## Appendix N Grid Resolution Journal Article

# Appendix N

Grid Resolution Journal Article

## Grid Resolution Journal Article Appendix N i The Charlotte-Gastonia-Rock Hill, NC-SC 8-Hour Ozone April 5, 2007 Pre-Hearing Draft –North Caro lina Attainment DemonstrationAtmospheric Environment 40 (2006) 5010–5026



# A quantitative assessment of the influence of grid resolution on

predictions of future-year air quality in North Carolina, USA

Saravanan Arunachalam a, 

#  

# , Andrew Holland a 

# , Bebhinn Do b



# , Michael Abraczinskas b

a Carolina Environmental Program, University of North Carolina at Chapel Hill, Bank of America Plaza, CB #6116, 137 E. Franklin St., Chapel Hill, NC 27599-6116, USA
bDivision of Air Quality, North Carolina Department of Environment and Natural Resources, 1641 Mail Service Center, Raleigh, NC 27699-1641, USA
Received 14 February 2005; received in revised form 5 January 2006; accepted 5 January 2006



### Abstract

Increased focus has been directed at fine-scale modeling for improving the ability of air quality modeling systems to capture local phenomena. While numerous studies have investigated model performance at finer resolution (4–5 km), there is relatively limited information available for choosing the optimum grid resolution for predicting future air quality in attainment demonstration studies. We demonstrate an evaluation of the MM5–SMOKE–MAQSIP modeling system for four 8-h ozone episodes in the summers of 1995, 1996 and 1997 in North Carolina using a one-way nested 36/12/4-km application. After establishing acceptable base-case model performance for ozone predictions during each episode, we developed future-year emissions control scenarios for 2007 and 2012, and finally computed relative reduction factors (RRFs) using model outputs from each of the three grid resolutions. Our analyses, based upon qualitative as well as quantitative approaches like the Student’s t-test, indicate that RRFs computed at specific monitoring locations—and hence predicted future-year air quality—are not very different between the 4- and 12-km results, while the differences are slightly larger between the 4- and 36-km results. The results imply that grid resolution contributes to a variability of about 1–3 ppb in the projected future-year design values; this variability needs to be incorporated into policy-relevant decision-making. Since this assessment was performed for four different episodes under diverse meteorological, physical and chemical regimes, one can generalize the results from this study. They are also relevant for regional modeling applications that are currently ongoing for studying PM 2.5 

### nonattainment issues, where the need for annual base-year and future-year simulations for demonstrating attainment may place a large demand on computing resources. Based upon the results from this study, future studies may consider using results from 12-km modeling to address future-year air quality goals for ozone and PM 2.5 

### and its components, and then incorporate grid-resolution uncertainties into the computed results. r 2006 Elsevier Ltd. All rights reserved.

Keywords: Emissions strategies; CMAQ; Student’s t-test; O 3 NAAQS; Attainment



### 1. Introduction

In 1997, the US Environmental Protection Agency (US EPA) revised the National Ambient 

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www.elsevier.com/locate/atmosenv

1352-2310/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2006.01.024

 Corresponding author. Tel.: +1 919 966 2126; fax: +1 919 843 3113. E-mail address: sarav@email.unc.edu (S. Arunachalam).

### Air Quality Standard (NAAQS) for ozone from a 1-h-based standard of 0.120 ppm to 0.080 ppm measured over an 8-h period; this is called the 8-h O 3 

### standard ( Federal Register, 1997 ). The new US NAAQS is met at an ambient air quality monitoringsite when the 3-year average of the annual fourthhighest daily maximum 8-h average O 3 

### concentration is p 0.080 ppm (i.e., the site is said to be in attainment). This revised NAAQS for O 3 

### is more stringent than the 1-h O 3 

### standard and more protective of public health. Based upon 8-h O 3 

### measurements from 2001 to 2003, the US EPA designated a total of 474 counties in the US as not attaining the 8-h O 3 

### standard in 2004 ( Federal Register, 2004). In North Carolina alone, 32 counties were designated nonattainment. The Clean Air Act Amendments of 1990 established selectedcomprehensive, three-dimensional (3-D) photochemical air quality simulation models as the required regulatory tools for analyzing the urban and regional problem of high ambient O 3 

### levels across the US ( US EPA, 1991 ). These models are currently applied to study and establish strategies for meeting the NAAQS for O 3 

### nonattainment areas, and State Implementation Plans resulting from these efforts must be submitted to the US EPA. The US EPA has developed a draft modeling guidance document ( US EPA, 1999 ) for demonstrating attainment of the NAAQS for 8-h O 3 

### . In this document, the US EPA recommends a methodology for applying air quality models to generate predictions that indicate whether a given set of emissions controls is likely to demonstrate attainment in the future. This involvesestablishing acceptable base-case model performance for the area of interest, then using the same system to model future-year emissions reductions strategies to test for attainment.

With this background, the use of grid-based photochemical models has expanded dramatically to include spatial scales varying from urban to regional. Users selecting a modeling system for a given application need to fully understand the structural and algorithmic differences between models and of their possible impacts on both operational and scientific inferences that may be drawn from the models’ respective simulations ( Russell and Dennis, 2000 ). These differences could significantly affect the development of emissions control strategies for attaining the O 3 

### NAAQS. Sillman et al. (1990) suggest that degrading the model horizontal resolution can cause a systematic positive bias in O 3 

### simulation, since the artificial dilution of NO x 

### emissions over relatively large grid volumes can increase the O 3 

### production efficiency per unit of NO x 

### oxidized ( Liu et al., 1987 ). Similar positive bias in predicted O 3 

### resulting from degradation of horizontal grid resolution has been reported in simulations over southern California by Kumar et al. (1994)

. Jang et al. (1995a, b) showed that grid resolution significantly influences both rates of chemistry and vertical transport processes, and that coarser grids tend to underpredict ozonemaxima over major source areas. Through boxmodel calculations of O 3 

### production efficiency for a variety of conditions, Liang and Jacobson (2000)suggest that coarsely resolved models might underpredict or overpredict O 3 

### production because they are unable to accurately represent the blending ofair masses of different origins. Recently, an operational assessment of the application of the draft guidance in demonstrating attainment of the O 3 

### NAAQS has shown that one needs to account formodel-to-model uncertainty in the attainment demonstration ( Sistla et al., 2004). The authors demonstrate that the choice of modeling systemmay bring an area into attainment or not, depending upon the estimated response of the chosen modeling system. Here, we present a case that the choice of grid resolution also needs to be judiciously made, as the results from our future-year modelingshow different sites being in attainment or nonattainment of the O 3 

### NAAQS depending upon the chosen model grid resolution.

2. Modeling systems

In the modeling performed to study O 3 

### nonattainment issues in North Carolina, we identified four ozone episodes that occurred during the summers of 1995, 1996 and 1997 and developed base-case applications using the MM5–SMOKE– MAQSIP modeling system. An iterative procedurewas adopted to refine the base-case model performance for each episode; each time, the overall modeling system was improved by either changingthe model configuration or by refining the meteorological and/or emissions inputs. Once acceptable base cases were developed per the US EPA guidance ( US EPA, 1991, 1999 ; Russell and Dennis, 2000 ), weperformed numerous emissions sensitivity simulations to develop future-year 2007 and 2012 attainment scenarios. We modeled a total of 16 episode days spanning the three summer periods: 12–15 July 1995, 21–24 and 27–30 June 1996 and 12–15 July 

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S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5011

### 1997. These episodes were chosen based upon extensive analyses of historical episodes in North Carolina ( STI, 1998 ); they represented typical meteorological conditions for the region, and included high 8-h ozone episodes closer to currentozone design values. For each episode, we performed simulations from 2 days prior to the actual episode start date, to provide ramp-up of the initialand boundary conditions (obtained from climatological data). The modeling domain ( Fig. 1a) used has a nested system of 36/12/4-km grids centered over North Carolina. Fig. 1b shows the zoomed-in 4-km modeling domain and the location of the air quality monitors that are the focus of this study. The various models used are described below.

2.1. Mesoscale meteorological model

The meteorological inputs for this study were derived from the Fifth-Generation Penn State/ 

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Fig. 1. (a) Nested air quality modeling domain (36-, 12- and 4-km grids) and (b) O 3 monitors in the 4-km grid (state boundaries shown in thicker/blue lines). S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5012

### NCAR mesoscale model (MM5) ( Grell et al., 1994). We used MM5 V1, V2.12 and V3.3 for the 1995, 1996 and 1997 episodes, respectively, since these were the latest versions that were available when we developed the base cases. We used one-way nesting in MM5, and the choices of cloud scheme and planetary boundary layer (PBL) scheme used for each grid resolution are shown in Table 1 . We employed observational nudging of winds (using surface reports, profilers and soundings when available) at 12- and 4-km resolutions, and we used grid nudging at 108/36/12

- km resolutions. An iterative procedure was applied to each episode to generate the best meteorological inputs possible. We changed either the PBL scheme and/or the cloud parameterization scheme during these iterations.The meteorological model performance was evaluated each time to measure improvements, by looking at the model’s capability to predict key meteorological variables such as wind speed, wind direction, PBL heights, temperature and moisture ( CEP, 2005 ).

The model was vertically resolved into 26 layers, and the top of the domain extends up to 100 mb. No interpolations were necessary from MM5 to theMultiscale Air Quality Simulation Platform (MAQSIP) model in the horizontal or vertical because the models used the same coordinate systems and grid resolutions. MAQSIP-ready meteorological inputs were derived using the meteorology-coupler (MCPL) ( Coats et al., 1998 ). MCPL is a drop-in MM5 output module designed for coupling MM5 to other environmental models, using the Models-3 Input/Output Applications Programming Interface ( Coats, 2005 ). 2.2. Sparse matrix operator kernel emissions (SMOKE) modeling system

Emissions inputs were developed using the SMOKE ( Houyoux and Vukovich, 1999 ; Houyoux et al., 2000 ) processing system. We used the beta version of SMOKE V2.0 for all emissions modeling presented here. Speciation was performed using the carbon bond mechanism-IV (CBM-IV) ( Gery et al., 1989 ). Nonroad emissions estimates were obtained using the US EPA’s NONROAD model. Biogenic emissions were processed using an implementation of the Biogenic Emissions Inventory System-3 (Vukovich and Pierce, 2002) within SMOKE. All episode-specific emissions inputs to the model for each of the four periods studied were continuously refined during development of the base-case model applications. Once acceptable model performance was established for the four episodes, we developed current-year emissions inputs (2000) and future-year emissions inputs (2007 and 2012). Emissions control strategies modeled for 2007 and 2012 include several Federal and State-specific control measures already in place or being implemented over the next few years for each state in the modeling domain. These measures will significantly reduce emissions from point, on-road mobile and nonroad mobile sources in North Carolina and neighboring states. Details of the actual emissions controls strategies modeled for the future years are discussed in NCDENR (2004)

. Fig. 2 shows changes in NO x 

### emissions in North Carolina by source category from 2000 to 2007 to 2012 for a typical episode day in 1996. Since thevolatile organic compound (VOC) emissions estimates are dominated by biogenic sources and do notchange much in the future years, only 2000 baseyear estimates for a typical 1996 episode day are shown in Fig. 2

. 2.3. Multiscale air quality simulation platform

MAQSIP ( Mathur et al., 2004) is a comprehensive urban- to intercontinental-scale atmosphericchemistry-transport model, developed in collaboration with the US EPA; the model also served as a prototype for the US EPA’s community multiscale air quality (CMAQ) modeling system ( Dennis et al., 1996 ; Byun and Ching, 1999 ). The MM5 model is used to provide meteorological inputs to MAQSIP. In its current form, MAQSIP has been applied to study issues related to tropospheric O 3 

### , acidic substances, and aerosol formation and pollutant 

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Table 1 Cloud scheme and PBL scheme used in MM5 for each episode/ grid resolution

Episode
year 36 km 12 km 4 km

Cloud Scheme 1995 KainFritsch KainFritsch Explicit

1996 KainFritsch KainFritsch Explicit

1997 Grell Grell Explicit

PBL Scheme 1995 Blackadar GaynoSeaman GaynoSeaman 1996 Blackadar Blackadar Blackadar 1997 Blackadar Blackadar Blackadar S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5013

### distribution on urban, regional and intercontinental scales for various geographic areas of the world.While MAQSIP can emulate many existing atmospheric chemistry-transport models, its modular and flexible structure facilitates incorporation of new, improved process representations and algorithms. This capability allows the system to be used as a comprehensive test-bed environment for exploring different process and algorithmic representations in situ in a 3-D modeling framework with other interacting physical and chemical phenomena. Its modularity also facilitates adaptation of the model to address a broad range of atmospheric chemistry and transport problems. MAQSIP is formulated with a generalized coordinate system to better interface the chemistry-transport calculations with various meteorological models. The formulation of MAQSIP supports multiple nesting of grids for efficient resolution of smaller-scale phenomena, and allows for one-way or two-way interaction between disparate spatial scales. Thus, the model can be adapted to a variety of spatial domains ranging from urban to interregional with flexible grid resolution; simulations to date have used 4 to 108-km grid resolutions. The model also has the flexibility to use different chemical mechanisms forrepresenting gas-phase chemistry or for incorporating explicit chemical schemes. We modeled only gasphase chemistry for this study, and used CBM-IV with updated isoprene chemistry ( Carter and Atkinson, 1996 ). The effects of cloud transport on the vertical distribution of trace species in the atmosphere are represented depending on the scale of model application and on the scheme used in MM5 ( Mathur et al., 2004). The modular design of MAQSIP permits a number of choices in the algorithm used for each modeled process. For this study, we modeled horizontal and vertical advection using the Bott scheme, horizontal diffusion using a
constant K h 

### , and vertical diffusion based upon K-theory. We used one-way nesting in MAQSIP for all the episodes, and did not use plume-in-grid technique for any of the three resolutions. Several of these modules have been evaluated in detail during the course of the model development, and for subsequent other model applications; descriptions and results of the evaluations can be found separately ( Kasibhatla et al., 1997 ; Kasibhatla and Chameides, 2000 ; Hogrefe et al., 2001 ; Fiore et al., 2003 ; Mathur and Dennis, 2003 ; Mathur et al., 1998, 2004, 2005 ).

2.4. Model performance evaluation

The US EPA has developed guidance documents for photochemical model performance evaluation (US EPA, 1991, 1999 ) that suggest specific tests and comparisons, recommend graphical methods for use in interpreting and displaying results, and identify potential issues or problems that may arise. We performed extensive evaluation of model performance for each of the episodes using observed data from the US EPA’s aerometric information retrieval system (AIRS) at these sites. The list of ozone monitors is shown in Table 2 . As a result of the iterative procedures adopted during the base-case development phase, we were able to achieve acceptable model performance for ozone on all 16 episode days. Fig. 3 shows daily mean normalized bias (acceptable performance is when 

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**2000 NO x** **Emissions (2,280 Tons/day)**

0 200 400 600 800 1000 1200 1400

Point Onroad Mobile Nonroad Mobile Area

**Source Category NO** **x Emissions (Tons/day)**  **2000**
**2007**
**2012 2000 VOC Emissions (14,028 Tons/day)** 

**3% 2%**  **2% 3%** 

**90%**

**Area Point Nonroad Mobile Onroad Mobile**  **Biogenics**

(b) (a)

Fig. 2. NO x (left) and VOC emissions (right) for a typical 2000 day in North Carolina. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5014

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Table 2 O 3 monitoring sites in North Carolina and DVCs (shown in ppm)

Region AIRS ID ID Site name Site in 4 km Ht (m) DVCa DVCb Max(DVC)

Charlotte 37-119-1009 CTYL County Line Yes 216 0.101 0.098 0.101 37-159-0021 ROCK Rockwell Yes 240 0.098 0.100 0.100 37-159-0022 ENVL Enochville Yes 270 0.099 0.099 0.099 37-119-0041 PLZA Garinger (Plaza) Yes 239 0.098 0.096 0.098 37-109-0004 CRSE Crouse Yes 270 0.091 0.092 0.092 37-119-1005 ARWD Arrowood Yes 195 0.092 0.084 0.092 37-179-0003 MONR Monroe Yes 200 0.087 0.088 0.088
Triangle (Raleigh–Durham–Chapel Hill) 37-183-0014 MLBK Millbrook Yes 100 0.094 0.092 0.094 37-077-0001 BTNR Butner Yes 91 0.092 0.094 0.094 37-183-0015 STAG St. Augustine Yes 127 0.093 0.091 0.093 37-145-0003 BSHF Bushy Fork Yes 198 0.089 0.091 0.091 37-069-0001 FRKL Franklinton Yes 135 0.086 0.090 0.090 37-063-0013 DUKE Duke St. Yes 390 0.087 0.089 0.089 37-183-0017 WRAL Tower Yes 320 0.088 0.085 0.088 37-183-0016 FUQV Fuquay-Varina Yes 117 0.086 0.088 0.088 37-101-0002 WJOH W. Johnston Yes 127 0.087 0.085 0.087 37-037-0004 PITT Pittsboro Yes 400 0.081 0.082 0.082
Triad (Greensboro–Winston– Salem–High Point) 37-059-0002 DAVI Cooleemee Yes 219 0.096 0.093 0.096 37-067-0022 HTAV Hattie Ave. Yes 287 0.094 0.093 0.094 37-067-1008 UCRS Union Cross Yes 241 0.093 0.089 0.093 37-157-0099 BETH Bethany Yes 277 0.085 0.091 0.091 37-033-0001 CHGR Cherry Grove Yes 285 0.090 0.088 0.090 37-081-0011 MLVL McLeansville Yes 229 0.090 0.089 0.090 37-067-0028 SHIL Shiloh Church Yes 294 0.089 0.088 0.089 37-151-0004 SOPH Sophia Yes 250 0.085 0.085 0.085 37-067-0027 POLL Pollirosa Yes 271 0.082 0.082 0.082

Asheville 37-199-0003 MTMI Mt. Mitchell Yes 1982 0.089 0.083 0.089 37-087-0035 FRYP Fry Pan Yes 1585 0.087 0.082 0.087 37-087-0036 PKNO Purchase Knob No 1494 0.087 0.085 0.087 37-099-0005 BKNO Barnet Knob No 1433 0.085 0.084 0.085 37-021-0030 BENT Bent Creek Yes 675 0.083 0.078 0.083 37-087-0004 WAYN Waynesville Yes 802 0.080 0.079 0.080
Greenville, Rocky Mount and Wilson (Down East) 37-065-0099 LEGT Leggett Yes 18 0.087 0.089 0.089 37-147-0099 FARM Farmville Yes 26 0.084 0.082 0.084 37-107-0004 KINS L. College No 29 0.082 0.081 0.082 37-061-0002 KVIL Kenansville Yes 34 0.082 0.079 0.082 37-117-0001 JVIL Jamesville No 6 0.080 0.081 0.081
Fayetteville 37-051-0008 WADE Wade Yes 43 0.088 0.086 0.088 37-051-1003 HOPE Golfview Yes 68 0.086 0.087 0.087
NW Piedmont (Hickory) 37-003-0003 ALEX Taylorsville Yes 339 0.087 0.088 0.088 37-027-0003 LENR Lenoir Yes 366 0.087 0.084 0.087

Various areas 37-131-0002 GAST Gaston Yes 40 0.082 0.084 0.084 37-029-0099 CAMD Camden No 3 0.080 0.081 0.081 37-011-0002 LINV Linville Yes 987 0.078 0.078 0.078 37-129-0002 WILM Castle Hayne Yes 12 0.075 0.078 0.078

CASTNET Sites 37-123-8001 CAND Candor Yes n/a 0.086 n/a 0.086 37-011-8001 CRAN Cranberry Yes 1219 0.083 n/a 0.083 37-113-8001 COWE Coweeta No 686 0.077 n/a 0.077 37-031-8001 BEAU Beaufort No n/a 0.076 n/a 0.076

Note : DVCs 4 0.084 ppm are shown in bold font. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5015

### MNB o 7 15%) and mean normalized gross error (acceptable performance is when MNGE o 35%) ( Russell and Dennis, 2000 ) for 8-h O 3 

### computed at North Carolina sites in each of the three model grid resolutions. These metrics correspond to the finalbase-case modeling that used episode-specific emissions. In computing these metrics, we used allhourly 8-h ozone modeled predictions that corresponded to an observed threshold of 0.060 ppm.Traditionally, for attainment demonstration purposes, the focus has been on using this threshold to evaluate the model’s capability to predict values that are closer to the NAAQS ( US EPA, 1991 ), and to help reduce apparent model errors (due to overpredictions of very low observations). However, we also computed MNB and MNGE for 8-h ozone using an observed threshold of 0.005 ppm (shown in Fig. 4), and one can see the relatively large bias andlarge errors when using low concentrations. Additional results from model performance evaluation performed for these episodes are also available (Arunachalam et al., 2001, 2002 ; CEP, 2005 ; NCDENR, 2004 ).

3. Attainment demonstration

This paper focuses on an evaluation of the MM5–SMOKE–MAQSIP modeling system for 

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**Mean Normalized Bias for 8-hr O 3** **(Obs Thresh = 60 ppb)**

-25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

950712 950713 950714 950715 960621 960622 960623 960624 960627 960628 960629 960630 970712 970713 970714 970715

**Episode Date % MNB**  4-km 12-km 36-km

(a)

**Mean Normalized Gross Error for 8-hr O 3**  **(Obs Thresh = 60 ppb)**

0% 10% 20% 30% 40% 50%

950712 950713 950714 950715 960621 960622 960623 960624 960627 960628 960629 960630 970712 970713 970714 970715

**Episode Date % MNGE**  4-km 12-km 36-km

(b )

Fig. 3. Mean normalized bias and mean normalized gross error for 8-h O 3 using an observed threshold of 60 ppb. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5016

### predicting future-year air quality using a demonstration of the US EPA’s modeled attainment test ( US EPA, 1999 ) in the North Carolina modeling domain ( Fig. 1a and b ). The attainment test to determine whether a given monitor meets the NAAQS or not by the mandated future year, recommends using modeled predictions in a relative sense rather than an absolute sense. A key assumption underlying the use of the relativereduction factor (RRF) in demonstrating attainment is that the uncertainty in the difference between the ozone maximum predictions for the base and emissions control scenarios is less than the uncertainty in the ozone maximum predictions themselves ( Hanna et al., 2001 ). Further, this attainment test is closely tied to the form of the NAAQS for 8-h ozone.

3.1. Modeled attainment test

For this study, we applied the modeled attainment test only to North Carolina O 3 

### monitors in the 

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**Mean Normalized Gross Error for 8-hr O 3**  **(Obs Thresh = 5 ppb)**

0% 20% 40% 60% 80% 100% 120% 140%

**Episode Date % MNGE**  4-km 12-km 36-km

950712 950713 950714 950715 960621 960622 960623 960624 960627 960628 960629 960630 970712 970713 970714 970715

(b) **Mean Normalized Bias for 8-hr O 3** **(Obs Thresh = 5 ppb)**

0% 20% 40% 60% 80% 100% 120% 140%

**Episode Date % MNB**  4-km 12-km 36-km

950712 950713 950714 950715 960621960622 960623 960624 960627 960628 960629 960630 970712 970713 970714 970715

(a)

Fig. 4. Mean normalized bias and mean normalized gross error for 8-h O 3 using an observed threshold of 5 ppb. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5017

### 4-km grid (see Fig. 1b ). The site-specific future-year air quality is computed as follows:

1. Calculate the site-specific current design values (DVCs) from monitored data. To be consistent with the form of the NAAQS, we calculated the DVC at each site by using the fourth-highest daily maximum 8-h O 3 

### concentration in each of three consecutive years (chosen as discussed next), and then finding their arithmetic mean. Because there is likely to be some variability in observed design values due to meteorological variations, the higher of the following two values was chosen: (a) average design value from the 3-year period ‘‘straddling’’ the year represented by the most recent available emissions inventory (1999–2001), indicated by DVCa in Table 2 ; and (b) average design value from the 3-year period (2001–2003) used to designate an area ‘‘nonattainment’’, shown as DVCb in Table 2 . Using the maximum of thesetwo values ensures that DVCs are not underestimated. Table 2 lists the monitors in North Carolina grouped by urban area, along with various site characteristics, including the DVC for each site. From Table 2 and from Fig. 1b , one can see that there is a very extensive monitoring network in North Carolina, and in some instances, the monitors are located very close to each other (within a few kilometers).2. Use air quality modeling results to estimate sitespecific RRFs. In this step, we identified surface grid cells that were considered to be ‘‘near’’ a monitoring site, rather than just the cell containing the monitor. Since it is hypothesized that RRFs can be underestimated due to potential migration of the predicted O 3 

### peak that results from a chosen control strategy, we identified a 15-km radius as being ‘‘near’’ a site, i.e., as an area consistentwith the intended representativeness for urbanscale O 3 

### monitors ( US EPA, 1999 ). The size of the array of ‘‘nearby’’ cells around each site varied for each grid resolution. For the 36-km resolution, it was a 1  1 array; for the 12 km, a 3  3 array; and for the 4 km, a 7  7 array. The spatial extents of these grid-cell clusters are shown in Fig. 5 using a typical episode day’s daily maximum 8-h O 3 

### predictions in the baseyear, i.e., for 22 June 2000. This figure also shows the spatial variability of the daily maximum values within the ‘‘nearby’’ cells at each site for each of the three grid resolutions. It can be hypothesized that the monitor is at the center of the cell in which it is located, and that this cell is at the center of the appropriate array (e.g., at the center of a 7  7 array of ‘‘nearby’’ cells in the case of the 4-km grid). The elevation of the monitor is not a factor while defining the ‘‘nearby’’ cells. We computed the site-specific RRFs for each grid resolution as follows: (a) Compute the daily maximum 8-h O 3 

### concentration in every grid cell for each modeledepisode day in the base case. (After establishing model performance for the base case with episodic emissions inputs, MAQSIP was run using the ‘‘current-year’’ emissions [i.e., 2000] for use in the base-year calculations.) (b) From these values, find each day’s highest predicted daily maximum 8-h O 3 

### concentration. (c) Compute the average of the highest values for all modeled episode days, using only those days when the highest was X 0.070 ppm, to get a site-specific mean base-year value (Mean_BY). The threshold of 0.070 ppm is applied to exclude low-value days that would cause overestimation of future-year design values (calculated in step 3 below). In some instances, this led to using fewer than 16 episode days in computing Mean_BY. (d) Repeat steps (a)–(c) for the future-year projected case, using the same days to average in the future-year calculation as wereused in the base-year calculation, to get a sitespecific mean future-year value (Mean_FY). Note that on any given day, the grid cell chosen for the future-year case need not be the same as the one chosen in the base-year case, and this helps to capture the ‘migration’ of a predicted peak from the base-year to the future-year case. (e) Calculate the relative reduction factor: RRF 1⁄4 Mean_FY = Mean_BY. 3. Compute site-specific future-year design values (DVFs): DVF 1⁄4 DVC  RRF. 4. Compare all DVFs to NAAQS for 8-h O 3 

### . If all the calculated DVFs are p 0.084 ppm, the modeled attainment test has been passed, and the modeling domain is set to be in attainment of the US NAAQS for 8-h O 3 

### in the modeled future year. Although the level of the 8-h O 3 

### NAAQS is 

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Fig. 5. ‘‘Nearby’’ grid cells around the monitors in 36- (top), 12- (middle) and 4-km (bottom) grid resolutions shown for a typical baseyear day’s daily maximum 8-h O 3 in 2000. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5019

### 0.080 ppm, the third decimal digit, in ppm, isrounded. Hence, 0.084 ppm is the largest concentration that is p 0.080 ppm.

4. Results and discussion

Using each episode’s meteorology, we performed current-year (2000) and future-year simulations for 2007 and 2012. We then postprocessed the model results as discussed above to compute Mean_BY and Mean_FY values (from the 16 episode days) and then finally the RRFs and DVFs for each of 2007 and 2012. Table 3 shows the 2007 and 2012 DVFs for all North Carolina ozone monitors. Fig. 6 (left column) shows the variation of DVCs and 2007 RRFs and DVFs vs. Mean_BY O 3 

### computed using model outputs from each of the 36-, 12- and 4-km grid resolutions. All North Carolina monitors in each of these grid resolutions are shown in these plots, and one should note that the 4-km domain consisted of less number of monitors than the other domains. Hence, the 36- and 12-km plots show more data points than the 4-km plot. A 0.085 ppm line is also shown as the level of the 8-h O 3 

### NAAQS exceedance. When we use the 36-km computed RRFs, only two sites— County Line (DVF of 0.086 ppm) and Enochville (0.085 ppm) in the Charlotte region—are still shown to be in nonattainment. Using the 12-km computedRRFs, four sites—County Line (0.087 ppm), Rockville (0.087 ppm), Enochville (0.086 ppm) and Plaza (0.085 ppm) in the Charlotte region—are shown to be in nonattainment. The 4-km computed RRFs yield an identical DVF of 0.087 ppm at all of these four sites. Similar metrics for the 2012 future-year scenario ( Fig. 6 , right column) indicate that all sites are in attainment of the 8-h O 3 

### NAAQS using RRFs from each of the three grid resolutions. As in 2007, the 2012 DVFs are also mostly similar between the 12- and 4-km resolutions, but show slightly larger differences between the 36- and 4-km modeled outputs. Interestingly, for both 2007 and 2012, the four Charlotte-region sites just referenced have higher base-year ozone concentrations with the 12-km grid than with the 36- or 4-km grids. Note that although the circles representing DVCs (a y

axis variable) change location as the grid-resolution changes, it is actually the change in Mean_BY values (x -axis) that cause the DVC circles to move. The DVCs themselves remain constant across all grid resolutions. To facilitate comparisons, the variations of the 36-, 12- and 4-km 2007 and 2012 RRFs vs. the corresponding DVCs are shown on the same plot in Fig. 7 , while Fig. 8 shows similar plots of DVFs vs. DVCs. These plots illustrate the almost identical response of the modeling system in the 12 km when compared to the 4 km. This seems to indicate that the artificial dilution of emissions within coarse-grid resolutions plays a relatively bigger impact in predicting model responses at 36 km than at 12-km grid resolution. Thus, the underlying combination of physical and chemical processes thatcontribute to ozone exceedances and their reductions is similar in the 12- and 4-km grid resolutions, but not at 36 km. Table 4 gives the number of monitors that show differences in RRFs when comparing 4-km model outputs to 12- or 36-km outputs. For 2007, the RRFs computed using 4-km outputs at 38 out of 42 sites have either 0% or o 3% difference compared to the 12-km outputs. Not a single site shows a difference of 4 5%. However, comparing the 4-km RRFs to the 36-km RRFs, only 26 sites have either 0% or o 3% differences, and six sites have differences of 4 5%. These differences in RRFs translate to DVF differences on the order of 1–3 ppb at most of these sites. These results corroborate the findings by Jones et al. (2005) where they showed that modeled DVFs can have uncertainties of about 2–4 ppb just through differences in alternate options to modeling. For the 2012 4-km RRFs, 37 and 21 sites have differences of o 3% when compared to the 12- and 36-km RRFs, respectively. Only one site (Fry Pan in the Asheville high-elevation region) shows 4 5% difference for the 2012 4-km RRF vs. 12-km RRF. Interestingly, all six sites (Bushy Fork, Pittsboro, Cherry Grove, Bent Creek, Waynesville and Castle Hayne) that have 4 5% difference in 2007 RRFs (4 vs. 36 km) show 4 5% differences in the 2012 RRFs (4 vs. 36 km) too. Also, all four sites (Pittsboro, Fry Pan, Bent Creek and Waynesville) that show differences of 4 3% in 2007 RRFs (4 vs. 12 km) also have differences of 4 3% in 2012 RRFs (4 vs. 12 km), with Fry Pan showing a notable increase from

3.4% (in 2007) to

7.1% (in 2012) difference in RRF.

4.1. Statistical significance

To further quantify the differences (or similarities) between the model responses in different grid resolutions, we used the Student’s t -test ( Steel et al., 1997 ) for the second part of the analyses. As we 

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Table 3 O 3 design values and p -values from Student’s t-tests

Region ID DVC 2007 DVF 2012 DVF p -Value (12 vs. 4)

36 km 12 km 4 km 36 km 12 km 4 km 2007 2012

Charlotte CTYL 0.101 0.086 0.087 0.087 0.079 0.080 0.081 0.79 0.57 ROCK 0.100 0.084 0.087 0.087 0.077 0.080 0.080 0.75 0.90 ENVL 0.099 0.085 0.086 0.087 0.078 0.080 0.081 0.39 0.47 PLZA 0.098 0.084 0.085 0.087 0.077 0.080 0.080 0.82 0.85 CRSE 0.092 0.078 0.079 0.080 0.072 0.074 0.076 0.56 0.38 ARWD 0.092 0.079 0.082 0.082 0.073 0.077 0.078 0.77 0.79 MONR 0.088 0.074 0.077 0.075 0.070 0.071 0.070 0.10 0.24
Triangle (Raleigh–Durham–Chapel Hill) MLBK 0.094 0.080 0.080 0.080 0.074 0.073 0.075 0.85 0.76 BTNR 0.094 0.078 0.079 0.079 0.072 0.075 0.074 0.57 0.78 STAG 0.093 0.079 0.080 0.080 0.073 0.074 0.074 0.87 0.84 BSHF 0.091 0.070 0.077 0.077 0.066 0.073 0.072 0.45 0.47 FKL 0.090 0.077 0.077 0.078 0.071 0.071 0.072 0.70 0.54 DUKE 0.089 0.076 0.077 0.075 0.070 0.070 0.070 0.76 0.97 WRAL 0.088 0.075 0.076 0.075 0.068 0.070 0.068 0.50 0.65 FUQV 0.088 0.075 0.073 0.075 0.070 0.068 0.070 0.54 0.46 WJOH 0.087 0.074 0.075 0.074 0.068 0.068 0.068 0.83 0.97 PITT 0.082 0.067 0.068 0.071 0.060 0.063 0.065 0.15 0.04
Triad (Greensboro–Winston Salem–High Point) DAVI 0.096 0.080 0.083 0.084 0.073 0.076 0.079 0.36 0.20 HTAV 0.094 0.078 0.079 0.080 0.073 0.074 0.075 0.93 0.82 UCRS 0.093 0.078 0.079 0.079 0.071 0.073 0.073 0.92 1.00 BETH 0.091 0.076 0.076 0.076 0.071 0.073 0.071 0.72 0.79 CHGR 0.090 0.070 0.074 0.076 0.064 0.071 0.072 0.68 0.57 MLVL 0.090 0.075 0.077 0.076 0.068 0.071 0.071 1.00 0.93 SHIL 0.089 0.073 0.078 0.076 0.068 0.072 0.072 0.26 0.49 SOPH 0.085 0.071 0.072 0.072 0.065 0.066 0.067 0.97 0.75 POLL 0.082 0.068 0.069 0.069 0.063 0.064 0.065 0.78 0.62

Asheville MTMI 0.089 0.072 0.074 0.075 0.067 0.070 0.071 0.58 0.58 FRYP 0.087 0.073 0.074 0.077 0.069 0.068 0.073 0.03 0.02 PKNO 0.087 0.073 0.075 n/a 0.066 0.070 n/a n/a n/a BKNO 0.085 0.070 0.073 n/a 0.066 0.068 n/a n/a n/a BENT 0.083 0.068 0.071 0.074 0.063 0.067 0.069 0.02 0.03 WAYN 0.080 0.067 0.068 0.071 0.060 0.064 0.067 0.20 0.10
Greenville, Rocky Mount and Wilson (Down East) LEGT 0.089 0.080 0.076 0.077 0.074 0.070 0.072 0.59 0.38 FARM 0.084 0.073 0.074 0.073 0.069 0.070 0.068 0.62 0.77 KINS 0.082 0.072 0.073 n/a 0.068 0.069 n/a n/a n/a KVIL 0.082 0.071 0.072 0.072 0.066 0.067 0.068 0.83 0.94 JVIL 0.081 0.073 0.073 n/a 0.070 0.070 n/a n/a n/a
Fayetteville WADE 0.088 0.077 0.077 0.078 0.070 0.071 0.073 0.90 0.70 HOPE 0.087 0.077 0.077 0.077 0.070 0.071 0.072 0.84 0.53
NW Piedmont (Hickory) ALEX 0.088 0.074 0.075 0.075 0.069 0.069 0.069 0.62 0.81 LENR 0.087 0.073 0.074 0.073 0.068 0.069 0.068 0.91 0.73

Various areas GAST 0.084 0.073 0.073 0.073 0.069 0.069 0.069 0.95 0.76 CAMD 0.081 0.073 0.076 n/a 0.071 0.074 n/a n/a n/a LINV 0.078 0.065 0.066 0.067 0.060 0.061 0.063 0.94 0.75 WILM 0.078 0.065 0.069 0.069 0.062 0.065 0.066 0.70 0.93

CASTNET Sites CAND 0.086 0.074 0.073 0.073 0.069 0.068 0.068 0.39 0.61 CRAN 0.083 0.068 0.069 0.070 0.063 0.065 0.066 0.77 0.99 COWE 0.077 0.066 0.066 n/a 0.062 0.060 n/a n/a n/a BEAU 0.076 0.066 0.067 n/a 0.063 0.064 n/a n/a n/a

Note : Design values 4 0.084 ppm are shown in bold font. S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5021

### discussed earlier, the only factor that changes DVFs (between future years or between grid resolutions) is the RRFs. Since DVCs remain constant for all grid resolutions, for the Student’s t-test it was appropriate to focus on RRFs, the key determinant for attainment. The test was to determine whether the daily RRFs for the 12-km grid are equal to the daily RRFs for the 4-km grid, for each monitoring site. The null hypothesis was defined as no difference between the mean daily RRFs from the 12-km grid and the 4-km grid, i.e., H 0 

### : m 12 

### m 4 

### 1⁄4 0 (or m 12 

### 1⁄4 m 4 

### ) and H 1 

### : m 12 

### m 4 

### a 0 (or m 12 

### a m 4 

### ). Assuming that the two populations from which the samples were drawn have unequal 

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0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor (RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(a)

0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor (RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(b)

0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor (RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(c) 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor (RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(d)

0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor(RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(e)

0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.70 0.75 0.80 0.85 0.90 0.95 1.00DVC or DVF (ppm)Relative Reduction Factor (RRF)

Mean_BY O 3(ppm) DVF DVC RRF 0.085 ppm

(f)

Fig. 6. Mean base-year O 3 vs. DVCs, RRFs and DVFs from 36- (top), 12- (middle) and 4-km (bottom) grid resolutions, shown for 2007 (left column) and 2012 (right column). S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5022

### variances ð s 2 12 

### a s 2 4 

### Þ , the appropriate variance for use in calculating t-statistics is computed as

s ð  ̄

Y 12  ̄ Y4 Þ 

### 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs 12 

### Þ 2



### n 12 

### þ ðs4 

### Þ 2



### n 4 

### s

, where n 12 

### and n 4 

### are the number of episode days used in calculating the mean daily RRFs for the 12- and 4-km grids, and hence had a maximum value of 16, ðs 12 

### Þ 2 

### and ðs4 

### Þ 2 

### are the sample variances for the 12- and 4-km grids, and  ̄ Y 12 

### and  ̄ Y4 

### are the monitor-specific mean daily RRFs for the 12- and 

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0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110Relative Reduction Factor (RRF)

Current-Year Desi g n Value ( DVC ) (pp m ) 4-km 12-km 36-km

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110Relative Reduction Factor (RRF)

Current-Year Desi g n Value ( DVC ) (pp m ) 4-km 12-km 36-km

( a) (b )

Fig. 7. Variation of DVCs vs. 2007 RRFs (left) and 2012 RRFs (right).

0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110Future-Year Design Value (DVF) (ppm)

Current-Year Desi g n Value (DVC) (ppm) 4-km 12-km 36-km 0.085 ppm

0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100

0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110Future-Year Design Value (DVF) (ppm)

Current-Year Desi g n Value (DVC) (ppm) 4-km 12-km 36-km 0.085 ppm

(a) (b)

Fig. 8. Variation of DVCs vs. 2007 DVFs (left) and 2012 DVFs (right).

Table 4 Number of sites that have differences in 12- and 36-km RRFs compared to 4 km

Magnitude of RRF differences (%) 2007 2007 2012 2012 4 vs. 12 km 4 vs. 36 km 4 vs. 12 km 4 vs. 36 km

0 15 7 11 9

o 3 2 3 1 9 2 6 1 2 3–5 4 10 4 12

4 5 0619 S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5023

### 4-km grids. The corresponding t-statistic is then defined as

t0 

### 1⁄4  ̄ Y 12 

###  ̄ Y4



### s
 ̄

Y 12  ̄ Y4 

### with an effective degree of freedom equal to

df 1⁄4 ðs2 12 

### = n 12 

### Þþðs2 4 

### = n 4 

### Þ 1⁄2ðs2 12 

### = n 12 

### Þ = ðn 12 

### 1 Þ þ 1⁄2ðs2 4 

### = n 4 

### Þ = ðn 4 

### 1 Þ .

One should note that the t-statistic presented in the paper is t0 

### . The prime indicates that, due to the test setup, the t-statistic is not distributed strictly as a Student’s t but as an approximation to it. The approximate nature dictates that we use an effective degree of freedom with the tabulated t as opposed to a more common calculation of the degrees of freedom.

Table 3 also shows the results of the t-test by presenting the p -values for each monitor, when comparing the RRFs from the 12 and 4 km for each of the two future years. Using a significance level of

a 1⁄4 0

: 05, any p -value o 0.05 would be significant, and the null hypothesis is rejected in favor of the alternative hypothesis. A low p -value for thestatistical test indicates rejection of the null hypothesis because it indicates how unlikely it is that a test statistic as extreme as, or more extreme than the one given by these data will be observed from this population if the null hypothesis is true. For example, if p 1⁄4 0

: 012, this means that if the population means were equal as hypothesized (under the null), there is a 12 in 1000 chance that a more extreme test statistic would be obtained using data from this population. If one agrees thatthere is enough evidence to reject the null hypothesis, one may conclude that there is significant evidence to support the alternative hypothesis. Applying the Student’s t-test on a per-monitor basis helps isolate areas (or monitors) that may benefit from the finer grid resolution. Of all the North Carolina sites analyzed, Bent Creek and Fry Pan accept H 1 

### , i.e., the 12- and 4-kmRRFs are different for both 2007 and 2012 futureyear emissions scenarios. Pittsboro rejected H 0 

### only for 2012. For all the other sites in North Carolina, the differences between the RRFs from the 12 and 4 km were statistically insignificant. Additional examination of the sites that reject H 0 

### reveal that all three sites have DVCs which are near attainment ( p 0.087 ppm), and DVFs well below the NAAQS ( p 0.077 ppm). Both Bent Creek and Fry Pan are situated at high elevations, and we believe that topography at these sites may contribute to significant differences in RRFs between the two grid resolutions; at these locations, the models are blending air masses of different origins and the 12- km grid artificially dilutes NO x 

### emissions over a relatively larger grid volume. Pittsboro is a special case since it is a rural site that lies at the edge of the Triangle urban area, and may also be affected by a major NO x 

### source (Cape Fear power plant) in its vicinity. Given these two reasons, the emissions gradient and hence the individual values in the daily maxima array in the ‘nearby’ cells in each of the 4- and 12-km grids may undergo a rapid transitionand hence contribute to different RRFs. Furthermore, the effect of NO x 

### titration from the Cape Fear source may also lead to differences in the RRFs between the two grid resolutions.

The US EPA draft guidance for demonstrating attainment of the NAAQS for PM 2.5 

### nonattainment areas (US EPA, 2001 ) recommends a similar approach for computing RRFs and then DVFs for future years. For urban areas, the US EPA recommends that states use a 12-km grid resolution for estimating RRFs for secondary particulate matter, but a much finer resolution of 5 km or less for primary particulate matter. Since there is an annual standard for PM 2.5 

### , states may resort toperforming annual base-year and future-year simulations to compute RRFs and DVFs; this will impose a huge burden on computational resources, especially for fine-grid modeling of longer periods. Based upon our application of the draft guidance for O 3 

### attainment purposes, we recommend that similar model evaluation be performed for PM 2.5 

### nonattainment areas to obtain ranges of variability for future-year PM 2.5 

### concentrations at various grid resolutions. States could then consider the use of coarse-grid resolutions, say 12 km for annual modeling to compute RRFs and DVFs for primary particulate matter as well, and then use the information gained from benchmark studies like these as bounds of variability to supplement the modeling results.

5. Conclusions

We used the MM5–SMOKE–MAQSIP modeling system to study future-year attainment of the 8-h O 3 

### NAAQS in several urban areas of North Carolina using a diverse set of meteorological (four different episodes in 1995, 1996 and 1997), chemical (two 

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S. Arunachalam et al. / Atmospheric Environment 40 (2006) 5010–5026 5024

### different future-year emissions scenarios—2007 and 2012) and physical (in three different model grid resolutions—36, 12 and 4 km) conditions. Using extensive model performance evaluation, we first established that the modeling systems performed well in capturing historical O 3 

### exceedances before using them in a relative sense for the future years. Using an illustration of the US EPA’s guidance for 8-h O 3 

### attainment demonstration in North Carolina, the results (focused on predicted RRFs and DVFs) show the potential uncertainty in modeled results due to grid resolution. Specifically, out of 42 sites analyzed in North Carolina, 38 (in the case of 2007) and 37 (in the case of 2012) sites have 12-km RRFs that differ by only o 3% when compared to the 4-km RRFs. However, only 26 (in the case of 2007) and 21 (in the case of 2012) sites show o 3% differences in the 36-km RRFs vs. 4-km RRFs, which indicates the sensitivity of the RRFs to the grid resolution modeled. In general, the coarser the grid resolution, the greater is the model response, and hence slightly lower are the RRFs. We were able to quantify the grid-resolution variability using the Student’s t-test, which showed that the differences between the 4- and 12-km computed RRFs were statistically insignificant except for three sites. These differences in RRFs (between the 36- and 4-km predictions) translate to an average difference of 1–3 ppb in the DVFs for some sites, and we recommend that this estimate of 1–3 ppb be considered as the estimate of variability due to grid resolution in the modeling. Based upon these results, future attainment demonstration studies (for ozone and perhaps PM 2.5 

### ) may consider using RRFs and DVFs from 12-km modeling and incorporate variability estimates into them.

Acknowledgments

The authors would like to thank the Division of Air Quality (DAQ) under the North CarolinaDepartment of Environment and Natural Resources for funding this work, under Modeling Assistance Contracts EA2012, EA03017 and EA05009. We also gratefully acknowledge Donald Olerud of Baron Advanced Meteorological Systems for the meteorological modeling and evaluation, the emissions modeling staff at DAQ for preparing the emissions inputs, Zac Adelman, Jeff Vukovich and Kim Hanisak of the Carolina Environmental Program for their assistance with preparing various other inputs, and George Bridgers of the DAQ for his contributions throughout this project. We also thank Jeanne Eichinger for her assistance with editing the final version of the manuscript. We finally thank the two anonymous reviewers for their valuable comments and suggestions that helped improve the overall quality of this paper.

References

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