Automated flask sampling aboard small charter aircraft has been proposed as a low-cost, reliable method to greatly increase the density of measurements of CO2 mixing ratios in continental regions in order to provide data for assessment of global and regional CO2 budgets. We use data from the CO2 Budget and Rectification-Airborne 2000 campaign over North America to study the feasibility of using discrete (flask) sampling to determine column mean CO2 in the lowest 4 km of the atmosphere. To simulate flask sampling, data were selected from profiles of CO2 measured continuously with an onboard (in situ) analyzer. We find that midday column means can be determined without bias relative to true column means measured by the in situ analyzer to within 0.15 and better than 0.10 ppm by using 10 and 20 instantaneously collected flask samples, respectively. More precise results can be obtained by using a flask sampling strategy that linearly integrates over portions of the air column. Using less than 8–10 flasks can lead to significant sampling bias for some common profile shapes. Sampling prior to the breakup of the nocturnal stable layer will generally lead to large sampling bias because of the inability of aircraft to probe large CO2 gradients that often exist very close to the ground at night and during the early morning.
 Low-cost, reliable methods are needed to obtain regular measurements of CO2 mixing ratio in the lower atmosphere over the continents [Wofsy and Harriss, 2002]. A method suggested by Tans et al.  is the use of automated flask sampling aboard small charter aircraft, allowing samples to be collected without the presence of a scientist. The National Oceanic and Atmospheric Administration (NOAA) Climate Monitoring and Diagnostics Laboratory (CMDL) has carried out a program of this type since 1992 at a site in northern Colorado, United States, and for shorter periods at several other sites around the globe. Added advantages of flask sampling over in situ instrumentation are that many trace gas mixing ratios and isotope ratios can be measured in the flask air, and analyses from a global network of sites can be carried out on a single set of laboratory instruments, alleviating possible problems of intercomparability.
 Measurements of the column mean of CO2 through the lower atmosphere could provide a strong constraint for inverse models of the global CO2 budget. Inverse methods use global circulation models (GCMs) to simulate atmospheric transport in order to calculate CO2 sources and sinks from spatial gradients of CO2 mixing ratios. Imperfect representation of atmospheric mixing, especially in the vertical, makes problematic the use of mixing ratio data obtained at the surface or at any discrete altitude. In particular, many GCMs currently have poor representation of the planetary boundary layer, which often has large vertical gradients of CO2. Column data will also be needed to calibrate CO2 data obtained from future satellite-based sensors. Measurements of the stable isotopic composition of CO2 (13C/12C and 18O/16O) provide additional information enabling the partition of CO2 sources and sinks into component processes such as ocean versus land net fluxes [Ciais et al., 1995], C3 versus C4 photosynthesis [Farquhar et al., 1989; Fung et al., 1997], and photosynthesis versus respiration [Francey and Tans, 1987; Peylin et al., 1999].
 The column mean CO2 could be very precisely determined (i.e., to within instrument precision) using linearly integrated flask samples that cover the entire profile. An additional benefit of integrated flask sampling is that small-scale atmospheric variability in the horizontal and vertical dimensions will be averaged out, providing a data set that may be well suited for use in transport models that have coarse spatial resolution. Key disadvantages of integrated sampling are that correlations between trace gases are smeared out, reducing the utility of the data for determining source signatures, and features of the atmospheric structure, such as the boundary layer top, cannot be accurately identified. Also, collecting air into flasks with linear weighting in time can be difficult, and most flask sampling systems introduce a weighting function that depends on system characteristics. Atmospheric Observing Systems (Niwot, Colorado), in collaboration with CMDL, has developed a simple system for collecting linearly integrated flask samples which is being tested for use aboard aircraft (J. Smith, personal communication, 2002).
 The extensive continuous in situ CO2 measurements obtained during the CO2 Budget and Rectification Airborne 2000 (COBRA-2000) campaign over the United States and Canada provide a useful data set to test strategies for defining column means using flask sampling. In this paper we use the COBRA-2000 data to determine the precision to which column mean CO2 can be determined using various flask sampling approaches.
 The COBRA-2000 campaign used instruments aboard the University of North Dakota (UND) Cessna Citation jet airplane to measure trace gas mixing ratios over North America during 28 July to 24 August 2000. Molar mixing ratios of CO2 and CO were measured continuously on board the airplane by the group from Harvard University (C. Gerbig et al., Toward constraining regional-scale fluxes of CO2 with atmospheric observations over a continent: 1. Observed spatial variability, submitted to Journal of Geophysical Research, 2003, hereinafter referred to as Gerbig et al., submitted manuscript, 2003), and flask samples were obtained for measurements at NOAA/CMDL of CO2, CH4, CO, H2, N2O and SF6, and at the University of Colorado Institute for Arctic and Alpine Research (CU/INSTAAR) of δ13C and δ18O in CO2. The flask samples allowed us to (1) measure several trace gases in order to give information about air mass history, (2) determine the isotopic signatures of CO2 sources and sinks, and (3) ensure that the in situ data were comparable to the WMO scales for CO2 and CO, which are maintained by CMDL [Zhao et al., 1997; Novelli et al., 1991]. Additional flask samples were collected for O2/N2 analysis at Scripps and were also analyzed at CMDL. Continuous measurements of water vapor and air temperature were made by the UND group.
 Flight patterns during COBRA-2000 were chosen to fulfill a variety of mission objectives, including boundary layer budget studies, Lagrangian budget studies, and regional surveys. In addition there were several transit flights. Ninety-six fairly complete continuous CO2 vertical profiles were obtained during the campaign. At times two or more profiles were flown in close proximity, such that the trace gas profiles were not completely independent. Nevertheless, in this analysis we treat each of the profiles as independent. All parameters measured aboard the aircraft were recorded at 1-s intervals, typically corresponding to an altitude increment of about 6 m. Generally, CO2 data were recorded at 4 Hz and processed into median filtered 0.5 Hz data [Daube et al., 2002]. Gaps in the CO2 profiles correspond to calibrations, which typically took about 90 s. The precision of the Harvard CO2 instrument was 0.25 ppm (Gerbig et al., submitted manuscript, 2003).
 On 23–24 August 2000, five flights were made over the Park Falls, Wisconsin, 447-m-tall tower site that has been operated by NOAA/CMDL since 1994. The landscape around the tower is quite flat and heavily forested. At the tower we measured CO2 mixing ratios at 11, 30, 76, 122, 244 and 396 m above the ground, with one measurement at each level about every 12 min [Bakwin et al., 1998]. We also measured wind speed and direction, temperature, humidity and surface pressure, as well as the atmosphere/surface exchange of CO2, H2O, heat and momentum [Berger et al., 2001; Davis et al., 2003]. Two profiles were obtained over the tower during each flight as the airplane descended in a spiral pattern, and then ascended while leaving the vicinity of the tower (Figure 1). Below 3 km above ground level (AGL) during the descents the average horizontal distance between the airplane and the tower was about 3 km.
 In order to obtain complete profiles between 0.25 and 4 km AGL for calculation of column means we filled the profiles by linear interpolation of the CO2 data to 6 m intervals. Surface elevation was determined using a digital elevation model. For profiles when the aircraft did not reach 4 km we assumed a uniform profile above the highest measured altitude, which is consistent with data collected above about 3 km. To simulate the effect of instrument noise and small-scale ambient variability, random, normally distributed (standard deviation = 0.2 ppm (Gerbig et al., submitted manuscript, 2003)) noise was added to the interpolated data. Subsequently, we refer to these as filled profiles. For most of the profiles we neglected variations of CO2 below 0.25 km AGL. Most aircraft will not fly much lower than this except during take off and landing. The influence of near-surface gradients of CO2 on the column means was examined using combined data from the airplane and the Wisconsin tower obtained on 23 and 24 August.
 Discrete flask sampling was simulated by selecting values from the filled profiles. Up to 20 flasks were sampled from the data either instantaneously or by averaging over 90 m intervals in height to simulate a finite time period for flask collection (equal to approximately 15 s). Samples were selected uniformly with height from 0.25 to 4 km AGL. Density-weighted CO2 column means were compared to those calculated from the original filled profiles. Real flask samples were obtained during most of the profiles, but with typically four or fewer samples collected below 4 km AGL during each profile it is impractical to compute column means from the real flask samples for comparison with the in situ data.
 Some sources of uncertainty were estimated by Monte Carlo methods. Uncertainty due to instrument noise was estimate by selecting samples from repeatedly interpolated profiles, and was generally about 0.05 ppm (1 standard deviation) for the column mean using 6–20 discrete samples. This corresponds to uncertainty due to the random error that was added to the interpolated segments of the profiles, and should be similar to the uncertainty of the column mean due to instrument noise. Uncertainty due to small-scale ambient variability of CO2 was estimated by randomly varying the sampling altitudes by up to ±60 m from the nominal values. An uncertainty in the column mean of about 0.1 ppm was obtained from the combination of these two factors, similar to the uncertainty of 0.19 ppm for the same data set determined by Gerbig et al. (submitted manuscript, 2003) by using an autocovariance method.
 The COBRA-2000 profiles were obtained during generally fair weather conditions in mid to late summer over biologically productive areas (Gerbig et al., submitted manuscript, 2003). Of the 96 aircraft profiles we examined all but 11 had lower CO2 in the lowest 1 km than above 3 km. Profiles obtained over the Wisconsin tower provide typical examples (Figure 1). A rapid change in CO2 with height at around 1–2 km AGL was usually observed, reflecting the top of the daytime convective boundary layer (CBL) [Yi et al., 2001]. Depletion of CO2 in the CBL is due to net sequestration by the vegetation and soils at this time of year [Davis et al., 2003]. Above the CBL, CO2 mixing ratios tended to be fairly uniform with height. During the afternoon of 24 August (Figure 1e), as during some other profiles, layers of high CO2 were observed above 3000 m and have been attributed to distant biomass fires (Gerbig et al., submitted manuscript, 2003).
 Early morning profiles at the Wisconsin tower (Figures 1a and 1c) are characterized by very high CO2 mixing ratios close to the ground, which result from nighttime buildup within the shallow, stable nocturnal boundary layer (NBL) of CO2 from respiration [Bakwin et al., 1995, 1998]. The layer of high CO2 is well below the altitudes accessed by the airplane, and is observed in the tower data only. The CO2 mixing ratio at 11 m above the ground (below the treetops) during the morning flight on 23 August was 410 ppm (Figure 1a). For the morning profiles, using only the aircraft data, and assuming that CO2 is constant below the lowest altitude reached by the airplane, would result in an underestimate of the column mean from the surface to 4 km of about 1 ppm (Table 1). The buildup of CO2 in the NBL is highly nonuniform in space and time. Therefore representative column means will be difficult to obtain from aircraft during the early morning hours, particularly if tower data are not available.
Table 1. Density-Weighted Column Averages of CO2 Mole Fraction From the Surface to 4 km AGL Calculated From Aircraft, Tower, and Simulated Flask Sample Data During COBRA-2000 Flights Over the Wisconsin Tower, 23–24 August 2000a
Profiles are shown in Figure 1, where times are listed.
Aircraft only (0–4 km) assumes constant CO2 below the lowest altitude sampled by the aircraft.
 Discrete sampling may not adequately capture the rapid change in CO2 at the CBL top, adding uncertainty (noise) to the column means computed from the discrete samples (Figure 2). Profiles sampled with 4 and 6 flasks overestimated the in situ column (0.25–4 km) averages by about 0.2 and 0.1 ppm, respectively. Since most of the profiles had roughly similar shapes (see Figure 1) this represents a true bias, that is, a consistent overestimate. With 10 or more samples, flask profile means were not significantly different from the nominal values (at the 95% level), and the uncertainty (1 standard deviation) of the mean was 0.15 ppm or less. Using a sampling strategy in which each flask linearly integrates over a 90 m layer did not significantly reduce the overestimate for profiles sampled by a small number of flasks but did reduce the uncertainty approximately in accord with the proportion of the total profile that was captured by the flasks; that is, with 20 samples almost one half of the 0.25–4 km column was sampled and the reduction of uncertainty was close to 50%. Integrating over larger vertical distances would obviously reduce the uncertainty further.
 Continuous profiles of water vapor, potential temperature (Θ) or other tracers could be used to identify the CBL top in order to improve the estimate of the column mean from discrete samples. Water vapor and Θ data for the profiles over the Wisconsin tower are shown in Figure 1. A distinct relic boundary layer is evident above the NBL in the morning profiles for 23 and 24 August (Figures 1a, 1c, and 1d). The vertical distributions of CO2 and H2O show considerable structure within the relic layer. The top of the relic layer can be accurately estimated as the point above which the variance of the H2O (or CO2) mixing ratio decreases markedly. These relic layers, which were about 2.4 and 1.5 km deep on 23 and 24 August, respectively, persisted throughout the day. As the day progresses the CBL grows into the relic layer. The top of the CBL can be identified as the point where Θ begins to increase rapidly with height. The CBL grew to about 2.0 and 1.2 km on 23 and 24 August, respectively (Figures 1b and 1e). A large gradient in CO2 exists between the top of the CBL and the top of the relic layer. With such complex atmospheric structure we have been unsuccessful in deriving a simple strategy to use Θ and H2O measurements to improve estimates of the column means from discrete sampling.
4. Discussion and Conclusions
 We determined the column mean for CO2 in a layer of the atmosphere up to 4 km above the ground using discrete sampling from continuous aircraft profiles to simulate flask sampling. We find that 10 and 20 instantaneously collected flasks can define the column mean without measurable bias to typically within about 0.15 and better than 0.10 ppm, respectively. More precise results can be obtained by using a flask sampling strategy that linearly integrates over portions of the air column. Using fewer than 8–10 flasks can lead to significant (at the 95% level) sampling bias for some typical profile shapes (Figure 2).
 The COBRA-2000 profiles were obtained mainly over productive continental regions during the growing season. Most of the profiles showed substantial depletion of CO2 in the CBL because of uptake by the vegetation (e.g., Figure 1). In winter in these areas, CO2 is likely to be higher in the CBL than aloft because of a net surface source from respiration and fossil fuel combustion. Higher CO2 in the CBL than aloft over Harvard Forest, Massachusetts, in winter is commonly observed in profiles that CMDL has obtained regularly since 1999 using an automated flask sampling system (NOAA/CMDL, unpublished data). When such profiles are sampled with a small number of flasks (i.e., less than 8–10) we would expect similar sampling bias, but of opposite sign, to that observed for the COBRA profiles. Over other areas where net surface fluxes are small, such as the oceans or desert regions, vertical profiles are likely to be more uniform and hence more easily characterized by discrete flask sampling.
 Aircraft sampling cannot capture strong gradients in CO2 that often exist very close to the ground during the nighttime and early morning. Tower data show large build up of CO2 below the nocturnal near-surface inversion, which is typically less than 200 m deep, and often less than 100 m. Usually by about 10:00 local time these gradients are dissipated by convective mixing [Bakwin et al., 1998]. Aircraft profiles that do not penetrate this layer underestimate the column mean below 4 km by about 1 ppm.
 Sources of uncertainty include instrument noise and small-scale atmospheric variability. We investigated these by using Monte-Carlo methods, and found that together they contribute about 0.1 ppm to the uncertainty in the column mean for our profiles. Differences between profiles obtained close in space and time were generally larger, averaging about 0.8 ppm for mixed layer means obtained 100 km apart (Gerbig et al., submitted manuscript, 2003). Frequent profiling using inexpensive methods such as automated flask sampling can provide a statistical representation of this large ambient variability.
 COBRA was funded by NSF (ATM-9821044), DOE (DE-FG02-98ER62695), NASA (NAG5-7950), and NOAA (NA06GP0406). Carbon dioxide mixing ratio measurements, and site infrastructure and maintenance at the Wisconsin tower were supported by the Atmospheric Chemistry Project of the Climate and Global Change Program of the National Oceanic and Atmospheric Administration, and work at the tower would not be possible without the gracious cooperation of the Wisconsin Educational Communications Board and R. Strand, chief engineer for WLEF-TV.