3.1. Campaign-Long Results
 It is of interest first to characterize the New Hampshire atmosphere during July and August of 2004 with respect to NOx constituents, NOy, CO, and O3. CO and O3 indicate the relative importance of primary emissions and secondary processing, respectively [Fishman and Seiler, 1983]. Figure 1 shows the 1-min average mixing ratios of NO and NO2 at TF for 26 July through 15 August 2004. During this time period, it can be seen that NO2 was generally higher than NO, except for occasional spikes of NO that generally occurred late morning local time, indicating that photolysis of NO2 at this time was occurring more rapidly than O3 was being titrated by NO. The range of NO measured was from 0.005 ppbv (= 5 pptv, the LDL of the instrument) to 6.45 ppbv, with a total of 17,642 measured points. The average NO mixing ratio was 0.26 ± 0.52 (SD) ppbv. Note that these values are calculated without consideration of those times when the NO mixing ratio was below the LDL of the instrument (total of 28 1-min points), meaning that the average values presented here are inflated very slightly. A Thermo Environmental Instruments (TEI, Woburn, MA) Model 42C-TL chemiluminescent NOx monitor operated without a converter so as to measure only NO was also operated at TF over the course of the ICARTT campaign. This instrument also provides 1-min average data. Details of its operation are discussed by Griffin et al. [2004a] and are available on the AIRMAP website. To confirm the operation of the new NO/NO2 instrument, the NO measurements from each instrument are compared. A linear regression between the NO mixing ratios of the TEI instrument (y variable) and those from the new combined NO/NO2 instrument (x variable) results in a slope of 0.96, an intercept of 0.01, and an R2 of 0.95 (not shown). Only times when both instruments measured NO above their individual LDLs are considered for this regression.
 Because of the lack of a photolytic loss process, NO2 mixing ratios were highest at night. Conversion of NO2 to nitric acid (HNO3) through reaction with the hydroxyl radical (OH) is also expected to lead to loss of NO2 during the day [Seinfeld and Pandis, 1998]. At night, NO2 conversion to dinitrogen pentoxide (N2O5) with subsequent conversion to HNO3 is also a chemical loss process for NO2 [Seinfeld and Pandis, 1998]. Over the course of the ICARTT campaign, the range of measured NO2 mixing ratios was 0.02 to 12.05 ppbv for 9,653 data points, with only a very small number (3) of measurements found to be below the LDL. The average NO2 mixing ratio at TF during this part of the ICARTT campaign was 2.07 ± 1.66 (SD) ppbv.
 The total NOx and NOy measured at TF during the same period are shown in Figure 2. NOx makes up a significant fraction of NOy under most scenarios, but times of definite deviation are observed (for example, 11 August 2004). Total NOx mixing ratios for times when both NO and NO2 are above the instrument LDLs range from 0.21 ppbv to 17.54 ppbv, with an average of 2.33 ± 1.93 (SD) ppbv. The corresponding NOy values ranged from 0.52 to 23.83 ppbv, with an average value of 3.67 ± 2.51 (SD) ppbv. The high end of the range of measured NOy values all occurred on 27 July 2004; this was the only date on which NOy levels exceeded 20 ppbv. NOy values greater than 20 ppbv have been associated with hydrocarbon-sensitive or NOx-saturated O3 chemistry [Sillman, 1995]. Similar levels of NOy were observed at this same site during a similar time period during the New England Air Quality Study (NEAQS) of 2002 [Griffin et al., 2004a].
Figure 2. Total measured NOx (shaded) and NOy (solid) mixing ratios (ppbv) at TF over the course of the ICARTT campaign.
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 The ratio of NOx to NOy indicates photochemical processing of pollutants because it can generally be assumed that the majority of NOy is emitted in the form of NOx [Nunnermacker et al., 1998]. In general, daytime values of this ratio below 0.3 indicate a highly processed air mass, while those above 0.3 are representative of fresher emissions [Trainer et al., 1993; Chin et al., 1994]. Values for this ratio approach unity at night. For those times when both NOx and NOy measurements are available, the ratio of NOx to NOy is shown in Figure 3, which also includes a solid line indicating a value of unity. In general, a diurnal pattern for this ratio is observed, with the minimum values (overall minimum value of 0.15 occurring at 2057 UTC on 29 July 2004, range of daily minimum values of 0.15 to 0.55) occurring during the afternoon (generally between 1600 to 0030 UTC). The value of this ratio approached unity daily during the 3-week sampling period, with this generally occurring overnight or early morning local time.
Figure 3. Ratio (dimensionless) of total measured NOx to total measured NOy at TF over the course of the ICARTT campaign.
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 Concentrations of HNO3 (a major component of NOy) in New England decrease overnight because of depositional losses and the lack of a photochemical source that outweigh its nighttime formation via hydrolysis of N2O5, as was observed during NEAQS [Brown et al., 2004; Dibb et al., 2004]. Other non-NOx contributors to NOy (including alkyl nitrates and peroxy acetyl nitrate) are also expected to decrease overnight as a result of the lack of a photochemical source. Therefore NO and NO2 are expected to be the major contributors to NOy overnight (leading to a ratio of unity) because NO is continually emitted from combustion sources regardless of time of day and because photolysis of NO2 ceases after sundown. The majority of NOx overnight is expected generally to be in the form of NO2 because any emitted NO will react rapidly with any residual O3 from the previous day. The lack of significant NO mixing ratios at night is confirmed by the measurements shown in Figure 1.
 The distributions of O3 and CO at TF during the same time period are shown in Figure 4. CO is used as a tracer of both short- and long-range transport of primary combustion emissions [Fishman and Seiler, 1983], while O3 is an indicator of photochemical activity, as discussed previously. In combination, these measurements give an overall picture of the atmosphere at TF.
 In general, CO varied between 100 and 200 ppbv diurnally, except for a pollution event that occurred 29 and 30 July 2004, when peak CO reached a value of 338 ppbv. This pollution event is also captured in the O3 temporal profile, as peaks in O3 reached upward of 90 ppbv during this time period; this value is significantly greater than the background mixing ratio of O3 during summer in southeastern New Hampshire [Mao and Talbot, 2004]. The minimum CO mixing ratio (68 ppbv) was observed on 31 July 2004. The average CO mixing ratio during this time period was 157 ± 40 (SD) ppbv. Because of the much stronger diurnal variability of O3, no range, average value, or standard deviation are given for this pollutant. However, it is interesting to note that a larger than average O3 peak (88 ppbv) occurred late on 11 August 2004, the same day on which significant deviations between NOx and NOy occurred, as shown in Figures 2 and 3. Ozone peaks and deviation between NOx and NOy indicate photochemical processing.
 Figure 5 indicates the values of Φ calculated using equation (2) when the requisite mixing ratios of NO, NO2, and O3 are available from the measurements. Values for jNO2 are also required, as is the temperature in order to calculate k1. In addition, certain data points have been removed from Figure 5. Times between 2000 and 0500 local time are not included. Only points in time with jNO2 values greater than or equal to 0.001 s−1 are considered. In addition, those points in time when jNO2 or the NO level changed rapidly were taken into account [Parrish et al., 1986; Carpenter et al., 1998]. A time interval, τ (min), required for NO to readjust to photostationary state at a level of 90% is defined, similar to Yang et al. :
When the change in jNO2 or NO mixing ratio between successive measurements was greater than 10%, calculated Φ values over the next τ minutes are removed from the analysis. For the remaining 3,561 data points, a regression of measured NO2 mixing ratios versus those calculated assuming that Φ = 1 yields a slope of 0.94 and a R2 of 0.97 when the intercept is forced to zero, as indicated in Figure 6. However, this type of regression is considerably misleading. Despite this strong correlation, 58% of the data points that are included in the regression fall outside of the 0.84 ≤ Φ ≤ 1.24 range indicated by the two additional solid lines in Figure 6.
Figure 5. Values of the Leighton ratio at TF over the course of the ICARTT campaign. Solid lines indicate the range of Φ values that would be considered within photostationary state on the basis of measurement uncertainties.
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Figure 6. A regression between measured and predicted mixing ratios of NO2. Predictions are based on an assumed Φ value of 1.0.
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 The values of Φ indicated in Figure 5 show the clear diurnal pattern of this parameter, with lowest values occurring at times of high solar zenith angle. Lowest values were less than unity, most likely because of uncertainty or error in the jNO2 values used; these values were generally within 10% of 0.84. In all, only 154 points (4% of all Φ data points) were associated with Φ values less than 0.84. The daily minimum values ranged from 0.5 (7 August 2004) to 1.07 (31 July 2004). Peak values generally occurred during times of peak photochemical activity. The daily peak values range from 1.41 (27 July 2004) to 5.87 (7 August 2004). Considering the entire 3-week data set and only those values included in Figure 5, the average value of Φ is 1.38 ± 0.44 (SD). However, it is of greatest interest to explain the points in time with larger deviations from the photostationary state, as discussed below.
3.2. Meteorological Controls on Φ
 It must be determined whether the observed deviations from photostationary state are a result of physical or chemical phenomena. To that end, the Φ values calculated using equation (2) and exhibited in Figure 5 have been compared to wind speed, wind direction, temperature, relative humidity (RH), and jNO2, which are all measured at TF with a resolution of 1 min.
 Regression analyses performed on a daily basis, as well as on the data set as a whole, indicated that values of the Leighton ratio are independent of wind speed and wind direction. For the entire data set, the R2 values are 0.06 and 0.02, respectively, for wind speed and wind direction. This indicates that the strong deviation from Φ values equal to unity is likely a local phenomenon that does not depend on transport or transport speed from a specific upwind location. On a daily basis, the R2 values ranged from 7.0E-05 to 0.53 for wind speed and from 1.0E-05 to 0.10 for wind direction. These findings are in contrast to calculations of Φ performed by Mannschreck et al.  for data collected on the Hohenpeissenberg, where Φ was only significantly greater than 2.0 when the measured air mass had been transported from a specific wind direction.
 Correlations of Φ with temperature and RH are moderately stronger than those for wind speed and direction but are also weak. For the entire data set, the R2 values are 0.13 and 0.20 for temperature and RH, respectively. The relationship with temperature is positive, and that with RH is negative. The daily ranges of R2 are 0.01 to 0.53 for temperature and 4.0E-03 to 0.54 for RH. During daylight, temperature is generally higher, and RH is generally lower, explaining the positive and negative relationship each variable has with Φ because of its diurnal profile. There are examples during the ICARTT period when no relationship between temperature or RH and Φ exists. From investigation of the data, steep temporal gradients in temperature and RH are observable during certain days. This occurred without strong simultaneous shifts in solar radiation and without notable changes in calculated Φ values. Therefore the improved regressions with temperature and RH are more likely to be related to diurnal solar patterns.
 Of the meteorological variables considered for regression with Φ, the strongest relationship was found for jNO2. For the entire data set, R2 is 0.41, which still indicates a fairly weak relationship, despite being significantly larger than all other regression coefficients when applied to the entire data set. The range for individual days ranged from 0.03 to 0.68. The weakest relationship was observed on days of weakest sunlight. Because of these weak, but improved, regressions, it is hypothesized that strong solar radiation controls some chemical process(es) that then exert(s) an influence on Φ.
3.3. Chemical Controls on Φ
 Besides the species that potentially influence PO2 or X levels, the other natural candidates to exert a chemical control on the Leighton ratio are the constituents of NOx themselves. Figure 7 presents the inverse relationship between the calculated Φ values and the measured total NOx. The range that is considered as adhering to photostationary state is indicated by the two solid lines. Larger mixing ratios of total NOx clearly show adherence to photostationary state, while smaller values (generally less than 3 ppbv) tend to show deviations, which is consistent with NOx dominating PO2 loss at higher values of NOx. It is of interest, therefore, to determine what other species may influence Φ values, particularly at times when total NOx mixing ratios are less than 3 ppbv.
Figure 7. Calculated Φ values versus total measured NOx (ppbv) over the course of the ICARTT campaign at TF. Solid lines indicate the range of Φ values that would be considered within photostationary state on the basis of measurement uncertainties.
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 In addition, the NOx to NOy ratio should be considered when investigating deviations from photochemical stationary state. Figure 8 indicates this relationship and shows that deviations of Φ from unity are more likely to occur when the NOx to NOy ratio is less than 0.5, indicating a more processed air mass. This relationship generally corresponds to Φ values that peak during the afternoon, as specified in Figure 5.
Figure 8. Calculated Φ values versus the ratio (dimensionless) of total measured NOx to total measured NOy over the course of the ICARTT campaign at TF. Solid lines indicate the range of Φ values that would be considered within photostationary state on the basis of measurement uncertainties.
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 As stated above, deviations from Leighton ratios of unity can generally be ascribed to the abundance of PO2 or to halogen chemistry. Biogenic hydrocarbons and CO dominate OH reactivity at this location in summer [Griffin et al., 2004a; M. White et al., Volatile organic compound measurements at Thompson Farm, NH, and Appledore Island, ME: A comparison of relative reactivities and variability, unpublished manuscript, 2007]. Therefore any deviation of Φ from photostationary state may be caused by PO2 related to these species. An overall regression between CO and Φ yields no relationship, with an R2 of 0.01 and a slightly negative slope (not shown). In addition, unlike NOx, Φ values show no inclination for higher values at a specific threshold mixing ratio. On a daily basis, the R2 value for this regression ranges from 4.0E-04 to 0.27. Despite this weak relationship, it cannot be concluded that HO2 formed from the oxidation of CO by OH is negligible with respect to the significant deviation from photostationary state observed at TF because HO2 variability is driven more by variability in OH than by variability in CO.
 A similar regression between isoprene (chosen as the predominant VOC based on reactivity) mixing ratios and Φ values is indicated in Figure 9a. Here, 10-min averaged Φ values are used, corresponding to the 10-min averaged mixing ratios of isoprene. Points are shaded by jNO2. It is clear from Figure 9a that no strong linear relationship exists between measured isoprene mixing ratios and calculated Φ values. However, as with NOx, a general increase in Φ can be observed at low mixing ratios of isoprene. Likewise, a scatterplot between the representative halogenated methane compound CH2ClI and Φ (Figure 9b) shows similar behavior. The low mixing ratios of representative species that are either anthropogenic or biogenic, high jNO2 values, and low ratios of NOx to NOy that are all coincident with the high values of Φ support the hypothesis that Φ values depend inherently on strong photochemistry. This is despite the fact that emissions of isoprene are likely highest under conditions of strong sunlight. In addition, the hypothesis that photochemistry, not different emissions sources, controls Φ is supported by the lack of a relationship between Φ and wind characteristics.
Figure 9. Calculated Φ values versus (a) isoprene and (b) CH2ClI mixing ratios at TF over the course of the ICARTT campaign shaded by jNO2. Considerably fewer data points are shown here because of the longer temporal resolution and less frequent measurements of organic gases compared to NOx. Leighton ratio values have been averaged to the same timescale as the organic gas mixing ratio. Solid lines indicate the range of Φ values that would be considered within photostationary state on the basis of measurement uncertainties.
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3.4. Estimates of PO2 Influence
 If it is assumed that PO2 is the sole contributor to the observed deviations from photostationary state, an estimated PO2 mixing ratio can be calculated by adding a second term (k2[NO][PO2]) to the denominator of equation (2), setting Φ equal to 1.0, and solving for [PO2]:
where k2 is the temperature-dependent rate coefficient (ppbv−1 s−1) for the reaction between HO2 and NO. It is assumed that the rate coefficients for reactions between individual RO2 molecules and NO are equivalent to this value [DeMore et al., 1997]. In this scenario, it is the PO2 reaction with NO that converts NO to NO2 in excess of the NO and O3 reaction. On the basis of equation (4), the required PO2 level for those times when calculated Φ is greater than 1.0 ranges from approximately 1.1E-04 ppbv to 0.33 ppbv, with an average of 0.04 ± 0.04 (SD) ppbv for the entire data set. An average PO2 mixing ratio between 0.02 and 0.03 ppbv was modeled for a similar time period during NEAQS (August 2002) at TF by Griffin et al. [2004a]; this value qualitatively agrees with the numbers indicated here. The time series of required PO2 needed to bring Φ values equal to 1.0 is shown in Figure 10. Clearly, the temporal profile of PO2 follows that of the Φ values presented in Figure 5.
Figure 10. Mixing ratios of PO2 (ppbv) that would force Φ values to be equal to 1.0 at TF at those times during the ICARTT campaign when Φ > 1.0.
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 Numerous studies have measured PO2 mixing ratios directly, used the method described here to quantify them, or applied radical budget or photochemical modeling techniques to estimate them. The variety of locations and seasons for which these measurements and calculations have been performed make a direct comparison difficult. However, a qualitative comparison is given here. Measurements of PO2 using chemical amplification and other techniques have shown average mixing ratios on the order of tens of pptv in locations ranging from Hawaii to the Canary Islands to Mace Head to rural Germany [Hauglustaine et al., 1996; Zenker et al., 1998; Carslaw et al., 1999; Mihelcic et al., 2003]. During the ROSE campaign during summer 1990, Cantrell et al.  measured PO2 mixing ratios as high as approximately 300 pptv in rural Alabama. Radical budget and photochemical steady state models predict PO2 mixing ratios that are generally on the same order of magnitude [Kleinman et al., 1995; Frost et al., 1998]. Calculations of PO2 from expressions similar to equation (4) result in estimates of the PO2 mixing ratio that are generally in accord with those presented here, despite differences in location and season [Ridley et al., 1992; Kleinman et al., 1995; Carpenter et al., 1998; Frost et al., 1998; Rohrer et al., 1998; Baumann et al., 2000; Duderstadt et al., 1998; Volz-Thomas et al., 2003; Yang et al., 2004]. In general, PO2 mixing ratios calculated by forcing Φ values to adhere to photostationary state are larger than those measured, indicating that there is likely another reaction occurring that converts NO to NO2. The ratio of estimated to measured PO2 on average is 1.23 for the work of Cantrell et al.  and in the range of 2.0 to 3.0 for that of Hauglustaine et al.  and Mannschreck et al. . PO2 mixing ratios calculated using some form of equation (4) also tend to be larger than those calculated using radical budget calculations or modeling techniques [Frost et al., 1998; Volz-Thomas et al., 2003], with this discrepancy being as much as two orders of magnitude [Carpenter et al., 1998]. However, adequate modeling results are achieved in some cases [Ridley et al., 1992; Kleinman et al., 1995].
 A zero-dimensional version of the Caltech Atmospheric Chemistry Mechanism (CACM) [Griffin et al., 2002] is used with observed meteorological conditions and species mixing ratios to estimate HO2 and total RO2 mixing ratios over the 10-min periods of interest when VOC and NOx measurements are temporally coincident. While the development of CACM was motivated by the desire to simulate SOA formation, particular attention was also paid to the chemistry of NOx and VOCs containing fewer than six carbon atoms so that accurate O3 prediction was also possible. CACM uses lumped (on the basis of structures and reaction rate constants) surrogates for VOCs and numerically solves kinetic rate expressions for over 120 different species. The pseudo steady state approximation is made for almost 70 individual organic radical species but is not made for HO2 and the total RO2 mixing ratio. The photolysis rates within CACM are scaled such that the jNO2 in the model is equivalent to that measured at TF. The performance and use of CACM has been documented previously [Griffin et al., 2002, 2004b]. While CACM was developed for use in a highly polluted urban air basin [Griffin et al., 2002], the chemistry occurring at TF is included in the mechanism because CACM considers the oxidation of C1–C10 VOCs, including explicit treatment of isoprene. The version of CACM used incorporates all of the model improvements described by Griffin et al. . A comparison between PO2 mixing ratios calculated using equation (4) for the relevant 10 min averages and PO2 estimated using CACM is shown in Figure 11. With the exception of a few points in which CACM predicts significantly higher PO2 mixing ratios than those determined using equation (4), it is observed that the majority of the points lie above the one-to-one line shown in Figure 11, as would be expected if species other than peroxy radicals were affecting the Leighton ratio values at this site.
 By including the reaction between NO and PO2, a new Leighton ratio, termed here Φ1, can be calculated as discussed previously:
 To calculate Φ1 using equation (5), measurements of NO, NO2, and O3 mixing ratios and jNO2 are used with calculated rate constants (based on measured temperatures) and estimated PO2 mixing ratios (from CACM). Figure 12 indicates both Φ and Φ1 values over the course of ICARTT to show how much of the deviation from unity can be attributed to PO2 chemistry. On average, estimated PO2 levels can account for approximately 71% of the observed departures of Φ from unity, which within uncertainty could be said to account for all of the deviation. It should also be noted that the PO2 values calculated using CACM have uncertainties associated with heterogeneous HO2 loss processes and halogen chemistry, as discussed by Griffin .
Figure 12. Comparison of Φ values (open diamonds) calculated using equation (2) and Φ1 values (solid squares) calculated using equation (5) with [PO2] from CACM model output. Solid lines indicate the range of Φ values that would be considered within photostationary state on the basis of measurement uncertainties.
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 It is assumed for the remainder of this discussion that the deviations of Φ1 from unity in Figure 12 are due to the presence of halogens in the atmosphere at TF, as discussed by Zhou et al. [2005, also submitted manuscript, 2006]. In a manner similar to that used to derive equation (4), the product of the reaction rate constant of a halogen atom, k3X, and the halogen atom concentration can be determined for those periods when Φ1 is greater than 1.0, assuming that the halogen monoxide (XO) is in steady state:
 When combined with numerical values for k3X for X = Cl or X = I [DeMore et al., 1997; Sander et al., 2006], it is possible to estimate the mixing ratios of Cl or I, assuming that they are the only halogen atom present. The possibility of X = Br is not considered here as the most photolabile halogenated methane compound observed at TF is CH2ClI (Varner et al., manuscript in preparation, 2007). The application of equation (6) in this analysis forces only one type of halogen to be present at a time.
 Figure 13 indicates the Cl and I mixing ratios that would force Φ1 to be 1.0, as calculated through equation (6). As would be expected, the temporal profiles of these halogen atoms follow those of Φ and Φ1. Necessary Cl mixing ratios range from 0 to 0.6 pptv and have an average value of 0.07 pptv. The required I mixing ratios reach up to 1.2 pptv and have an average value of 0.14 pptv. On the basis of the relative strengths of the carbon-Cl and carbon-I bonds (Varner et al., manuscript in preparation, 2007), it is more likely that I is the halogen atom that is responsible for deviations of Φ from unity if it is assumed that CH2ClI is the primary source of the halogen atoms. It should be noted that it is likely that Cl and I are each present and working in concert to lead to deviations of Φ from unity; however, a method that would allow an estimation of the combined effect of multiple halogens is not possible given the species currently measured at TF.
 It is possible to estimate the associated ClO and IO mixing ratios using a temperature-dependent rate constant for the reactions between XO and measured NO [DeMore et al., 1997; Sander et al., 2006]. The corresponding average ClO mixing ratio was 3.9 pptv (range up to 27 pptv). Chang et al.  modeled summer Cl and ClO mixing ratios in the coastal marine boundary layer of Taiwan, with average respective values being approximately 0.01 pptv and 2.0 pptv. These estimates are on the same order of magnitude for those calculated for TF. The corresponding average IO mixing ratio was 8.7 pptv, with a maximum value of 64 pptv. Peters et al.  observed average levels of IO up to 7.7 pptv during daylight hours in coastal European locations. While the IO levels calculated here are somewhat larger than those measured at Appledore Island during ICARTT (Varner et al., manuscript in preparation, 2007), the halogen levels estimated for TF appear to be atmospherically realistic given the level of qualitative agreement with values measured and modeled for other locations.