CO2 storage in a 30-min period in a tall forest canopy often makes significant contributions to net ecosystem exchange (NEE) in the early morning and at night. When CO2 storage is properly measured and taken into account, underestimations of NEE on calm nights can be greatly reduced. Using CO2 data from a 12-level profile at the Missouri Ozark flux site (an oak-hickory forest in central Missouri, USA), we demonstrate that the lower canopy layer (below the thermal inversion) is a disproportionately large contributor to the total CO2 storage. This is because time derivative of CO2 density (Δc/Δt) generally shows increasing magnitude of mean and standard deviation with decreasing heights at night and from sunrise to 1000 h in both growing and dormant seasons. Effects of resolution and configuration in a profiling system on the accuracy of CO2 storage estimation are evaluated by comparing subset profiles to the 12-level benchmark profile. It is demonstrated that the effectiveness of a profiling system in estimating CO2 storage is not only determined by its number of sampling levels but, more importantly, by its vertical configuration. To optimize a profile, one needs to balance the influence of two factors, Δc/Δt and layer thickness, among all vertical sections within a forest. As a key contributor to the total CO2 storage, the lower canopy requires a higher resolution in a profile system than the layers above. However, if the upper canopy is oversparsely sampled relative to the lower canopy, the performance of a profile system might be degraded since, in such a situation, the influence of layer thickness dominates over that of Δc/Δt. We also find that because of different level of complexity in canopy structure, more sampling levels are necessary at our site in order to achieve the same level of accuracy as at a boreal aspen site. These results suggest that in order to achieve an adequate accuracy in CO2 storage measurements, the number of sampling levels in a profile and its design should be subject to the site properties, e.g., canopy architecture and the resulted thermodynamic and flow structures. If CO2 density from a single profile is averaged in time and then used in assessing CO2 storage to reduce random errors, biases associated with this averaging procedure become inevitable. Generally, larger window sizes used in averaging CO2 density generate poorer estimates of CO2 storage. If absolute errors are concerned, it appears that the more significant the CO2 storage is during a period, the larger effects the averaging procedure has.
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 Net ecosystem exchange (NEE) of CO2, derived from mass conservation principles, can be formulated as
if molecular diffusion and horizontal divergence of turbulent flux are neglected and incompressible flow is assumed. In equation (1), c is CO2 density, t is time, zr is the height of eddy covariance measurement, and ui (i = 1, 2, and 3) is the velocity component in x, y, and z (or x1, x2, and x3) direction, respectively. The overbar denotes Reynolds averaging, while the single prime indicates departures from the Reynolds averaging. The repeated index in the second term on the right-hand side indicates a summation over each value for i. The three terms on the right-hand side of equation (1) are storage, advection, and vertical flux (or eddy flux), respectively. The first two terms are vertically integrated, while the third term is measured at height zr. Following convention, negative values of NEE mean uptake of CO2 by the ecosystem from the atmosphere, while positive values indicate a reverse process.
 Under ideal conditions, such as strong turbulent mixing, horizontal homogeneity of canopy, a steady atmosphere, and flat terrain with an extended upwind distance, vertical flux can be a close estimation of NEE [Aubinet et al., 2000; Baldocchi, 2003]. However, these ideal conditions are often not met in field, which leads to frequent underestimation of NEE because of omission of considerable contributions from advection and storage.
 The importance of the advection term was recently realized in the flux community. Vertical advection of CO2 (i = 3 for the second term on the right-hand side of equation (1)) could be significant over tall vegetation under conditions of nonzero mean vertical velocity [Lee, 1998; Paw U et al., 2000], and inclusion of vertical advection improved the accuracy of NEE estimates [Baldocchi et al., 2000]. Further studies suggested that horizontal advection (i = 1 and 2 for the second term on the right-hand side of equation (1)) could also be significant at field sites over sloped terrain, where drainage flow is very likely under stable condition at night and CO2 leaks from the sides of the control volume [Baldocchi et al., 2000; Aubinet et al., 2003; Staebler and Fitzjarrald, 2004]. Moreover, drainage flow over sloped terrain often results in nonzero mean vertical motion and, under such circumstances, both vertical and horizontal advection should be taken into account simultaneously [Aubinet et al., 2003; Marcolla et al., 2005].
 Although its mean over long periods (e.g., a day or a month) is close to zero, CO2 storage in the vertical air column beneath the height of eddy covariance measurement can be significant over short-term intervals (e.g., 30 min) and must be taken into account in assessing NEE [Aubinet et al., 2000]. Previous studies have shown that CO2 storage makes considerable contributions to NEE in a forest ecosystem at night, when wind is calm and atmosphere is thermally stable, and during the early morning, when accumulated CO2 in the previous night is flushed from the forest into the atmosphere by the onset of turbulence [Baldocchi et al., 2000; Fan et al., 1995; Goulden et al., 1996; Grace et al., 1995; Hollinger et al., 1998; Jarvis et al., 1997; Yang et al., 1999]. For example, most of these studies found that hourly or half-hourly values of CO2 storage typically ranged from −2 to −5 μmol m−2 s−1 in the morning hours immediately after sunrise and from 1 to 3 μmol m−2 s−1 at night, while Grace et al.  measured as high as −20 μmol m−2 s−1 and 10 μmol m−2 s−1 for the two periods in a tropical rain forest.
 Neglect of CO2 storage in estimating NEE could lead to misinterpretation of biological activities in a forest ecosystem. For example, a positive spike of eddy flux of CO2 (the third term on the right-hand side of equation (1)) is usually observed in the early mornings as a result of CO2 “flush” [Grace et al., 1995; Yang et al., 1999]. This alone would mistakenly indicate that the ecosystem is a CO2 source in these hours. Once CO2 storage is properly included, however, NEE can become negative [Grace et al., 1995; Yang et al., 1999] and the transition of the ecosystem from a CO2 source to a sink may actually occur earlier than indicated by eddy flux alone [Jarvis et al., 1997].
 Another widely known problem in the flux community is the frequent underestimate of NEE by eddy covariance technique at night, when a portion of the respiratory CO2 from soil and plants is trapped near the ground surface and takes the form of CO2 storage as a result of calm wind and stable atmosphere. However, previous studies did not reach a consensus on whether inclusion of CO2 storage could bring nighttime NEE under low wind conditions to the same level as measured under high wind. While Grace et al.  and Hollinger et al.  showed that nighttime NEE no longer depended on wind intensity after CO2 storage was taken into account, others [Fan et al., 1995; Goulden et al., 1996; Jarvis et al., 1997; Yang et al., 1999] found that it was not the case even though inclusion of CO2 storage could reduce the underestimate of NEE to a certain degree. In the latter case, advection might also play a role, as Marcolla et al.  showed that nighttime NEE was independent of wind intensity after both CO2 storage and advection were included.
 Typically, a vertical profiling system is used at flux sites to measure the CO2 storage in the air column from the ground level to the eddy covariance measurement height. A survey of several studies revealed that the number of measurement levels varied from 4 to 8, covering a vertical distance of 21 to 45 m [Baldocchi et al., 2000; Cook et al., 2004; Fan et al., 1995; Goulden et al., 1996; Grace et al., 1995; Hollinger et al., 1998; Jarvis et al., 1997; Schmid et al., 2000; Yang et al., 1999]. In these experiments there were 3 to 7 measurements arranged below the canopy top (canopy height from 6.5 to 30 m) and 1 to 3 measurements above. A logical question arises as to whether such a sampling resolution and arrangement in these CO2 profiles are adequate in estimating the storage term. In an attempt to address this issue, Yang et al.  used an eight-level profile as a reference to test the subsets of this profile. They divided these subsets into seven groups on the basis of the number of measurement levels in each profile and defined the error of the storage term as the difference between each subset profile and the reference. Their major findings were (1) standard errors of estimate decrease as the number of measurement levels in a profile increases, (2) a profile containing no measurement below the thermal inversion (at 9 m in their experiment) produces relatively large errors and cannot be used to estimate CO2 storage no matter how many measurement levels there are in a profile, and (3) when the number of measurement levels is four or more, all three measurement levels below the thermal inversion must be included in order to construct the best profile (minimal error) within each group. Their analyses showed that the standard error of estimate of CO2 storage was about 0.87 and 0.58 μmol m−2 s−1 in the growing season for the best two- and three-level profiles, respectively. It is unclear which period of the day was included in their error analyses, but one would expect that errors resulting from the inadequate sampling must be higher during the period when CO2 storage is significant (night and hours just after sunrise) than when CO2 storage is negligible (late morning and afternoon).
Finnigan  addressed another issue regarding the CO2 storage term. In principle, if measurements of CO2 exchange between an ecosystem and atmosphere take place over an inhomogeneous surface, one would like to average the three terms in equation (1) over a volume or over the plane capping that volume. When a single tower is used at flux sites, however, we are forced to perform time-averaging instead of volume-averaging. In doing so, eddy flux term in equation (1) becomes a mean quantity for a short period (flux-averaging period, usually 30 min at most flux sites) while the CO2 storage term in its exact form is the vertical integration of the difference between instantaneous CO2 density at the beginning and end of this flux-averaging period, divided by the length of this period [Finnigan, 2006]. This often leads to noisy CO2 storage (random errors) because instantaneous CO2 density can be easily influenced by wind gusts and/or electronic noises associated with the instruments. Many workers practically replace instantaneous CO2 profiles by time-averaged ones to reduce the random errors. However, the tradeoff is that CO2 storage could be underestimated because of the removal of high-frequency information by the averaging procedure and underestimation of CO2 storage can be 50% or more depending on the time of the day and the sizes of the window in which CO2 profiles are averaged [Finnigan, 2006].
 In this study, we extend the work conducted by Yang et al.  and Finnigan  using a high-resolution CO2 profile system operating in an upland oak forest. Our tasks are (1) to examine the effects of resolution and configuration of a profiling system on CO2 storage estimates, (2) to test in a vertically complex forest canopy the suggestion made by Yang et al.  that CO2 storage could be reasonably estimated by a three-level profile (one above the thermal inversion height and two below), and (3) to test the theoretical prediction by Finnigan  on the underestimation of CO2 storage caused by the CO2 density averaging.
2. Site, Measurements, Data, and Methods
 As a component of AmeriFlux, the Missouri Ozark flux (MOFlux) site (38°44′ N, 92°12′ W) is located at the Baskett Research and Education Area (BREA; owned and managed by the University of Missouri) 30 km southeast of Columbia, Missouri, USA. This research area is part of the Ozark border forest and in an ecologically important transition zone from deciduous forests in the eastern United States to tallgrass prairie in the Great Plains. The vegetation at the site is an oak-hickory forest dominated by white oak (Quercus alba) and with contributions of several other oak species (black oak, Quercus velutina; northern red oak, Q. rubra; Shumard oak, Q. shumardii; chinkapin oak, Q. muehlenbergii; and post oak, Q stellata) and hickories (primarily shagbark hickory, Carya ovata). A dense understory of sugar maple (Acer saccharum) is found beneath the canopy, along with eastern redcedar (Juniperus virginiana) (the latter in localized disturbed areas) [Pallardy et al., 1988]. Forest density is about 583 trees ha−1 (≥9 cm in diameter at the breast height) and tree basal area around 24.2 m2 ha−1. Canopy height ranges from 17 to 20 m and leaf area index (LAI), measured by leaf litter collection, is about 4.2. The vegetation sampling reported above was conducted in spoke-like transects around the tower in dominant wind directions (SE, S, SW, W, NW). Each transect contains five plots (except the NW one with only four plots because of a small pond at the end of it) at a 50 m interval and extends to 250 m from the tower.
 Dominant soils are a broadly distributed type classified as Weller silt loam and another type “Steep Stony Land” localized to limestone outcrop areas [Krusekopf and Scrivner, 1962]. The climate of the area is warm, humid and continental. The monthly mean temperature (1971–2000) is −2.3°C in January and 25.2°C in July. Annual precipitation averages 1023 mm from 1971 to 2000. These climatic data can be found in the category of “Free Data B, 1971–2000 U.S. Climate Normals Products” at the National Climatic Data Center (http://www.ncdc.noaa.gov).
 The topography of the area surrounding the site comprises flat to rolling upland areas dissected by forested drainages. In the forested areas, ridges alternate with relatively gentle side slopes leading to ephemeral streams in the shallow valleys with a total local elevation range of 175–245 m. The eddy flux tower is located on the top of a ridge surrounded by an approximately 1 km diameter circular drainage basin. The ridge extends from N to S into the basin and has gently sloping SE- and NW-facing sides.
 An eddy covariance system is installed at a height of 31 m at the top of the tower. It consists of a RM Young 81000 three-dimensional sonic anemometer (R. M. Young Company, Traverse City, Michigan, USA) and a LI-7500 open path gas analyzer (LI-COR Inc., Lincoln, Nebraska, USA). Data are recorded at 10 Hz by a personal computer sheltered in a support building at the base of the tower. Vertical fluxes of CO2, water vapor, temperature, and momentum are carried out every 30 min after two-dimensional coordinate rotation, despiking, and Webb correction [Webb et al., 1980] are performed.
 Also in operation are CO2/water vapor and air temperature/relative humidity profile sampling systems. Atmospheric CO2 concentration and water vapor content are measured by a LI-7000 gas analyzer (LI-COR Inc., Lincoln, Nebraska, USA) at heights of 0.15, 0.30, 0.61, 0.91, 1.52, 3.05, 6.10, 9.14, 12.19, 16.76, 22.86, and 30.48 m. The LI-7000 gas analyzer also resides in the support building that is temperature-controlled by an air conditioning/heating unit. Air samples are drawn continuously from the 12 heights through 6.4 mm diameter Teflon tubes at a flow rate of 9–10 L min−1. All tubes are cut into the same length to ensure the same amount of traveling time by air samples in the tubes between different heights and are heated by electric wires to prevent condensation. The tube inlets are filtered with Teflon filters and placed downward to minimize intake of water, insects, and dust particles. Downstream of these tubes is a manifold that diverts the air samples to the LI-7000 gas analyzer one at a time at a flow rate of 0.7 L min−1. Air samples are measured from top to bottom levels in a recurring cycle. Each level is measured for a period of 60 s (30 s before 7 October 2004) at an interval of 5 s, but only the last reading is recorded to avoid influence from the previous sample. The LI-7000 gas analyzer is manually calibrated every month using N2 as the zero-CO2 gas and a commercially prepared CO2 standard (430.1 μmol mol−1) as the span gas. During the period when CO2 concentrations from the profile were collected for this study, our monthly calibration records showed that zero drift of LI-7000 ranged from −0.65 to 0.05 μmol mol−1 and span drift was from −1.3 to 0.1 μmol mol−1.
 The temperature/relative humidity profile is composed of 8 HMP45C probes (Campbell Scientific Inc., Logan, Utah, USA) at heights of 0.61, 1.52, 6.10, 9.14, 12.19, 16.76, 22.86, and 30.48 m. Air temperature and relative humidity are measured once every minute for all heights but reported as 30-min averages. CR10X data-loggers (Campbell Scientific Inc., Logan, Utah, USA) are employed to record data from both profiles. To avoid any possible influence of the concrete tower base on the samplings, the air inlets and temperature/relative humidity probes below 6 m are mounted on a 3.3 m pole, which is about 15 m from the tower in an area of undisturbed forest, while the rest of the profile sensors and sample tubes are mounted on the tower.
 Other regular measurements at this site include those of a subcanopy eddy covariance system located east of the tower, a variety of meteorological and environmental variables, soil respiration (by eight automated chambers), and individual tree sap flow rates (by 24 sap flow gauges). Additional periodic measurements obtained within 24 permanent plots located along the transects from the tower include tree growth (by band dendrometers), litter production (by randomly located baskets), canopy assimilation and photosynthetic attributes, water relations, and phenology.
2.3. Data and Methods
 The first data set used in this paper covers a period from the initiation of measurements on 16 June 2004 to 31 March 2005 so that data periods considered are about equal between growing season (before 1 November 2004) and dormant season. This data set includes measurements from the eddy covariance system and from the two profiling systems and is used to demonstrate the importance of CO2 storage (section 3.1) and to test the influence of profile resolution and configuration on the storage term (section 3.2). Since CO2 concentration from the profile is measured in a 12-min recurring cycle and therefore not always recorded at the exact beginning or end of each 30-min period, we use a cubic spline function [Press et al., 1992, pp. 113–116] to interpolate CO2 concentration on a 1-min basis before CO2 storage is computed for each 30-min period. Atmospheric pressure (measured by Vaisala PTB101B; Vaisala Inc., Helsinki, Finland) and air temperature from the air temperature/relative humidity profile are involved in computing air density at each height so that unit conversion for CO2 (from μmol mol−1 to g m−3 or μmol m−3) can be carried out. At the CO2 measurement levels where air temperature is not measured, we obtain air temperature by applying linear interpolation to the two adjacent measurements. The CO2 storage (first term in equation (1)) within each 30-min period is evaluated in a discrete format,
where z is the aboveground height for each measurement level, Δc/Δt is the time derivative of interpolated CO2 density, k is the index for vertical levels, and n is the total number of measurement levels in the profile. We average Δc/Δt over a 3-min period centered at the beginning and end of each 30-min period to reduce the random error associated to the instantaneous CO2 profile [Finnigan, 2006]. We also average Δc/Δt between levels k and k−1 so that it is more representative for the layer zk−zk−1 than using either of them alone. At the bottom level (k = 1), however, Δc/Δt is not averaged because of the unavailability of measurement right at the ground surface. By doing this, we assume an vertically invariant Δc/Δt below the lowest measurement level [Jarvis et al., 1997; Yang et al., 1999] without regard to the absolute value of CO2 density or its height dependence within this bottom layer.
 To examine how resolution and vertical configuration of a profiling system may influence the accuracy of CO2 storage, we used our 12-level profile as a benchmark to test subsets of the full profile system. The subset profiles are grouped on the basis of the total number of measurement levels in each profile. Within a group, all profiles contain the same number of measurement levels but different combinations of measurement heights. For convenience, we use “group 1” in the following text to denote the group in which all profiles contain one-level measurement, “group 2” for the group of profiles containing two-level measurements and so on. The topmost level (30.48 m) is always included as the top boundary in all subset profiles and thus the number of possible combinations in group m (2 ≤ m ≤ 11) is 11Cm−1. Group 1 is not tested since it has only one combination (the topmost level). After the CO2 storage term is computed for every 30-min period and for all subset profiles, root-mean-square error (RMSE) is calculated for each subset profile using the 12-level benchmark as the standard. Therefore RMSE measures the mean error of 30-min CO2 storage from a subset profile when compared to the benchmark. We finally determine the best and worst profiles within each group on the basis of the RMSE and these results are discussed in section 3.2.
 In the following analyses, NEE refers to the sum of eddy flux (at 31 m) and storage terms (from ground up to 30.48 m) owing to unavailable measurement of CO2 advection. No attempt has been made to fill any gaps in this data set. A 30-min period is rejected if any of NEE, eddy flux or storage exceeds 50 μmol m−2 s−1 in magnitude. This threshold represents the upper bound for NEE during the season in which the data are chosen.
 The second data set in this study contains 10 Hz CO2 density measured at the tower top by the LI-7500 open path gas analyzer from 28 March 2006 to 20 July 2006 (data from 17 May to 7 June are missing). These data are used to test the theoretical prediction from Finnigan  on how the size of averaging window centered at the beginning and end of each 30-min period affects the accuracy of CO2 storage term (section 3.3). They are screened by the diagnostic flags (indicating the instrument status) from the LI-7500 and by limit test (0.35 to 1.05 g m−3, approximately corresponding to 200 to 600 μmol mol−1 under condition of 15 °C air temperature and 105 Pa atmospheric pressure).
3.1. Importance of CO2 Storage and Disproportional Contributions From Different Vertical Sections to the Total CO2 Storage
 Seasonally averaged NEE (Figure 1a) and storage terms (Figure 1b) exhibit a clear diurnal cycle as observed at other sites [Baldocchi et al., 2000; Fan et al., 1995; Jarvis et al., 1997; Yang et al., 1999]. CO2 storage in general makes significant contribution at night and from sunrise to about 1000 h (referring to local time and thereinafter). The magnitude of mean CO2 storage in the growing season is about 1.2 to 2.6 μmol m−2 s−1 at night and up to 6.5 μmol m−2 s−1 around 0830 h, comparable to the reported values from other temperate forests [Baldocchi et al., 2000; Goulden et al., 1996]. Not surprisingly, both NEE and storage of CO2 show much greater magnitude in both daytime and nighttime for the growing season than for the dormant season. However, the seasonal difference is greatly reduced when ratios of storage to NEE are concerned (Figure 1c). Storage/NEE varies from 0.23 to 0.64 at night in the growing season, while it is from 0.1 to 0.5 at night in the dormant season with exception of outliers. Curves for storage/NEE are erratic from sunrise to 1000 h because this ratio can be extremely large when NEE is close to zero. From 1000 h to sunset, CO2 storage is of negligible importance as the value of storage/NEE is very small for all seasons.
Figure 2 shows eddy flux of CO2 and NEE as a function of friction velocity (u*) at night for the growing season. Here and in the following text, we use a threshold of 10 W m−2 incoming global radiation to define daytime and nighttime. With storage excluded, mean CO2 eddy flux exhibits a nearly linear relationship with u* at u* < 0.3 m s−1 and a considerable underestimate of the respiratory CO2 on calm nights. In contrast, the slope of this linear relationship is greatly reduced when mean NEE (sum of CO2 eddy flux and storage) is plotted against u*. The respiratory CO2 flux measured at u* < 0.3 m s−1 is increased from 0.15 to 5.8 μmol m−2 s−1 (by eddy flux only) to a range of 3.4–6.8 μmol m−2 s−1 (by both eddy flux and storage). These storage-adjusted values are very close to the values at u* > 0.3 m s−1. In the dormant season (not shown), dependence of NEE on u* at the low end is also reduced but by a smaller degree. It is clear from Figure 2 that nighttime CO2 storage is a greater contributor to the NEE at low values of u* than high values. When u* < 0.3 m s−1, for example, 67% of measurements suggest that nighttime CO2 storage accounts for at least 50% of the NEE in the growing season; it is only 13% when u* > 0.3 m s−1. In the dormant season, the corresponding values are 62% and 26%, respectively.
 Seasonally averaged CO2 concentration in a time- and height-coordinate is presented in Figure 3. CO2 buildup at night and rapid depletion after sunrise are clearly shown. These correspond to the positive CO2 storage at night and large magnitudes of negative storage from sunrise to 1000 h observed in Figure 1. As a result of turbulent mixing, CO2 is relatively uniform in vertical direction during the daytime. In contrast, large vertical gradients of CO2 concentration are observed at night owing to the nonuniform source distribution in vertical direction and lack of mixing mechanisms (calm wind conditions). Our data show that instantaneous CO2 concentration near the ground surface sometimes reaches 500 μmol mol−1 or more at night in the growing season and is about 100 μmol mol−1 greater than at the canopy top. Such a vertical gradient suggests that different vertical sections of the forest may contribute unequally to the CO2 storage term.
 To further support this assertion, we present statistics of the time derivative of CO2 density (Δc/Δt) over 30 min in Figure 4. By definition, the vertical integration of Δc/Δt yields the storage term (equation (2)). Generally, the magnitude of mean Δc/Δt and its standard deviation decreases with height at night and from sunrise to 1000 h in both the growing and dormant seasons. These results suggest that a layer in the lower canopy very likely contributes more to the seasonal mean CO2 storage than does a layer with the same thickness in the upper canopy. Additionally, indicated by its larger standard deviation of Δc/Δt, the lower canopy experiences more occurrences of relatively large values of Δc/Δt than the upper canopy and thus plays a dominant role in contributing to 30-min CO2 storage as well.
 A noticeable phenomenon in Figure 3 is the rapid fall of CO2 concentration in the early morning after turbulent mixing and photosynthesis resume. This CO2 reduction is especially large in the lower canopy, as indicated by the most compacted contour lines in that region. Therefore a large mean and standard deviation of Δc/Δt near the surface from sunrise to 1000 h are expected (Figure 4). On the other hand, large variation of Δc/Δt in the lower canopy layer at night is probably attributable to a combination of proximity to active CO2 sources at the ground represented by respiration in the soil and litter, a prevalent nighttime thermal inversion aloft and the intermittence of turbulence at night. Air temperature profiles at our site show that a thermal inversion frequently forms above 6.10 m at night (Figure 5) because of the strong radiative cooling associated with the maximum leaf area density at this height. Although seasonally averaged Δc/Δt is positive at night, there sometimes is negative Δc/Δt for 30-min periods. The large magnitude of Δc/Δt (both positive and negative) in the lower canopy often occurs on nights with strong inversion. The CO2 released by soil respiration readily accumulates in the layer below 6.10 m and its upward transport is prevented by negative buoyancy imposed by the inversion layer. Consequently, large positive Δc/Δt events take place. In contrast, the large negative Δc/Δt events in the layer below 6.10 m are a result of horizontal air motion or intermittent turbulence that occasionally penetrates the inversion and quickly removes CO2 in a brief period of time [Salmond, 2005].
Figure 6 compares the mean CO2 storage per unit height from different vertical sections (0.00–6.10 m, 6.10–16.76 m, and 16.76–30.48 m) of the forest during the growing season. We first calculated the CO2 storage in each vertical section and then divided it by the thickness of that section; therefore values in Figure 6 quantitatively equal the layer-thickness weighted-mean of Δc/Δt. Figure 6 confirms our inference from Figure 4 that a layer below the thermal inversion contributes more to the seasonal mean CO2 storage from sunset to 1000 h the next morning than does a layer above 6.10 m with the same thickness. In other words, the contribution from each vertical section to the total CO2 storage is disproportional to its volume. For example, the volume proportions are 20%, 35%, and 45% in the three sections (from bottom to top), but their respective contributions to the total CO2 storages are 27% (23%), 40% (35%), and 33% (42%) in average from sunrise to 1000 h (at night) during the growing season.
3.2. Biases of CO2 Storage Related to the Configuration of a Vertical Sampling Profile
 Since CO2 storage has much larger magnitudes at night and from sunrise to 1000 h in the growing season than in the dormant season (Figure 1), we used CO2 storage from sunset to 1000 h the following morning in the growing season to determine the best and worst configurations in each subset profile group (method described in section 2.3). After the best and worst configurations were identified, time series of 30-min CO2 storage from these selected profiles were paired with that from the benchmark for the purpose of statistical analysis. Coefficients of determination and slopes of linear-regression lines from these pairs were computed and plotted in Figure 7 along with the RMSE. Coefficients of determination measure how much variance of 30-min CO2 storage from the benchmark can be explained by the time series from a subset profile and slopes of linear-regression lines measure how much the time series from a subset profile is systematically biased from the benchmark. The best and worst configurations from all subset profile groups are presented in Figures 8 and 9, respectively.
 It is clear from Figure 7 that an increase of measurement levels in a profiling system (increasing resolution) generally improves the accuracy of CO2 storage term relative to the benchmark. As expected, the worst configurations result in much larger RMSE, smaller coefficients of determination and larger departures from the unit for the slopes than the best configurations from the same group. When total number of sampling levels in a profile increases from 4 to 8 (corresponding to typical profiles operated at flux sites), coefficients of determination and slopes of linear-regression lines from the best configurations do not change significantly but the RMSE drops from 1.4 to 0.3 μmol m−2 s−1. A profiling system with 4 sampling levels or fewer, even if optimized, is not adequate for CO2 storage measurements in a forest with vertical structure as complex as at our site because its mean error is on the same order of magnitude as the nighttime NEE (1.0 to 5.8 μmol m−2 s−1 in the growing season from Figure 1).
 Comparison of Figures 8 and 9 suggests that the best configured profiles are among those in which sampling levels are close to a uniform distribution, while the worst profiles are those in which the vertical distribution of sampling levels is extremely uneven. Although we concluded in section 3.1 that the layer below 6.10 m is a key section in contributing to the total CO2 storage, an overdense coverage in this layer that in the meantime leaves a large void between 6.10 and 30.48 m inevitably produces the largest RMSE and becomes the worst configurations (Figure 9). If a profile is not optimally arranged, the deduced CO2 storage can be less accurate than others that have much smaller number of sampling levels but are properly configured (compare the worst profiles from groups 9 and 10 to the best profiles from groups 3 and 4 in Figure 7).
 A close look at the best configured profiles reveals that they are not exactly evenly distributed (Figure 8). First, the lowest sampling level in the best configured profiles is usually located below the geometric center of a layer that crosses this sampling level, and nearer to the respiratory CO2 source at the ground. If the lowest sampling level is relocated to the geometric center of that layer or above, RMSE increases and this increase largely depends on layer thickness (Table 1). The displacement of the optimal sampling level from the geometric center reflects the observation in Figure 4 that Δc/Δt is highly variable with height and has relatively large magnitudes of mean and standard deviation near the ground. Second, the layer below the thermal inversion (<6.10 m) requires a higher resolution than layers above. This principle is illustrated by comparing the best configured profiles from groups 6 and 7 (Figure 8). The best configured profile in group 7 is constructed by adding a sampling level at 0.91 m (covering a thickness of 3.05 m, RMSE = 0.515 μmol m−2 s−1) to the best one in group 6 rather than by adding at 9.14 m (covering a thickness of 6.09 m, RMSE = 0.620 μmol m−2 s−1). In other words, a profile with an unsampled thin layer below 6.10 m can produce larger errors than a profile from the same group with an unsampled thick layer above 6.10 m. More such examples are listed in Table 2.
Table 1. Comparison of Root-Mean-Square Error (RMSE) Before and After the Lowest Sampling Level is Relocated to the Geometric Center (or Above) of the Lowest Layera
Number of Sampling Levels (Group ID)
Sampling Levels, m
RMSE, μmol m−2 s−1
Sampling Levels, m
RMSE, μmol m−2 s−1
Data are from sunset to 1000 h the following morning during the growing season.
Data are from sunset to 1000 h the following morning during the growing season.
Here r2 is coefficient of determination and a is slope of linear regression.
30.48, 22.86, 16.76, 12.19, 9.14, 6.10
6.10 m between ground and 6.10 m
30.48, 22.86, 16.76, 12.19, 6.10, 3.05
6.09 m between 6.10 and 12.19 m
30.48, 22.86, 16.76, 9.14, 6.10, 3.05
7.62 m between 9.14 and 16.76 m
30.48, 22.86, 12.19, 9.14, 6.10, 3.05
10.67m between 12.19 and 22.86 m
30.48, 16.76, 12.19, 9.14, 6.10, 3.05
13.72 m between 16.76 and 30.48 m
 However, the statement above may not apply when the difference of layer thickness between the thin and thick layers becomes very large. In equation (2), two parameters determine the magnitude of CO2 storage, Δc/Δt and the thickness of the layer across the sampling level. In the above case and those in Table 2, the effect of Δc/Δt dominates over that of layer thickness. A contrasting situation is that contribution to total storage from a level above 6.10 m with a relatively small magnitude of Δc/Δt but covering a much thick layer may outweigh that from a lower level with a large magnitude of Δc/Δt but covering a very thin layer. Supporting examples are (1) a sampling level at 22.86 m (covering a layer of 13.72 m), rather than any level below 3.05 m (covering a layer of 3.05 m), is added to the best configuration in group 4 to construct the best one in group 5 (Figure 8); (2) a sampling level at 9.14 m (covering a layer of 6.09 m), rather than any level below 0.91 m (covering a layer of 0.91 m), is required in constructing the best configuration in group 8 from that in group 7 (Figure 8); (3) in the worst configured profiles (Figure 9), relocating any single sampling level from below 6.10 m to the big gap above can certainly improve that profile. In brief, an overdense coverage below 6.10 m constructed at the expense of upper layers is likely to degrade the accuracy of CO2 storage term.
3.3. Effects of CO2 Density Averaging on CO2 Storage
 According to Finnigan , spatially averaged instantaneous CO2 densities are required to calculate the storage term. With 10 Hz CO2 density measured only at the top level of a single tower at our site, however, we were forced to obtain the “true” storage from this single-level profile, that is, Δc/Δt at tower top from instantaneous CO2 density within a 30-min interval multiplied by the vertical distance from the ground to tower top (30.48 m). We acknowledge that it is improper to estimate CO2 storage from a single-point measurement, but the focus in this section is on the effects of CO2 density averaging on the estimate of CO2 storage. To do so, time series of 30-min CO2 storage were calculated using time-averaged CO2 density under different window sizes from 10 s to 1800 s and then tested against the “true” storage from the instantaneous density. We computed RMSE, coefficient of determination and slope of the linear regression line for CO2 storage under each averaging-window size for two periods, early growing season (28 March 2006 to 16 May 2006) and peak growing season (8 June 2006 to 20 July 2006). The results are presented in Figures 10 and 11, respectively.
 This analysis demonstrated that, first, as the window length used in averaging CO2 density becomes longer, time series of CO2 storage estimated from the averaged CO2 density generates larger mean errors (RMSE) and larger systematic biases (slopes of linear regression) and becomes less correlated (coefficients of determination) with the reference. The y-intercepts of the linear regression line (each symbol-labeled point in the bottom panels of Figures 10 and 11 represents one regression line) vary from −0.51 to 0.36 μmol m−2 s−1 in the early growing season and from −0.72 to 0.66 μmol m−2 s−1 in the peak growing season. This suggests that all linear regression lines cross the y-axis near the origin and slopes of linear regression largely represent the fraction of “true” CO2 storage returned by the time series of averaged CO2 density. Therefore large departures from the unit in the slopes of linear regression mean large systematic biases. Second, the averaging procedure appears to cause larger errors (RMSE) at night and from sunrise to 1000 h, when CO2 storage is significant, than from 1000 h to sunset when CO2 storage is relatively small. If errors are quantified in their relative magnitudes (slopes of linear regression), however, the averaging procedure affects the period from 1000 h to sunset the most and the period from sunrise to 1000 h the least. Third, if the same window length is used in averaging CO2 density in both early and peak growing seasons, this averaging procedure results in larger RMSE in the peak growing season although there is no significant difference for coefficient of determination and slope of linear regression between two seasons. This can be explained by the fact that the amplitude of diurnal cycle of CO2 density is greater in the peak growing season and thus its temporal variation is suppressed more by the averaging procedure.
Aubinet et al.  examined the CO2 storage and advection terms at multiple European flux sites and found that CO2 storage during the second part of the night was three times smaller than during the first part of the night. They attributed this decline of CO2 storage to the increase of advection term. Following their interpretation, we believe that advection may also play a role at our site as seasonally averaged CO2 storage decreases slightly from the early evening to midnight and then retains a lower value after midnight than before midnight (Figure 1b). Neglect of advection term may explain that inclusion of CO2 storage only is unable to completely bring the NEE at small u* values to the same level as at the large u* values (Figure 2). It is worth pointing out that the advection at our site may not be as strong as reported by Aubinet et al.  since CO2 storage only drops by about 40% from the first half of night to the second half (Figure 1b). Differences in strength of advection may provide an explanation to the disagreements among researchers at different flux sites about whether inclusion of CO2 storage can bring nighttime NEE at the low wind condition to the same level measured under high wind conditions (see literature review in section 1).
 The partition of CO2 storage among different vertical sections at our site (Figure 6) is different from that in a boreal aspen forest [Yang et al., 1999]. In that study, they showed that the layer below the inversion (<9 m at their site) accounted for 65–90% of the seasonally averaged CO2 storage between 1700 and 2200 h, but less than 15% from 2200 h to sunrise as a result of quasi-stationary CO2 concentration below 9 m. In short, the layer below 9 m played a contrasting role in contributing to total CO2 storage before and after 2200 h at night. This was not the case at our site, where mean CO2 storage per unit height below inversion (<6.10 m at our site) is generally greater than or at least equal to the values in the layers above 6.10 m (Figure 6). Consequently, the average contribution from the layer below 6.10 m to total CO2 storage is 27% from sunset to 0100 h and 20% from 0100 h to sunrise, higher or at least equal to its volume proportion (6.10 m/30.48 m = 0.2). This result suggests that the quasi-stationary state of CO2 concentration below the inversion observed by Yang et al.  may not be a universal feature and could be related to site topography (advection), canopy structure, and wind conditions.
 Difference also exists between Yang et al.  and the present study in regard to the best configuration of a CO2 profiling system and the number of measurement levels required to achieve the same degree of accuracy in CO2 storage estimate. Yang et al.  reported that, using their eight-level profile as a reference, the RMSE was about 0.87 and 0.58 μmol m−2 s−1 in the growing season for the best two- and three-level profiles. These RMSE values largely correspond to the best six- and seven-level profiles at our site (Figure 7). Moreover, Yang et al.  found that, when the total number of sampling levels is four or more, all three levels below the thermal inversion (including 9 m) had to be included in order to construct the best profiles at their site. At our site, however, containing three sampling levels below the inversion (including 6.10 m) for a profile of 4–6 levels would be the case of overdense coverage below 6.10 m (in comparison to the best profiles in Figure 8) relative to above. The difference could be explained mainly by the different level of complexity in canopy structures and the resulted flow structures (both dynamic and thermal).
 Our data presented in Figures 10 and 11 qualitatively agree with the theoretical predication on the underestimation of CO2 storage associated with the density averaging [Finnigan, 2006]. In that study it was predicted that when the averaging window is 1800 s in length (the typical time interval for most flux sites to average fluxes), the ratios of CO2 storage calculated from the averaged CO2 density to the true value decrease when turbulent conditions change from nonstationary (transition periods of the day such as sunrise and sunset, characterized by longer integral timescale) to stationary (noontime, characterized by shorter integral timescale). Moreover, smaller averaging windows result in less underestimation of CO2 storage than larger ones. These two conclusions are consistent with our findings. Compared to our data, however, Finnigan  overpredicted the underestimations of CO2 storage caused by the averaging procedure. Under stationary conditions (integral timescale is about 10 s), for example, Finnigan  predicted that CO2 storage was about 44% of its true value when the averaging window is 10 times the integral timescale and about 10% when averaging window is 1800 s. Under nonstationary conditions (integral timescale is about 200 s), it was predicted that time series of the averaged CO2 density returned about 40% of the true CO2 storage no matter what averaging window sizes were used. These predicted percentages are much smaller than the corresponding ones in Figures 10 and 11. These quantitative differences can be explained by three reasons. First, as stated by Finnigan , the mathematical expression of CO2 storage derived from the power spectra of CO2 density can only be regarded as the upper bound of the true storage. Second, the integral timescales for both stationary and nonstationary conditions used in the work of Finnigan  are smaller than our field measurements. The averaged integral timescales for stationary conditions (1000 h to sunset) computed from our 10 Hz CO2 density are about 100 s in the early growing season and about 50 s in the peak growing season; for nonstationary conditions (sunrise to 1000 h), the corresponding values are 370 s and 310 s. Third, the “true” CO2 storage at our site used in above analysis was from a single-point measurement and its exact amount is unknown.
 CO2 storage in a tall forest canopy often makes significant contributions to the forest CO2 budget in the early morning owing to reactivation of turbulence, and also at night because of low wind speeds, thermal inversion, and the intermittence of turbulence. We have demonstrated that underestimations of NEE on calm nights, which are typical at many flux sites, can be greatly reduced if CO2 storage is properly measured and taken into account.
 CO2 density and its time derivative, Δc/Δt, can vary greatly in the vertical extent of a forest because of the nonuniform distribution of CO2 sources, complexities of the canopy architecture and the deduced thermodynamic structures in the atmosphere below the canopy height. We have showed that the magnitude of mean and standard deviation of Δc/Δt generally increases with decreasing heights at night and from sunrise to 1000 h in both growing and dormant seasons. This suggests that different vertical sections in a forest make disproportional contributions to the total CO2 storage. Our data showed that the proportion to the total CO2 storage from the lower canopy layer (below the thermal inversion) was greater than or at least equal to its volume proportion throughout the night and from sunrise to 1000 h in the growing season.
 Increasing the number of measurement levels in a CO2 profiling system generally increases the accuracy in estimating CO2 storage. If not optimized, however, a profile with more sampling levels could produce larger biases than an otherwise optimized one with fewer sampling levels. A profiling system with four sampling levels or fewer is not adequate for CO2 storage measurements in a complexly structured forest at our site (Figure 5), because the RMSE value generated by an optimized four-level profile for the period from sunset to 1000 h the following morning is about the same order of magnitude as nighttime NEE in the growing season.
 As a key contributor to the total CO2 storage, the canopy layer below the thermal inversion requires a relatively detailed coverage in sampling. If the number of sampling levels is fixed, a profile with an unsampled thin layer below the thermal inversion is likely to produce larger biases than another one with an unsampled thick layer above the inversion. It is equivalent to say that poor resolution of a profile sampling system in the lower canopy is likely to result in larger storage errors than poor resolution in the upper canopy. However, layer thickness may come into play when its effect on estimating CO2 storage dominates over that of Δc/Δt. We showed by examples that an overdetailed coverage below the thermal inversion in a profiling system, which is built at the expense of upper canopy layers and therefore leaves very large gaps in the upper canopy layers, actually degrades the accuracy of CO2 storage term. One needs to balance these two factors, Δc/Δt and layer thickness, in designing and optimizing a profiling system.
 By comparing our results with Yang et al. , we found that vertical distribution of Δc/Δt and the partition of CO2 storage among different vertical sections in a forest are mainly determined by site properties, such as topography, canopy structures, and prevailing wind conditions. It implies that the best design and the number of sampling levels in a profile required to achieve an adequate accuracy in storage measurements should reflect these properties, especially the complexity of canopy structure at individual site.
 If CO2 density from a single profile is averaged in time and then used in assessing CO2 storage to reduce the random errors, one needs to be aware that this averaging procedure results in biases. Generally, larger window sizes used in averaging CO2 density generate poorer estimates of CO2 storage. In terms of absolute error, the more significant the CO2 storage is during a period of a day (night and sunrise to 1000 h versus 1000 h to sunset) or in a season (peak growing season versus early growing season), the more the averaging procedure affects estimate of CO2 storage. If the ratios of CO2 storage calculated from the averaged CO2 density to the true storage are concerned, however, the averaging procedure affects more when CO2 storage is negligible compared to the eddy flux such as from 1000 h to sunset. The relative magnitude of CO2 storage underestimation resulted from CO2 density averaging, quantified from our 10 Hz CO2 density, qualitatively agrees with the theoretical prediction by Finnigan . However, the latter appeared to overpredict the effects of density averaging.
 This research was supported by U.S. Department of Energy, Office of Science, Biological and Environmental Research (BER), as a part of the Terrestrial Carbon Processes (TCP) Program and conducted at Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725 and by the University of Missouri under U. S. Department of Energy, grant DE-FG02-03ER63683. The helpful comments made by three anonymous reviewers are greatly appreciated. This research was supported in part by an appointment to the ORNL Postdoctoral Research Associates Program which is sponsored by Oak Ridge National Laboratory and administered jointly by Oak Ridge National Laboratory and by the Oak Ridge Institute for Science and Education under contracts DE-AC05-00OR22725 and DE-AC05-00OR22750, respectively. First author thanks Wilfred M. Post for being his mentor during his postdoctoral program at ORNL.