Measurements of carbon sequestration by long-term eddy covariance: methods and a critical evaluation of accuracy

The turbulent exchanges of CO2 and water vapour between an aggrading deciduous forest in the north-eastem United States (Harvard Forest) and the atmosphere were measured from 1990 to 1994 using the eddy covariance technique. We present a detailed description of the methods used and a rigorous evaluation of the precision and accuracy of these measurements. We partition the sources of error into three categories: (1) uniform systematic errors are constant and independent of measurement conditions (2) selective systematic errors result when the accuracy of the exchange measurement varies as a function of the physical environment, and (3) sampling uncertainty results when summing an incomplete data set to calculate long-term exchange. Analysis of the surface energy budget indicates a uniform systematic error in the turbulent exchange measurements of -20 to 0%. A comparison of nocturnal eddy flux with chamber measurements indicates a selective systematic underestimation during calm (friction velocity < 0.17 m s"^) nocturnal periods. We describe an approach to correct for this error. The integrated carbon sequestration in 1994 was 2.1 t C ha'^ y"' with a 90% confidence interval due to sampling uncertainty of ±0.3 t C ha~^ y"' determined by Monte Carlo simulation. Sampling uncertainty may be reduced by estimating the fiux as a function of the physical environment during periods when direct observations are unavailable, and by minimizing the length of intervals without fiux data. These analyses lead us to place an overall uncertainty on the annual carbon sequestration in 1994 of -0.3 to +0.8 t C ha"^ y '.


Introduction
Long-term measurements of the exchange of COj between natural vegetation and the atmosphere have the potential to markedly improve understanding of the role terrestrial ecosystems play in the global carbon cycle. Eddy covariance is a micrometeorological technique that allows a non-invasive measurement of the exchange of CO2 between the atmosphere and a several hectare area of forest, shrubland, or grassland (Baldocchi et al. 1988). Recent technical advances have made long-term eddy covariance measurements practical {Wofsy et al. X993), opening the possibility of a global network of field Correspondence: Michael L.  Stations for monitoring biosphere-atmosphere CO2 exchange (Baldocchi et al. 1996). However, investigators must first establish that the accuracy and predsion of eddy covadance is sufficient to allow a reliable assessment of carbon sequestration over time .scales ranging from hours to decades.
We have used the eddy covariance technique throughout the last four years to monitor the net exchanges of CO2 and H2O above the Harvard Forest, an aggrading deciduous forest in the northeastern United States. The observations span a range of climatic conditions, allowing a quantitative assessment of the physical and biological controls on whole-forest activity. In this paper we (i) describe the methods in use at Harvard Forest (ii) sum-marize the observations of carbon flux, and (iii) evaluate the predsion and accuracy of these measurements.
We partition the sources of error into three categories, and proceed by assessing each category separately (1) Uniform systematic errors are constant and independent of measurement conditions (e.g. an error in the span of a gas analyser). A uniform error of 15% in the hourly measurements results in a 15% error in the calculation of long-term carbon sequestration. (2) Selective systematic errors result when the accuracy of the exchange measurement varies as a function of the physical environment. Because carbon sequestration reflects the difference between two larger fluxes, respiratory efflux during the night and photosynthetic uptake during the day, a small selective underestimation of nocturnal flux can cause a large overesHmation of long-term sequestration. (3) Sampling uncertainty occurs when summing an incomplete data set to estimate long-term exchange. The observations at Harvard Forest are interrupted for maintenance, equipment failure, and unsuitable atmospheric conditions. Day-to-day variability in carbon balance creates uncertainty in the calculation of long-term flux.

Site description
The measurements are made on the Prospect Hill tract of the Harvard Forest, near Petersham, Massachusetts (42°32' N, 72°ir W, elevahon 340 m), an area typical of rural New England (Foster 1992). The forest is 50-to-70years old, dominated by red oak and red maple, with scattered stands of hemlock, and white and red pine. The canopy height is 20-24 m. Nearly continuous forest extends for several km to the south-west and the northwest of the site, the dominant wind directions. The site is centred in a small level drainage, with a stream running from the north-west to the east within 50 m of the tower, and a gentle upward slope for several hundred meters to the south-west (5° facing north). Soil type, soil drainage, forest age, and land-use history are patchy on the scales of 50-200 m (Foster 1992).
The measurements are made from a 31-m-tall, 30-cmcross-section tower of the type used to support radio antennas (Rohn 25G, Peoria IL). The small diameter tower was selected to minimize wind distortion. Most of the instruments and the data acquisition system are housed in a hut 15 m east of the tower base. The hut is climate controlled and receives electrical and phone service. The site is accessible by a dirt road which is closed to public traffic. The area is sparsely populated with no occupied dwellings to the south-west and north-west closer than 2 km. The nearest secondary road is 2 km to the west and the nearest highway is 5 km to the north. The nearest urban areas are 100 km east (Boston) and 100 km southwest (Hartford). Additional site details are included in Munger et al. (1996), Moore et al. (1996), andWofsy et ai (1993).

Tower measurements
The eddy fluxes of sensible heat, latent heat, COj, and momentum are measured at 30 m on the tower. Wind and temperature are measured with a 3-axis sonic anemometer (Applied Technologies, Boulder CO) pointed into the prevailing wind direction (west). The mixing ratios of COT and H2O are monitored by sampling 6-8 standard litre min^' (sipm) through an inlet located 0.5 m behind the vertical axis of the anemometer. The error due to separation of the inlet from the anemometer should be small at 30-m altitude (1-2% during unstable periods. Lee & Black 1994). The sample is drawn down the tower in a 50-m, 0.5-cm inner diameter (id) Teflon tube and through a CO2/H2O infrared gas analyser (IRGA; Model 6262, LiCor, Lincoln NH) located in the instrument hut.
A 2-(im, 47-mm diameter Teflon filter at the inlet on the tower is changed every 2-4 weeks, and a second filter immediately before the IRGA is changed every 6 months. The inner surface of the sampling tube is cleaned periodically using a moist cotton ball. The pressure immediately after the IRGA is monitored and actively controlled at 60 kPa using a variable valve (MKS Instruments, Andover MA). The sample stream reaches an equilibrium temperature before entering the IRGA, removing the effects of coincident sensible heat flux (e.g. Webb et al. 1980). The effects of coincident water vapor fluctuations are removed by the IRGA software. The gain of the IRGA is automatically determined every 5 h by addition to the main sample stream near the inlet of 1% CO2 gas mixture at 30 standard ml min"' (seem). The response time of the IRGA to a step change in CO2 is also determined during this procedure.
The data acquisition and control systems are fully automated, allowing extended periods of unattended operation. The system records outputs from the sonic anemometer and the IRGA at 4 Hz. A spectral analysis of data collected at 10 Hz revealed no appreciable underestimation of flux due to 4 Hz sampling (Moore et al. 1996). The data are stored on disk at the site and transferred every two to four days for processing. Eddy CO2 flux is calculated as the 30 minute covariance of vertical wind velodty (w') and CO2 concentration (c'). The CO2 record is detrended using a linear least squares fit. The time lag required to draw air down the tower is determined by maximizing the correlation between w' and c'. The lag is extremely consistent due to the active pressure control at the IRGA. The flux is rotated to the plane where the mean vertical wind is zero (McMillen 1988).
The closed-path IRGA and long sampling tube result in a small underestimation of CO2 flux due to the damping ot" high-frequency fluctuations (Leuning & King . 1992). The magnitude of underestimation varies with atmospheric stability, creating a possible selective systematic error. We determine the magnitude of this underestimation by recalculating the sensible heat flux after numerically slowing the response of the temperature detector to simulate the slower response of the CO2 analyser (exponential time constant = 0.2 s as determined by GO2 addition on the tower). We then increase the calculated CO2 flux by the ratio of the fast-response heat flux to the slow-response heat flux. The response-time correction is determined for each 30 minute run, and is typically 0-2% during the day and 0-5% during the night. We assure the quality oi data by discarding periods with water on the sonic transducers as indicated by an unreasonable temperature signal (low a, too hot or cold), periods with spiking on any sonic axis as indicated by the ratios between aw, GU, OV, and u*, or periods with unusual flow or pressure at the eddy IRGA.
We use a second IRGA (Binos, Hanau Germany) to sequentially measure the mixing ratio of CO2 at 8 levels through the canopy (0. 05, 0.85, 2.8, 6.2, 9.5, 18.2, and 30.8 m). The hourly change in CO2 beneath 30 m {storage, Wofsy et al. 1993) is calculated by interpolation through space and time to synchronize the profile and eddy observations. The eddy fliix and storage observations are added to calculate the hourly net ecosystem exchange {NEE, Wofsy et al. 1993). The flux of photosynthetically active photons (PPFD) to the forest is measured with a silicon quantum sensor (LiCor, Lincoln NE). The net radiation at 30 m is measured with a thermopile net radiometer (REBS Q*6, Seattle WA). Air temperature and water vapor content are measured at the top of the tower with an aspirated thermistor and solid-state humidity probe (Vaisala, Wobum MA). Soil temperature is measured with an array of thermistors buried at the base of the litter layer. Soil water content is measured hourly by time domain reflectometry using six 15-cm and two 50cm sets of wave guides placed vertically (Campbell Scientific, Logan UT).

Chamber measurements
We used a multiplexing gas exchange system to measure the efflux of CO2 from soil, stems, and leaves over diel courses during summer 1992. The system sequentially sampled 10 open chambers (Field et al 1989;Mosier 1989) deployed in a semi-circle, completing a circuit every 2 h. The system was moved among 10 sites around the tower, allowing measuremenLs at 50 soil and 50 stem locations.
The soil chambers consisted of a 27-cm id by 10-cm long by 0.5-cm thick polyvinyl chloride (PVC) collar with a removable solid FVC lid. The collars were inserted to a depth of 2-4 cm during June 1992. Air was drawn at = 5 slpm from a sample port on the chamber top through the sample cell of a differential infrared gas analyser (LiCor 6251, Lincoln NE). Ambient air entered the chamber through a 10-cm tall, 4-cm id chimney on the side of the lid opposite the sample port. A subsample from the chimney was drawn through the reference cell of the IRGA at = 0.5 slpm. A measurement was made over a 12 minute period by (i) selecting a chamber with a solenoid valve (Skinner Valves, New Britain CT), (ii) measuring flow through the chamber with a mass flow meter (MKS Instruments, Andover MA), and (iii) measuring the difference in CO2 between the inlet and outlet of the chamber.
The data were recorded and the system managed using a data logger (Campbell Scientific, Logan UT). The IRGA and mass flow meter were zeroed every 2 h, and the ambient concentration of CO2 entering a chamber determined after each observation. Soil temperature at 2-cm and 5-cm depth was measured within each chamber using type T thermocouples. The chambers remained in place between measurements and flow was maintained at 5 slpm. The system was moved to a new site every one to four days, and the chamber tops removed when the system was deployed at other sites. Five soil collars were measured at least once at each of the 10 sites.
We established the analytical accuracy of the system with a series of standard additions. When a small flow of 1% CO2 was metered into a chamber, the increase in flux matched the rate of CO2 addition to within 5%. Errors caused by aspirating air from the soil are a particular problem with open-type chambers (Mosier 1989). We checked for this possibility by measuring the resistance to mass flow from the soil. When combined with the expected pressure drop through the chimney (10"^ Pa at 5 slpm) these observations indicate a forced flow from the soil at the leakiest collars of a few seem. Assuming a soil CO; concentration of 4000 ^L L'^ the maximum overestimation due to aspiration is 0.2 (imol m ^ s '. The stem respiration chambers consisted of 0.01-cm polyethylene sheet wrapped around 500-3000 cm^ of stem. The chambers were placed at a height of 1-2 m, and sealed around the trunks using caulking compound and tape. The sample port consisted of a perforated 1to-4-m length of tubing wrapped around the stem within each chamber Ambient air entered a chamber through an opening in the sheet held open by an inlet tube (4-cm id). A subsample from the inlet tube was drawn through the reference cell of the IRGA. The respiration of five stems representing various spedes was measured at each of the 10 sites. The absolute rates of CO2 efflux from the 50 stems were well correlated with both the volumes and the areas enclosed within the chambers. The relationship between enclosed area and CO2 efflux was linear with a large zero offset such that small diameter stems had a greater flux per area, whereas the relationship between volume and efflux was linear with a zero intercept such that flux per volume was constant over a range of diameters. Respiration was therefore calculated on a volume basis and converted to ground area based on a survey of wood volume in 40 10-m radius plots within 500 m of the tower. Most of the stem respiration measurements were made after the period of maximum secondary growth (April through June), and the observed flux is likely dominated by maintenance respiration.
Leaf respiration in the canopy was measured by deploying branch chambers from a pair of 20-m tall scaffolding towers. The branch chambers consisted of 50cm long by 30-cm diameter by 0.01-cm thick polyethylene bags held open by a frame of 0.64-cm outer diameter coated aluminium tube (Dekoron, Aurora OH). The chambers enclosed 20-50 leaves. Sample air was drawn through a series of perforations in the Dekoron frame. Measurements were made on a total of 10 branches representing 3 spedes during two nights in August 1992. Respiration was calculated per leaf and converted to ground area based on leaf litter collections in autumn 1992.

Turbulence measurements
The tilt of the mean wind at the top of the Harvard Forest tower generally does not vary by more than a few degrees from a fixed horizontal plane, indicating that flow distortion due to local topography or tower shadowing is minor (Fig. 1). The rotation angle varies as a function of wind direction in a manner consistent with a simple 2°o ffset between the plane through the u and v axes of the anemometer and the local topography (McMillen 1988). The relationship between rotation angle and wind direction is consistent from day to night, summer to winter, and calm to windy periods. The rotation angle is relatively variable when wind is blowing from behind the tower (45-135"), suggesting the possibility of modest distortion despite the tower's small cross section. The ratio of aw to u* is consistent as a function of direction with a modest increase in variability from 45 to 135°, also suggesting the possibility of modest tower shadowing (Moore et al. 1996). Fortunately wind from behind the tower is infrequent (« 14% of the time). We do not remove these periods from the main data set as they are often assodated with cloud cover and we do not want to introduce a bias. Spectral analyses of the fluctuations in atmospheric CO2, T, and H3O assodated with turbulent transport provide a useful tool for assessing the reliability of flux measurements (Kaimal et al 1972). Under ideal drcumstances the shapes of the w'CO2', wT', and w'H2O' cospectra should be similar (Ohtaki 1985). An incomplete resolution of small eddies, a common error when making eddy covariance measurements, is indicated by the loss of power at high frequencies (Leuning & King 1992). The power spectrum of the CO2 time series, the cospectrum of vertical wind and CO2, and the cospectrum of vertical wind and air temperature, indicate that the closed-path IRGA records nearly all of the fluctuations in CO2 assodated with turbulent transport (Fig. 2). The CO2 spectrum decreases through the subinertial range at the expected 2/3 power to a frequency of 1 Hz (Fig. 2a). The cospectrum of w'CO2' is similar to that of w'T' (Fig. 2b). Both cospectra indicate that large eddies with frequency less than 0.1 Hz dominate flux (cf. Hollinger et al. 1994). The cospectrum of w'H2O', also measured with the closed-path IRGA, shows a nearly complete lack of flux at n > 0.2 Hz, and a modest underestimation of flux at n > 0.01 Hz (data not shown). The damping of high frequency water vapor fluctuations, which presumably is due to adsorption and desorption on the walls of the sample tube, results in an underestimation of evaporation by 20%.

CO2 exchange at Harvard Forest
Measurements of CO2 exchange were made during 20 300 of the 35 000 hours from Oct. 1990 to Oct. 1994 (Fig. 3), with interruptions for calibration, data transfer, maintenance, rain, and equipment failure. Notable gaps occurred when an IRGA failed repeatedly in spring 1991, when a with a midday uptake of 20-30 ^mol m"^ s"^ from June iluough August a peak ni^ttime efflux of 5-10 |imol m~^ 8~^ from June through August, and an efflux during day and night of 0-5 ^unol m"^ s~^ from October April. A more detailed look reveals several differences between yean including a notable increase in efflux from Dec 1992 to Teb. 1993 ( Fig. 3; Goulden et al. 1996).
A typical summer day of turbulent fluxe6 is shown in Fig. 4. Respiratory efflux of 3-5 ^lmoI m"^ s"' during the first night was followed by photosynthetically driven net uptake of 14-19 junol m~^ s~^ during the day and respiratory efflux of 0-1 nmol m"^ s"^ during the second ni^t (Fig. 4a). The difference in flux between nights was assodated with a difference in turbulence; the first night was windy whereas the second night was calm with a friction velodty that often approached zero (Fig. 4b).
Carbon dioxide storage was quite variable from hour to houc wife a general increase at night and a general decrease during the morrung (Fig. 4a). Nocturnal storage was not well correlated widt turbulence, and the differ-eiKe in eddy flux between ni^ts was not offset by storage. The relationships between eddy flux, CO2 storage, and turbulence on calm nights are discussed further in the section on selective systematic errors. The sum of sensible and latent heat was 100 W m~^ less than net radiation as the forest warmed in the morning, and 0-50 W m~^ less than net radiation in ^e afternoon and early evening (Hg. 4c). The outgoing radiation at night exceeded tfie influx of sensible heat by 25-75 W m"^ and summed over die 24-hour period the turbulent fluxes were vrtthin 10% of the net radiation.
Nocturnal NEE over a whole year was exponentially related to surface soil temperature with Qio = 2.1 (Fig. 5;Wofsy et al 1993;Hollinger et al 1994;Fan et al 1995), Similarly, soil CO2 efflux measured with an automated diamber was tigjitly correlated with temperature at 2 cm depth (Fig. 6a), and bole respiration measured wi^ a duunber was tightly correlated with temperature averaged over the outer 2 cm of stem (Fig. 6b). The complete set of soil chamber measurements was exponentially related to the soil temperature monitored at die tower with QiQ " 2.2 (rt = 2450, data rtot shown). The diamber measurements were made over diel cydes, and most of the range in soil temperature was due to the difference between days and nights. The Qio observed with the chambers is tiierefore appropriate for extrapolating nighttime observations of respiration to daytime as a function of soil temperature at the tower.
The relationship between nocturnal NEE and soil temperature allows a separation of fee processes that contribute to daytime NEE. Net ecosystem exdiange at night should equal die combined rates of autotrophic and heterotrophic respiration. During the day NEE should equal the combined rates of rubisco carboxylation and oxygenation (gross ecosystem production, GEF), and autotrophic respiration and heterotrophic respiration. We separate daytime NEE into respiration and GEF by first determining the expcmential fit with Qjo • 2.2 between NEE during well-mixed nocturnal periods (see section on selective systematic errors) and soil temperature within time blocks that indude 100 h of valid nocturnal observations (2-4 weeks). We then calculate GEP as the difference between NEE and the respiration estimated from soil temperature. Our sign convention is that a râ ddition of CO2 to the atmosphere is a positive flux and hence GEP is negative. However, we discuss all processes, induding photosynthesis and carbon sequestration, as positive.
Hourly GEP during the summer was well correlated with inddent light (Fig. 7; Wofsy et al. 1993). The slope at low ligjit indicated a quantum yield of 0.055 pjnol C per timol inddent photon. The maximum photosynthetic rate was 20-25 ^mol tn'^ s'^, with moderate saturation beginning around 400 ^iinol photons m~^ s'*. The relationship between photosynthesis and light was very ti^t, with an absolute scatter similar to that observed at night, approximately ±5 ^imol m"^ s"^ ( Fig. 7, Fig. 5). This fidelity is remarkable since a range of phenomena, induding measurement variability due to the finite sampling interval (Baldocchi et al 1988), physiological processes that modulate photosynthesis, variability in die respiration fiux (Fig. 5), and spatial heterogeneity in photosynthesis, could lead to high variance in daytime flux.

Effects of turbuknce on CO2 exchange
Tbibulence may affect CO2 ei&ax in several ways. During calm periods turbulence limits the transport of CO2 throu^ the atmosphere as discussed in the section on selective systematic errors. During windy periods turbulence appears to affect the movement of CO2 out of the soil as discussed in this section. The winter observations of whole-forest exchange indicate a positive correlation between effiux and friction velodty during very windy periods (Fig. 8, u* > 0.8 m s"'). This correlation likely reflects the aspiration of CO2-ridi air from soil and snow pore space, rather than a short-tenn increase in CO2 production. The increase in CO2 effiux during windy periods was especially pronounced in winter 1993 (Fig. 3, 9;Goulden ei al 1996). Rates of efflux exceeding 10 \xino\ m""^ 5"^ were repeatedly observed when the friction velodty exceeded 0.8 m s"^ (Fig. 9a). TTw enhanced efflux was observed only when the tower sampled regions to the nor^-west, a poorly drained area dominated by a maple bog and old stands of hemlock. Fluxes of CO2 to the south-west, an upland area of oaks and maples, were similar to those in other winters. The fluxes of latent and sensible heat (Fig. 9b), the response and gain of the CO2 analyser, and the flow through the CO2 analyse^, did not give any indication of experimental problems during these periods. TTie soil chambers were designed to allow the entry of static pressure fluctuations associated with overiying Bg. S Nocturnal COj efflux measured by the tower as a function of soil temperature during 1992. Points are hourly averagw during periods wirii u' > 0.17 tn s-^ Flux (nmol m"^ s*^) • exp<0-129 + 0.073 • T ('Q), n -1800. turbulence, a property tfiat we confirmed by measuring the pressure within a chamber (data not shown; Sigmon et al. 1983). Contrary to the pattern observed in winter and also to reports suggesting that Suctuations in static pressure increase gas exchange from forest soils (Baldocchi & Meyers 1991), we found no consistent relationship during the summer between CO2 efflux into the soil or stem chambers and above-<aTiopy turbulence (Fig. 6a, b, c). Similarly, we have not observed a tight correlation between eddy CO2 flux and friction velocity during windy summer periods (u* > 0.17 m s"'). The difference from winter to summer in the sensitivity of efflux to strong turbulence may be a consequence of tiw canopy. The canopy may reduce ground-level turbulence in summer preventing it from reaching ^ intensity where aspiration occurs.

Long-term predsion
Based on instrument specifications and cabltration protocols we estimate a long-term precision for die eddy CDvariance measurements of better than ±5%. Similar infrared gas anal)^ers have been used for the flux measurements since April 1991. The performance of the IRGA is monitored closely widi a calibration every 5 h to determirw both instrument gain and response time. The CO2 standard used in ti\e calibration has been replaced twice during tiw study, with an intercomparison between standanis to within 1%. Ilie zero offsets of the mass flow meters used in the calibration are determined every 2-4 days, and the meters are calibrated at least once every year Similar sonic anemometers have been used throughout the study,, with only a modest change in the on-line shadowing correction, providing long-tenn stability of Pig. 8 CO2 efflux diiring periods with air temperature less than -4 *C as a function of friction velodty. Points are medians ±1 standard deviation measured by tihe tower during 1992. Data were sorted by u* into 10 intervals, with each interval during the night (R < 0 W m"^) containing 30 observations, and eadi interval during the day (R > 0 W m'^) containi:^ 16 observations. better than 1% (Kaimal et al. 1990; H. A. Zimmermaiv personal commtinication). 'Hie locations of d\e sonic and the IRCA inlet, ^ flow and time lag, and ^e IRGA response time have remaii^ relatively constant over the study. We store and archive all (he raw data, allowing recalculation of the entire record of CO2 exchange in the event of significant d\anges to the data analysis software.

Uniform s}fstematic errors: Accuracy of daytime measurements
Experience has shown fl\at eddy covariance works beat during windy periods. Errors during these periods are presumably uniformly systematic (e.g. inaccurate concervtrations of calibration gases), and should apply equally to all periods. An analysis of the surface energy budget provides a useful approach for evaluating the measurements of latent heat, sensible heat, and, based on spectral siniilarity (Fig. 2b), CO2 flux. A convincing closure of the energy budget at Harvard Forest is difficult due to the underestimation of latent heat flux revealed by die spectral analysis, and also due to uncertainty in the rate of heat storage. When these factors are taken into account (Verma et al, 1986;Moore 1986;Leuning & King 1992) good agreement is obtained between the loss and storage of energy at ihe surface, and the net flux of radiation to the forest (Fig. 10). The comparison indicates a tendency for the turbulent Oiwes to underestimate exchange by 5-10%, An additional ±10% should be added to account for uncertainties in the measurement of net radiation, in the calculation of heat storage, and in the correction of latent heat flux. The confidence interval for the measurement of daytime turbulent exdiange is -20 to 0%. Additional analyses support this conclusion. The daily evaporation at the site measured by eddy covariance during 20 summer days in the later stages of drying cydes was 0.14 cm day~^, while the evaporation estimated horn time domain reflectcmetry in the top 50 cm of soil was 0.16 cm day"^ (data not shown). The mean photosynthesis at die site measured by eddy covariance e 1996 Btadcwell Sdence Ltd., Glohal Change Biology 2,169-182

Selective systematic errors: UTiderestxmation of nighttime flux
Selective systematic enors, which result when tfiere is a correlation between the direction of surface exchange and the accuracy of the exdiange measurement represent a seriotis problem when summing short-term measurements (hourly NEE) to longer intervals (annual carbon sequestration). Of particular concem is the possibility that noctuma] exchange may be imdeiestimated. The reliability of the daytime flux measurements is not nirprising; die methods in use at Harvard Forest are comparable to those used wi^ success above odur forested sites (Denmead & Bradley 1985;Verma et al. 1986;Kelliher et al 1992). In contrast the applicability of eddy covariance during nocturnal periods has not been completely established (Fig, 4;Fitzjarrald & Moore 1990). Nocturnal periods indude conditions that may challenge o&erwise reliable methods. These indude cold air drainage, sporadic mixing, a spectral shift towards high-frequency eddies, fluctuations in vertical wind too small to be The observations of nocturnal CX)2 exchange at Harvard Forest indicate a selective underestimation of flux during calm periods. TTiere is a reduction in the measured vertical flux of CO2 at 30 m during poorly mixed periods (u* < 0.17 m 5"^ Fig. 11a) that is not due to a reduction tn the flux of CO2 from the soil (Fig. lie). This discrepancy cannot be explained entirely by increased storage. The rate of CX)} accumulation during calm periods is only 20-30% of tfie eddy flux during windy intervals (Fig. 11a). The fluw of CO2 at 30 m immediately following the resumption of mixing is not unusually hi^ (Fig. lib) as wciild be expected with flushing of accumulated COj. Carbon dioxide evidently escapes from the forest during poorly mixed periods by an undetected route. Similar pattems have been observed in boreal forestŝ .L Goulden, personal observation; TA. Black, personal communication; P.G. jarvis, personal communication). Howevet Grace Q. Grace, personal communication) observed that storage quantitatively offset the reduction in eddy flux during calm ru>chiinal periods in a tropical forest.
The cause of flux underestimation during stable periods has not been identified. Orw possibility is that COj leaves the forest in drairung cool air that subsequently mixes upwards away from the tower. Alternatively, CC)2 may leave the forest in fluctuations diat are too small or too short to be resolved with the available instrumentation. A third possibility is that the Oux calculation is inadequate for calm nocturnal periods, and a longer averaging time or a different detrending algorithm is required due to the dominance of sporadic mixing events.
The efflux of CO3 during summer nights becomes insensitive to atmospheric turbulence at u* > 0.17 m s" {  Fig. 11a). A critical question is whether eddy covariance provides an accurate measure of ecosystem respiration during d\ese periods. The fiux of CO3 during windy nights is insensitive to net radiation (Fig. 12a), to the temperature gradient beneath the canopy (Fig. 12b), and to ti\e temperature gradient above the canopy (Fig. 12c)ê stablishing that there is no apparent difference between periods tiiat are thermally stratified to ^ose that are unstratified. Since there is no apparent selective error between daytime periods that are neutral and those that are unstable, we conclude that night-time observations at u* > 0.17 m s~^ axe reliable. TTie ccmtention tfiat flux measurements in windy dark periods are not systematically different from those in light periods is supported by &e observation that the relationship between u* and CO2 flux does not vary from day to night during the winter (Fig. 8).
We correct for the selective underestimation of respiration at u* < 0.27 m s'' by substituting the respiration predicted from soil temperature (Fig. 5) for die observed flux. The buildup of carbon dioxide beneath 30 m during calm periods is relatively small (Fig. lib), minimizing problems with double counting. The replacement of data during calm periods increases the calculated aruiual respiration by 0.5-1.0 t C ha~V This correction is largely responsible for a revision of our estimate of 1991 caibon sequestration from 3.7 t C ha'^ to 2.8 t C ha"^ (Goulden et al. 19%), a somewhat larger effect than the 051 C ha"â nticipated by Wofsy et al (1993).

Comparison of chamber and eddy-flux measurements of ecosystem respiration
The average respiration measured by eddy covariance during windy nights in summer 1992 was 4. 6.5 )ano\ temperature of 6.5 nmol m"^ s"* (Table 1). Botii numbers are based on a large numbet of observations and tius discrepancy is beyond the expected eiTors. The discussion in d\e previous section provides evidence for die reliabil-ity of noctumal eddy flux measurements during wellmixed periods. Additionally, a selective systematic underestimation of NEE during windy periods is difficult to reconcile with observations of wood productioa A 33% underestimation of respiration during mixed periods would result in a revised annual net caibon sequestration of less than 11C ha~^ Allometric observations in hardwood stands at Harvard Forest indicate wood production of -25 t C ha""' (Aber et al 1993), implying an unlikely annual loss of more than a ton of C ha~' from the soil.
A possible explanation is that the chamber measurements overestimate respiration. The most likely candidate is-soil respiration; stem respiration is insufficient to account for d\e discrepancy (Table 1), and dte rate of leaf respiration is about 10% of the maximum rate of canopy photosynthesis (Fig. 7), a pattem cortsistent with observations on individual leaves (Aber et d. 1995). Measurements of soil trace-gas exdiange are extremely difficult to verify. Tl\e rates of respiration measured with the open chambers are comparable to those measured around the tower using a dc»ed diamber (UCor 6000-09, Uncoln NE; data not shown), but higher than l}\Dse measured within a few km of die tower using a static chamba (Kicklighter et al 1994;3.1 nmol m"^ s'^ at 17 'Q. An altemative explanation is tfwt botii sets of respiration measurements are correct, but that different areas were measured. A survey of mid-day sott respiration during August and September 1993 using a dosed dumber (UCor 6000-09) foimd considerable heterogeneity around the tower (data not shown). For example, respiration at 19-21 "C in an extensive poorly drained area to the north-west of the tower averaged 3,8 |imol m"^ s"', while respiration in an upland area to 'ivt sou^-west averaged 7,5 pimol m~' s"^ The depth and width of the nocturnal footprint from ground-level sources is unknown. Without diis information it is not possible to , rule out spatial heterogerwity as a cause of die discrepancy. Ensuring that point measurements (e.g. diamber fiuxes, foliar chemistry) are representative of the area sampled by micrometeorological observations represents a major challenge to interdisdpliruiry investigations. The establishment of a dear set of gvidelines for distributing point measurements around eddy flux sites will be a necessary component of a successful flux network.

Sampling uncertainty
One of our goals is to determine dw annual rate of carbon sequestration (annual net ecosystem production, NEP). We assume that NEP is equal to the annual net exdiange of CO2 widi the atmosphere (integrated NEE) since dve site has not burned during the study, and carbon exdianges in forms other dian CO^, and by processes other than turbulent transport are likely small Our current approach for calculating Iong-tenn carbon sequestration involves: (i) Estimating COj exdiange as a function of soil temperature (Fig. 5) for d.ark periods when u* < 0.17 m s"* or when flux measurements are unavailable. Estimating CO2 exchange as a function of PPED (Fig. 7) and soil temperature (Fig. 5) for summer light periods when flux measurements are unavailable, (ii) Dividing the record of hourly CO3 exchange intD intervals that encompass four days with complete observations. (Most of the intervals are 4 days, but longer periods may be required due to equipment malfunction.) (iii) Averaging by hour within each interval, (iv) Summing to calculate the carbon balance of each interval, (v) Summing through the year assuming for each interval that tfie carbon balance calculated from the 4-days of observations is representative of the complete interval (Fig. 13a). Sampling uncertainty arises in step 1 when an empirical relationship is used to fill missing periods, and in step 5 when the carbon balance determined from 4 days of observations is assumed representative of a longer interval.
We estimated tfus uncertainty using a Monte Carlo method to simulate the sampling process. We assembled a total of eight populations of daily carbon balances that were intended to represent the typical patterns of dayto-day variation. Each population consisted of the daily carbon balances of 30 nearly consecutive days drawn from observations during 1994, with a pair of populations representing each season. One population within eadi season was composed of the actual measurements of daily carbon balance, arul ^e other of the simultaneous carbon balances calculated from the empirical telatiorw ships (Figs 5, 7). For each interval we sampled from tiie appropriate population one hundred randomly selected sequences of the interval length. The average of 4 randomly selected days within each sequence was compared with the true sequence average to simulate the sampling error for eadi of the 100 cases. The sampling error for each of the 100 cases was accumulated through the year and sorted to determine the 5th and 95th percentiles.
The integrated carbon sequestration from Day 301, 1993 through Day 300,1994 was 2.11C ha'^ y "^ ( Fig. 13a, negative cumulative NEE refers to a loss of carbon from the atmosphere and a piositive net sequestration of carbon by the forest), and the 90% confidence interval due to sampling uncertainty was ±0.3 t C ha~^ y"^ (Fig. 13b). About half of the annual sampling uncertainty resulted from missing flux and meteorological observations in July following lightning damage (Fig. 3). Missing observations in winter did not cause appreciable uncertainty because CO2 exchange was relatively low and consistent from day to day.
Two strategies are important for reducing sampling uncertainty. First, a continuous set of climate data may Nov Sep Fig. 13 (a) Cumulative net caibon exchange (points) and 90% confidence interval (shading) from Day 301, 1993to Day 300, 1994. Points are at intervals with A oomplete days of observations, (b) Increase through the year in 90% confidence interval due to sampling uncertainty. The anntjal net exchange during 1994 wa£ -ZI t C Ka'^ widi an accum^ulated sampling uncertainty of ±03 t C ha-1.
be collected aiui used to £31 periods when flux observations are unavailable. The xmcertainty caused by filling missing periods as a function of the physical environment is smaller d\an that caused by assuming that the days with observations are representative. Second, the sampling strategy should minimize the length of intervals without flux data. The correlation at Harvard Forest between the carbon balance on days that are separated by less than a week is high (i.e. the lag correlation, r^ -0.6-0.7), whereas die correlation between days that are separated by longer than two weeks is low (i^ -0.2-03). The correlation between days separated by more ihzn a week is especially low in spring and fall when die carbon balance Is changing rapidly. Long gaps create disproportionately large uncertainty, whereas short gaps (a few days) spread throughout the year are acceptable. This pattern supports die deployment of unattended monitoring systems, provided that malfimctions can be repaired quiddy. Periodic breakdowns of unattended systems are inevitable, but the uncertainty caused by these gaps is offset by the advantage of year-round monitoring.
Condusiona 1 Long-term eddy covariance provides an effective tedinique for measuring the hourly, daily, monthly, and axmual rates of carbon exchange by terrestrial ecosystems.
The long term precision of the approach is very good (±5%). Long-term eddy covariance is particularly well suited for quantifying the effects of stress, climate, and phenology on carbon exchange, and for developing and testing mechanistic models and remote-sensing algorithms.
2 We observe a selective systematic underestimation of flux during calm (u* < 0.17 m s"') noctumal periods at Harvard Forest, for which we compensate using an estimation of ecosystem respiration based on temperature. Additional work is needed to fully establish the reliability of eddy covariance during nocturrwl periods. In particular, we are unable to fully account for a discrepancy between the ecosystem respiration at Harvard Forest measured as NEE during mixed nocturnal periods, and that measured using chambers. 3 The uncertainty in the measurement of carbon exchange at Harvard Forest due to uniform systematic errors is -20 to 0%. The annual carbon sequestration in 1994 was 2.1 t C ha"' y "^ with a 90% confidence interval due to sampling uncertainty of ±0.3 t C ha"' y"'. Sampling uncertainty is reduced by estimating the flux as a function of the physical environment during periods when direct observations are unavailable, and by minimizing the length of intervals without Qux data, espedally during spring and fall. The combined effects of uruform systematic errors, sampling uncertainty, and ^e estimation of respiration during calm noctumal periods leads to an overall confidence interval for carbon sequestration in 1994 of -03 to +0.8 t C ha"> y^\