Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ doi:10.5194/amt-7-2787-2014 © Author(s) 2014. CC Attribution 3.0 License. Ecosystem fluxes of hydrogen: a comparison of flux-gradient methods L. K. Meredith1,*, R. Commane2, J. W. Munger2, A. Dunn3, J. Tang4, S. C. Wofsy2, and R. G. Prinn1 1Center for Global Change Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 2School of Engineering and Applied Sciences and Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA 3Department of Physical and Earth Science, Worcester State University, Worcester, Massachusetts, USA 4Ecosystems Center, Marine Biological Laboratory, Woods Hole, Massachusetts, USA *now at: Environmental Earth System Science, Stanford University, Stanford, California, USA Correspondence to: L. K. Meredith (predawn@stanford.edu) Received: 10 March 2014 – Published in Atmos. Meas. Tech. Discuss.: 25 March 2014 Revised: 29 July 2014 – Accepted: 31 July 2014 – Published: 3 September 2014 Abstract. Our understanding of biosphere–atmosphere ex- change has been considerably enhanced by eddy covariance measurements. However, there remain many trace gases, such as molecular hydrogen (H2), that lack suitable analyt- ical methods to measure their fluxes by eddy covariance. In such cases, flux-gradient methods can be used to calculate ecosystem-scale fluxes from vertical concentration gradients. The budget of atmospheric H2 is poorly constrained by the limited available observations, and thus the ability to quan- tify and characterize the sources and sinks of H2 by flux- gradient methods in various ecosystems is important. We de- veloped an approach to make nonintrusive, automated mea- surements of ecosystem-scale H2 fluxes both above and be- low the forest canopy at the Harvard Forest in Petersham, Massachusetts, for over a year. We used three flux-gradient methods to calculate the fluxes: two similarity methods that do not rely on a micrometeorological determination of the eddy diffusivity, K , based on (1) trace gases or (2) sensi- ble heat, and one flux-gradient method that (3) parameter- izes K . We quantitatively assessed the flux-gradient meth- ods using CO2 and H2O by comparison to their simultane- ous independent flux measurements via eddy covariance and soil chambers. All three flux-gradient methods performed well in certain locations, seasons, and times of day, and the best methods were trace gas similarity for above the canopy and K parameterization below it. Sensible heat similarity required several independent measurements, and the results were more variable, in part because those data were only available in the winter, when heat fluxes and temperature gradients were small and difficult to measure. Biases were often observed between flux-gradient methods and the inde- pendent flux measurements, and there was at least a 26 % difference in nocturnal eddy-derived net ecosystem exchange (NEE) and chamber measurements. H2 fluxes calculated in a summer period agreed within their uncertainty and pointed to soil uptake as the main driver of H2 exchange at Harvard Forest, with H2 deposition velocities ranging from 0.04 to 0.10 cm s−1. 1 Introduction Atmospheric H2, with a global average mole fraction of 530 ppb (parts per billion; 10−9, nmol mol−1), exerts a no- table influence on atmospheric chemistry and radiation. H2 is scavenged by the hydroxyl radical (OH radical), thereby attenuating the ability of OH to scavenge potent green- house gases, like methane (CH4) from the atmosphere, which classifies H2 as an indirect greenhouse gas (Novelli et al., 1999). H2 is also a significant source of water vapor to the stratosphere, and as such may adversely perturb strato- spheric ozone chemistry (Solomon, 1999; Tromp et al., 2003; Warwick et al., 2004). The two major atmospheric H2 sources are photochemical production from methane and non-methane hydrocarbons and combustion of fossil fuels and biomass (Novelli et al., 1999). The major H2 sinks are Published by Copernicus Publications on behalf of the European Geosciences Union. 2788 L. K. Meredith et al.: A comparison of flux-gradient methods soil consumption, representing about 81± 8 % of the total sink, and oxidation by OH being about 17± 3 % based on a global inversion of sparse atmospheric H2 measurements (Xiao et al., 2007). The major sources and sinks are nearly balanced so atmospheric H2 concentrations are stable. Al- though the global atmospheric H2 budget has been derived through a variety of methods, it remains poorly constrained at the regional level and disputed at the global level, and a process-based understanding is lacking (as reviewed by Ehhalt and Rohrer, 2009). Therefore, there are large uncer- tainties in the estimated impact of changes to the H2 biogeo- chemical cycle that might arise from changes in energy use, land use, and climate. Field and laboratory measurements are needed to improve the process-level understanding of atmo- spheric H2 sources and sinks, especially regarding its sensi- tivity to biological activity in the soils. The paucity of data on key H2 processes is related to dif- ficulties in measuring sources and sinks in situ, in particular the soil sink. H2 soil uptake is typically measured using soil flux chambers (e.g., Conrad and Seiler, 1980; Lallo et al., 2008; Smith-Downey et al., 2008). Chamber measurements are labor intensive and typically yield infrequent and discon- tinuous data that are difficult to scale up to the landscape scale, especially in ecosystems with high spatial heterogene- ity (Baldocchi et al., 1988). Although chambers are subject to artifacts if not implemented carefully (Davidson et al., 2002; Bain et al., 2005), they are well suited for process-level stud- ies. Boundary layer methods have been used to calculate H2 soil uptake rates from H2 mole fraction measurements and assumptions about atmospheric winds and mixing, bound- ary layer height, and/or the uptake rates of other trace gases (Simmonds et al., 2000; Steinbacher et al., 2007). The need for assumptions in these methods can introduce large uncer- tainties into reported H2 fluxes. Most studies have focused on soil processes, and we have little information about any other processes in the canopy that affect H2. Despite the limitations of these traditional methods, few alternatives are available for the measurement or estimation of atmospheric H2 fluxes. The gas chromatographic methods used to measure H2 are slow (> 4 min), which precludes use of eddy covariance techniques that rely on high-frequency measurement of the covariation of the trace gas mole frac- tion with the vertical wind component. In such cases, where no high-accuracy fast-response instrument (≥ 1 Hz sampling frequency) is available, a variety of micrometeorological methods under the umbrella of flux-gradient theory can be used to non-intrusively measure the biosphere–atmosphere exchange of trace gases from relatively slow ( 1 Hz) mea- surements of vertical gradients of trace gas mole fractions (Fuentes et al., 1996; Meyers et al., 1996). Flux-gradient methods assume that fluxes are equal to the gradient of the quantity in question scaled by the rate of turbulent exchange. These methods can be automated for near-continuous data collection, and by averaging over time, the spatial hetero- geneity within the tower footprint is integrated (Baldocchi et al., 1988). As a result, flux-gradient methods avoid some of the aforementioned problems that arise from the use of flux chambers and box models. These methods are also useful in cases where fluxes are small and fast-response instruments lack the precision to resolve deviations in trace gas mole fraction from background levels (Simpson et al., 1998). The structure of the turbulence below the canopy can make eddy covariance measurements difficult, and flux-gradient meth- ods may be a superior choice (Black et al., 1996). Flux- gradient methods do rely on simplifying assumptions, such as the one-dimensional representation of a three-dimensional process, the existence of steady-state conditions, horizontal homogeneity in the source–sink distributions, and flat topog- raphy (Baldocchi et al., 1988). Recognizing the potential for flux-gradient methods for determining the H2 flux, we designed, constructed, and eval- uated a fully automated, continuous measurement system for determining H2 fluxes in a forest ecosystem by three different flux-gradient methods: (1) trace gas similarity, (2) sensible heat similarity, and (3) K parameterization. Critical issues in instrument design and performance for making flux-gradient measurements were considered, including instrument preci- sion, sampling error, and measurement accuracy. The valid- ity of each flux-gradient method was demonstrated by ap- plication to CO2 and H2O fluxes, for which simultaneous eddy covariance or chamber flux measurements were avail- able for comparison. Finally, H2 fluxes were calculated using the flux-gradient methods in the above- and below-canopy environment. The approach and findings could be extended to other trace gases that present similar measurement chal- lenges to H2. 2 Experimental 2.1 Measurement site The study site, Harvard Forest (42◦32′ N, 72◦11′ W; eleva- tion 340 m), is located in Petersham, Massachusetts, approx- imately 100 km west of Boston, Massachusetts. The largely deciduous 80- to 115-year old forest is dominated by red oak, red maple, red and white pine, and hemlock (Urbanksi et al., 2007). Harvard Forest soils are acidic and originate from sandy loam glacial till (Allen, 1995). Measurements presented in this study were made from November 2010 to March 2012 at the Environmental Measurement Station (EMS) (Wofsy et al., 1993), located in the Prospect Hill tract of Harvard Forest. The station is surrounded for sev- eral kilometers by moderately hilly terrain and forest that has been relatively undisturbed since the 1930s. Previous work at the site found no evidence for anomalous flow patterns that would interfere with eddy-flux measurements (Moore et al., 1996), the local energy budget has been balanced to within 20 % (Goulden et al., 1996), and about 80 % of the turbulent Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2789 Vent nulling line NO COM NC IRGA 1 IRGA 2 Pump to ventBallast volume Flow controllers Pressure controllers Infrared gas analyzers (IRGA) Bypass Reference cell CO2/H2O scrubber HI M LO CO2 calibration standards Zero air Bypass Tubing to tower Nulling volume Shed wall H2 calibration standard Pump Integrating volume Naon dryer Stream selection valve Pressure transducerFlow controller NO COM NC NC NO Counter purge ow COM Sampling valve (load position) Gas chromatograph (GC) NO CO M NC Pump to vent PC AC He CG 1 2 6 12 11 10 3 4 5 7 89 NV VPHI RS HeP HeP HeP SI SO SL DPO RG HeP V EPC3 EPC4 HePDD RS Key: AC = analytical column CG = carrier gas DPO = discharge purge outlet EPC = electronic pressure controller HeP = helium purier HePDD = He pulsed discharge detector NV = needle valve PC = pre-column RG = regulator RS = restrictor SI = sample in SL = sample loop SO = sample out V = vent VPHI = valve purged housing inlet Figure 1. Schematic of the flux-gradient instrument system, which includes a gas chromatograph (GC-HePDD, H2 measurements), infrared gas analyzers (IRGA, CO2, and H2O measurements), and the gas stream selection system. fluxes originate within a 0.7–1 km radius of the tower (Sakai et al., 2001; Urbanski et al., 2007). 2.2 Instrumentation An instrument system was designed to measure mole frac- tion gradients and ancillary variables needed to calculate H2 fluxes above and below the forest canopy at four heights (Fig. 1). H2 mole fractions were measured with a gas chromatograph (GC, model 6890, Agilent Technologies) equipped with a pulsed discharge helium ionization detec- tor (HePDD, model D-3 PDD, Valco Instruments Co. Inc. (VICI)) and two columns (HayeSep DB, 1/8 in. OD stainless steel, 2 m pre-column 80/100 and 4.5 m analytical column 100/120, Chromatographic Specialties). A 2-position, 12- port injection valve (UW type, 1/16 in. ports, M-type rotor, purged housing, VICI) was used to introduce 2 mL samples and control the chromatographic timing. The GC-HePDD was run with research-grade helium carrier gas (99.9999 % purity, Airgas) and was configured as in Novelli et al. (2009), with the exception of a shorter pre-column to reduce the anal- ysis time to 4 min (Meredith, 2012, Fig. 2-3). Sample loop pressure (transducer model 722B13TFF3FA, MKS Instru- ments) and temperature (thermistor affixed to sample loop) were measured to quantify the exact number of moles of sam- ple air injected. The GC sample stream was dried using a Nafion drying tube (MD-070-12S-2, Perma Pure). CO2 and H2O mole fractions were measured at four heights using a pair of nondispersive, infrared gas analyzers (model 6262, LI-COR) configured to measure vertical gradients (Dunn et al., 2009). Gas sampling inlets were installed at 24 and 28 m on the EMS tower and at 0.5 and 3.5 m on a small tower erected 14 m to the north-northwest of the EMS tower in an area of undisturbed vegetation and soil (Fig. 2). The leaf foliage dis- tribution (Fig. 2) during summer at the Harvard Forest EMS site is top heavy and is important to consider for its inter- actions with the turbulent structures at the site (Parker, un- published data). In this manuscript, we refer to measurement heights by their relation to the median forest canopy height (18 m; Fig. 2) when relevant to the topic at hand: above canopy for 24 and 28 m and below canopy for 0.5 and 3.5 m. Tubing lines (OD 1/4 in., Synflex®) of lengths 45–55 m were installed with inline PFA filter holders (47 mm PFA, Cole Palmer) containing 0.2 µm pore size filters (Zefluor™, Pall Corporation) and inverted Teflon funnels to protect the tubing inlet from precipitation. During the normal sampling routine, H2 GC-HePDD measurements were made at 28, 24, 3.5, and 0.5 m over a 16 min cycle. Meanwhile, the IRGAs measured 1 Hz CO2 and H2O mole fractions in either the 28 and 0.5 m or the 24 and 3.5 m gas sample streams (250 mL min−1), switching on 1 min intervals. Each sample stream was mixed in 2 L glass integrating volumes with fans (Meredith, 2012; Fig. A1). Three times per week, we used a nulling procedure to assess measurement accuracy, in which all gas streams sampled a common gas inlet installed at 2 m connected to an unmixed 25 L nulling reservoir (glass carboy). Custom-designed small-footprint aspirated temperature shields (Dunn et al., 2009) containing thermistors (YSI) were colocated with the gas inlets. Temperature data were corrected for offsets between the sensors, which were www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2790 L. K. Meredith et al.: A comparison of flux-gradient methods 0 5 10 Leaf Foliage Distribution % 28 m 24 m Above Below 3.5 m 0.5 m 14 m Figure 2. Meteorological equipment and gas inlets installed on the Environmental Measurement Site (EMS) tower and a small tower installed 14 m to the north-northwest of the EMS tower over undis- turbed soil. Squares represent gas inlets and temperature shield lo- cations. Sonic anemometers, sketched in gray, were installed at 2 and 29 m. The distribution of foliage per meter of height (leaf fo- liage distribution) at the Harvard Forest EMS site in summer has a median height of 18 m. determined on two occasions by temporarily colocating temperature shields. Three-dimensional sonic anemometers were installed on the small tower at 2 m (CSAT3, Camp- bell Scientific) and on the EMS tower at 29 m (Applied Technologies). Three-dimensional winds are rotated to the plane where the mean vertical wind is zero (Wilczak et al., 2001). Data acquisition/logging and sample valve con- trol was handled by Campbell Scientific CR10X data log- gers. GCwerks (version 3.02-2, Peter Salameh, Scripps Insti- tute of Oceanography, http://gcwerks.com) was used for gas chromatograph control and peak integration (example chro- matogram in Meredith, 2012, Fig. 2-4). Independent eddy covariance CO2 and H2O flux mea- surements were made at 29 m (Urbanski et al., 2007). The soil–atmosphere flux of CO2 was measured using an auto- mated flow-through flux chamber system located approxi- mately 0.6 km south of the EMS tower with similar soils and vegetation. The system consisted of an infrared gas analyzer (IRGA, LI-7000, Li-Cor Inc., Lincoln, NE), six automated soil chambers (20 cm diameter), a data logger, and the gas control system. Only data from the three control chambers not placed on a root-exclusion plot are used here. Every half- hour all six chambers were measured in succession. Chamber air was circulated through a flow meter to the IRGA and back to the chamber, and pressure was equalized in and out of the chamber by venting. CO2 fluxes were calculated from the in- crease in CO2 concentration following chamber lid closure over the 2–3 min measurement period. 2.3 Calibration Trace gas measurements were calibrated every 1.5 and 3 h for H2 and CO2, respectively. GC-HePDD calibrations were based on duplicate sampling from an H2 calibration stan- dard of compressed air from Niwot Ridge in an electropol- ished stainless steel tank (34 L, Essex Industries) referenced against the NOAA Earth System Research Laboratory Global Monitoring Division (ESRL/GMD) primary standards on their in-house instrument before (501.5 (±10) ppb) and after (499.0 (±7.5) ppb) the experiment. H2 mole fractions were stable in our calibration cylinder, as has been reported for other steel cylinders, but not for many aluminum tanks (Jor- dan and Steinberg, 2011). The GC-HePDD response was sta- ble over the study period (Meredith, 2012, Figs. 2-9 and 2- 10). CO2 calibrations were performed using three CO2 span gases (HI ∼ 500 ppm, MID ∼ 420 ppm, and LO ∼ 350 ppm) traceable to the NOAA and World Meteorological Organi- zation (WMO) CO2 scales. IRGA zeros were determined by periodically passing ambient air through a CO2 scrubber (soda lime) and desiccant (magnesium perchlorate) trap. Wa- ter vapor measurements were calibrated on one occasion with a dew point generator (model 610, LI-COR). Simultaneous, colocated mole fraction measurements of CO2 and H2O (in- strument from this study versus the independent EMS sys- tem) were used to derive scaling factors for comparison to the EMS eddy covariance fluxes from the slope of the linear regression forced through the origin: CO2 (slope = 1.0047, R2 = 0.84) and H2O (slope = 1.085, R2 = 0.98). A detailed description of the instrument design, parts, and calibration is available online (Meredith, 2012). 2.4 Gradient measurement considerations 2.4.1 Instrument precision Application of the three flux-gradient methods relies on the ability to resolve vertical gradients in mole fraction or tem- perature. The problem is not trivial as vigorous turbulent mixing can cause the gradients, even those originating from strong source or sink processes, to be quite small. In this study, we aimed to resolve H2 gradients both above and be- low the forest canopy at Harvard Forest. In previous work over a grassland in Quebec, H2 gradients were typically < 5 % between inlets at 3.5 and 0.5 m (Constant et al., 2008), but somewhat larger at night under stable nocturnal condi- tions. Although there were no previous measurements above a forest canopy in the literature, H2 mole fraction gradients in the turbulent above-canopy environment were expected to be much smaller than below the canopy. Assuming that H2 up- take fluxes, FH2 , are represented by FH2 =−vd [H2], where vd is the H2 deposition velocity of 0.07 cm s−1 and [H2] is the hydrogen concentration (Conrad and Seiler, 1980), we antici- pated needing relative mole fraction measurement precisions Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2791 for high levels of turbulence of 0.07 and 0.7 % to resolve meaningful gradients under unstable and stable stratification, respectively (Wesely et al., 1989). The required precisions would be 0.4 and 4 % under unstable and stable stratification under low-turbulence conditions, but under the latter, eddy covariance measurements may not be valid. Commonly used H2 detectors were not adequate for the desired measurement precision: reported precisions were 0.5–5 % for mercuric oxide reduced gas detectors (Novelli et al., 1999, 2009; Constant et al., 2008; Simmonds et al., 2000) and 1.1–2 % for N2O-doped electron capture detec- tors (Barnes et al., 2003; Moore et al., 2003). Therefore, we used the GC-HePDD to measure H2 mole fractions because it had been used to measure H2 with precisions of 0.06 % (1σ) under laboratory conditions (Novelli et al., 2009). Our system achieved median H2 measurement precisions over the field study between 0.06 and 0.11 %, and nearly always bet- ter than 0.3 % (95 % level) (Meredith, 2012, Fig. 2-8), which were on par with the laboratory-based configuration (Novelli et al., 2009) and at a 10-fold improvement over methods pre- viously deployed to the field. The IRGA instruments mea- sured mole fractions of CO2 and H2O with high precisions as well: between 0.025 and 0.043 and between 0.04 and 0.05 % (Meredith, 2012, Fig. 2-12). The high precision capability was critical for measuring the small vertical differences in mole fractions (Sect. 3.1). 2.4.2 Sampling error We used well-mixed integrating volumes to smooth out the temporal fluctuations in gas sample streams to retain rele- vant information from each gradient level and reduce sam- pling error (Woodruff, 1986). An integrating volume (V ) acts as an exponential filter on a gas flow (Q) with an e-folding timescale (τV = V/Q) that is set to span the time (Tc) to measure both H2 mole fractions of a given gradient pair: specifically, τV ∼ Tc = 8 min. The sampling error increases with the ratio of the timescale of the measurement cycle (Tc) to the timescale of the scalar in turbulent flow (τT ). Specif- ically, percent sampling error = 6 ( Tc τT )0.8 , and sampling er- rors can be in excess of 50 % for a 90 min GC-based mea- surement cycle (Woodruff, 1986; Meyers et al., 1996). The integrating volumes avoided sampling errors of around 10 % for our GC configuration that would have resulted from in- termittent sampling with a single instrument (see Sect. 2.4.3) assuming τT = 200–300 s (Baldocchi and Meyers, 1991). Sampling intervals interact systematically with the autocor- relation of the time series arising from the eddy structures (Woodruff, 1986). Integrating volumes (known also as buffer volumes) have been used in previous studies to dampen tem- poral fluctuations in trace gas mole fractions for flux-gradient measurements (Griffith et al., 2002), for contributions of ad- vection (Yi et al., 2008), and for flask sampling (Bowling et al., 2003). A block-averaging effect is accomplished in flux-gradient measurements that trap the compound of in- terest over periods of minutes or hours (Müller et al., 1993; Goldstein et al., 1995, 1996, 1998; Meyers et al., 1996) and eddy accumulation methods that use high-precision differen- tial collection apparatus to trap and then sample air from up- and down-drafts to determine the flux (Businger and Onlcey, 1990; Guenther et al., 1996; Bowling et al., 1998). The effect of the integrating volumes is shown by exam- ple with our CO2 measurements during a period when one gas stream (3.5 m level) passed through the well-mixed in- tegrating volume, while the other (0.5 m level) stream by- passed its integrating volume at a flow rate of 500 mL min−1. Each point represents the mean of the last 45 s of 1 Hz mole fraction measurements made for 1 min intervals at each level. The variability of CO2 mole fractions in the bypassed stream was higher than the stream passing through the integrating volume, and that variability carried over to the mole fraction gradients (Fig. 3). The effect of the integrating volume was simulated by the exponential moving average (τV = 2 min) of the 0.5 m level data. This example provides insight into the natural variability in trace gas mole fractions at the for- est. Without using integrating volumes to reduce sampling error, the lower-frequency measurements of H2 (Tc = 8 min) would poorly represent the true vertical distribution of H2 at the forest, which would increase the error in the flux-gradient calculations. 2.4.3 Measurement accuracy High measurement accuracy was required to measure small differences in concentration between two sampling inlets. Any inherent nonzero differences in the measurement, here referred to as measurement bias, would cause errors in the gradient measurement and had to be accounted for. To avoid one potential source of measurement bias, we measured mole fraction gradients using a single instrument that alternately sampled from a pair of inlets. The alternative – simultane- ously sampling a pair of gas inlets using separate instruments – could produce a measurement bias due to mismatch in the calibrations or drift between the two instruments (Woodruff, 1986). Only with very rigorous application of zeroing and intercomparison procedures can that method be applied with confidence, and even then, sudden changes in the offset between instrument sensitivity may occur without obvious causes (Bocquet et al., 2011). Operating two GC-HePDD in- struments or separate columns would have a high potential for bias due to chromatography effects or differential detec- tor sensitivity. In addition to choosing a single instrument setup, we in- corporated a nulling routine into the sampling procedure to diagnose measurement biases under a null condition when no difference should be detected. Differences may arise in the sample line segments dedicated to each inlet level due to leaks or physical interactions. During the nulling routine, run three times weekly at different times of the day, each inlet www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2792 L. K. Meredith et al.: A comparison of flux-gradient methods 14:30 15:00 15:30 16:00 407 408 409 410 411 a) CO2 mole fractions [pp m] 3.5 m 0.5 m: bypass IV 0.5 m: exp lter 14:30 15:00 15:30 16:00 −0.4 −0.2 0 b) CO2 gradients [pp m m− 1 ] 2 m: bypass 1 IV 2 m: exp lter Figure 3. Two-hour period highlighting the importance of using integrating volumes for our mole fraction gradient measurements. During this period, the 0.5 m inlet sample stream bypassed the in- tegrating volume (a, blue diamonds), while the 3.5 m inlet sample stream passed through the integrating volume and was physically smoothed (a, pink points). The effect the integrating volume would have had on the 0.5 m inlet measurements was simulated with an exponential moving average (a, dark-blue points). The mole frac- tion gradients from the physically smoothed 3.5 m inlet data and the 0.5 m inlet measurements bypassing the integrating volume (b, blue diamonds) were more variable than the physically smoothed 3.5 m inlet data and the computationally smoothed (exponential fil- ter) 0.5 m inlet data (b, dark-blue points). sampled ambient air from a 25 L glass carboy, which can be thought of as a large integrating volume. The volume was pre-flushed at 3 L min−1 (τV = 8.3 min) and then sampled by all sample streams at 2 L min−1 total flow (τV = 12.5 min). Similar systems have been engineered to sample air from the same inlet height by temporarily placing inlets at the same height or frequently interchanging the inlet positions (Goldstein et al., 1995; Meyers et al., 1996; Wesely et al., 1989), but that ambient air is still subject to atmospheric vari- ability. Our goal was to have an automated nulling procedure where all inlets would sample from the same reservoir of air that had nearly the same thermal, barometric, and chemical characteristics as the ambient air, but with the high-frequency atmospheric variability filtered out. An example of our nulling procedure on the morning of 2 August 2011 (Fig. 4) shows the transition of the CO2 sam- pling system from tower measurements to the nulling vol- ume as the integrating volumes flushed. The null bias be- tween inlet heights for each H2, CO2, and H2O gradient pair was calculated after detrending with a second-order polyno- mial to account for the drift in concentrations due to lower- frequency atmospheric variability. In this example, the appar- ent null bias between the 24 and 28 m (0.5 and 3.5 m) canopy inlets was 1.06 (1.63) ppb and 0.92 (−0.33) ppm for H2 and CO2, respectively. Over the entire study period, the median  18   358   Figure 4. Nulling procedure example: 2 August 2011. Around 05:50 local time, the 359   nulling valves were activated to draw air through the nulling volume (flushed for 40 min 360   prior) each of the four gas lines that were usually connected to the 28 m, 24 m, 3.5 m, and 361   0.5 m inlets. The full CO2 time series (upper plot) shows that it took over 20 min to flush 362   the integrating volumes and sample lines of the memory of the strong nighttime CO2 363   mole fraction gradient. Over the procedure, each inlet was sampled twice for H2 (lower 364   right) and eight times for CO2 (lower left; shaded portion upper plot) and H2O (not 365   shown). Second-order polynomials were used to detrend the data to remove the drift in 366   mole fractions of CO2 and H2 over the nulling period. 367   368   05:50 06:00 06:10 06:20 06:30 400 450 500 Time CO 2 [ pp m ] Flushing of nulling volumes and nulling period (gray shading) 28 m 24 m 3.5 m 0.5 m 0 2 4 6 8 10 12 14 16 460 465 470 475 480 Nulling time (min) CO 2 [ pp m ] CO2 nulling Fit above Fit below 0 4 8 12 16 20 24 28 32 410 420 430 440 H2 nulling H 2 [p pb ] Nulling time (min) Example nulling procedure Figure 4. Nulling procedure example for 2 August 2011. Around 05:50 local time, the nulling valves were activated to draw air thr ugh the nulling volume (fl hed for 40 min prior) each of the four gas lines that were usually connected to the 28, 24, 3.5, and 0.5 m inlets. The full CO2 time series (upper plot) shows that it took over 20 min to flush the integrating volumes and sample lines of the emory of the strong nighttim CO2 mole fraction gradient. Over the procedure, each inlet was sampled twice for H2 (lower right) and eight times for CO2 (lower left, shaded portion upper plot) and H2O (not shown). Second-order polynomials were used to detrend the data to remove the drift in mole fractions of CO2 and H2 over the nulling period. H2 null bias was −0.17 and −0.01 ppb for the respective gradient pairs, and was approximately normally distributed (1σ ; −077 to 0.52) (Fig. 5). The observed null bias was smaller than the combined analytical uncertainty (minimum detectable difference given instrument precision √ 2σ), so it was not possible to distinguish it from zero, and the H2 bias between the inlet lines could be ignored. The nulling procedure was a valuable tool to diagnose bias to between sampling lines, though in retrospect mixing the reservoir, increasing its volume, using multiple reservoirs in series, or filling the reservoir from a level with less variability (i.e., farther from the soil) in order to reduce concentration variability and drift over the nulling procedure would yield better data on the null bias. 3 Gradients and flux-gradient methods In this section, we present mole fraction gradients measured at Harvard Forest. The theory and applicability of three flux- gradient methods are discussed and the filtering criteria are described. 3.1 Gradient measurements This study was the first application of the GC-HePDD to measure H2 gradients in the field. We observed statistically Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2793   19   369   Figure 5. Time series (upper plots) and distributions (lower plots) of the measurement 370   bias between sampling lines for the 24 m and 28 m (left plots) and the 0.5 m and 3.5 m 371   (right plots) H2 measurements as determined by the nulling procedure. The median and 372   the 1σ confidence intervals are reported for each distribution and are compared with 373   minimum detectable difference given the median instrument 1σ precision (grey shading). 374   375   The nulling procedure was a valuable tool to diagnose bias to between sampling 376   lines, though in retrospect mixing the reservoir, increasing its volume, using multiple 377   reservoirs in series, or filling the reservoir from a level with less variability (i.e., farther 378   Nov10 Apr11 Sep11 Feb12 −2 0 2 24 m and 28 m inlets H 2 n ull b ias [p pb ] Nov10 Apr11 Sep11 Feb12 −2 0 2 0.5 m and 3.5 m inlets H 2 n ull b ias [p pb ] −2 0 2 0 10 20 Median, −1m, 1m −0.17, −0.77, 0.35 H2 null bias [ppb] Co un ts −2 0 2 0 10 20 H2 null bias [ppb] Co un ts Median, −1m, +1m −0.01, −0.60, 0.52 Figure 5. Time series (upper plots) and distributions (lower plots) of the measurement bias between sampling lines for the 24 and 28 m (left plots) and the 0.5 and 3.5 m (right plots) H2 measurements as determined by the nulling procedure. The median and the 1σ confi- dence i tervals a e reported for ea distribution and are compared with minimum detectable difference given the median instrument 1σ precision (gray shading). significant H2 gradients both above and below the canopy at Harvard Forest. Below-canopy H2 gradients were typi- cally larger than above canopy by a factor of 10 because of the reduced turbulence and proximity to the H2 sink be- neath the forest canopy (Fig. 6). Gradients exhibited a di- urnal pattern, with stronger gradients at night during calm atmospheric conditions when H2 lost to soil uptake was not replenished by H2 in the overlying air mass. The 26 m H2 gradients were often close to the precision of the GC-HePDD system, especially during turbulent daytime periods. As a re- sult, raw measurements were averaged to reveal the environ- mental gradients and fluxes, as has been previously required for these types of measurements above the forest canopy (Simpson et al., 1997). For example, the 26 and 2 m gradients of H2 and CO2 averaged into 2 h bins for the month of July clearly showed the underlying environmental signal (Fig. 7). Soil uptake of H2 led to positive H2 gradients at both levels. Above-canopy CO2 gradients oscillated from positive during the day, when photosynthetic uptake of CO2 by the forest canopy was the dominant process, to negative at night, when ecosystem respiration was the overwhelming process. Respi- ration was the dominant process below the forest canopy, as indicated by consistently negative 2 m gradients. Our CO2 mole fraction measurements agree well with simultaneous CO2 profile measurements at the EMS site (unpublished Har- vard Forest EMS data; Urbanski et al., 2007; Wehr et al., 2013). Higher signal-to-noise ratios could have been achieved for H2 gradients measured over a larger vertical height (1z) dif- ference. However, the 4 m 1z for the 24 and 28 m inlets was   21   at night when ecosystem respiration was the overwhelming process. Respiration was the 402   dominant process below the forest canopy, as indicated by consistently negative 2 m 403   gradients. Our CO2 mole fraction measurements agree well with simultaneous CO2 404   profile measurements at the EMS site (unpublished Harvard Forest EMS data; Urbanski 405   et al., 2007; Wehr et al., 2013). 406   407   408   Figure 6. Example of mole fraction gradients of hydrogen (ppb H2 m-1) above (26 m) and 409   below (2 m) the forest canopy: a) both levels compared side-by-side in the same scale 410   and b) above canopy at a magnified scale. Black whiskers represent instrument precision 411   (median 1σ bracketed precision scaled over the vertical distance in ppb H2 m-1). Grey 412   shading designates nighttime hours. 413   07/16 07/17 07/18 07/19 07/20 07/21 07/22 07/23 0 10 20 30 40 50 [p pb H 2 m −1 ] a) 07/16 07/17 07/18 07/19 07/20 07/21 07/22 07/23 −1 0 1 2 3 4 [p pb H 2 m −1 ] b) above canopy (26 m) below canopy (2 m) Figure 6. Example of mole fraction gradients of hydrogen (ppb H2 m−1) above (26 m) and below (2 m) the forest canopy: (a) both levels com ared sid by side in the same sc le and (b) above canopy at a magnified scale. Black whiskers represent in- strument precision (median 1σ bracketed precision scaled over the vertical distanc in ppb H2 m−1). Gray shading designates night- time hours. limited by the height of the tower above the forest canopy. Close to the soil sink, H2 gradients were greater in mag- nitude than the instrument precision. For future studies, in- lets below the canopy could be installed farther from the soils (> 0.5 m) and placed closer together (1z < 3 m) so as to still measure statistically significant gradients that may be more linear than observed here. For studies with taller tow- ers extending beyond the vegetative canopy, a greater dis- tance between the inlets (1z > 4 m) could increase the mole fraction gradient signal-to-noise ratio, but should not exceed relevant eddy length scales, which can range from the me- chanical eddy size forced by obstruction of the wind by the trees (∼ 5 m) to the lower planetary boundary layer buoyant eddy size (∼ 100 m). At Harvard Forest, the dominant flux- carrying eddy frequency is between 0.01 and 0.2 Hz, which corresponds to eddy scales of 10 to 200 m for mean winds around 2 m s−1 (Goulden et al., 1996) 3.2 Flux-gradient methods Flux-gradient methods were used to calculate the flux of a trace gas from the measured gradient and a number of differ- ent parameters. In most presentations of flux-gradient meth- ods, an analogy is drawn to Fick’s first law for molecular diffusion, such that it is directly or implicitly stated that con- servative fluxes, FC1 , of gas molecules (Eq. 1) are equal to the product of their mole fraction gradient (1C1/1z) in the down-gradient direction and the eddy diffusivity, K , which depends on the intensity of turbulent mixing over time inter- vals appropriate to the scale of the process (Baldocchi et al., 1995; Goldstein et al., 1996, 1998; Dunn et al., 2009). www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2794 L. K. Meredith et al.: A comparison of flux-gradient methods  22    414   Figure 7. Two-hour mean mole fraction gradients of H2 and CO2 versus the hour of day 415   (hod) above (26 m) and below (2 m) the Harvard Forest canopy in July 2011. Bars 416   indicate 95% confidence interval of the sample mean of mole fraction gradients in 2-hour 417   bins. Grey shading designates nighttime hours. 418   419   Higher signal-to-noise ratios could have been achieved for H2 gradients measured 420   over a larger vertical height (Δz) difference. However, the 4 m Δz for the 24 m and 28 m 421   inlets was limited by the height of the tower above the forest canopy. Close to the soil 422   sink, H2 gradients were greater in magnitude than the instrument precision. For future 423   studies, inlets below the canopy could be installed farther from the soils (> 0.5 m) and be 424   placed closer together (Δz < 3 m), to still measure statistically significant gradients that 425   0 6 12 18 24 −0.2 0 0.2 0.4 0.6 [p pb m −1 ] 6H2/6z 26m 0 6 12 18 24 −1 −0.5 0 0.5 [p pm m −1 ] 6CO2/6z 26m 0 6 12 18 24 5 10 15 [p pb m −1 ] 6H2/6z 2m hod 0 6 12 18 24 −20 −10 [p pm m −1 ] 6CO2/6z 2m hod Figure 7. Two-hour mean mole fraction gradients of H2 and CO2 versus the hour of day (hod) above (26 m) and below (2 m) the Har- vard Forest canopy in July 2011. Bars indicate 95 % confide ce in- terval of the sample mean of mole fraction gradients in 2 h bins. Gray shading designates nighttime hours. FC1 =−K 1C1 1z ρn (1) In this context, 1 denotes the mean difference between 30 min measurements at each level of a vertical gradient pair and ρn is the molar density of air. The turbulent mixing co- efficient K is inferred or parameterized, unlike the molecular diffusion coefficient in Fick’s first law that can be derived from first principles using molecular kinetic theory. Flux- gradient methods assume that, at a given time and place, the eddy diffusivity is invariant for mass, heat, and momentum (e.g., Reynold’s analogy) (Garratt and Hicks, 1973; Sinclair and Lemon, 1975; Baldocchi et al., 1988). In general, to calculate trace gas fluxes, flux-gradient methods require that there are no sources or sinks of the trace gas or the reference species between the gradient in- lets. This was not a problem in our study because gradient pairs were located either above or below the forest canopy (Fig. 2), and whole-canopy gradients were only used when gas fluxes from the canopy should have been minimal. For the methods to work, trace gas species should not have sig- nificantly different vertical distributions of sources and sinks. Furthermore, the trace gas in question should be inert over the timescale of the flux-gradient measurement, meaning that the timescale of turbulence (200–300 s in such ecosys- tems) should not exceed the timescale of chemical reactions (Baldocchi et al., 1988; Baldocchi and Meyers, 1991). Flux-gradient theories have been found to overestimate scalar fluxes within the roughness sublayer, which is the re- gion from the ground to 2 or 3 times the canopy height because the turbulent structure is influenced (mechanically and thermally) by the canopy elements (Raupach and Thom, 1981; Baldocchi and Meyers, 1988; Högström et al., 1989; Simpson et al., 1998) and tall vegetation (Garratt, 1978). That said, the theory might be less compromised than previ- ously thought above forests even at just 1.4 times the canopy height (Simpson et al., 1998). In our case, the tower height (30 m) constrained the height of the above-canopy inlets, which were centered on approximately 1.2 times the canopy height within the roughness sublayer. We evaluated the per- formance of flux-gradient methods against independent flux measurements of CO2 and H2O to validate the use of flux- gradient theories in this region. Below-canopy environments are characterized by low wind speeds and intermittent turbulent events that can violate flux-gradient theory assumptions. Counter-gradient transport of heat, momentum, and trace gases has been documented beneath plant canopies and may severely compromise flux- gradient methods (Shaw, 1977; Raupach and Thom, 1981; Baldocchi and Meyers, 1988; Amiro 1990; Baldocchi and Meyers, 1991). On the other hand, flux-gradient methods have been preferred over eddy covariance techniques for measuring surface–atmosphere fluxes within a few meters of the surface layer (Fitzjarrald and Lenschow, 1983; Gao et al., 1991; de Arellano and Duynkerke, 1992; Wagner-Riddle et al., 1996; Taylor et al., 1999; Dunn et al., 2009). Intermittent turbulent transport events may become less important near the ground, where the sources or sinks of tracers can be large; therefore, Meyer et al. (1996) argue that the flux-gradient re- lationships near the forest floor are valid and their application is justified. The availability of different parameters and the applicabil- ity of a given flux-gradient method varied with time and loca- tion in our experiment (Table 1). Whole-canopy fluxes could not be calculated during the growing season daytime because of canopy interference. The sensible heat flux method was only applied outside the 2011 growing season because the fans in the aspirated temperature shields were damaged by a lightning strike on 28 May 2011, which was not appar- ent from the data, and was only discovered 6 months later. In this study, we determined H2 fluxes using three different flux-gradient methods: trace gas similarity, sensible heat (H) similarity, and K parameterization. 3.2.1 Trace gas similarity The first method, trace gas similarity, assumes similarity of H2 fluxes and gradients to CO2 or H2O flux-gradients that can be measured by an independent method and is often re- ferred to as a modified Bowen ratio (MBR) technique. The flux (FC1) of a given trace gas is calculated from its mole fraction gradient (1C1/1z) and measurements of the flux (FC2) and gradient (1C2/1z) of a second reference trace gas using Eq. (2) (Meyers et al., 1996; Goldstein et al., 1996, 1998; Lindberg and Meyers, 2001). Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2795 Table 1. The type, location, and availability of the ancillary measurements required for each flux-gradient method. Method Measured parameters Location applied Period available Trace gas similarity CO2 and H2O eddy flux, Above canopy (28 & 24 m) All CO2 chamber flux, Whole canopy (24 & 3.5 m) All (nighttime)CO2 and H2O gradients Outside growing season (daytime) Below canopy (3.5 & 0.5 m) All after start of chamber measurements (April 2011) Sensible heat similarity Sonic heat flux, temperature Below canopy (3.5 & 0.5 m) Winter and spring 2011, winter 2012 gradient, H2O gradient K parameterization Sonic u∗ Below canopy (3.5 & 0.5 m) All FC1 = FC2 1C1 1C2 (2) The trace gas eddy diffusion coefficients (K) for CO2 and H2O were compared (slope = 1.07, R2 = 0.68) at Harvard Forest in the past (Goldstein et al., 1996). However, it is important to note that the idea of similarity applied in this method is more general than diffusional theory and calcula- tion of K . Trace gas similarity only assumes linear transport of trace gases considered to be inert over the spatial and tem- poral scale of the measurement and that have a similar spa- tial distribution of sources and sinks. The method is there- fore more general than is often attributed to flux-gradient methods. K is not calculated explicitly by similarity meth- ods. These points also apply to the sensible heat similarity method. In previous work, the trace gas similarity method was used to derive H2 fluxes using CO2 as the reference gas over a weeklong manual collection experiment in an Alaskan bo- real forest with promising but limited results (Rahn et al., 2002). In this study, independent flux measurements of CO2 and H2O via eddy covariance and of CO2 via automated flux chambers were available above and below the forest canopy, respectively. We applied the trace gas similarity method both above and below the canopy all year round and to the whole- canopy gradient outside the growing season as data availabil- ity allowed. 3.2.2 Sensible heat similarity The second method, sensible heat similarity, assumes simi- larity of H2 fluxes and gradients to the sensible heat flux and temperature gradient (Meyers et al., 1996; Liu and Foken, 2001; Dunn et al., 2009). The sensible heat flux (H) and temperature gradient (1T/1z) are related by the turbulent transfer coefficient for heat KH (Businger, 1986), H =−KH 1T 1z ρmcp, (3) where ρm is the mass density of air and cp is the specific heat capacity of air. Following Liu and Foken (2001) and Dunn et al. (2009), the sensible heat flux was obtained by applying a water vapor correction to the buoyancy flux derived from sonic anemometer temperature measurements, and the cross- wind term was neglected because it should be small com- pared to the other terms, H = w ′T ′s 1T 1z + 0.51T 1q 1z 1T 1z ρmcp, (4) where w′T ′s is the sonic heat flux and q represents the spe- cific humidity (kg H2O kg air−1). Equation (4) gives the flux- gradient form (Eq. 1) for sensible heat, which can then be used to determine the H2 flux (Eq. 5) by inferring KH . FC1 =H 1C1 1T ρn ρmcp (5) The eddy diffusion coefficients for trace gases (K) and heat (KH ) were measured at Harvard Forest in the past, agree- ing within 12± 10 % when compared to both H2O and CO2 (Goldstein et al., 1996). The method has been applied to de- termine hydrocarbon fluxes above a forest canopy (Goldstein et al., 1996) and the specific method adopted in our study was developed for the calculation of CO2 and H2O fluxes close to the ground (Dunn et al., 2009). This is an MBR technique (Liu and Foken, 2001) that can be used to determine sensible (and latent heat) fluxes (errors of less than 10 %) and it cir- cumvents errors (often on the order of 20–30 %) associated with methods that require closure of the measured surface energy budget, such as the modified Bowen ratio energy bal- ance (MREB) method (Sinclair and Lemon, 1975; Baldocchi et al., 1988; Liu and Foken, 2001, and references therein). In previous work, annual H2 fluxes were determined using the MREB method over grassland in Quebec (Constant et al., 2008). In this study, the sensible heat similarity method was applied below the canopy during months when the aspi- rated temperature shields were functioning (November 2010 to May 2011 and December 2012 to March 2012). 3.2.3 K parameterization The third method, K parameterization, invokes Monin– Obukhov similarity theory to parameterize a turbulent www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2796 L. K. Meredith et al.: A comparison of flux-gradient methods exchange coefficient (K) from sonic anemometer measure- ments, and is often referred to as an aerodynamic method (Monin and Obukhov, 1954; Simpson et al., 1998). K can be estimated by means of a variety of aerodynamic methods de- rived from energy or momentum balances (Högström et al., 1989; Celier and Brunet, 1992; Simpson et al., 1998; Foken, 2006). For example, K can be determined from K = u ∗ k(z− d) φm , (6) where u∗ is the friction velocity (a characteristic velocity scale calculated from the square root of covariance between vertical and horizontal wind), k is von Karman’s constant (taken as 0.4), z is the height above the ground, d is the zero-plane displacement height, and φm is the diabatic influ- ence function for momentum (Monin and Obukhov, 1954; Simpson et al., 1998). The Monin–Obukhov length (L= −u3∗ k g T H ρmcp ) is used to determine φm from the empirical de- scriptions outlined by Eqs. (22a) and (22b) in Foken (2006). The method has been applied close to the surface (Fritsche et al., 2008) and above the forest canopy (Simpson et al., 1997, 1998). In this study, the K parameterization method was applied below the canopy. Assuming that z= 2 m (the height of the u∗ measurement), the displacement height was inferred empirically to be around 1.63 m (z−d = 0.37 m) by comparing parameterized K values to the values for K de- termined from the chamber flux and concentration gradient using Eq. (1). The determination of d is often problematic (Raupach and Thom, 1981). Physically, d represents an ad- justment of the basis height to reflect the displacement by the surface features of the profiles of micrometeorological vari- ables fundamental to the K parameterization at hand. The inferred value for d was consistent throughout the study pe- riod and may reflect the effect of below-canopy environment on the turbulent fluxes at the EMS site. 3.3 Data filtering Data were filtered to reject unrealistic values and to appro- priately apply flux-gradient methodology. By their nature, the trace gas similarity and sensible heat similarity methods are not valid when the gradient of the comparative species (Eqs. 2 and 5, denominator) approaches zero or changes sign over the measurement period. Similarity methods can- not work during such periods, so we limited flux calculations to periods when gradients in the denominator exceeded their measurement precision. In general, the fluxes calculated dur- ing dawn and dusk periods are not included in averages or comparative assessments because of the tendency for condi- tions to change such that the observed fluxes and gradients provide no information about the turbulence. For example, conditions pass through an isothermal point when air and sur- faces have the same temperature so that there is no gradient driving a heat flux; when air is saturated, there is no gradient driving a water vapor flux; and when photosynthesis ceases, CO2 gradients change sign. Data were rejected during rainy periods with more than 0.2 mm of rain per 30 min (Baldocchi and Meyers, 1991). Periods with u∗ < 0.07 m s−1 and u∗ < 0.17 m s−1 were ex- cluded for below- and above-canopy data, respectively, be- cause of poorly developed turbulent conditions (Goulden et al., 1996; Liu and Foken, 2001; Bocquet et al., 2011) and po- tential for advective fluxes driven by drainage flows on slop- ing terrain (Yi et al., 2008). We excluded unrealistic values of the implied turbulent transfer coefficients, K , such that 0 ≤K ≤ 0.5 m2 s−1 and 0 ≤K ≤ 5 m2 s−1 for the below- canopy and the whole/above-canopy fluxes, respectively. We did not filter based on the wind sector because we found no interference from the tower and instrument shed to the east (45 to 180◦). We considered quantile–quantile plots of the residual between flux-gradient methods and eddy covariance fluxes, and excluded clear outliers: residual absolute values > 20 and > 10 mmol m−2 s−1 for CO2 and H2O fluxes. Ad- ditional filters were applied to the sensible heat flux method to retain only reasonable sonic and sensible heat flux val- ues: ∣∣∣w′T ′s ∣∣∣ < 0.1 K m s−1 and −100 0.05, α = 0.05). A text-type flaga is assigned to each flux-gradient method to indicate the level of performance against the inde- pendent flux methods: good (bold), fair (underlined italic), and poor (plain text). Data are grouped into summer (23 June 2011 to 16 Octo- ber 2011) and winter (15 November 2011 to 28 February 2012) and daytime (10:00–16:00 LT) and nighttime (21:00–05:00 LT) periods. The comparison is not made for the chamber–chamber comparison, for periods with no data (nd), and across the canopy when in-canopy fluxes are significant (c). Chamber K (2 m) Sensible heat Trace gas Trace gas Eddy or chamber (0 m) parameterization similarity (2 m) similarity (10 m) similarity (26 m) flux median Trace gas flux Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter CO2 chamber (0 m) Day 0.48∗ 0.46∗ nd 0.62∗ c 0.47∗ c −0.17∗ 5.4 0.6 0.0† −0.1 0.3 0.8 −0.1† Night 0.50∗ 0.63∗ nd 0.44∗ −0.04 0.25∗ −0.10 0.22∗ 5.6 0.6 −1.1 0.2 −0.1† −0.9† 0.4 −4.3 −0.4 CO2 eddyb (26 m) Day c 0.0 c −0.04 nd −0.10 c 0.07 0.68∗ 0.20∗ −19 0.8 0.3 −0.1† −0.8 0.1† 0.3† 0.0† Night 0.19∗ 0.32∗ 0.24∗ 0.23∗ nd 0.05 0.31∗ 0.24∗ 0.33∗ 0.23∗ 4.3 1.2 1.1 −0.7 0.7† −0.4 −0.8 −0.7 −0.4 −3.3 −0.8 H2O eddy (26 m) Day nd nd c 0.25∗ nd 0.19∗ c 0.34∗ 0.65∗ −0.21 4.5 0.4 −0.35 −0.25 −0.02† −0.41 −0.63 Night nd nd 0.28∗ 0.44∗ nd 0.46∗ 0.14∗ 0.32∗ 0.22∗ 0.37∗ −0.04 0.006 0.07 0.02 0.02† 0.13 0.08 0.03† 0.02 a Text-type flags are assigned in this manner: (1) good (bold) r >= 30 and |% bias |< 50 %, (2) fair (underlined italic) r >= 10 and |% bias |< 100 %, and (3) poor (plain text) remainder, where the % bias is the tabulated bias relative to the median eddy flux or chamber flux for the period (right columns). b The eddy CO2 flux is used for 10 to 26 m comparisons, and the net CO2 ecosystem exchange (NEE) is used for 0 to 2 m comparisons to account for the CO2 storage flux. 0 6 12 18 24 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 CO 2  u x [µm ol m − 2 s − 1 ] 29 m: eddy covariance 26 m: trace gas similarity 10 m: trace gas similarity 0 6 12 18 24 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 CO 2  u x [µ m ol m − 2 s − 1 ] 2 m: sensible heat similarity 2 m: K parameterization 29 m: respiration model Figure 9. Comparison of wintertime (1–14 February 2012) CO2 fluxes determined by eddy covariance, K parameterization, trace gas similarity (corrected; Sect. 4.2), sensible heat similarity, and respiration model throughout the forest canopy in the winter. Data points represent 3 h aggregate mean and 95 % confidence intervals. the summer period (Table 2) and for the whole measurement period (CO2: r = 0.88∗, bias=−0.1† µmol m−2 s−1; H2O, r = 0.71∗, bias=−0.39 mmol m−2 s−1). The whole-canopy trace gas similarity method (Sect. 3.2.2; centered on 10 m) could only be applied in the absence of interfering canopy sources or sinks be- tween the gradient inlets (24 and 3.5 m), making this method more restricted in its application than the above-canopy method. However, we found that the whole-canopy method was an equal or superior method in some cases when trace gas gradients were small and difficult to detect above the forest canopy, such as during the winter and at night (Table 2). For example, day- and wintertime H2O fluxes from whole-canopy trace gas similarity were good, while that method applied above the canopy had poor performance (Table 2). An example of the 10 m trace gas similarity CO2 fluxes is shown in Fig. 9. CO2 fluxes calculated by the sensible heat similarity method (Sect. 3.2.2; 2 m) were significantly correlated with chamber measurements all year (daytime: r = 0.67∗, bias= 1.1 µmol m−2 s−1), but tended to overestimate day- time fluxes (Table 2). The method was only available during the wintertime, when heat fluxes and temperature gradients were small, which contributed to higher uncertainty in the results than for the other methods, as shown in Fig. 9. Agree- ment of the wintertime sensible heat similarity and eddy flux data across the forest canopy was poor for CO2 and poor to fair for H2O (Table 2). The performance of the K parameterization method be- low the forest canopy (Sect. 3.2.4; 2 m) versus chamber measurements was good throughout the year (daytime: r = 0.74∗, bias=−0.12 µmol m−2 s−1). These fluxes were sig- nificantly correlated with chamber data, and bias was low or insignificant (Table 2). K parameterization fluxes were cor- related with eddy covariance fluxes in most cases, but typ- ically were biased positively in the summer and negatively in the winter, as can be seen from the comparison with the Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2799 NEE-derived simple ecosystem respiration model in Figs. 8 and 9. The overestimation of nocturnal summertime fluxes by K parameterization was likely related to the large and nonlinear CO2 gradients (determined from profile measure- ments) that arise under calm nocturnal conditions. In con- trast, trace gas and sensible heat similarity methods use ra- tios of vertical mole fraction or temperature gradients, which can compensate for nonlinear vertical concentration gradi- ents. The K parameterization has been shown to agree with trace gas similarity and eddy covariance-derived fluxes in the past (Fritsche et al., 2008). A larger period of overlap- ping data for the sensible heat similarity method was avail- able with K parameterization results than chamber data, and the two flux-gradient methods were highly correlated but had a relative positive bias of the CO2 flux in the sensible heat method relative to K parameterization over the whole period (day r = 0.63∗, bias= 0.37 µmol m−2 s−1; night r = 0.42∗, bias= 0.10 µmol m−2 s−1). 4.3 Flux-gradient method application: H2 gradient fluxes Summertime H2 fluxes were calculated for the 15– 22 July 2011 period above the canopy by the trace gas similarity methods using the CO2 and H2O eddy fluxes, and below the canopy from trace gas similarity to CO2 us- ing CO2 chamber measurements and the K parameteriza- tion method (Fig. 10). The H2 fluxes were characterized by net ecosystem H2 uptake and were consistent with our expectation that H2 uptake by soil would be the dominant ecosystem process. The below-canopy fluxes were −8 and −10 nmol m−2 s−1 during midday over this period for the K parameterization and chamber-based trace gas similarity methods, respectively. The above-canopy trace gas similar- ity average midday H2 fluxes via CO2 and H2O were −21 and −15 nmol m−2 s−1, respectively. Larger trace gas fluxes were calculated using CO2 as the correlative variable than H2O, but in the case of H2 this difference (and the differ- ence with the below-canopy fluxes) fell within the 95 % con- fidence intervals because of the higher uncertainty in H2 gra- dients measurements above the canopy. Potential systematic differences in the trace gas similarity fluxes of H2 were not corrected for as was done for CO2 and H2O in Sect. 4.2 be- cause the true relationship of KH2 with KCO2 and KH2O was unknown. Storage fluxes of H2 were calculated, but were typ- ically small (<| 1 nmol m−2 s−1 |), and were therefore not in- cluded in the comparison. The midday summertime H2 up- take rates correspond to H2 deposition velocities of 0.04 to 0.10 cm s−1, which were within the range of previously re- ported soil H2 deposition velocities, so our results support the previously reported values that typically range between 0.01 and 0.10 cm s−1 (Ehhalt and Rohrer, 2009). Wintertime H2 fluxes were calculated for the 1–14 Febru- ary 2012 period using the whole-canopy trace gas similar- ity, K parameterization, and sensible heat methods (Fig. 11). 0 6 12 18 24 −50 −40 −30 −20 −10 0 10 20 30 H 2  u x [nm ol m − 2 s − 1 ] 26 m: trace gas similarity (CO2) 26 m: trace gas similarity (H2O) 0 6 12 18 24 −50 −40 −30 −20 −10 0 10 20 30 H 2  u x [nm ol m − 2 s − 1 ] 2 m: K parameterization 2 m: trace gas similarity (CO2) Figure 10. Comparison of summertime H2 fluxes (15–22 July 2011 period) above (left) and below (right) the canopy: trace gas similar- ity via CO2 or H2O, eddy covariance (eddy), K parameterization, and trace gas similarity via flux chamber data. Data points represent 6 h aggregate mean and 95 % confidence intervals. The wintertime H2 fluxes were −4 and −6 nmol m−2 s−1 for the whole canopy using the trace gas similarity via CO2 and H2O, respectively, and −0.5 to −0.8 nmol m−2 s−1 be- low the canopy using the K parameterization and sensible heat similarity methods, respectively. H2 soil uptake has been shown in previous work to persist at low rates in the winter (Constant et al., 2008; Lallo et al., 2008). The apparent H2 flux divergence below and above the canopy was consistent with the diagnosed median daytime biases for each method: compared with the wintertime CO2 chamber data, K parame- terization tended to slightly underestimate CO2 fluxes, while uncorrected trace gas similarity (10 m) and sensible heat sim- ilarity methods overestimated CO2 fluxes (Tables 2 and A1). However, we cannot exclude the effect of different source– sink distribution for H2 versus CO2 and H2O or the measure- ment of different patches of forest and H2 exchange rates as a result of the difference in the 2 m versus 10 m footprints. The uncertainty in the H2 gradient fluxes depended on the method used and the location applied. The uncertainty was large for H2 fluxes calculated by trace gas similarity above the canopy due to the low signal-to-noise ratio of those H2 gradients. For example, the summer daytime median propa- gated relative error (using the mean and uncertainty for terms in Eq. 2 and a 15 % uncertainty in eddy covariance fluxes fol- lowing Urbanski et al., 2007) was 200 % for H2 fluxes during the day and night, while CO2 flux relative error in the same period was around 40 % for each measurement. Therefore, H2 flux calculations were aggregated into hourly bins to re- duce the uncertainty around each measurement such as in the weeklong summer and winter examples (Figs. 10 and 11). In those cases, the relative error in aggregated H2 fluxes (calcu- lated from the 10:00 to 16:00 LT mean and 95 % confidence intervals) in the summer was 80 % for trace gas similarity (26 m) both via CO2 and H2O, 10 % for trace gas similarity (2 m) via CO2, and 10 % for parameterization (2 m), and in the winter it was 22 and 16 % for trace gas similarity (10 m) www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2800 L. K. Meredith et al.: A comparison of flux-gradient methods 0 6 12 18 24 −10 −5 0 5 hour of day H 2  u x [nm ol m − 2 s − 1 ] 10 m: trace gas similarity (CO2) 10 m: trace gas similarity (H2O) 0 6 12 18 24 −10 −5 0 5 H 2  u x [nm ol m − 2 s − 1 ] hour of day 2 m: sensible heat similarity 2 m: K parameterization Figure 11. Comparison of wintertime (1–14 February 2012) H2 fluxes above (left) and below (right) the canopy determined by trace gas similarity via CO2 and H2O, K parameterization, and sensible heat similarity in the winter. Data points represent 6 h aggregate mean and 95 % confidence intervals. via CO2 and H2O, respectively, 92 % for sensible heat simi- larity (2 m), and 30 % for K parameterization (2 m). There was uncertainty due to the choice in flux-gradient method, which we calculated as the relative error in the in- ferred K from the available flux-gradient methods by as- suming that each have equal validity (the same H2 gradi- ent was applied to each K in a given location). Over the whole year, the uncertainty across flux-gradient methods for the above-, whole-, and below-canopy environments was 46, 74, and 76 % in the median, respectively. The trace gas sim- ilarity uncertainty was smaller above the canopy than for the whole-canopy measurement, where there was more potential for canopy source–sink interference. Greater uncertainty be- tween the methods existed below the forest canopy where three different flux-gradient methods were compared: trace gas similarity via chamber fluxes, sensible heat similarity, and K parameterization (Table 2). 5 Summary and conclusions This paper describes design factors in the experimental setup that were key to the success of the flux-gradient method. Perhaps the most critical factors were the ability to measure H2 mole fraction gradients with high instrumental precision (0.06 to 0.11 %), with low sampling error (by use of inte- grating volumes), and without significant measurement bias (determined by a frequent nulling procedure). By addressing these three potential sources of error, we were able to mea- sure statistically significant above-canopy H2 fluxes, which still had relatively large uncertainty, but were consistent with the below-canopy results. Furthermore, the choice to design a system that could use multiple flux-gradient methods was im- portant, especially given the possibility for one method to fail or to suffer from large data losses (e.g., failure of temperature shields over the growing season for the sensible heat simi- larity method). Validating the flux-gradient method(s) using trace gases with independent flux measurements such as eddy covariance and/or chamber measurements gave us the confi- dence to apply the flux-gradient methods to H2. Finally, we encourage the use of independent flux measurements to cor- rect for any systematic biases in the flux-gradient methods (i.e., from different source–sink distributions), which should be determined for the particular ecosystem and time period of interest. This study provides a temporal guide to the suitability of each flux-gradient method at Harvard Forest. We found that all three flux-gradient methods (trace gas similarity, sensible heat similarity, and K parameterization) had good and fair performance in certain locations, seasons, and times of day. In general, the best agreement between flux-gradient meth- ods and the independent eddy covariance and chamber flux measurements was observed for measurements made on the same side of the canopy; that is, the correlation was typi- cally reduced when the eddy or chamber measurements were located on the opposite side of the forest canopy to the flux- gradient method. This is not surprising given the separation of dynamical flows above and below the canopy. Large rel- ative biases were observed for flux-gradient methods tested against H2O eddy covariance measurements at night because of the low signal-to-noise ratio in H2O gradients and fluxes. The trace gas similarity method performed the best above the forest canopy, and when applied to the whole canopy the per- formance was also good to fair. The whole-canopy approach provides a useful alternative to the above-canopy method during periods with low signal-to-noise ratio in the mole frac- tion gradients. Flux-gradient methods performed well below the forest canopy, despite the potential pitfalls in such loca- tions (Sect. 3.2). The relatively open and top-heavy canopy at Harvard Forest may foster a turbulent environment con- ducive to flux-gradient methods at this site. We found the K parameterization method to perform best below the canopy. An instrument failure meant that the sensible heat similarity method could not be used in the summer, but all indications are that the method would have worked if this instrument had been operational (e.g., Dunn et al., 2009). However, prob- lems with the aspirated temperature shields were not obvious in situ, which could be a risk for future studies as well. This paper shows that a variety of flux-gradient techniques can be used at Harvard forest to study the ecosystem ex- change of H2. We observed net uptake of H2 by the bio- sphere both above and below the canopy during the exam- ple periods, which point to the particular sensitivity of H2 to soil uptake, and uptake was stronger in summer than win- ter, as is presented over the entire study period in Mered- ith (2012) and Meredith et al. (2014). The H2 gradient fluxes were generally consistent across methods and with previous measurements. The flux-gradient approach generated auto- mated, continuous results representing a larger, spatially av- eraged, undisturbed measurement footprint than possible us- ing chamber techniques. The uncertainty in H2 fluxes for a given method ranged between 10 and 92 % and across all Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2801 available flux-gradient methods at a location ranged between 46 and 76 %. Further analyses of H2 gradient fluxes will weigh uncertainty against data availability for each method. These methods can be used to partition the net ecosystem H2 flux between above- and below-canopy contributions to yield additional information regarding the underlying fluxes. These measurements will help to elucidate specific process rates and reduce uncertainty in the H2 budget. In this study, we demonstrate that flux-gradient methods can inform our understanding of ecosystem processes for H2, and presum- ably, a wide variety of trace gases. www.atmos-meas-tech.net/7/2787/2014/ Atmos. Meas. Tech., 7, 2787–2805, 2014 2802 L. K. Meredith et al.: A comparison of flux-gradient methods Appendix A Table A1. Same as Table 2, but for uncorrected trace gas similarity fluxes (Sect. 4.2). Quantitative comparison of CO2 and H2O fluxes determined by flux-gradient methods and by independent eddy covariance and chamber measurements. First, the correlation between flux method pairs (r , Pearson’s linear correlation coefficient) is given, and statistically significant correlations are indicated by ∗ (Student’s t test, p value < 0.05, α = 0.05). Second, the median of the bias over the period (column header minus row) is given in µmol CO2 m−2 s−1 and mmol H2O m−2 s−1, and instances when this mean bias is not significantly different from zero are indicated by † (Student’s t test, p value > 0.05, α = 0.05). A text-type flaga is assigned to each flux-gradient method to indicate the level of performance against the indepen- dent flux methods: good (bold), fair (underlined italic), and poor (plain text). Data are grouped into summer (23 June 2011 to 16 October 2011) and winter (15 November 2011 to 28 February 2012) and daytime (10:00–16:00) and nighttime (21:00–05:00) periods. The comparison is not made for the chamber–chamber comparison, for periods with no data (nd), and across the canopy when in-canopy fluxes are significant (c). Chamber K (2 m) Sensible heat Trace gas Trace gas Eddy or chamber (0 m) parameterization similarity (2 m) similarity (10 m) similarity (26 m) flux median Trace gas flux Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter CO2 chamber (0 m) Day 0.48∗ 0.46∗ nd 0.62∗ c 0.47∗ c −0.20∗ 5.4 0.6 0.0† −0.1 0.3 0.4 −0.3 Night 0.50∗ 0.63∗ nd 0.44∗ −0.12 0.18∗ −0.10 0.22∗ 5.6 0.6 −1.1 0.2 −0.1† −1.9 0.1 −4.5 −0.5 CO2 eddyb (26 m) Day c 0.0 c −0.04 nd −0.10 c 0.06 0.62∗ 0.16∗ −19 0.8 0.3 −0.1† −0.8 −0.2 5.5 −0.23† Night 0.19∗ 0.32∗ 0.24∗ 0.23∗ nd 0.05 0.47∗ 0.13∗ 0.27∗ 0.21∗ 4.3 1.2 1.1 −0.7 0.7† −0.4 −0.8 −1.5 −0.6 −3.4 −0.9 H2O eddy (26 m) Day nd nd c 0.25∗ nd 0.19∗ c 0.34∗ 0.65∗ −0.21 4.5 0.4 −0.35 −0.25 −0.02† 1.13 −0.57 Night nd nd 0.28∗ 0.44∗ nd 0.46∗ 0.14∗ 0.32∗ 0.22∗ 0.37∗ −0.04 0.006 0.07 0.02 0.02† 0.17 0.08 0.06 0.03 a Text-type flags are assigned in this manner: (1) good (bold) r >= 30 and |% bias |< 50 %, (2) fair (underlined italic) r >= 10 and |% bias |< 100 %, and (3) poor (plain text) remainder, where the % bias is the tabulated bias relative to the median eddy flux or chamber flux for the period (right columns). b The eddy CO2 flux is used for 10 to 26 m comparisons, and the net CO2 ecosystem exchange (NEE) is used for 0 to 2 m comparisons to account for the CO2 storage flux. 0 6 12 18 24 0 2 4 6 8 10 12 H 2O u x [ mm ol m − 2 s − 1 ] 29 m: eddy covariance 26 m: trace gas similarity (TGS) 26 m: TGS, uncorrected 2 m: K parameterization Figure A1. Comparison of summertime H2O fluxes (15–22 July 2011 period) throughout the forest canopy: eddy covariance, trace gas similarity via CO2 (corrected and uncorrected; Sect. 4.2), and K parameterization. Data points represent 3 h aggregate mean and 95 % confidence intervals. Atmos. Meas. Tech., 7, 2787–2805, 2014 www.atmos-meas-tech.net/7/2787/2014/ L. K. Meredith et al.: A comparison of flux-gradient methods 2803 Acknowledgements. The authors are grateful to Peter Salameh for providing the GCwerks automated gas chromatograph software and support (http://www.gcwerks.com), and to Andrew Crotwell for training on use of GC-HePDD systems for H2 measurement. We would also like to thank Elaine Gottlieb, Brad Hall, Paul Novelli, and Duane Kitzis for help with standard tank calibrations, and Alfram Bright and Bruce Daube for their contributions to the IRGA system. Furthermore, the authors are grateful for help at Harvard Forest from Emery Boose, Mark VanScoy, Josh McLaren, Leland Werden, Rick Wehr, and Ben Lee. L. K. Meredith was supported through the following funding sources: NSF Graduate Research Fellowship, multiple grants from NASA to MIT for the Advanced Global Atmospheric Gases Experiment (AGAGE), MIT Center for Global Change Science, MIT Joint Program on the Science and Policy of Global Change, MIT Martin Family Society of Fellows for Sustainability, MIT Ally of Nature Research Fund, MIT William Otis Crosby Lectureship, and MIT Warren Klein Fund. Operation of the EMS flux tower was supported by the Office of Science (BER), US Dept. of Energy (DE-SC0004985), and is a component of the Harvard Forest LTER, supported by National Science Foundation. Edited by: D. Heard References Allen, A.: Soil science and survey at Harvard Forest, Soil Surv. Horiz., 36, 133–142, 1995. Amiro, B. 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