fit. Based on an analysis for all the representative SJV monitoring sites (not shown here) that are included in the SIP, we

selected the 60-ppb threshold (with at least three bands that

have simulated O3 mixing ratio 90 ppb) for the band-RRF

regression. This choice increases the number of bands available

Figure 2. An illustration of the band-RRF procedure for the Edison monitoring site. The top left panel shows the time series of observed (black circles) and simulated

(black line) daily maximum 1-hr O3

for the simulation period (May–September 2007). The top right panel shows the scatter plot of binned band-RRF for 1-hr O3from

60 to 120 ppb (in 5-ppb increments) vs. the number of bands. The bottom left panel shows the time series of observed (black circles) and simulated (black line) daily

maximum 8-hr O3 for the simulation period (May–September 2007). The bottom right panel shows the scatter plot of binned band-RRF from 60 to 100 ppb (in 5-ppb

increments) for 8-hr O3 vs. the number of bands. S.RRF and B.RRF denote single- and band-RRFs, respectively.

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for the regression and provides more stability. It also ensures that

low mixing ratios will not dominate the regression. In addition,

including only the reference year data that fall within 20% of

the measured values in the RRF calculations further constrains

the band-RRF regression fit.

We have used the RRFs on the regression line for all bins

instead of the actual band-RRF points when available, since the

regression fit represents the average site specific RRF for that

particular mixing ratio range. This approach also reduces the

uncertainty caused by a band with very few data points (that are

used in the RRF calculation for that particular band) and prevents it from having a disproportional impact on the future DV

calculations.

The decrease in RRF with increasing band number raises an

issue with respect to multiplying the reference year DV directly

by the appropriate band-RRF. If the individual observations used

to determine the reference year DV were to be projected into the

future with their corresponding band-RRF and the fourth highest

future value was selected as the future DV, it is possible that this

future DV could be different from a future DV that was projected

directly from the reference year. For example, the order of values

when projected to the future year could be different from the

order of values in the reference year. This possibility was recognized in a different context (24-hr PM2.5) in the 2011 addendum

to the 2007 EPA modeling guidance (EPA, 2011).

To account for this potential reshuffling of values, the new

future DVs were calculated by multiplying the top 10 observed

1-hr daily maximum O3 mixing ratios from the 3 years ending in

the reference year (i.e., 2005–2007) by their corresponding

band-RRF values. The future year values were then re-sorted

and the value of the fourth highest 1-hr O3 was selected as the

future 1-hr O3 DV for that monitor. The future 1-hr O3 DVs,

calculated using this procedure, are shown in the fourth column

of Table 1 and are in general lower than the corresponding

single-RRF DVs shown in third column of Table 1 (e.g., at the

Edison monitoring site, the band-RRF-based future DV of 108.1

ppb is ~4 ppb lower than the corresponding single-RRF-based

DV of 111.9 ppb).

8-Hour O3 RRF calculation methodology

In this section, the procedure to calculate the 8-hr O3 RRFs is

described. The 8-hr O3 DV is the average of the annual fourth

highest daily maximum 8-hr O3 mixing ratios over 3 consecutive

calendar years (EPA, 2008). The 2007 8-hr O3 DVs (based on the

2005–2007 measurement period) are shown in the sixth column of

Table 1 for representative sites in the SJV region. These DVs are

highly variable across the region and range from 77 ppb at

Stockton (not shown in Table 1) to 107 ppb at Arvin Bear

Mountain (see Figure 1 for site locations). The ordering (ranking)

of the 2007 DVs for the 1-hr and 8-hr O3 DVs is different. For

instance, the highest 1-hr O3 DV is at the Edison site, while this

site is ranked third for the 8-hr O3 DVs. This is expected, given the

differences in the form of the two O3 standards.

Single-RRF. We now discuss the single-RRF calculations for

8-hr O3 values. In this study, we followed the procedure to

calculate the single-RRFs for the 8-hr O3 standard as described

in the EPA modeling guidance (EPA, 2007) with one notable

exception: We calculated the RRFs based on the subset of the

data with the reference year simulated values that are within

20% of the corresponding observed values (to maintain consistency with the 1-hr O3 calculations described earlier). In this

study, we have used 70 ppb as the minimum threshold value for

8-hr daily maximum O3 values that are included in the RRF

calculations (EPA 2007). This minimum threshold is based on

the 84-ppb standard and may need to be reassessed in the future

to reflect the current 75 ppb 8-hr O3 standard. The future 8-hr O3

DVs, calculated by multiplying the reference year (i.e., 2007) 8-

hr O3 DVs with the corresponding 8-hr O3 single-RRF values,

are shown in the seventh column of Table 1.

Band-RRF. We now describe the procedure of applying the

band-RRF concept to the 8-hr O3 standard using the same

example of the Edison monitoring site used earlier in the 1-hr

O3 band-RRF section. The time series (bottom left panel of

Figure 2) of the observed (solid black circles) and simulated

“nearby” (i.e., in a grid cell within a 15-km radius of the monitor)

daily maximum 8-hr O3 values (black solid line) at Edison shows

good agreement (~52% of the simulated days meet the model

performance criteria outlined earlier in the modeling system

section) and follows the similar trend seen in corresponding 1-

hr O3 values (top left panel of Figure 2). Further details of the

model performance statistics for 8-hr O3 are presented in the

Supplemental Materials.

We applied an analogous procedure for 8-hr O3 band RRF

analysis (similar to the 1-hr O3 band-RRF calculations described

in previous sections) but with two notable exceptions. First, an

RRF was calculated for each 5 ppb bin in the 60–100 ppb range,

where the upper bound of 100 ppb is less than the corresponding

120 ppb used in the 1-hr O3 calculations. Second, the bands with

missing RRFs were represented by the band-RRF regression and

this regression was applied only when at least three bands with

simulated 8-hr O3 mixing ratio 70 ppb were available. Note

that this criterion was set to 90 ppb for the 1-hr O3 band-RRF

regression calculations. The bottom right panel of Figure 2

clearly shows that the simulated higher 8-hr O3 values are

more responsive to emission controls through the decreasing

trend in RRF values with increasing band number (consistent

with the corresponding 1-hr O3 values).

To account for potential reshuffling of the annual fourth

highest mixing ratio, as in the case of 1-hr O3 described earlier,

a larger number of days (10 days per year with a total of 30 days

during 3 years) were projected to the future and subsequently

used in the future year DV calculation. This is different from the

1-hr O3 procedure, where the 10 highest measured O3 mixing

ratios from the entire 3-year measurement period were used in

calculating the future 1-hr O3 DV at each monitor. The top 10

daily maximum 8-hr O3 mixing ratios from each of the 3 years

(i.e., 2005–2007) were projected to the future using the corresponding band RRFs, re-sorted, and the fourth highest value was

calculated at each monitor. The future 8-hr O3 DV is then

calculated as the three-year average of the annual fourth highest

8-hr O3 mixing ratio at each monitor (eighth column of Table 1).

These DVs are in general lower than the corresponding singleRRF DVs (seventh column of Table 1), and this is consistent with

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the trend seen in the 1-hr O3 future DVs. For instance, at the

Edison monitoring site, the band-RRF-based future DV of 81

ppb is ~2 ppb lower than the corresponding single-RRF DV of

83.2 ppb.

The EPA modeling guidance (EPA, 2007) recommends simulating a full O3 season for demonstrating compliance with the 8-

hr O3 standard using the RRF methodology. In this study, singleand band-RRFs are calculated based on modeling results from a

single O3 season (i.e., 2007 reference year) projected to the

future, consistent with the EPA recommendation. Since the

reference year DVs are based on 3 years of ambient O3 mixing

ratios, ideally 3 years should be simulated and used in the future

year DV calculation. This would allow the use of year-specific

regression curves to select appropriate band-RRFs for each of

the top 10 values. However, it is currently not feasible to conduct

three annual simulations within the context of a SIP, primarily

due to computational limitations. Therefore, the standard practice in SIP preparation is to simulate a single O3 season

(e.g., http://www.dec.ny.gov/chemical/37012.html) or a shorter

period in some cases (e.g., http://www.tceq.texas.gov/airquality/

airmod/data/dfw8h2).

It is known in California that high O3 mixing ratios occur

within very specific meteorological regimes, and they occur

repeatedly over time (Beaver and Palazoglu, 2009). Thus, it

may be reasonable to assume that these meteorological

regimes are represented in the RRFs developed for 1 year

and they can be reasonably applied to high O3 mixing ratios

over the 3 years.

Extension of the Band-RRF Concept to

PM2.5

Before we discuss the extension of the band-RRF procedure

to the PM2.5 standards, we first demonstrate in Figure 3 that, as

for O3

, high PM2.5 concentrations respond more to emissions

controls of the limiting precursors in the SJV region. The four

panels in Figure 3 show daily 2019/2007 PM2.5 concentration

ratios as functions of 2007 simulated PM2.5 concentrations for

four representative locations in the SJV. The solid line is the

nonlinear regression line generated using the power form. The

simulated PM2.5 concentrations used in Figure 3 are described in

Chen et al. (2014).

The 24-hr PM2.5 DV is based on the average of the annual 98th

percentile of observed 24-hr PM2.5 values over a period of 3

consecutive years (40 CFR Part 50, Appendix N). The procedure

to test for attainment of this standard (EPA, 2011) already has

some elements of the band-RRF method in it. For example, after

determining the rank of the 98th percentile value for a given

reference year, the top eight measured values per calendar quarter

(32 values/year) are projected into the future, one component

(e.g., nitrate, sulfate, ammonia, etc.) at a time, using quarter- and

component-specific single-RRFs. The projected future components are then combined into a future total PM2.5 concentration,

sorted in descending order, and the value of the rank that corresponds to the 98th percentile in the reference year is selected as the

future 98th percentile. The future DV is the average of future 98th

percentile concentrations for three consecutive years. The only

modification needed in this case is to introduce band-RRFs for

each calendar quarter for each component. The same procedural

steps that were described in the 1-hr O3 standard can be followed

in this case. Other processing steps (e.g., determining the speciation, calculating the particle bound water, etc.) would remain the

same.

The demonstration for attainment of the annual PM2.5 standard

requires that quarterly averages of the reference year be used to

form the annual average and that three consecutive years be

averaged to form the annual DV (EPA, 2007). In the procedure

to demonstrate attainment of the annual PM2.5 standard, each

quarterly average is projected to the future using quarter- and

component-specific RRFs. Then the future DV is calculated

using the same averaging procedure followed in the reference

year (EPA, 2007). Again, the only modifications needed are to

introduce band-RRFs for each calendar quarter for each component and to project all measurements into the future. The same

procedural steps that were described for the O3 standards can be

followed to calculate the quarter- and component-specific RRFs.

All the other processing steps would remain unchanged.

It may appear to be a daunting task to calculate band-RRFs,

particularly for PM2.5, where multiple components are involved.

However, nearly all steps can be automated with spreadsheet

software that is readily available. We are currently in the process

of conducting photochemical model simulations for the future

PM2.5 SIPs. At the conclusion of those simulations we will

provide operational details and numerical examples on how to

apply band-RRFs to both 24-hr PM2.5 and annual PM2.5

standards.

Figure 3. The total PM2.5 daily concentration ratios (2019/2007) at Modesto,

Fresno, Visalia, and Bakersfield monitoring sites in the SJV region. The solid line

represents the power form of the regression. (See Chen et al. [2014] for further

details on the simulated PM2.5 concentrations.)

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Conclusion

In this study, we have developed and applied the band-RRF

concept, which addresses the observed phenomenon that simulated

high O3 mixing ratios are, in general, more responsive to emission

controls of limiting precursors than lower mixing ratios are. The

concept of band-RRF is a logical extension to the currently used

single-RRFs and can be applied to estimate varied model responses

for different ranges of O3 mixing ratios. Since the reference year DVs

are typically based on 3 years of ambient O3 mixing ratios, it would

be ideal to simulate all 3 years and then calculate an individual dayspecific RRF to estimate the future DV at each monitoring site.

However, computational limitations do not make it viable to conduct

three annual simulations within the context of a SIP. The band-RRF

concept makes it possible to calculate the day-specific RRFs without

simulating the three measurement years by estimating average site

specific RRFs for different ranges of O3 mixing ratios.

The band-RRF based future DVs are generally lower than

those calculated with single-RRFs. However, there can be cases

(e.g., 8-hr O3 DV for the Sequoia National Park Site in this

study) where the band-RRF procedure results in a higher DV if

higher O3 mixing ratios are less responsive to emissions controls

(e.g., due to long-range O3 transport). The single-RRF procedure, due to its averaging nature, may not be able to represent this

situation accurately. The concept of the band-RRF is only marginally more complex than that of the single-RRF. It is readily

extendable to any standard that uses RRFs and can be easily

implemented using spreadsheet software.

The width of the bands should be selected carefully to prevent

having too few points for regression analysis (if the bands are too

wide) and calculating RRFs for a given band with too few points

(if the bands are too narrow). However, as seasonal (May–

September 2007 in this case) and annual air quality simulations

become commonplace in regulatory modeling, the selection of

the width of the bands would become less critical.

Here, we have presented an improved approach to using RRFs to

account for the deficiencies of the photochemical model. However,

using the modeling results in a relative sense may not be the only

solution. Another potential strategy may be to correct the biases in

the reference year using the observations (Kang et al., 2010, Zhang

et al., 2012). In the simplest case, if it is assumed that the biases in

the future year are identical to those in the reference year, then the

same bias adjustment can be applied to the future year simulation.

Such a bias-corrected future year could then be used directly to

calculate the future DVs without resorting to RRFs.

Disclaimer

This paper has been reviewed by the staff of the California

Air Resources Board and has been approved for publication.

Approval does not signify that the contents necessarily reflect

the views and policies of the California Air Resources Board,

nor does mention of trade names or commercial products

constitute endorsement or recommendation for use.

Acknowledgment

The authors thank Karen Magliano, Mena Shah, and

Lawrence Larsen of the California Air Resources Board and

Scott Bohning of the EPA Region 9 for providing them with

helpful comments.

Supplemental Material

Supplemental data for this paper can be accessed at http://dx.

doi.org/10.1080/10962247.2014.936984.

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About the Authors

Sarika Kulkarni, Ph.D., and Daniel Chau, Ph.D., are air resources engineers in

the Modeling and Meteorology Branch of the Air Quality Planning and Science

Division of the California Air Resources Board.

Ajith P. Kaduwela, Ph.D., is a staff air pollution specialist in the Modeling and

Meteorology Branch of the Air Quality Planning and Science Division of the

California Air Resources Board. He is also affiliated with the Air Quality

Research Center at the University of California, Davis.

Jeremy C. Avise, Ph.D., is an air resources supervisor in the Modeling and

Meteorology Branch of the Air Quality Planning and Science Division of the

California Air Resources Board. He is also affiliated with the Department of Civil

and Environmental Engineering at Washington State University, Pullman.

John A. DaMassa, M.S., is Chief of the Modeling and Meteorology Branch of the

Air Quality Planning and Science Division of the California Air Resources Board.

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