Measurements of several short-lived photochemical species (e.g., OH, HO2, and CH2O) were obtained from the DC-8 and P3-B aircraft during the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) campaign. To assess fast photochemical theory over the east Asian coast and western Pacific, these measurements are compared to predictions using a photochemical time-dependent box model constrained by coincident measurements of long-lived tracers and physical parameters. Both OH and HO2 are generally overpredicted by the model throughout the troposphere, which is a different result from previous field campaigns. The calculated-to-observed ratio of OH shows an altitude trend, with OH overpredicted by 80% in the upper troposphere and by 40–60% in the middle troposphere. Boundary layer and lower tropospheric OH ratios decrease from middle tropospheric values to 1.07 for the DC-8 and to 0.70 for the P3-B. HO2 measured on the DC-8 is overpredicted by a median of 23% and shows no trend in the agreement with altitude. Three subsets of data which compose 12% of the HO2 measurements represent outliers with respect to calculated-to-observed ratios: stratospherically influenced air, upper tropospheric data with NO > 135 pptv, and data from within clouds. Pronounced underpredictions of both HO2 and OH were found for stratospherically influenced air, which is in contrast to previous studies showing good agreement of predicted and observed HOx in the stratosphere. Observational evidence of heterogeneous uptake of HO2 within low and middle tropospheric clouds is presented, though there is no indication of significant HO2 uptake within higher-altitude clouds. Model predictions of CH2O are in good agreement with observations in the median for background concentrations, but a large scatter exists. Factors contributing to this scatter are examined, including the limited availability of some important constraining measurements, particularly CH3OOH. Some high concentrations of CH2O near the coast are underpredicted by the box model as a result of the inherent neglect of transport effects of CH2O and its precursors via the steady state assumption; however, these occurrences are limited to ∼1% of the data. For the vast majority of the atmosphere, transport is unimportant in the budget of CH2O, which may be considered to be in steady state.
 NASA's Transport and Chemical Evolution over the Pacific (TRACE-P) field campaign was conducted along the Asian Pacific Rim and the western Pacific during February–April 2001 [TRACE-P Science Team, 2003]. In situ sampling of a broad suite of trace gases, aerosols, and meteorological parameters were provided from two aircraft, NASA's DC-8 and P3-B. The goals of TRACE-P were (1) to determine the composition of Asian outflow over the western Pacific in spring in order to understand and quantify the export of chemically and radiatively important gases and aerosols and their precursors from the Asian continent and (2) to determine the chemical evolution of the Asian outflow over the western Pacific in spring and to understand the ensemble of processes that control this evolution.
 An examination of fast photochemical cycles and their role in altering the chemical composition of Asian outflow is central to the second objective. These cycles involve short-lived chemical species that can be measured as well as theoretically predicted from in situ conditions. Test species available for examination in the TRACE-P data include the hydroxyl (OH) and hydroperoxyl (HO2) radicals and formaldehyde (CH2O). This paper presents results of a diurnal steady state modeling analysis of fast photochemistry using measurements during the TRACE-P campaign.
 The role of HOx as central in the determination of the atmosphere's oxidative capacity has been well established. OH is pivotal to understanding photochemical ozone formation, removal of pollutant gases, and new particle formation. In the lower troposphere, the principal source of HOx is from the reaction of the excited state O(1D) with water vapor following O3 photolysis, and in the presence of extremely low water vapor (such as in the upper troposphere), photolysis of acetone can become the dominant source [Singh et al., 1995]. Secondary production of HOx stems from the oxidation of hydrocarbons. Though this process initially consumes OH, further reactions of products from hydrocarbon oxidation such as formaldehyde (CH2O) can in turn produce multiple HO2 radicals. Additionally, species such as peroxides that are typically considered to be in equilibrium with HOx can become local sources when transport-induced nonequilibrium conditions occur, such as the convective transport of abundant peroxides from the boundary layer into the free troposphere [Jaeglé et al., 1997; Prather and Jacob, 1997]. HOx losses include the self-reaction of HO2 to form H2O2, reaction of OH with HO2, and reaction of OH with NO2 to form HNO3. Internal recycling of HOx is largely dependent on NO and CO and is important both in the definition of the O3-forming potential of the environment and in the efficiency of the HOx sinks.
 Formaldehyde plays an important role in the cycling of HOx, particularly as it relates to the oxidation of hydrocarbons. CH2O is an intermediate product in the oxidation by OH of methane and other hydrocarbons; its major global source is photochemical production. In addition, CH2O is directly emitted from industrial combustion and biomass burning, though these sources are expected to be relatively minor [Sigsby et al., 1987; Lee et al., 1997]. CH2O losses include oxidation by OH and photolysis. Photolysis proceeds through two branches, one of which leads to formation of HOx, while a secondary branch leads to stable products. Thus the photochemical cycling of CH2O is intimately tied to both hydrocarbon degradation, which itself has considerable uncertainty, and to HOx formation. This, along with the fact that CH2O can be more sensitive than HOx to changes in precursor species, makes it a particularly important test species for improving our understanding of photochemical cycling [Crawford et al., 1999].
2. Model Description
 The analysis presented here is based on calculations from a time-dependent photochemical box model, which has been described in detail in several previous studies [e.g., Crawford et al., 1999]. The approach used is diurnal steady state modeling, whereby long-lived precursor species are constrained to observations. Model-calculated species are then assumed to be at diurnal steady state, meaning that these predicted concentrations are integrated in time until their diurnal cycles no longer vary from day to day. The model chemistry includes basic HOx-NOx-CH4 gas phase reactions based on the recommendations of Atkinson et al. , Sander et al. , and Ravishankara et al. . Nonmethane hydrocarbon (NMHC) chemistry is based on the condensed mechanism of Lurmann et al.  with modifications included to address remote low-NOx conditions and to represent explicit chemistry for acetone, propane, and benzene. Surface and heterogeneous losses for soluble species are simulated as by Logan et al. .
 Photolysis rate coefficients are based on measurements. A DISORT four-stream implementation of the National Center for Atmospheric Research Tropospheric Ultraviolet-Visible (TUV) radiative transfer code is first used to calculate the diurnal variations of photolysis coefficients for clear-sky conditions. To account for local radiative conditions, these modeled clear-sky photolysis rates are then normalized throughout the day using a cloud correction factor (CCF) such that in situ spectroradiometer photolysis measurements are exactly matched at the time of the measurement [Shetter and Müller, 1999].
 Model calculations use the 1-min merged data set available on the GTE TRACE-P public data archive (http://www-gte.larc.nasa.gov). Model calculations require a minimum set of input constraints; these include observations of O3, CO, NO, NMHC, temperature, H2O (dew/frost point), pressure, and photolysis rates. Nonmethane hydrocarbons are constrained to observations where available (53% of the data) and are interpolated from adjacent measurements in data gaps of <5 min (37% of the data). Data gaps of >5 min were interpolated and examined subjectively for adequacy (10% of the data). Acetone and methyl ethyl ketone (MEK) are constrained to observations when data are available and are filled in the upper troposphere using an empirical relationship with CO. Missing data for methanol are filled throughout the troposphere. Model analysis is also limited to conditions with solar zenith angles <80°. There are 5167 points from the DC-8 (59% of the total) that meet the criteria for modeling, and 6621 points from the P3-B (70% of the total) are analyzed.
 In addition to the required constraints described above, the model constrains the following species when measurements are available: Hydrogen peroxide (H2O2), methyl hydrogen peroxide (CH3OOH), nitric acid (HNO3), and peroxy acetyl nitrate (PAN). If unavailable, these species are calculated to be in diurnal photochemical equilibrium. Impacts on model results from the limited availability of observations for these species are addressed in sections 3.2 and 4.2.2.
 With the exception of NO, constraining parameters are held constant throughout the diurnal cycle. Short-lived nitrogen (NO + NO2 + NO3 + 2N2O5 + HONO + HNO4) is photochemically partitioned at each time step, while the total short-lived nitrogen is held constant to a value such that predicted NO matches the measurement at the time of observation.
3. Observational Data and Modeling Approach
3.1. Oxygenated Hydrocarbon Data
 At upper tropospheric altitudes (e.g., above 7 or 8 km), oxygenated hydrocarbons such as acetone, MEK, methanol, and ethanol can constitute an important primary source of HOx [e.g., Singh et al., 1995; Jaeglé et al., 1998, 2000; Crawford et al, 1999]. Measurements of these oxygenates were obtained from the DC-8, which has a flight ceiling of 12 km and therefore flies within the altitudes where these species are expected to influence HOx. The median value of acetone measurements was 565 pptv at these upper altitudes, while that for MEK was 26 pptv. The alcohols methanol and ethanol were measured at median values of 711 and 33 pptv, respectively. No measurements of oxygenates were made on board the P3-B during TRACE-P. However, the P3-B flight ceiling is 7 km, below the altitude at which oxygenates are expected to become important components of the HOx budget.
Figure 1 shows the altitude dependence of oxygenate influence on HOx. Results are shown relative to base calculations that neglect oxygenates, illustrating the impact on HO2 from ketones (acetone and MEK, open boxes) and the combined impact from both ketones and alcohols (solid boxes). Increases in HO2 due to oxygenates are most significant in the upper troposphere (>11 km), with enhancements of up to 60–80%. The importance of oxygenates declines with decreasing altitudes; below 7 km, the median increase to HO2 is <5%, and the impact on OH is <1% (not shown). From this it can be concluded that an analysis of HOx data from the P3-B aircraft is not compromised by the absence of oxygenate data. Note that the majority of the increases due to ketones in Figure 1 are attributed to acetone; MEK has only a limited role in the HOx increases. Figure 1 also illustrates that the impact from alcohols is significantly less than the impact from ketones.
 Data coverage for oxygenate measurements on the DC-8 was ∼25% from 8 to 12 km, necessitating a method of estimation for points with missing values. At these altitudes, median measured CO was 117 ppbv. An empirical relationship for acetone and CO was derived from data at 8–12 km and was used to fill missing measurements for acetone as
The relation in equation (1) gives an r2 coefficient of 0.81 for observed versus calculated acetone and is notably similar to that derived by McKeen et al.  for data above 9 km in the western Pacific during February and March 1994 during the Pacific Exploratory Mission (PEM) West B field campaign (acetone (pptv) = −126.8 + 6.12*[CO(ppbv)]). Similarly, missing methanol values are filled on the basis of an empirical nonlinear relation to acetone derived from the TRACE-P data. MEK is assumed to equal a 5% fraction of the acetone mixing ratio, and ethanol is assumed to equal a 5% fraction of methanol.
 The oxidation of methanol via OH represents a small but nonnegligible source of CH2O throughout the troposphere. Thus it is necessary to extend data filling for methanol to altitudes below 8 km, where the coverage for CH3OH measurements on the DC-8 is 30%. Methanol was measured at these altitudes during TRACE-P at a median value of 895 pptv, and at these concentrations, the model calculations show the impact on CH2O predictions is on the order of 10%, similar to results presented by Frost et al. . Missing methanol data points at these lower altitudes are therefore also filled on the basis of empirical nonlinear fits to CO derived from the TRACE-P measurements.
3.2. Peroxide Data
 Another source of uncertainty in model predictions of HOx results from the limited availability of peroxide data. Measurements are available 48% of the time for H2O2 and 47% of the time for CH3OOH. The median measured value of H2O2 in the lower troposphere (below 4 km) during TRACE-P was 635 pptv, which decreased to 165 pptv at altitudes >8 km. The median measurement of CH3OOH was 215 pptv at altitudes below 4 km and was 80 pptv in the upper troposphere. For points without available measurements, concentrations are calculated by the model in photochemical diurnal steady state. Deviations from this equilibrium are expected, however, because of physical processes such as wet removal and transport influences (e.g., convective transport of peroxides into the upper troposphere). Test model simulations were conducted, calculating peroxides at points with available measurements in order to test both the ability of the model to predict peroxides and the influence of nonequilibrium peroxides on HOx. H2O2 is generally overpredicted by the model by 30–40%. Prominent exceptions are for the 1–2 km layer, which showed model overpredictions of factors of 2–3 due to the model assumption limiting H2O2 surface deposition to a 1-km boundary layer depth and at altitudes above 10 km, which had a median model underprediction of 25%. CH3OOH is overpredicted below 4 km by a median of 40% and is underpredicted by 40% in the upper troposphere, similar to results from previous studies [e.g., Olson et al., 2001]. Despite the differences in calculated versus observed peroxides, Figure 2 shows that the ultimate impact on calculated HO2 is minimal. The results are shown as the ratio of predicted HO2 for model simulations using observed peroxides versus calculated peroxides; thus the ratio is a measure of the influence of nonequilibrium peroxides on HOx during TRACE-P. While it may be argued that some increase in HO2 (∼10%) occurs above 10 km as a result of using observed peroxides, the median ratio is near 1 throughout most of the troposphere, indicating that while nonequilibrium conditions do exist for peroxides on a point-by-point basis, the overall bulk statistics for comparing measured and calculated HOx should be relatively insensitive to the availability of peroxide observations during TRACE-P. This conclusion is also supported by the analysis by Davis et al. .
4. Discussion of Results
 Direct measurements of HOx have been implemented from airborne platforms only since the 1990s, and results of comparison with theory have yielded inconsistencies from campaign to campaign. Measurements from the Stratospheric Tracers of Atmospheric Transport (STRAT) and Subsonic Aircraft Contrail and Cloud Effects Special Study (SUCCESS) campaigns indicated large HOx model underpredictions in the upper troposphere by up to 50–75% [Jaeglé et al., 1997; Wennberg et al., 1998; Brune et al., 1998]. HOx predictions during SASS (Subsonic Assessment) Ozone and Nitrogen Oxides Experiment (SONEX) were generally good, though some trends in the agreement related to solar zenith angle and NOx were discussed [Jaeglé et al., 2000; Brune et al., 1999]. In contrast, predictions of upper tropospheric HO2 were ∼10% larger than measurements during PEM-Tropics B [Olson et al., 2001]. While suggestions of convective transport of peroxides and formaldehyde could explain the upper tropospheric HOx imbalance during STRAT and SUCCESS, the lack of measurements for these precursors prevented a definitive investigation [Jaeglé et al., 1997, 1998]. Evidence of significant influence of these precursors on HOx was not found during the SONEX or PEM-Tropics B campaigns, however.
 Predictions of the upper tropospheric HO2/OH ratio have likewise been inconsistent between campaigns. While this ratio was in general agreement with observations during STRAT and SONEX [Jaeglé et al., 1997, 2000], it was underpredicted during SUCCESS by 30% [Brune et al., 1998]. Conversely, the HO2/OH ratio was overestimated by models in the upper troposphere during PEM-Tropics B by 30% [Olson et al., 2001].
 Agreement of models and measurements for HOx in the lower troposphere has been somewhat more consistent, although the quantity of the measurements is limited. Analysis of OH in the lower troposphere from the ACE-1 [Mauldin et al., 1998; Chen et al., 2001], PEM-Tropics A [Mauldin et al., 1999] and PEM-Tropics B [Olson et al., 2001] field campaigns showed modeled OH values that were typically slightly higher than measurements. The only field campaign measurements of HO2 in the lower troposphere (PEM-Tropics B) also showed slight model overpredictions in the boundary layer and good agreement in the middle troposphere [Olson et al., 2001].
4.1.1. HOx Model-to-Observations Comparisons During TRACE-P
 OH measurements were made on the P3-B using a multichannel selected ion chemical ionization mass spectrometer system with a reported error of 60% [Mauldin et al., 2003] and a data coverage of 75% of the modeled points. While HO2 measurements were also obtained, using a chemical ionization mass spectrometer [Cantrell et al., 2003], coverage with this technique was sparse and is not included in this analysis.
 On board the DC-8, OH and HO2 measurements were obtained with the Penn State Airborne Tropospheric Hydrogen Oxides Sensor (ATHOS) which employs a laser induced fluorescence technique, the same instrument used during the SUCCESS, SONEX, and PEM-Tropics B field campaigns [Brune et al., 1995]. Measurements of OH and HO2 are reported at a frequency of every 10 s with an estimated absolute accuracy of 40% and a limit of detection of 0.1 pptv for HO2 and 0.01 pptv for OH. HOx measurements are reported for 93% of the modeled data points on the DC-8 (over 4800 points). Eisele et al.  compare OH measurements obtained from the two aircraft from several intercomparison flights and determine that while 90% of the measurements from the two instruments agreed to within the stated instrument uncertainties, an overall bias pointed to possible problems with instrument calibration.
 On the DC-8, 75% of HO2 and 48% of OH model predictions fall within the stated measurement accuracies, and 85% of the calculated P3-B OH points are within the measurement accuracy. Model-to-measurement comparisons are shown in Figure 3 for OH and in Figure 4 for HO2. In contrast to previous campaign studies outlined above, this study shows a persistent model overprediction of DC-8 HO2 throughout all altitudes of ∼23%, with no evident altitude trend. OH is also overpredicted but with an altitude trend; the overprediction increases from 7% for altitudes below 1 km to 60% in the middle troposphere and 80% at the highest altitudes, giving an overall median overprediction of 40%. The trend in model-measurement agreement with altitude is duplicated with the P3-B OH data, though the profile is shifted toward lower ratios; boundary layer P3-B model-generated OH is underpredicted by 30% relative to measurements and is overpredicted by 40% at altitudes near 6 km [see also Mauldin et al., 2003]. There was no trend in the agreement found associated with time of day (solar zenith angle).
 While both OH and HO2 measured on the DC-8 have reported accuracies of ±40%, the broader range of ratios for OH reflects the lower measurement precision for this species which is derived from a much smaller signal than for HO2 [Faloona et al., 2000]. Note that the outlier points for HO2 which fall below the agreement line at low mixing ratios on Figure 4b are largely associated with stratospheric air and will be discussed section 4.1.2. Similar outlier points at low mixing ratios for the DC-8 OH (Figure 3b) are associated with higher solar zenith angles. Notably, while HO2 on the DC-8 shows a bias of 23%, the point-to-point correspondence is quite compact (r2 = 0.88).
 From the lack of an altitude dependence in HO2 calculated/observed (calc/obs), it follows that the calc/obs HO2/OH partitioning is inversely related to the altitude dependence of OH, with a 20% overprediction near the surface, decreasing to an underprediction above 8 km of 23%, a value similar to the upper tropospheric underpredictions of this ratio during SUCCESS and similar in magnitude but opposite in sign to that found during PEM-Tropics B.
4.1.2. Examination of Upper Tropospheric Outliers
 Three subsets of HO2 calc/obs ratios constituting a total of 12% of the modeled HO2 points, are identified in Figure 5a as distinct from the majority of the data. To illustrate the magnitudes of the highlighted populations, these points are also indicated in Figure 4b with the colored symbols. Subsets are defined as high O3 or stratospheric (2.3%), high-altitude/high NO (3.3%), and in-cloud data (6.4%).
Table 1 shows median observations and calc/obs ratios relevant to the two outlier subsets predominantly in the upper troposphere (>7 km): the stratospheric and high NO data points. Statistics for the remaining data points at upper altitudes are also shown, identified here as “majority data.” The high O3 points (O3 > 120 ppbv) are shown with blue diamonds in Figures 4b and 5a, and Table 1 confirms that these points are consistent with stratospheric influence as they are associated with high O3; low water vapor, CO, and hydrocarbons; and moderate NOx. In contrast to the majority data, HOx is significantly underpredicted for these stratospherically influenced points, with calc/obs values of 0.63 for HO2 and 0.77 for OH. These points span a range of solar zenith angles (SZA) from 40° to 80°, with no correlation between the calc/obs ratio and SZA. These results are in contrast to good agreement of modeled and measured stratospheric HOx given by Wennberg et al.  and Jaeglé et al. . Note, however, that for this subset the 23% underprediction of the HO2/OH partitioning ratio calculated for the majority subset is essentially retained, with a median underprediction of HO2/OH of 20% (Table 1).
Table 1. Median Observations and Calculated/Observed Ratios for Subsets at Altitudes > 7 kma
Stratospheric Points (O3 > 120 ppbv)
High NO Points (NO > 135 pptv)
Calculated (calc) and observed (obs).
Number of points
Obs HO2, pptv
Obs OH, pptv
Obs O3, ppbv
Obs CO, ppbv
Obs H2O, molecules cm−3
1.38 × 1015
1.0 × 1014
8.1 × 1014
Obs C2H6, pptv
Obs acetone, pptv
Obs NO, pptv
Calc NO2, pptv
 The high NO data (NO > 135 pptv) are shown with red triangles in Figures 4b and 5a, and these points are likely associated with convected pollutants, since CO, O3, and hydrocarbons are slightly elevated above that for the majority subset (Table 1). While the HO2 calc/obs ratio is 0.97, it is low relative to the majority subset ratio. Note that a decrease in ratio with higher NO concentrations is consistent with the general behavior found by Faloona et al.  on examination of SONEX and SUCCESS data. In contrast to HO2, however, the OH calc/obs ratio for the high NO data is quite large, with a median value of 2.01. The resulting calc/obs ratio for HO2/OH partitioning is 0.46, significantly lower than that for the stratospheric and majority subsets (0.8, see Table 1). Such behavior suggests an uncertainty related to the rate of HOx recycling by NO. Note that data with NO > 135 pptv also occur in the lower troposphere, indicated in Figures 4b and 5a by gray triangles. However, only those high NO points at altitudes greater than ∼6 or 7 km show a consistent HO2 calc/obs behavior distinct from the preponderance of the data. Below 6 km, the median HO2 calc/obs ratio for the high NO data is 1.23, identical to the bulk median, though there is a large scatter to the ratios. Therefore the calc/obs HO2 discrepancy associated with high NO in this study appears limited to the upper troposphere.
 Selected HOx source and loss terms are shown in Table 2 and reveal differences in the dominant instantaneous processes affecting HOx between the subsets. For example, while the water vapor reaction with O(1D) is clearly the dominant HOx primary source for the stratospherically influenced data, higher concentrations of acetone in the majority subset and particularly in the high NO subset results in an increased importance of acetone photolysis for those data.
Table 2. Selected Instantaneous HOx Budget Terms for Subsets at Altitudes > 7 km
Gross Production and Loss Terms, 103 molecules cm−3 s−1
Stratospheric Points (O3 > 120 ppbv)
High NO Points (NO > 135 pptv)
Model-calculated HOx gross production
O1D + H2O
Acetone photolysis (assume yields of 2, 3)
Model-calculated HOx gross loss
OH + HO2
HO2 + HO2
Total for HOx-driven losses
OH + NO2
Model-calculated HOx gross production from HNO4 cycling
HNO4 thermal decomposition
Model-calculated HOx gross loss from HNO4 cycling
HO2 + NO2
HNO4 + OH
 Because HOx is a highly buffered system, it is difficult to significantly impact calculated HOx by minor adjustments to the sources or losses [Wennberg et al., 1998; Crawford et al., 1999]. To bring the calc/obs ratio for the stratospheric HO2 into agreement with measurements, an HO2 increase on the order of 60% is required, and to come into agreement with the majority data subset (where the median calc/obs is 1.24) an increase on the order of 100% is required.
 To test the uncertainty related to water vapor measurements in stratospherically influenced air, model calculations were conducted for the stratospheric subset using water vapor measurements from a diode laser instrument, which, during dry conditions, recorded data 2.4 times larger than that from the cryogenic hygrometer, the measurement used for the base model simulations. The resulting HO2 increase was ∼17%. Similarly, because acetone photolysis is a significant primary source in the high NO subset, the uncertainty in those measurements was tested by increasing acetone by the stated measurement uncertainty of 25%. The resulting impact on HOx is <5%.
 Recent studies have suggested that photodissociation of HNO4 in the near-infrared spectrum could significantly impact the budget of HOx, particularly in the lower stratosphere and upper troposphere [Wennberg et al., 1999; Salawitch et al., 2002; Evans et al., 2003]. To test the potential impact of this additional photolysis, we conducted model simulations including HNO4 near-infrared photolysis as described by Roehl et al. . For the stratospheric subset, median predicted HOx increased by 17% when this photolysis was included. The impact on HOx for the high NO subset was only ∼3%, and the median impact on the majority data was negligible.
 Another possibility is that uncertainties in the NO measurement may have contributed to differences in the HO2 calc/obs ratios among the subsets. Model sensitivity calculations show that an assumption of a consistent NO measurement bias of −30% is sufficient to increase predicted HO2 within the high NO subset by 20%, resulting in a median calc/obs ratio of 1.18. Meanwhile, the impact on the majority data from this bias is limited to a few percent change in HO2 so that differences in the calc/obs ratios between the high NO and majority subsets are no longer clearly evident. Note, however, that the distinction in the median calc/obs HO2/OH partitioning between the two subsets remains; that is, while this assumed NO measurement bias improves the calc/obs partitioning ratio to near 1 for the majority data, a calc/obs value of 0.65 is calculated for the high NO subset. For the stratospheric subset, the impact of an assumed −30% NO measurement bias is a 27% increase in HO2.
 For the stratospheric subset, the combined impact of the assumed −30% NO measurement bias, the additional HNO4 photolysis, and the higher water vapor measurements is nonlinear, with a total increase in HO2 of 54%, resulting in a calc/obs ratio of 0.93. Therefore, while these combined uncertainties have the potential of significantly improving the HO2 calc/obs ratio in the stratospheric subset, the ratio remains distinct from the majority data.
 Additional rate sensitivity calculations were conducted to examine uncertainties in reaction rates that contribute to the loss of HOx (see Table 2). Because HOx self-reactions are disproportionately dominate over HNO3 formation for the majority data relative to the stratospheric or high NO subsets, uncertainties in these rates can be expected to have a larger influence on the majority data. Holding the rates for OH + HO2 and HO2 + HO2 to the higher ends of their respective uncertainties as defined by DeMore et al.  and Sander et al.  resulted in HOx concentration decreases <10% larger for the majority data relative to the other subsets. Thus, though the makeup of these subsets reveals different dominating processes in the HOx budget along with different behaviors of the HO2 calc/obs ratios, uncertainties in primary source components or HOx loss processes are not sufficient to explain all of the differences.
 Discrepancies between the stratospheric subset and the majority data subset extend beyond HOx to CH2O. As discussed earlier, CH2O photolysis can be an important secondary source of HOx in the upper troposphere; CH2O is a photochemical byproduct of acetone and hydrocarbon degradation. For the stratospheric subset, the median measurement reported for CH2O is 55 pptv. An important caveat to note, however, is that most of these reported values are below the instrument limits of detection (LOD) [Fried et al., 2003a]. Nevertheless, this implies that measured CH2O may be up to 3 times larger than that calculated by the model, which has a median value for the stratospheric subset of 17 pptv. If the stratospheric points are modeled while constraining CH2O to the median measured value of 55 pptv, median predictions of OH and HO2 increase by 71% and 79%, respectively, increasing the median OH calc/obs ratio to 1.28 and the HO2 calc/obs ratio to 0.95. Note, however, that CH2O levels of 55 pptv cannot be supported by the concentrations of acetone or other hydrocarbons measured.
4.1.3. Examination of In-Cloud Data
 The data points marked with a green asterisk in Figures 4b and 5a indicate the third subset, within-cloud data as determined by a combination of visual inspection of flight videos and measurements of particles in the 10–20 μm range from the Forward Scattering Spectrometer Probe (FSSP). Using this approach, data points were classified as in-cloud, intermediate, hazy, or clear air. There is a compelling distinction between the behaviors of calc/obs HO2 for in-cloud points versus those in clear air, supporting a significant heterogeneous loss of HO2 within clouds (Figure 5a). The median HO2 calc/obs ratio for all clear air data points is 1.20, while that for in-cloud data is 25% larger, at 1.51. While the analysis of Jaeglé et al.  suggested evidence of HO2 heterogeneous uptake within cirrus clouds, significant model overpredictions spanned regions well outside of cloud areas as well. This data analysis shows large model overpredictions that are clearly located directly within and limited to clouds (Figure 5a). Note that the few points around 4 km that show relatively large HO2 calc/obs ratios and are not identified as in-cloud data are all from flight 15 and were located within the heavily polluted haze layer of the Yellow Sea; these points are all identified as either “intermediate” or “hazy” using the cloud index described above and were intermixed with points identified as “in-cloud.”
 Further, most evidence of in-cloud HO2 loss is limited to the lower and middle altitudes. For data points within clouds at altitudes below 6 km, the HO2 calc/obs ratio is 1.55, while that for in-cloud points above 6 km is 1.32. Contrary to previous studies [e.g., Jaeglé et al., 2000], this suggests that cloud uptake plays only a minor role in upper tropospheric HOx chemistry.
 To expand the investigation of heterogeneous impacts to aerosol in both cloudy and in clear air, a theoretical heterogeneous loss of HO2 was added to the model. The heterogeneous loss rate (khet) is parameterized as
where a is the effective particle radius for a given observational size bin, n(a) is particle number size distribution, Dg is the gas-phase molecular diffusion coefficient of HO2, υ is the mean molecular speed, and γ is a reaction probability which is set to 0.2, as suggested by Jacob . The integral is evaluated over all the available particle size spectrum observations by the FSSP and optical particle counter instruments on board the DC-8 aircraft. The observations are reported in six size bins and span the size range of 0.1–50 μm. The median decrease in calculated HO2 due to in-cloud heterogeneous loss is 70%, reducing the median in-cloud calc/obs HO2 ratio to 0.42 (Figure 5b, green asterisks). Thus the loss calculated using the simple parameterization in equation (2) is shown to be quantitatively inconsistent with that suggested by these observations. However, note that the error in estimated cloud aerosol number/size distribution data is on the order of 100% so the parameterization is highly uncertain, and there may be additional HO2 loss limiting factors which are not described in equation (2). Furthermore, heterogeneous losses to HOx precursors and/or reservoir species were not considered in this assessment (e.g., CH2O and H2O2 [see Fried et al., 2003a]).
 The estimated impact on HO2 from heterogeneous loss to aerosol in clear air (no cloud) can also be seen in Figure 5b and is calculated to be on the order of a 4% decrease, with minimum decreases in the upper troposphere (1–2%) and maximum decreases in the boundary layer (12%). The boundary layer heterogeneous losses therefore could explain about half of the median model boundary layer overestimate; however, the HO2 measurement is not sensitive enough to independently verify the existence or magnitude of this HO2 loss.
 During TRACE-P, two independent instruments measured formaldehyde on board the DC-8: a coil enzyme method [Heikes et al., 1996] and a tunable diode laser absorption spectrometer [Fried et al., 2003a]. Measurements from the coil enzyme method [Heikes et al., 1996] are on the order of ∼30% higher than the laser spectrometer [Fried et al., 2003a]. A more detailed comparison of the two CH2O measurements is presented by Eisele et al. ; 60% of the compared points fall within measurement uncertainties. For this analysis, we focus on model comparisons with data from the laser spectrometer, which has a data coverage much larger than that from the coil enzyme. Note that a CH2O model-measurement comparison using these data and model results are also discussed by Fried et al. [2003a].
 Values of the 2σ LOD for the laser spectrometer were typically between 60 and 80 pptv [Fried et al., 2003a], and one third of all measured CH2O was at LOD. This percentage is greatest at upper altitudes, with 60% of the measurements above 8 km below LOD. As discussed by Fried et al. [2003a], CH2O concentrations are reported for all data, including those at and below LOD. Though these LOD data are, by definition, are too noisy to give information on a point-by-point basis, by including their statistical impact in the running median, we are able to avoid biasing our comparison at the low end of the concentration range.
 A scatterplot of modeled versus observed formaldehyde is shown in Figure 6a, with a smoothed version of the data used in Figure 6b. Note that some of the data below LOD were reported as negative and do not appear on these logarithmic plots. To create the smoothed data, measurement-model data pairs were first sorted by model concentration, and measurements were then smoothed using a 1% running average. By sorting the data pairs using model concentration rather than measurement, the smoothing process eliminates negative values and allows for an assessment of the reported LOD.
 For the full raw data set (Figure 6a), the median calc/obs ratio for CH2O is 0.92, with an r2 correlation coefficient of 0.85. However, the general behavior of the calculated-to-observed comparison differs distinctly across the spectrum of measured CH2O mixing ratios. This behavior within the data is more clearly evident when smoothing the data (Figure 6b). In Figure 6b, calculated CH2O agrees well with observed values for mixing ratios of roughly 60–500 pptv. Here, the slope of the agreement equals 1.02, indicating no bias in the model-to-measurement comparison. These results corroborate those shown by Fried et al. [2003a], who employ a binned regression analysis approach. Below ∼60 pptv, the measurement-model correlation degrades for this comparison, which agrees with the reported 1-min LOD of Fried et al. [2003a]. Note, however, that as discussed by Fried et al. [2003a], longer measurement averages can, in some instances, be employed during stable horizontal flight legs to improve the measurement precision. For concentrations >500 pptv, the slope differs markedly, with a value of 0.37, as the model increasingly underpredicts CH2O at the highest concentrations.
4.2.1. Impact of Transport on CH2O Predictions
 One explanation for the underprediction of CH2O at highest concentrations is that direct transport of CH2O and its precursors (such as ethene or methanol) can shift the concentration of CH2O away from photochemical steady state. However, because the median lifetime of CH2O for the daylight TRACE-P calculations is 2.2 hours, evidence of transport influence on these calculations of CH2O is expected to be limited to within a few hours of large emission areas. Note that the transport impact distance would increase for nighttime emissions, when the instantaneous CH2O and precursor lifetime is longer.
Figure 7 shows the geographical locations of high-concentration CH2O measurements and of significant model underestimations. Figure 7a shows the location of all CH2O measurements, and in Figure 7b, all measurements >500 pptv, constituting ∼7% of the data, are identified. While several isolated measurements exceed 500 pptv, given the scatter seen in Figure 6a, it is difficult to arbitrate the model versus measurement disagreement. Therefore extended periods of high CH2O concentration (>500 pptv) are identified based on averaging over horizontal flight legs (Figure 7c). These occurrences reduce the number of identified points to 3% of the data set and are limited to the Yellow Sea and a few locations farther offshore. Figure 7d shows points within these identified flight legs for which the calc/obs ratio is <0.7, which constitute ∼1% of the total CH2O observations. For the remainder of points with flight leg averages larger than 500 pptv, the median calc/obs ratio is 0.96, indicating no substantial bias in the model prediction. The fact that the large underpredictions are exclusively located in the Yellow Sea and at altitudes below 2.5 km suggests the possibility of transport influence. However, back trajectories using Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT, http://www.arl.noaa.gov/ready/hysplit4.html, NOAA Air Resources Laboratory, Silver Spring, Maryland) run from the locations in Figure 7d show that while slightly more than half of these observations were subjected to <6 hours of day lit transport time from the coast, the remainder indicated transport times in excess of 1 day. This qualitative examination suggests that during the overall TRACE-P campaign, transport influences on CH2O, while probably present, were quite rare, impacting on the order of only a few percent of the data at most.
 To further verify the diurnal steady state assumption for CH2O, an exercise was undertaken using results from version 4.33 of the Harvard 2 × 2.5 GEOS-CHEM global model simulation for the TRACE-P time period in place of observational data (http://www-as.harvard.edu/chemistry/trop/geos/geos_version.html; M. Evans et al., manuscript in preparation, 2004). The box model analysis was repeated using GEOS-CHEM global model parameters from along simulated flight tracks through the model environment as box model constraints, and box model predictions for formaldehyde, based on diurnal photochemical steady state, were then compared to those predicted by GEOS-CHEM, which includes simulated effects of both photochemistry and transport. The resulting median box model/GEOS-CHEM CH2O ratio is 0.92, a bias determined to be a result of minor input and mechanistic differences between the two models. The agreement between the two models is compact, however (r2 = 0.93), which supports the assumption of steady state for formaldehyde throughout most of the TRACE-P region. Figure 8a shows the box model/GEOS-CHEM CH2O ratios for the upper 50th percentile of the GEOS-CHEM concentrations, while a similar plot for the calc/obs ratio using observational data is shown in Figure 8b. Median ratios for segments of tenths of percentiles are indicated near the top of Figures 8a and 8b. The uppermost 10th percentile segment ratio for GEOS-CHEM decreases abruptly from 0.91 to 0.85, similar to but not as pronounced as the decrease to 0.69 for the upper 10th percentile of observed data.
 Similar to results described for the observations, large box model underpredictions (calc/obs < 0.7) of high concentrations of GEOS-CHEM CH2O (>500 pptv) constitute only 1.1% of the Harvard data set. About half of these identified points reside near coastal regions in the Yellow Sea or off the coast of Taiwan, with the remainder located more than a day's transport time from the coast. Therefore, while the box model analyses using both the observational data and the GEOS-CHEM analysis suggest that there are isolated cases where transport may influence CH2O, these cases are rare, with the portion of the data affected on the order of a few percent or less.
4.2.2. Impact of Constraining Species on the Model-Measurement Comparison
 Agreement between calculations and observations is quite good for CH2O data falling between the measurement LOD and 500 pptv, but this agreement is not readily apparent without smoothing the data. The comparison in Figure 6a is quite scattered for data below 500 pptv (r2 = 0.46), and this noise is likely to be due to a variety of causes. Some of these include uncertainties in the measurement (2σ LOD ∼ 60–80 pptv) or in the model mechanism, uncertainties in the modeling approach (e.g., treatment of clouds), and uncertainties in formaldehyde precursors, which encompass both the limited availability of precursor constraints and also measurement issues (e.g., unmeasured hydrocarbon species or uncertainties in measurements of precursors such as CH3OOH). Fried et al. [2003a] also discuss some aspects of measurement and model uncertainties.
 As noted earlier, this modeling study is limited by the availability of several important but noncritical model inputs (H2O2, CH3OOH, PAN, and HNO3), which are constrained to observations at points where data are available and are calculated where observations are missing. The uncertainty imposed by the limited availability of these constraining species becomes most obvious in calculations for periods of flight through homogeneous air masses. If model predictions of these species are significantly different than adjacent measurements, the resulting fluctuations in the flight data time series between the measured value (when available) and the calculated value can be large. Depending on the sensitivity of CH2O to variations in these constraining species, this in turn can potentially introduce noise into the time series of calculated CH2O; this is particularly so for CH3OOH. Further complicating things, some of these periods of large fluctuations between adjacent measurements and calculations for CH3OOH in the TRACE-P data are seen where the presence of a constraining measurement improves model-measurement agreement for CH2O while other periods clearly exhibit better agreement when constraining species are absent. This type of behavior is also described by Fried et al. [2003a].
 To evaluate the sensitivity of CH2O to the availability of noncritical constraint species, we conducted several independent model tests. For each noncritical constraint species, a set of model simulations was conducted with the test species calculated, rather than constraining it to the observed value. Differences in predictions of CH2O were then examined as a function of the differences in the calculated and observed values of the test species. The total dynamic range of model over and under predictions was similar for all of the constraint species. The impacts of HNO3, H2O2, and PAN constraints on CH2O were relatively low. The sensitivity of CH2O to HNO3 was always <2% and was <20% for H2O2 and PAN.
 In contrast, the response in CH2O to variations in CH3OOH were large. Results from test simulations for CH3OOH are shown in Figure 9. The x axis on Figure 9a shows CH3OOH calc/obs ratios, with values greater than one indicating a model overprediction, and the y axis shows the resulting relative differences in predicted CH2O. While the median CH3OOH calc/obs ratio is 1.06, the agreement is altitude-dependent. Below 4 km, there is a median overprediction of 40–50%, and above 8 km, there is a median underprediction of 40. Figure 9b shows absolute differences for CH3OOH (calc-obs) and for resulting predictions of CH2O. The response in CH2O, with absolute differences of several hundred parts per trillion by volume and relative ratios ranging from 0.3 to 3.5, may be interpreted as a measure of the variance potentially introduced as a result of the limited availability of CH3OOH.
 The colors in Figure 9 indicate the level of NO; blue points show data where NO was <5 pptv, and red points show data where NO was measured at >50 pptv. Figure 9a indicates that CH2O is particularly sensitive to CH3OOH when NO levels are very low. Under these conditions, formaldehyde production becomes dominated by photolysis of CH3OOH as the production from the methyl peroxy radical reaction with NO becomes small. Note that CH3OOH is frequently overpredicted by the model under low NO conditions (i.e., 80% of the blue points in Figure 9a are greater than one). One possible explanation for this is a box model overestimation of the peroxy radical production of CH3OOH by the steady state approach which neglects any time evolution of intermediate-lived species such as NOx, particularly in the presence of upstream emissions. A similar effect is also suggested by Wang et al.  in a steady state box model analysis using data over the northern and middle high latitudes from the TOPSE field campaign. Additionally, Fried et al. [2003a] propose the possibility that reactions of CH3OOH on aerosols and/or with halogens may be important and result in model underpredictions of this species under low NO conditions.
 While these exercises illustrate the theoretical sensitivity of CH2O predictions to CH3OOH, it is useful to determine how often the large fluctuations actually occur in the field data and whether the resulting introduction of noise impacts the gross statistics of the CH2O comparison seen in Figure 6. Within the lowest 2 km, we identified 175 CH2O data points that were located within seven constant-altitude legs where differences in calculated and observed CH3OOH were at least 250 pptv and where resulting model predictions of CH2O differed by at least 30%. These 175 flagged points constitute ∼13% of all CH2O data at those altitudes. Above 2 km, such fluctuations are much rarer; affecting only ∼2% of the data. The overall median CH2O calc/obs ratio for altitudes below 2 km is 1.03, with a calculated versus observed r2 correlation of 0.2. For the subset of these points with observations of CH3OOH, the median calc/obs CH2O decreases to 0.91, and for the subset of points using calculated CH3OOH, the median ratio increases to 1.12. While this establishes that limited observations of CH3OOH is a source of uncertainty in model calculations versus observations, it is interesting to further note that the r2 correlation between model predictions and observations of CH2O remains unchanged when limiting the comparison to either of the subsets using observations or calculations of CH3OOH. Thus other sources of uncertainty must dominate the scatter for the CH2O comparison seen in Figure 6. These of course include uncertainty in both the CH2O measurements themselves as well as the uncertainty in constraining measurements. What is clear from this exercise is the sensitivity of CH2O predictions to presumed concentrations of CH3OOH. Therefore, in order to more accurately assess formaldehyde measurements, accurate measurements of CH3OOH, particularly in low NOx regimes, are critical.
4.2.3. Impact of Clouds on Predictions of CH2O
Fried et al. [2003a] discuss the role of local in-cloud heterogeneous loss of CH2O. This in situ loss is not specifically reproduced by the box model, which assumes a climatological wet loss throughout the troposphere but does not simulate instantaneous in-cloud removal. Fried et al. [2003a] conclude that model predictions of CH2O can be up to 56% larger than observed within cloudy regions as a result of this effect.
 Another impact related to clouds that affects predictions of CH2O is the application of the cloud correction factor (CCF; see section 2). For example, at very low or very high CCF (i.e., when in an environment with heavy cloud attenuation or high reflectance), the assumption that these extreme cloud influences persist throughout the diurnal cycle is most likely erroneous. Approximately 10% of CH2O data below 500 pptv fall under these extreme conditions, identified as CCF (JO1D) <0.5 or >1.7. For CCF (JO1D) values <0.5, CH2O is underpredicted, with a median calc/obs ratio of 0.67, and for CCF (JO1D) >1.7, the median calc/obs ratio is 1.3, indicating a model overprediction. However, when removing extreme CCF data and in-cloud data points (identified as described in section 4.1.3) from the analysis, the correlation coefficient between calculated and observed CH2O is essentially the same (0.46 versus 0.49), and the median calc/obs ratio is unchanged from the bulk value. This suggests that the assumption of diurnal persistence of clouds, while clearly introducing uncertainty, does not introduce bias into the comparison, and is insufficient to explain the large amount of scatter in agreement seen in Figure 6a.
 Model predictions of HOx showed good agreement relative to measurements from TRACE-P; 75% of OH and HO2 predictions for DC-8 data fell within the stated instrument uncertainties, and 85% of the P3-B OH predictions were within the stated uncertainties. HOx was generally overpredicted throughout the troposphere, in contrast to results from several previous field campaigns. The calc/obs ratio for OH on the DC-8 indicated a median overprediction of 40% and a trend with altitude; measurements were overpredicted by 7% at altitudes below 1 km, increasing to a 80% overprediction at the highest altitudes. This trend was duplicated with the P3-B OH data, though shifted toward lower ratios, with boundary layer OH underpredicted by 30% relative to measurements and overpredictions of 40% at 6 km altitude. The calc/obs ratio for HO2 on the DC-8 showed a consistent 23% model overprediction bias throughout all altitudes and a high point-to-point correspondence, with a correlation coefficient (r2) of 0.88. Three subsets stood out as distinct from the preponderance of the data, however: stratospherically influenced data, upper tropospheric data with high NO (>135 pptv), and data obtained within clouds.
 Median HO2 calc/obs ratios in the stratospheric subset were quite low (0.63) relative to a median ratio of 1.24 for the majority data. Likewise, the stratospheric median OH calc/obs ratio was also low, with a value of 0.77 relative to 1.81 for the majority data. These findings are in contrast to previous studies of stratospheric OH which indicated good agreement between models and measurements [e.g., Wennberg et al., 1998; Jaeglé et al., 1997]. Several sensitivity studies were conducted to examine influences on HOx pertinent to the stratospheric subset. Even with the combined effects of an increase in stratospheric water vapor by a factor of 2.4 to measurements taken from the laser hygrometer, the inclusion of the near-IR HNO4 photolysis [Roehl et al., 2002], and an assumed −30% NO measurement bias, the resulting increase in predicted HO2 within the stratospheric subset of 54% was not sufficient to explain the disconnect from the majority data.
 The subset with high NO (>135 pptv) in the upper troposphere had a median HO2 calc/obs ratio of 0.97, also lower than the 1.24 ratio for the majority data. A tendency for a lower HO2 calc/obs ratio with higher NO is consistent with findings by Faloona et al.  during the SUCCESS and SONEX field campaigns. In contrast, OH was overpredicted in this subset by a median calc/obs ratio of 2.01, compared to the majority data OH calc/obs ratio of 1.81. The resulting HOx partitioning ratio (HO2/OH) was therefore underpredicted, with a calc/obs value of 0.46. This is significantly lower than that for the stratospheric and majority data (both equal to 0.8), suggesting an uncertainty related to the rate of HOx recycling by NO. While the assumed −30% bias in the NO measurement resulted in a 20% increase in predicted HO2 for this subset, the impact on the majority data was minimal, so that the distinction between calc/obs HO2 for these two subsets was no longer evident. However, differences in the calc/obs HOx partitioning remained, with an increase in the ratio to near 1 for the majority data versus a value of 0.65 for the high NO subset.
 The third subset included data obtained within clouds. Elevated calc/obs HO2 ratios were directly correlated to in-cloud data at lower and middle altitudes. The median in-cloud HO2 ratio below 6 km was 1.55, substantially higher than that for data identified as in clear air (1.20). There was no evidence of significant HO2 uptake within cirrus and other high-altitude clouds (above 6 km), however, which is a result in contrast to previous studies suggesting a significant loss of HO2 to cirrus clouds [e.g., Jaeglé et al., 2000]. Heterogeneous loss of HO2 to aerosol outside of clouds had a much smaller impact on HO2, and these HO2 measurements are not sensitive enough to independently verify the magnitude of this HO2 loss.
 Measurements of formaldehyde from the tunable diode laser absorption spectrometer were compared to model predictions. Similar to previous analyses, methanol observations were shown to increase predicted CH2O by ∼10% throughout the TRACE-P domain. The median calc/obs agreement was very good for data falling between the measurement LOD and 500 pptv, with a value of 1.02. However, the agreement was marked by large scatter (r2 = 0.46). The general behavior of the model-to-measurement comparison differed across the spectrum of measured CH2O mixing ratios, however. For concentrations >500 pptv (∼7% of the data), the model increasingly underpredicted CH2O with a median ratio of 0.66. While some transport influences on CH2O are evident in the data, it was found that no more than a few percent of the data set could be conclusively determined to be impacted by transport. These conclusions were further supported by a test of the steady state assumption for CH2O using a simulation of TRACE-P conditions by the Harvard GEOS-CHEM global model in place of the real atmosphere.
 For the CH2O data between LOD and 500 pptv, the large scatter is likely due to a variety of causes, including finite measurement imprecision (2σ LOD ∼ 60–80 pptv), uncertainties in the modeling approach (e.g., treatment of clouds), and uncertainties in CH2O precursors, encompassing issues such as the limited availability of precursor measurements and also measurement issues such as unmeasured hydrocarbon species or uncertainties in measurements of precursors such as CH3OOH. Specifically, CH2O was determined to be quite sensitive to CH3OOH, particularly at low altitudes and under low NOx conditions where predicted CH2O could vary by more than a factor of 2 (several hundred parts per trillion by volume) as a result of the differences between measured and predicted CH3OOH. During TRACE-P, ∼13% of the CH2O data was impacted by the limited availability of CH3OOH measurements. However, correlation between model predictions and measurements did not improve when limiting the analysis to only those points with measured CH3OOH, suggesting that other uncertainties must play a dominant role. Similarly, while clouds were shown to introduce some uncertainty due to potential heterogeneous losses of CH2O and also due to the assumption of diurnal persistence of extreme local radiative deviations, these effects did not introduce bias into the model-to-measurement comparison. Further, the removal of those points had no impact on the calculated correlation between model predictions and measurements.
 This work was supported by the NASA Tropospheric Chemistry Program. The authors would also like to thank the pilots and crew of the NASA's DC-8 and P3-B aircraft for their efforts in support of the TRACE-P flights.