Isotopic signatures of production and uptake of H 2 by soil

Molecular hydrogen (H2) is the second most abundant reduced trace gas (after methane) in the atmosphere, but its biogeochemical cycle is not well understood. Our study focuses on the soil production and uptake of H2 and the associated isotope effects. Air samples from a grass field and a forest site in the Netherlands were collected using soil chambers. The results show that uptake and emission of H2 occurred simultaneously at all sampling sites, with strongest emission at the grassland sites where clover (N2 fixing legume) was present. The H2 mole fraction and deuterium content were measured in the laboratory to determine the isotopic fractionation factor during H2 soil uptake (αsoil) and the isotopic signature of H2 that is simultaneously emitted from the soil (δDsoil). By considering all netuptake experiments, an overall fractionation factor for deposition of αsoil = kHD / kHH = 0.945± 0.004 (95 % CI) was obtained. The difference in mean αsoil between the forest soil 0.937± 0.008 and the grassland 0.951± 0.026 is not statistically significant. For two experiments, the removal of soil cover increased the deposition velocity (vd) and αsoil simultaneously, but a general positive correlation between vd and αsoil was not found in this study. When the data are evaluated with a model of simultaneous production and uptake, the isotopic composition of H2 that is emitted at the grassland site is calculated as δDsoil = (−530± 40) ‰. This is less deuterium depleted than what is expected from isotope equilibrium between H2O and H2.


Introduction
H 2 is considered an alternative energy carrier to replace fossil fuels in the future.However, the environmental and climate impact of a potential widespread use of H 2 is still under assessment.Several studies suggested that the atmospheric H 2 mole fraction might increase substantially in the future due to the leakage during production, storage, transportation and use of H 2 , which could significantly affect atmospheric chemistry (Schultz et al., 2003;Tromp et al., 2003;Van Ruijven et al., 2011;Warwick et al., 2004).
In the troposphere, H 2 has a mole fraction of about 550 parts per billion (ppb = nmol mol −1 ) and a lifetime of around 2 years (Novelli et al., 1999;Price et al., 2007;Xiao et al., 2007;Pieterse et al., 2011;2013).H 2 can affect atmospheric chemistry and composition in several ways.Firstly, it increases the lifetime of the greenhouse gas methane (CH 4 ) via its competing reaction with the hydroxyl radical (OH) (Schultz et al., 2003;Warwick et al., 2004).Additionally, H 2 affects air quality because it is an ozone (O 3 ) precursor and indirectly increases the lifetime of the air pollutant carbon monoxide (CO) through competition for OH.In the stratosphere, H 2 O that is produced through the oxidation of H 2 increases humidity, which can result in increased formation of polar stratospheric clouds and O 3 depletion (Tromp et al., 2003), but this effect may be weaker than estimated initially (Warwick et al., 2004;Vogel et al., 2012).
The main sources of tropospheric H 2 are the oxidation of CH 4 and non-methane hydrocarbons (NMHC) (48 %), biomass burning (19 %), fossil fuel combustion (22 %) and biogenic N 2 fixation in the ocean (6 %) and on land (4 %), while the main sinks are soil uptake (70 %) and oxidation by OH (30 %) (Pieterse et al., 2013).The biogenic soil sink of H 2 is the largest and most uncertain term in the global atmospheric H 2 budget.Conrad and Seiler (1981) assumed that the soil uptake of atmospheric H 2 is most likely due to consumption by abiotic enzymes, since there were no soil microorganisms known to be able to fix H 2 at the low atmospheric mole fraction at that time.This remained the basic hypothesis of many further soil uptake studies (Conrad et al., 1983;Conrad and Seiler, 1985;Ehhalt and Rohrer, 2011;Guo and Conrad, 2008;Häring et al., 1994;Smith-Downey et al., 2006).However, Constant et al. (2008a) were first to identify an aerobic microorganism (Streptomyces sp.PCB7) that can consume H 2 at tropospheric ambient mole fractions and suggested that active metabolic cells could be responsible for the soil uptake of H 2 rather than extracellular enzymes.Further studies showed that uptake activity at ambient H 2 level is widespread among the streptomycetes (Constant et al., 2010) and it was postulated that high-affinity H 2 -oxidizing bacteria are the main biological agent responsible for the soil uptake of atmospheric H 2 (Constant et al., 2011).Khdhiri et al. (2015) suggested that the relative abundance of high-affinity H 2 -oxidation bacteria and soil carbon content could be used as predictive parameters for the H 2 -oxidation rate.Determining the dominant mechanism of the H 2 soil uptake activity is still an active area of research.

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It has been shown that soil uptake of H 2 can coexist with soil production (Conrad, 1994).H 2 is produced in the soil during N 2 fixation (e.g., by bacteria living symbiotically in the roots of legumes such as clover or beans) and dark fermentation.Although the H 2 produced in the soil by, e.g., N 2 fixation can be largely consumed within the soil, a significant amount of H 2 escapes to the atmosphere (Conrad andSeiler, 1979, 1980).Conrad and Seiler (1980) estimated that 2.4 to 4.9 Tg a −1 of H 2 is emitted into the atmosphere through N 2 fixation on land.
One approach to better understand the sources and sinks of H 2 is to investigate the isotopic fractionation processes involved, which act as a fingerprint for H 2 emitted from different sources or destroyed by different sinks.The isotopic composition of H 2 is expressed as where R sa is the D / H ratio of the sample H 2 and R VSMOW = (155.76± 0.8) parts per million (ppm = mmol mol −1 ) is the same ratio of the standard material, Vienna Standard Mean Ocean Water (VSMOW) (De Wit et al., 1980;Gonfiantini et al., 1993).For brevity, we will use the notation δD (= δD(D, H 2 )) throughout the rest of this paper.The δD values are usually given in per mill (‰).Recent studies showed that the global mean δD value of atmospheric H 2 is about +130 ‰ (Batenburg et al., 2011;Gerst andQuay, 2000, 2001;Rice et al., 2010).
The HH molecule is consumed preferentially over HD during both OH oxidation and soil uptake, with OH oxidation causing a much stronger isotope fractionation effect.Only a few studies have investigated the soil uptake of H 2 with isotope techniques.Gerst and Quay (2001) carried out field experiments in Seattle, USA, and found α soil (= k HD / k HH ) to be 0.943 ± 0.024 (1σ ).Note that k HD and k HH are removal rate constants for HD and HH, respectively.Rahn et al. (2002a) collected air samples from four forest sites in ecosystems of different ages in Alaska, USA, in July 2001 and obtained a similar average value (0.94 ± 0.01).They suggested that α soil depends on the forest maturity, with smaller fractionation for more mature forests.Since the more mature forests showed larger deposition velocity (v d ) of H 2 , they further suggested that lower uptake rates involve greater isotopic fractionation (α soil further from 1) than fast uptake rates.Rice et al. (2011) performed deposition experiments in Seattle and found α soil varying from 0.891 to 0.976, with a mean of 0.934.They found α soil to be correlated with v d , with smaller isotope effects (α soil closer to 1) occurring at higher v d , which agreed with the suggestion by Rahn et al. (2002a).In addition, unpublished experiments from Rahn et al. (2005) yielded α soil = 0.89 ± 0.03 in three upland ecosystems that were part of an Alaskan fire chronosequence.The data suggest that variability in the soil/ecosystem affects α soil but no significant variability of α soil with season was detected.Hitherto, only α soil values from studies in Seattle and Alaska are available, and values from other locations and ecosystems are needed to learn more about the factors influencing α soil .
The δD of H 2 from various surface sources has been reported as about −290 ‰ for biomass burning (Gerst and Quay, 2001;Haumann et al., 2013) and between −360 and −200 ‰ for fossil fuels combustion (Rahn et al., 2002b;Vollmer et al., 2012).So far no field studies have determined the isotopic composition of H 2 emitted from soil.Two laboratory studies examined the isotopic signature of H 2 produced from N 2 fixation.Luo et al. (1991) reported a fractionation factor α H 2 /H 2 O = R(D / H, H 2 ) / R(D / H, H 2 O) = 0.448 ± 0.001 between the H 2 produced from N 2 fixation and the H 2 O used to grow the N 2fixing bacteria for Synechococcus sp. and 0.401 ± 0.002 for Anabaena sp., respectively.Walter et al. (2012) reported α H 2 /H 2 O = 0.363 ± 0.019 for the N 2 -fixing rhizobacterium Azospirillum brasiliensis.It has been proposed that microbiological H 2 consumption and production could modify the thermal isotopic equilibrium between H 2 and H 2 O in lowtemperature hydrothermal fluids (Kawagucci et al., 2010).Compared to the surface sources, H 2 produced from CH 4 and NMHC oxidation is isotopically strongly enriched in deuterium, with δD between +120 and +180 ‰ (Rahn et al., 2003;Röckmann et al., 2003a;Pieterse et al., 2011).
Here we report measurements of the isotopic fractionation factors of H 2 during soil deposition at two different sites in the Netherlands, a forest and a grassland site.For the grassland site we also determine the apparent isotopic composition of H 2 that was simultaneously emitted from soil during the experiment.

Sampling
Air samples were collected from a soil chamber at two locations in the Netherlands (Fig. 1): a grass field around the Cabauw tall tower (51 • 58 N, 4 • 55 E) and a forest site near Speuld (52 • 13 N, 5 • 39 E).Two types of ground cover (grass with and without clover) were sampled at Cabauw, while three types of forest (Douglas fir, beech and spruce) were selected in Speuld.More information about the soil and vegetation type can be found in Beljaars and Bosveld (1997) for the Cabauw site and in Heij and Erisman (1997) for the Speuld site.
Flask samples were filled with air from a soil chamber, using a closed-cycle air sampler (Fig. 2).The soil chamber consisted of two parts: the chamber body with a metal base at the bottom that was inserted about 2 cm into the soil and a removable transparent lid with two connections for air sampling.The chamber had a height of 40 cm, an area of 570 cm 2 and a volume of 22.8 L; the air inside was mixed by a fan.The sampler could hold four flasks installed in series, which could be bypassed independently; the flow and pressure in the flasks were controlled.The air was dried using Mg(ClO 4 ) 2 .After passing through the flasks the air was returned to the soil chamber, which kept the pressure inside the chamber approximately constant during sampling.
Air samples were collected from the chamber in 1 L glass flasks at 0, 10, 20 and 30 min after closing the chamber (time interval changed to 5 min in Speuld because of the faster uptake).The gas flasks (Normag, Ilmenau, Germany) were made of borosilicate glass 3.3 with O-ring-sealed stopcocks made of PCTFE (Kel-F) and covered with a dark hose.Thorough tests have demonstrated that air samples with typical trace gas content are stable in these flasks (Rothe et al., 2004).In the beginning, the whole sampling unit (all lines, connections and flasks) was flushed with ambient air for about 10 min at a flow rate of 2 L min −1 and a pressure of 100 kPa, with all flasks open and the chamber lid open.This initial flushing process was designed to fill the flasks with background air.The air pressure inside the flasks was increased to 200 kPa (180 kPa for Speuld samples) by adjusting the flow control valve and the valves on two pressure gauges (Fig. 2) before chamber closing and then maintained constant during the whole sampling time.The flow rate was maintained at 2 L min −1 at ambient pressure and temperature with a rotameter and the pressure inside the chamber was maintained at 100 kPa during the whole sampling time.The temperature was not recorded during the sampling.After the initial flushing, the first flask was closed and then the chamber was closed as well.Afterwards, the air was flushed from the chamber through three flasks (the first flask was bypassed) and back to the chamber.After 10, 20 and 30 min, the second, third and fourth flasks were closed.
A total of 36 sets of air samples were collected in Cabauw during summer (June, July and August) 2012 and 12 sets were collected in Speuld in September 2012.Each set contains four air samples.In total, 186 valid samples were analyzed for H 2 mole fraction and its deuterium content (six were lost during sampling, transportation and measurement).All the Speuld samples and about half of the Cabauw samples were further used for analysis in this study.The reason why 50 % of the Cabauw experiments were not used is that these experiments showed neither strong H 2 emission nor H 2 uptake and the isotopic signals were weak.Most experiments were conducted with the 22.8 L volume soil chamber as described above, while 10 experiments were conducted with a larger automated soil chamber with a volume of 125 L and a height of 22.5 cm.

Laboratory determination of H 2 mole fraction and deuterium content of air samples
The mole fraction and δD of H 2 were measured with a gas chromatography isotope ratio mass spectrometry (GC/IRMS) setup (Rhee et al., 2004).For H 2 mole fractions, the laboratory working standards are linked to the MPI-2009 scale (Jordan and Steinberg, 2011).The δD values of the laboratory reference gases are indirectly linked to mixtures of synthetic air with H 2 of known isotopic composition, certified by Messer Griesheim, Germany (Batenburg et al., 2011).Most of the samples collected from Cabauw were measured within 2 months after sampling, while the samples from Speuld were kept in a dark storage room for around 4 months before measurement.
The operational principle of the GC/IRMS system is to separate H 2 from the air matrix at low temperature (about 36 K) and measure the HH and HD content with a mass spectrometer.The measurement includes four main steps.
-A glass sample volume (750 mL) is evacuated and subsequently filled with sample air to approximately 700 mbar.This volume is then exposed to a cold head (36 K) of a closed-cycle helium compressor for 9 min.During this stage, all gases except H 2 , helium (He) and neon (Ne) condense.
-The remainder in the headspace of the cold head and sample volume is then flushed with He carrier gas to a pre-concentration trap where H 2 is collected on a 25 cm long, 1/8 inch OD (outside diameter) stainless steel tube filled with fine grains (0.2 to 0.5 mm) of 5 Å molecular sieve, for 20 min.The pre-concentration trap is cooled down to the triple point of nitrogen (63 K) by keeping it in a liquid N 2 reservoir that is further cooled down by pumping on the gas phase.
-After the collection of H 2 , the pre-concentration trap is warmed up to release the absorbed H 2 , which is then cryo-focused for 4 min on a capillary (25 cm long, 0.32 mm inside diameter) filled with 5 Å molecular sieve at 77 K.After that, the cryo-focus trap is warmed up to ambient temperature and the H 2 sample is flushed with He carrier gas onto the GC column (5 Å molecular sieve, ≈ 323 K) where H 2 is chromatographically purified from potential remaining interferences.
-In the end, the purified H 2 is carried by the He carrier gas via an open split interface (Röckmann et al., 2003b) into the IRMS for D / H ratio determination.
More details about the GC/IRMS system and measurement steps can be found in Rhee et al. (2004) and Röckmann et al. (2010).The data correction procedures and isotope calibration are similar to those described in Batenburg et al. (2011).Four reference gases were used to determine the δD values of the samples.Two of them (Ref-1 and Ref-2) with δD values of (+207.0 ± 0.3) ‰ and (+198.2± 0.5) ‰ were calibrated and used previously in Batenburg et al. (2011).The other two new reference gases

Non-linearity of the GC/IRMS system
Ideally, the δD of H 2 measured with the GC/IRMS should not depend on the total amount of H 2 used for analysis, but in practice a dependence of the isotopic composition on the amount of H 2 is observed for low mole fractions.This is called non-linear behavior, and it is a particularly severe limitation for soil uptake studies, since the mole fraction in such samples can decrease by more than an order of magnitude.For comparison, in ambient background air the H 2 mole fraction variations are usually no more than 20 %.
Experiments were carried out with different quantities of air from various laboratory reference bottles with known δD . Difference of δD from the assigned value for different gases including reference gases (Ref1-3) and laboratory flask samples (S1-7).A linear function (y = 54.6x) was fit to the data with peak area between 0.2 and 1.0 Vs (green solid line; the dashed lines represent the 95 % confidence interval of the fit).This function was used to correct the soil experiment data that were measured at low peak areas.
to determine a suitable correction for the non-linear behavior.The measured δD increases with the mass 2 sample peak area, which is proportional to the H 2 quantity in the sample.In the peak area range of 0.2 Vs to 1 Vs this relation can be parameterized by a logarithmic function δD = 54.6 ln (peak area (Vs) −1 ) ‰, which is used as correction function for the measurements at low peak areas (Fig. 3).The linearity correction introduces an additional uncertainty due to uncertainties in the logarithmic fit, particularly at low peak areas.The total assigned uncertainty for each measurement is calculated from the analytical and fitting uncertainty, as a function of peak area (Fig. 4).It is 2 ‰ for ln (peak area (Vs) −1 ) of 1.5 or more (equivalent to more than 600 ppb H 2 in an air sample) but increases to 32 ‰ when ln (peak area (Vs) −1 ) drops to −1.6 (≈ 20 ppb H 2 in air sample).In total, the δD results of 18 Speuld samples that were measured at these low peak areas were corrected with this linearity correction.Possible additional systematic errors (a few ‰ ) may arise from uncertainties in the initially assigned δD values of the commercial calibration gases, changes of these values in the process of creating calibration mixtures with near-ambient H 2 concentration, and the calibration measurements themselves (Batenburg et al., 2011).

Data evaluation
Assuming first order kinetics for H 2 removal and a constant production rate P over the course of a deposition experiment, the time evolution of the mole fraction c of non-deuterated H 2 (HH) inside the soil chamber can be expressed as where k is the first order uptake rate constant of HH.For well-mixed air in the chamber, k = v d / h, where v d is the gross deposition velocity of H 2 and h is the chamber height.The gross deposition velocity is the deposition velocity corrected for production, which is different from the net deposition velocity reported in some studies in the past that showed the effective uptake of H 2 from the atmosphere.The solution of Eq. ( 1) is of the form where c, c i and c e (= P / k) are the mole fractions of HH at time t, initially and at equilibrium, respectively.Therefore, P and k can be obtained by fitting an exponential function to the time evolution of HH inside the chamber.Similarly, we can obtain P and k from the time evolution of HD.
where c , c i , c e (= P / k ), P and k are the corresponding parameters for HD.Equations ( 2) and ( 3) constitute the mass balance model that we used to analyze our data.When k, k , P and P have been determined, α soil and δD soil can be calculated simply as However, fitting an exponential curve to only four sample data yields relatively large errors for k, k , P and P , which propagate to large errors for α soil and δD soil if they are determined directly from Eqs. ( 4) and (5).

Q. Chen et al.: Isotopic signatures of production and uptake of H 2 by soil
In Rice et al. (2011), Eqs. ( 2) and (3) were combined to calculate α soil in the presence of both source and sink of H 2 using c e and c e from the exponential fits:  5).

Flask sampling model
The advantage of sampling with the soil chamber system described in Sect.2.1 was that the pressure in the soil chamber stayed constant even when several large samples (2 L each) were taken.A disadvantage was that the volume of air inside the flasks (8 L of air in total) was considerable compared to the volume of air inside the soil chamber (22.8 L).This had two effects: (1) a significant part of the air was at each time separated from the chamber and thus from the soil production and uptake and, (2) because of the time lag to flush the samples, the air in a flask was not the same as the air in the chamber at the same time.
We built a flask sampling model to derive correction factors that take into account the influence of the flask sampling system.For a given combination of uptake and production rates, the model simulates the evolution of the H 2 mole fraction in two configurations: the soil chamber alone and the soil chamber plus four flasks as in our experiments.The model is described in detail in Appendix A. An example of a simulation is shown in Fig. 5. Compared to the situation without flasks, there is a time lag in the decay of H 2 for both the chamber and the flasks after introducing four flasks in the model.The time lag for the second flask is about 2.5 min.It increases to 5 min for the third flask and is even longer for the fourth flask.
It is obvious that the sampling process strongly affects the uptake rate k app and production rate P app obtained from the direct flask measurements, so we corrected all k app and P app values with the correction coefficients derived from this flask sampling model (Appendix A).For a fixed chamber volume, sample pressure, flow rate and time interval of the flask collection that are all recorded for each experiment, the relationship between the actual uptake rate constant k true and apparent uptake rate constant k app can be obtained (see Appendix A).Under the same sampling conditions for a fixed value of P app , the relationship between actual production rate P true and apparent production rate P app depends on k true (Fig. 10b).
To evaluate the data, we first applied an exponential fit as in Eq. ( 2) to the measured HH mole fractions for the four flasks in each experiment and obtained apparent values k app , P app and c e,app from the fit parameters.Then we used the correction factors derived from the flask sampling model to retrieve true values k true and P true from the apparent values k app and P app .One can obtain k true and P true by applying the same method to HD mole fractions inside four flasks.
To determine α soil , we plotted ln  c 1 −c e,app (Fig. 9), and calculated δD soil,app by use of Eq. ( 5).Then we retrieved δD soil,true by use of the flask sampling model (Fig. 10d).The corresponding correction coefficients for δD soil,app for each net-emission experiment are shown in Table 3.More + c e,app , where c 1 and c e,app are the H 2 mole fractions initially and in equilibrium, and k app is the apparent soil uptake rate constant for H 2 .A similar exponential function is applied to the HD data.Error estimates for H 2 , HD and δD are shown.The connecting lines for δD data are included to guide the eye.information about the retrievals of α soil,true and δD soil,true can be found in Appendix A.
Overall, the sampling effect on δD soil is small (less than 22 ‰).This means that the flask sampling system strongly affects the temporal evolution of HH and HD individually (Fig. 5), and the uptake and production rates derived from flask measurements, but the effects on the computed isotopic signature of the source and sink are relatively small.More de-tails and discussion of the flask sampling model corrections are provided in Appendix A. c 1 −c e,app for all Speuld and Cabauw net-uptake experiments.The slope of the linear fit to the data returns the fractionation factor α soil,app = 0.947 ± 0.004 (95 % CI).Errors in x and y direction for each data point were considered.One outlier ("CBW-18") was not included in the fitting.The 95 % confidence intervals of the fit line are included as dashed lines but largely overlap with the fit line.cluded.The errors for H 2 and HD are about 4 % of the respective mole fraction.The error for δD ranges from 2 to 17 ‰.Some of our Cabauw experiments show net soil emission of H 2 (upper panels) and some show net soil uptake (middle panels), while all Speuld experiments show net uptake of H 2 (lower panels).In the Cabauw net-emission experiments, the increase in H 2 mole fractions is associated with a strong decrease in δD, showing a strongly depleted H 2 source.However, the net-uptake experiments at Cabauw show also a decrease in δD, albeit smaller.In the Speuld experiments, the uptake of H 2 is much faster; the δD increases in the beginning but then decreases again towards the end of the sampling, when the H 2 mole fractions are low.

Temporal evolution of H 2 , HD and δD
As mentioned in the introduction, soil uptake tends to increase δD while soil emission tends to decrease δD of H 2 .The continuous decrease of δD with time in all Cabauw experiments and the eventual decrease of δD in all Speuld experiments clearly show that there is concurrent soil emission even with net uptake.Thus, the equilibrium H 2 concentration in our experiments is not just a threshold concentration where microbial uptake stops, but the isotopic evolution shows that there is an active overlapping emission (Conrad, 1994).

Emission and uptake strength of H 2
The production rate P = P true and uptake rate constant k = k true were obtained by applying exponential fits to the temporal evolution of H 2 and applying the corrections derived from the flask sampling model (Appendix A) to the P app and k app obtained from the exponential fits (Fig. 6).The deposition velocity (v d ), production flux (F p ), initial uptake flux (F u ) and net flux at the beginning of the experiment (F n ) were then calculated as follows: where h, V M and c 1 are the chamber height, standard molar volume (= 22.4 L mol −1 ) and H 2 mole fraction of the first flask, respectively.We note that with our method we derive v d as deposition velocity for the gross uptake, unlike most of the results reported in the literature that just measured net uptake.

Fractionation during soil uptake
Soil uptake and soil emission have opposite effects on the isotopic composition of H 2 and can partly cancel each other.This will lead to additional uncertainty and we expect to obtain the most robust fractionation factor for soil uptake when the soil uptake is larger than the soil emission (Table 1a, b).
The resulting α soil for Speuld (Table 1a) varies from 0.913 to 0.955, with a mean value of 0.937 ± 0.008 (2 SE, n = 12).Error estimates for HH and HD mole fraction at time t and at equilibrium are considered for the final error estimates of α soil for each experiment.
Table 1b shows α soil of the Cabauw net-uptake experiments.It should be noted that the soil-emitted H 2 interferes much more with the fractionation during uptake in these Cabauw net-uptake experiments than in the Speuld experiments, which is illustrated by the consistent decrease in δD in the middle panel of Fig. 6.The derived values for α soil vary from 0.911 to 1.019 with a mean value of 0.951 ± 0.026 (2 SE, n = 8) for these eight selected Cabauw net-uptake experiments.Both the mean and the standard error are higher than in the Speuld experiments (0.937 ± 0.008), but the difference is not significant at the 0.1 confidence level.
To graphically illustrate the calculation of α soil with the mass balance model, we plot ln c 1 −c e,app for all Speuld and Cabauw net-uptake experiments in Fig. 7.A linear fit is applied to all the data and the overall α soil,app is found to be 0.947 ± 0.004 (95 % CI).Applying a correction factor is not straightforward now because this analysis combines the results from different experiments.If we use the average of α soil,true / α soil,app ratios (0.998) for all net-uptake experiments in Table 3 as the correction coefficient for this overall α soil,app , the overall α soil is 0.945 ± 0.004 (95 % CI).
Figure 8 shows α soil as a function of v d for all Speuld experiments and Cabauw net-uptake experiments.The R 2 value is nearly 0 and the p value is 0.53 for the linear regression of all experiments, so no significant correlation between α soil and v d is found.Also, no significant correlation is found when considering the Speuld and Cabauw net-uptake experiments separately.

Isotopic signature of H 2 emitted from soil
As discussed in Sect.2.4, the isotopic signature of H 2 emitted from the soil (δD soil ) can be obtained from the mass balance model.In order to minimize the influence of soil uptake on the computed δD soil and obtain the most robust result, we only consider the Cabauw experiments with strong soil emission and weak soil uptake (c e,app > 1500 ppb).In total, nine Cabauw experiments are selected (Table 2) and a linear fit is applied to the plot of c e,app ln c −c e,app c 1 −c e,app vs. c e,app ln c−c e,app c 1 −c e,app for each experiment (Fig. 9).It can be seen that the linear function fits the data very well for each experiment.The slope of the linear fit yields P app / P app .This P app / P app ratio is used to calculate δD soil,app (Eq.5).After correcting for the flask sampling effects (see Appendix A), the corresponding δD soil values are shown in Table 2.The δD soil value ranges from −629 to −451 ‰, with a mean value of (−530 ± 40) ‰ (2 SE, n = 9), which is very D depleted, but still considerably enriched relative to the value around −700 ‰ expected for thermodynamic equilibrium between H 2 and H 2 O (Bottinga, 1969).

Emission and uptake strength of H 2
The deposition velocity v d is a measure of the strength of soil uptake.Both microbial removal and diffusion can affect v d , and they can both be influenced by the temperature and moisture content of the soil (Ehhalt and Rohrer, 2013a, b).On average, the v d obtained in this study is larger in the forest region (Table 1a) than in the grass/clover region (Table 1b  and 2), in agreement with the conclusion from Ehhalt and Rohrer (2009).
The v d of (0.06 ± 0.03) cm s −1 found in our Cabauw netemission experiments (Table 2) is similar to those reported in Conrad and Seiler (1980) (0.07 cm s −1 , both grass and clover) and Gerst and Quay (2001) (0.04 cm s −1 , grass), while the v d of (0.13 ± 0.06) cm s −1 in Cabauw net-uptake experiments (Table 1b) is larger than those studies with similar soil cover but close to values of 0.12 to 0.14 cm s −1 found in savanna soil (Conrad and Seiler, 1985).The stronger soil uptake in Speuld forest ((0.17 ± 0.02) cm s −1 ) agrees well with the beech forest results (0.06 to 0.22 cm s −1 ) in Förstel (1988) and Förstel and Führ (1992).However, other studies at forest sites cited in Ehhalt and Rohrer (2009) showed lower v d than our Speuld results.We note here that the v d values reported in Conrad andSeiler (1980, 1985) were gross deposition velocities while those reported in Gerst and Quay (2001) were net deposition velocities.The specific method used to obtain v d was not documented in the other studies.v d values obtained from our experiments are gross deposition velocities.
The net-uptake flux F n in our Speuld experiments and Cabauw net-uptake experiments is much larger than those found in Smith-Downey et al. (2008).They found a F n of about −8 nmol m −2 s −1 for the forest, desert and marsh, which was similar to that for loess loamy soil in Schmitt et al. (2009).Our results are within the F n range found in the mixed wood plains by Constant et al. (2008b) and the Harvard forest by Meredith (2012).Previously at our Cabauw site, Popa et al. (2011) obtained a F n of only −3 nmol m −2 s −1 by using the radon tracer method.However, the Cabauw net-uptake experiments used for this evaluation were from selected places where uptake was strong, while the results in Popa et al. (2011) represented the overall uptake in the footprint of the Cabauw site, which is a much larger area (tens of km 2 ).Khdhiri et al. (2015) performed microbiological analyses on soil samples from the Cabauw and Speuld sites in order to find the drivers of soil H 2 uptake.They observed that the H 2 uptake rate under standard incubation conditions was significantly lower for the Cabauw soil samples than for the Speuld ones, which is consistent with our findings.The main factors that explained the differences were the relative abundance of high-affinity H 2 -oxidizing bacteria and the soil carbon content, both lower on average for the Cabauw site.The emission of H 2 from the soil is large for the Cabauw net-emission experiments, with F n ranging from 13.7 to 150.2 nmol m −2 s −1 and a median value of 41.0 nmol m −2 s −1 (Table 2).One experiment, "CBW-28", shows unusually high emission, with H 2 increasing to 3010 ppb within 30 min.In comparison, Conrad and Seiler (1980) found a F n of 23-32 nmol m −2 s −1 for a clover field.Except for the experiments "CBW-28" and "CBW-31", our Cabauw net-emission experiments are close to the F n found by them.The variability in F n could be attributed to different N 2 fixation flux in our experiments, which could be affected by both spatial density of N 2 fixation organisms and their N 2 fixation activities.The N 2 fixation activity could be regulated by various factors including temperature, moisture, light availability and carbon storage (Belnap, 2001), which were not measured are therefore not discussed here.

Fractionation during soil uptake
Fractionation during soil uptake of H 2 can happen during the diffusion into the soil and due to microbial removal within the soil.To further investigate the factors determining α soil , information about the soil cover is provided in Table 1a, b.It is evident that no large differences exist between the Douglas fir, spruce and beech sites, i.e., the variability between sites is similar to the variability within sites.The small number of experiments impedes examining the possible small differences between sites.In order to investigate the diffusion effect, we removed the soil cover in experiments "SPU-8" and "SPU-12" at the same place of experiments "SPU-7" and "SPU-11".The removal of leaves ("SPU-8") and needles ("SPU-12") increased α soil by ≈ 0.014, thus towards smaller fractionation, which indicates that diffusion contributes to the fractionation.As v d also increases when the soil cover is removed, faster deposition is associated with smaller fractionations in these experiments, which is similar to the results from Rice et al. (2011).
The α soil for the Cabauw net-uptake experiments is higher and more scattered than that for the Speuld experiments (0.951 ± 0.026 vs. 0.937 ± 0.008).This could be caused by the interference of D-depleted H 2 from the strong soil emission in Cabauw, which may not be perfectly captured via the mathematical models applied.As can be seen from the strong decline of δD with time in the middle panel of Fig. 6, though soil uptake of H 2 dominates for the Cabauw net-uptake experiments, soil production is still considerable.If part of the source signature is not taken into account properly and appears in α soil , then α soil will be larger, because soil production tends to decrease δD of H 2 .This could explain why α soil is even larger than 1 in "CBW-7".
The overall α soil (0.945) obtained by plotting ln c −c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c e,app and applying the average correction factor for all the Speuld and Cabauw net-uptake experiments is similar to the results of 0.943 ± 0.024 from Gerst and Quay (2001), 0.94 ± 0.01 from Rahn et al. (2002a), and the overall α soil (0.943) from Rice et al. (2011).Rice et al. (2011) suggested that the overall α soil is more accurate as it is less susceptible to outliers.We argue here that the average α soil of all individual experiments in Speuld (0.937) and Cabauw (0.951) is representative for a spatially averaged fractionation factor for those sites and is useful for, e.g., characterizing the phenomenon and comparing with other fractionation results.If all experiments are included in one fit, their weight for determining the slopes depends on how much H 2 has been removed, so experiments with a lower c e,app have a larger weight than experiments with a higher c e,app (i.e., experiments with a higher v d have a larger weight than experiments with a lower v d ).The fractionation factor obtained by fitting all data together is therefore representative for a flux weighted average, which is the relevant number for the global atmospheric isotope budget.Rice et al. (2011) proposed a significant positive correlation between α soil and deposition velocity v d in their soil uptake experiments.Figure 8 shows that no significant correlation between α soil and v d is found when considering all Speuld and Cabauw net-uptake experiments.The uptake rate is much stronger in the Speuld experiments (v d ≈ 0.17 cm s −1 ) than in the study of Rice et al. (2011) (v d ≈ 0.04 cm s −1 ), but the α soil is virtually identical (0.937 vs. 0.934).Therefore, when the results from both studies are combined, the correlation reported in Rice et al. (2011) between α soil and v d disappears.We suggest that a positive correlation between α soil and v d may exist for a specific site where microbial species are similar.This was suggested from the simultaneous increase of both α soil and v d in two experiments ("SPU-8" and "SPU-12"), when soil cover was removed at the same sampling location, as mentioned in Sect.4.2.

Relationship between α soil and v d
We conclude that there is certainly not one single correlation between α soil and v d that holds globally and the soil type might play an important role.Measurements at more sites may be needed to positively confirm whether local positive correlations between α soil and v d are common.

δD of H 2 emitted from the soil
The present study is the first field study to report δD of H 2 emitted from soils.The δD soil values (−629 to −451 ‰) shown in Table 2 are less depleted than the H 2 in isotopic equilibrium with water (≈ −700 ‰).Previous observations from environmental H 2 production yielded a δD of −628 ‰ for two seawater samples (Rice et al., 2010), −778 ‰ for a termite headspace sample and −690 ‰ for two headspace samples from a eutrophic water pond (Rahn et al., 2002b).Kawagucci et al. (2010) proposed that microbiological H 2 consumption and production could destroy the thermal isotopic equilibrium between H 2 and H 2 O in low-temperature hydrothermal fluids.Luo et al. (1991) and Walter et al. (2012) found fractionation factors of 0.448, 0.401 and 0.363 for H 2 generated from water by different N 2 -fixing bacteria in the laboratory.
In order to compare our δD soil with the fractionation factors between H 2 and H 2 O found by Luo et al. (1991) and Walter et al. (2012), we converted their fractionation factors to δD(H 2 ) by assuming the δD(H 2 O) to be the same as that of global rainwater (−37.8 ‰, Hoffmann et al., 1998).This results in δD(H 2 ) values of −651 to −569 ‰ for their N 2fixing bacteria.Although the ranges are considerable, it appears that the mean δD soil (−530 ‰) obtained in our field study is even higher than what was found for nitrogenasederived H 2 in laboratory experiments.
It is known that H 2 produced by biogenic N 2 fixation can be largely recycled within the soil before entering the atmosphere (Evans et al., 1987;Conrad andSeiler, 1979, 1980).If this uptake process within the soil tends to increase the δD of the remaining H 2 , as the soil uptake process for atmospheric H 2 does, then the H 2 entering the atmosphere will be less D depleted than pure biogenic H 2 .However, if the fractionation factor of removal in the soil is similar to that determined from the net-uptake experiments (≈ 0.94), a large fraction (f in ) of H 2 needs to be removed in the soil before release to explain the D-enriched δD soil compared to the values reported in the literature.The fraction f in could in principle be estimated from the Rayleigh equation: where α in is the fractionation constant of H 2 within soil, δD 0 is the δD value of initial H 2 produced by N 2 -fixers, and δD soil is the δD value of remaining H 2 emitted from soil that is measured in our experiments.By assuming α in = 0.945 (overall fractionation factor as determined in our deposition experiments), δD soil = −530 ‰ (averaged δD soil of Cabauw net-emission experiments) and δD 0 = −611 ‰ (averaged of δD(H 2 ) derived from laboratory experiments in Luo et al. (1991) and Walter et al., 2012), we would obtain f in = 0.97.That is, 97 % of H 2 produced by N 2 fixation would be removed within soil before entering atmosphere.This is higher than the estimate from Conrad and Seiler (1979), which was from 30 to 90 %.It should be noted that the estimation of f in is very uncertain due to the lack of information about α in and δD 0 .By using the lower limit of α in (0.911) in our experiment and the upper limit of δD 0 Q.Chen et al.: Isotopic signatures of production and uptake of H 2 by soil (−569 ‰) in Luo et al. (1991) and Walter et al. (2012), we calculate a lower limit of f in to be 0.62.The upper limit of f in is 1.00 when α in approaches 1.For these calculations we have used a δD soil of −530 ‰ , but it varies from −629 to −451 ‰ in our experiments.We cannot rule out cases with δD soil = δD 0 , which yields a f in of 0. The deuterium enrichment in the emitted H 2 , compared to the value expected in isotopic equilibrium with water, could also be caused by different fractionations induced by different enzymes and/or a potentially enriched deuterium content of the substrate water available for H 2 production in Cabauw.H 2 is generated from the reduction of hydrogen ions (H + or D + ) in intracellular water (Yang et al., 2012).It was found that the isotopic composition of intracellular water can be different from that of extracellular water due to metabolic processing (Kreuzer-Martin et al., 2006).Due to the differences in H bonding and hydrogen ion transport, the fractionation may be different for different microbe species, which could result in different isotopic signatures of the produced H 2 .Measurements of the isotopic composition of produced H 2 may be a tool to investigate such effects.
Finally, we note that if our Cabauw net-emission experiments are analyzed with a simple Keeling plot approach (i.e., without considering uptake), the y axis intercept is −703 ‰.We know from the temporal evolution of H 2 , HD and δD that this model is not adequate and that uptake was significant in our experiments, so a simple Keeling plot analysis can be misleading if uptake is not considered.

Conclusions
This study investigated the isotope effects associated with the production and uptake of atmospheric H 2 by soil.Our aim was to quantify the fractionation factor α soil for H 2 deposition and the isotopic signature of H 2 emitted from the soil (δD soil ) from experiments carried out at Speuld and Cabauw.
The experiments covered a wide range of conditions from situations with very strong net H 2 uptake to situations with very strong net H 2 emission.The superposition of deposition and production made the analysis with simple models like Rayleigh plot and Keeling plot impossible.Therefore, the mass balance model suggested by Rice et al. (2011) was used for evaluation.
The mean fractionation factors α soil are 0.937 ± 0.008 for the Speuld forest soil experiments and 0.951 ± 0.026 for the Cabauw grassland experiments, which are representative for a spatial average and useful for comparisons with other fractionation studies.The Cabauw results may be affected by the relatively strong concomitant soil emissions.The overall α soil by considering all net-uptake experiments is 0.945 ± 0.004, which is representative for a flux weighted average and useful for global isotope budget estimates.The fractionation factors found in this work are in good agreement with previous studies.
No significant correlation between α soil and deposition velocity v d was found while considering all of our experiments.The v d were overall much larger in our study than those in Rice et al. (2011) and we obtained similar values for α soil .This demonstrates that the positive correlation that was found previously does not hold globally.From two of our Speuld experiments, α soil increased after the removal of leaves or needles above the soil.This indicates that there may be a fractionation associated with diffusion through the surface layer of leaves or needles during soil uptake, but more experiments are required to confirm this.
The isotopic analysis clearly showed that the net uptake was always a superposition of a larger gross uptake and a gross emission flux.In Cabauw, the emission strength was very large at locations where clover was present.Using a simple mass balance approach, the isotopic composition of the emitted H 2 was determined to be (−530 ± 40) ‰, which is significantly higher than the value expected for H 2 O-H 2 isotope equilibrium.Although limited, other published data on H 2 produced biologically via nitrogenase show also a tendency to more enriched values.An additional isotope enrichment in our field soil study could originate from fractionation during the recycling of H 2 within the soil before it enters the atmosphere.

Appendix A A1 Flask sampling model
A mathematical model is used to simulate the sampling and to correct for the effects of the flask sampling method on the values of uptake rate constant (k), production rate (P ), fractionation factor (α soil ) and isotopic signature of H 2 produced from soil (δD soil ).We start with a pair of known (true) uptake and production rates and simulate the evolution of the mole fractions of H 2 and HD in the flasks and chamber.From the modeled mole fractions we calculate the apparent uptake and production rates and derive the correction needed to obtain the true uptake and production rates from measurement of the apparent rates in actual experiments.

A1.1 Mathematical description of the flask sampling model
The sampling setup is shown in Fig. 2 of the main paper.
After 10 min of flushing, the chamber and the flasks contain ambient air with the prevailing H 2 and HD mole fractions.In the following we denote c 1 (t), c 2 (t), c 3 (t), c 4 (t) and c 0 (t) the H 2 mole fractions for the first, second, third and fourth flask and the chamber, respectively.The moment when the first flask and the chamber lid are closed is considered the starting time of the experiment (t = 0).From this point on, only the chamber and the second, third and fourth flask are connected, and the initial H 2 mole fraction inside them is c 0 (0) = c 2 (0) = c 3 (0) = c 4 (0) = c 1 .We start a simulation with an input uptake rate constant (k true ) and an input production rate (P true ).The simulation of the flask sampling is based on Eqs.(A1)-(A4) shown below.
Assuming that the air in each flask and in the chamber is well mixed during the entire sampling process, the time evolution for the second flask c 2 (t), third flask c 3 (t), fourth flask c 4 (t) and the chamber c 0 (t) in the first 10 min after starting the experiment can be expressed as where V and V are the air volumes of the flask and chamber, and f is the flow rate.These differential equations are solved using the Matlab ODE solvers at time steps of 0.01 min.The input parameters are c 0 (0), P true , k true , V , V and f .For each time step the solvers calculate the hydrogen flux into and out of the chamber and each flask, as well as the new mole fractions there.
After 10 min, the second flask is closed and now contains air with mole fraction c 2 = c 2 (10 min).From this point on, only the chamber, the third and the fourth flask are connected, and the time evolution of the mole fractions can be expressed as After another 10 min of sampling, the third flask is closed c 3 = c 3 (20 min), and only the chamber and the fourth flask are connected.Then, the time evolution for the fourth flask and the chamber can be expressed as The H 2 mole fraction inside the chamber and the fourth flask at time t = 30 min is c 0 (30) and c 4 (30).
In the end, a set of four flasks with mole fractions c 1 (0), c 2 (10 min), c 3 (20 min) and c 4 (30 min) is obtained.By fitting this set of four data points with an exponential function c = ae −k app t + c e,app (see Eq. 2 in the main paper), we can obtain the apparent soil uptake rate constant (k app ) and equilibrium concentration (c e,app ) and further calculate apparent production rate (P app = k app c e,app ).These apparent rates k app and P app are different from the assumed true rates k true and P true .The flask sampling model enables us to establish a relation between k app and P app and k true and P true , so that k true and P true can be derived from k app and P app in actual experiments, where the true values are unknown.To accomplish this, simulations are carried out with a wide range of values for k true and P true , and a corresponding data set of k app and P app is generated.Similarly, we use a new set of input uptake rate constant k true and production rate P true for HD and generate a corresponding data set of k app and P app .

A1.2 The correction coefficients for k and P
Here we discuss an example of the relationship between k true and k app for the setup used in some Cabauw experiments (V = 22.8 L, f =2 L min −1 and t = 10 min).The pressure inside the flasks is 200 kPa and the pressure inside the chamber is 100 kPa.The relationship between k true / k app and k app is shown in Fig. 10a.The ratio k true / k app varies between 1.45 to 1.61 for our k app range of 0.04 to 0.30 min −1 .This relationship does not depend on P true (with P true varying from 50 to 650 ppb min −1 ).An additional uncertainty can arise from incorrect timing of the flask sampling, but sampling times should be correct within few seconds, which may lead to an additional uncertainty of below 1 %.The uncertainty of the Q.Chen et al.: Isotopic signatures of production and uptake of H 2 by soil flow rate obtained from the rotameter due to variations in ambient pressure and temperature that were not recorded is less than 4 %, and the effect on the ratio k true / k app ratio is below 1 %.We can retrieve k true by multiplying k app with the modeled value of k true / k app for each experiment.The ratio k true / k app for each experiment is shown in Table 3.It depends on experimental setup and k app of each experiment, with a range of 1.177 to 1.589.
After retrieving k true from k app , we investigate the relationship between P true / P app and P app for a fixed value of k true (Fig. 10b).The ratio P true /P app depends slightly on P app and k true , ranging from 1.40 to 1.59 for a wide P app range of 30 to 450 ppb min −1 and a wide k true range of 0.05 to 0.45 min −1 .As for the correction of k, uncertainties arising from incorrect timing of the flask sampling and from pressure and temperature variations and their effect on the flow rate lead to additional uncertainties of P true / P app ratio below 1 %, which are not considered.We can retrieve P true by multiplying P app with P true / P app for each experiment after having determined k true from k app .The ratio P true / P app for each experiment is shown in Table 3 and depends on the experimental setup, P app and k app of each experiment.It ranges from 1.152 to 2.759 for most experiments, with an exception of 7.472 for experiment SPU-2 where a very small P app of 0.67 ppb min −1 is found.Although the ratio P true / P app of experiment SPU-2 is high, P true of SPU-2 is still smaller than the rest of the experiments.P true / P app ratios for experiments SPU-10 and SPU-11 are null because these two experiments show a P app of 0.

A1.3 The correction coefficients for α soil and δD soil
In our experiments, the uncertainties of k app and k app derived from exponential fits to the time evolution of HH and HD are rather large, which results in a large scatter of α soil,app if α soil,app is calculated directly as k app / k app .Thus, we obtained α soil,app by plotting ln c −c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c e,app (Fig. 7) for each experiment which yields a smaller scatter for α soil,app .
Correction coefficients to convert α soil,app to α soil,true are obtained using the flask sampling model by comparing α soil,true used as input for the model run to α soil,app derived from the plot of ln   10c shows α soil,true / α soil,app as a function of α soil,app for a wide δD soil,true range of −750 to −250 ‰ with the sampling setup described above (V = 22.8 L, f = 2 L min −1 and t = 10 min) for k true = 0.25 min −1 and P true = 50 ppb min −1 .In this case the correction factor α soil,true / α soil,app varies from 0.98 to 1.00 for a α soil,app range of 0.90 to 1.00, and it does not depend on δD soil,true .Thus, after retrieving k true and P true as described in Sect.A1.2, we can retrieve α soil,true from α soil,app for each experiment.The correction factors range from 0.984 to 1.007, depending on the experimental setup and α soil,app of each experiment (Table 3).
Similarly, in our experiments, the uncertainties of P app and P app derived from exponential fits of time evolution of HH and HD are large, which results in a large scatter of δD soil,app if δD soil,app is calculated directly from these P app and P app .We therefore obtained the ratio P app / P app by plotting c e,app ln c −c e,app c 1 −c e,app vs. c e,app ln c−c e,app c 1 −c e,app (Fig. 9) and calculated δD soil,app from Eq. ( 4).This yielded smaller scatter for δD soil,app .After retrieving k true , P true and α soil,true as described above, we used the flask sampling model again to derive correction factors by comparing δD soil,true used as model input with δD soil,app obtained from c e,app ln c −c e,app c 1 −c e,app vs. c e,app ln c−c e,app c 1 −c e,app of the model output and to retrieve δD soil,true from δD soil,app for each experiment.Figure 10d shows (δD soil,true +1) / (δD soil,app +1) as a function of (δD soil,app +1) for a α soil,true range of 0.90 to 1.00 with the sampling setup described above (V = 22.8 L, f =2 L min −1 and t = 10 min) for k true = 0.25 min −1 and P true = 50 ppb min −1 .The ratio (δD soil,true +1) / (δD soil,app +1) changes from 0.99 to 1.05 for a wide (δD soil,app +1) range of 0.25 to 0.65.It can be seen that the (δD soil,true +1) / (δD soil,app +1) ratio depends slightly on α soil,true at a fixed (δD soil,app +1), with a maximum difference of about 1 % for a α soil,true range of 0.90 to 1.00.The ratio (δD soil,true +1) / (δD soil,app +1) for each net-emission experiment is shown in Table 3, ranging from 1.007 to 1.048.The largest difference between δD soil,true and δD soil,app is 21 ‰ for CBW-8.The mean δD true and δD app for these netemission experiments are −530 and −538 ‰, respectively.
In conclusion, the effect of the flask sampling process is relatively small for α soil and δD soil but considerable for the uptake rate constants k and k and emission rates P and P .The flask sampling model allows us to derive corresponding corrections that have been applied to correct for the bias introduced by the flask sampling system.
Publications on behalf of the European Geosciences Union.13004 Q. Chen et al.: Isotopic signatures of production and uptake of H 2 by soil

Figure 1 .Figure 2 .
Figure 1.The location of the two sampling sites (Cabauw and Speuld) in the Netherlands, as well as the plant species there.
were calibrated vs. Ref-1 and Ref-2.The δD value of Ref-3 was (−183 ± 2.4) ‰.Ref-4 was a fre-quently measured reference gas that was measured usually about five times per sequence of measurement, while other three reference gases were measured about one to three times per sequence of measurement.The δD value of Ref-4 dropped linearly with time from −115 to −157 ‰ between 1 June 2012 and 15 February 2013, while the other three reference gases were stable.

Figure 4 .
Figure 4. Calculated total assigned uncertainty of δD (consisting of analytical uncertainty and uncertainty arising from the linearity correction) for air samples with ln(peak area) ranging from −1.6 to 1.5.
) α soil = k / k can be obtained by plotting ln c −c e c i −c e vs. ln c−c e c i −c e and fitting a linear function.In the absence of soil emission (c e = c e = 0), Eq. (6) collapses to the well-known Rayleigh fractionation equation that is used to quantify the isotope fractionation during single stage removal processes in the absence of sources.For the high emission measurements, where production overwhelms consumption, we use the relations c e = P / k and c e = P / k and obtain P / P from the slope of c e ln c −c e c i −c e against c e ln c−c e c i −c e .Then δD soil is calculated from Eq. (

Figure 5 .
Figure5.Results of the flask sampling model with the following parameters: k = 0.1 min −1 , P = 10 ppb min −1 and c 1 (t = 0) = 530 ppb.The figure shows the evolution of H 2 mole fraction in the chamber (green curve), in flask 2 (blue curve), flask 3 (red curve) and flask 4 (magenta curve) as a function of time and what would be expected for a chamber without flasks (black curve).Flask 1 was closed before closing the chamber (at time 0 when all volumes contained the same air).

c
−c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c e,app (Eq.6, Fig.7) and obtained α soil,app from the slope of the linear regression.Here, c and c are HH and HD mole fractions in each of the four flasks; c 1 and c 1 are HH and HD mole fractions of the first flask; c e,app and c e,app are apparent HH and HD equilibrium mole fractions obtained from the exponential fits of HH and HD mole fractions inside the four flasks.We determined the relationship (Fig.10c) between α soil,true and α soil,app obtained from ln c −c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c

Figure 6 .
Figure 6.Time evolution of H 2 , HD and δD in Cabauw (upper and middle panels) and in Speuld (lower panel) for representative experiments.HD is calculated from H 2 and δD.The H 2 data are fitted with an exponential function of the form c = c 1 − c e,app e −k app t+ c e,app , where c 1 and c e,app are the H 2 mole fractions initially and in equilibrium, and k app is the apparent soil uptake rate constant for H 2 .A similar exponential function is applied to the HD data.Error estimates for H 2 , HD and δD are shown.The connecting lines for δD data are included to guide the eye.

Figure 6 Figure 7 .
Figure6shows examples for the temporal evolution of H 2 , HD and δD in Cabauw and Speuld, with error estimates in-

Figure 8 .Figure 9 .
Figure 8. Correlation between α soil and v d for all Speuld experiments and Cabauw net-uptake experiments.The errors for α soil were taken fromTable 1.

c
−c e,app c 1 −c e,app vs. ln c−c e,app

c
−c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c e,app of the output values, like in the experiments. Figure e,app using the flask sampling model (see Appendix A1.3).The correction coefficients for each experiment are given in Table3.Similarly, we obtained P app /P app by plotting c e,app ln c −c e,app c 1 −c e,app vs. c e,app ln c−c e,app

Table 1 .
The deposition velocity (v d ), fractionation factor (α soil ) as well as its error estimate and soil cover information for each Speuld experiment (a) and Cabauw net-uptake experiment (b).The SD represents standard deviation and SE represents standard error.The errors of α soil represent the 95 % confidence interval (CI) for α soil,app obtained from ln c −c e,app c 1 −c e,app vs. ln c−c e,app c 1 −c e,app .

Table 2 .
Net flux, deposition velocity and δD soil (including error) obtained from the mass balance model for the net H 2 emission experiments.