The FLUXNET2015 dataset (Pastorello et al., 2017) aggregates measurements of land–atmosphere fluxes of CO2, H2O, momentum, and heat at sites around the world (http://fluxnet.fluxdata.org/data/fluxnet2015-dataset; last access: 24 February 2017). Measurements are made with the eddy covariance method on towers above vegetation canopies (Baldocchi et al., 2001; Anderson et al., 1984; Goldstein et al., 2000) with consistent gap filling (Reichstein et al., 2005; Vuichard and Papale, 2015) and quality control across sites (Pastorello et al., 2014). Flux and meteorological quantities are reported in half-hour intervals. We analyze data from all sites in the United States and Europe in the FLUXNET2015 Tier 1 dataset. This analysis is restricted to the US and Europe because these regions have dense O3 monitoring networks, described below. There are 103 sites meeting these criteria, all listed in Table S1 in the Supplement with references to full site descriptions. Three of these sites – Blodgett Forest, Harvard Forest, and Hyytiälä Forest – measure O3 flux with the eddy covariance method, which we will use in Sect. 3 to evaluate our methods.

SynFlux aims to constrain O3 deposition and stomatal uptake as much as possible from measured water, heat, and momentum fluxes, in contrast to other methods (Finkelstein et al., 2000; Mills et al. 2011; Schwede et al., 2011; Yue et al., 2014) that rely more heavily on atmospheric models or parameterizations of stomatal conductance. From the eddy covariance measurements, we derive the resistance components of Eq. (2) using methods similar to past studies (Kurpius and Goldstein, 2003; Gerosa et al., 2005; Fares et al., 2010). The aerodynamic and quasi-laminar layer resistances (ra and rb, respectively) are derived from measured wind speed, friction velocity, and fluxes of sensible and latent heat every half hour using Monin–Obukhov similarity theory (Foken, 2017). The stomatal conductance for O3 (gs) is derived from the measured water vapor flux and meteorological data every half hour with the inverted Penman–Monteith equation (Monteith, 1981; Gerosa et al., 2007). Supplement S1 provides further details of the resistance and conductance calculations. Some studies instead calculate gs from gross primary productivity (Lamaud et al., 2009; El-Madany et al., 2017), but that method is less widely used than the Penman–Monteith approach adopted here. The Penman–Monteith method of calculating stomatal conductance has been successfully applied across FLUXNET sites previously (Medlyn et al., 2017; Novick et al., 2016; Knauer et al., 2017; Lin et al., 2018). Those studies and others caution that, since evapotranspiration measurements include evaporation from ground, the stomatal conductance could be overestimated. While there are methods for quantifying and removing the evaporative fraction of evapotranspiration from eddy covariance data (Wang et al., 2014; Zhou et al., 2016; Scott and Biederman, 2017), a more common approach is to restrict analysis to conditions when transpiration dominates. We follow this second approach, analyzing only daytime data during the growing season, and use filtering criteria similar to Knauer et al. (2017). We define daytime as Sun elevation angle above 4∘ and the growing season as days when gross primary productivity (GPP) exceeds 20 % of the annual maxima in GPP. To avoid complications to the Penman–Monteith equation from wet canopies, we exclude times when dew may be present (RH > 80 %), and days with precipitation (> 5 mm). We also exclude the top and bottom 1 % of gs values, which include many unrealistic outliers (e.g., gs>0.5ms-1). Figure 1 shows the mean stomatal conductance during the growing season at all sites.

The terms in Eqs. (1)–(3) that cannot be derived from FLUXNET2015 measurements are O3 mole fraction and non-stomatal conductance. The O3 mole fraction is taken from a gridded dataset of hourly O3 measurements that spans the contiguous United States and Europe (Schnell et al., 2014). This dataset has 1∘ spatial resolution, so some differences from measured O3 abundances at individual sites are inevitable. Schnell et al. (2014) estimated these errors to be 6–9 ppb (rms) or about 15 % of summer mean O3 in the US and similar in Europe. Figure 2 shows that the daytime gridded O3 concentrations correlate well with observations at three flux tower sites where O3 was measured (R2=0.63–0.87) and have modest negative bias (5–10 ppb, -12 % to -28 %), consistent with the accuracy reported by Schnell et al. (2014). We use the Zhang et al. (2003) parameterization of non-stomatal conductance, which accounts for O3 deposition to leaf cuticles and ground and was developed from measurements in the eastern United States. The parameterization requires leaf-area index, which we take from satellite remote sensing (Claverie et al., 2014, 2016), snow depth, which we take from MERRA2 reanalysis (GMAO, 2015; Gelaro et al., 2017), and standard meteorological data provided by FLUXNET2015. Uncertainties in these variables are described in Sect. 2.4. Performance of the non-stomatal parameterization is examined in Sect. 3.2.

Figure 3 shows the stomatal O3 flux at each site calculated with Eq. (3), and then averaged over the growing season. Figure S1 shows the corresponding total O3 flux (Eq. 1). We refer to these products as the “synthetic” total O3 flux (FO3syn) and synthetic stomatal O3 flux (Fs,O3syn). Superscript “syn” distinguishes these synthetic quantities from the FO3Fs,O3 observed total O3 flux (FO3obs) and observation-derived stomatal O3 flux (Fs,O3obs), which are only available at a few sites. Together, we refer to FO3syn and Fs,O3syn as SynFlux. In total, the measurements required to calculate Fs,O3syn are O3 mole fraction, sensible and latent heat fluxes, friction velocity, temperature, pressure, humidity, canopy height, and leaf-area index. There are 43 sites in the US and 60 sites in Europe within the FLUXNET Tier 1 database with sufficient measurements to calculate Fs,O3syn.

We evaluate SynFlux and its inputs at three sites where O3 flux measurements are available: Harvard Forest, Massachusetts, United States (Munger et al., 1996); Blodgett Forest, California, United States (Fares et al., 2010); and Hyytiälä Forest, Finland (Keronen et al., 2003; Mammarella et al., 2007; Rannik et al., 2009). These forest sites sample a range of environmental and ecosystem conditions summarized in Table 1. All three sites have at least 6 years of half-hourly or hourly flux measurements. Two sites are evergreen needleleaf forests (Blodgett and Hyytiälä), while one is a deciduous broadleaf forest containing some scattered stands of evergreen needleleaf trees (Harvard). Climate also differs across these sites. Blodgett Forest has a Mediterranean climate with cool, wet winters and hot, dry summers. Hyytiälä and Harvard forests have cold winters and wetter summers, with Harvard Forest being the warmer of the two.

Harvard Forest water vapor flux measurements were recalibrated for this work based on matching water vapor mixing ratio measured by the flux sensor to levels calculated from ambient relative humidity and air temperature, resulting in a 30 % increase in evapotranspiration during the 1990s and no change since 2006. In addition, we remove sub-canopy evaporation from the measured water vapor flux before the Penman–Monteith calculation. Based on past measurements at these sites, the sub-canopy fraction of evapotranspiration is 20 % at Hyytiälä Forest and 10 % at Harvard Forest in summer (Moore et al., 1996; Launiainen et al., 2005). We are unable to make this correction at all FLUXNET sites since water vapor flux is typically measured only above canopy.

At these three sites, observation-derived vd, gns, and Fs,O3 can be derived from the FO3 measurements with methods that differ slightly from Sect. 2.1. O3 deposition velocity is inferred from measurements of O3 concentration and flux via vd=FO3nχ-1. Resistance or conductance terms ra, rb, and gs are calculated as described in Sect. 2.1, and then both canopy and non-stomatal conductance are derived from observations via gc=vd-1-ra-rb-1 and gns=gc-gs, respectively. With those values, Eq. (3) gives the observation-derived stomatal O3 flux. Synthetic and observation-derived stomatal O3 fluxes are both calculated with Eq. (3) and use the same observation-derived gs, ra, and rb but different values of gns,vd, and O3 mole fraction.

The FLUXNET2015 dataset uses gap filling for most flux and meteorological measurements (Vuichard and Papale, 2015), but not for friction velocity (u∗), which is required to calculate vd and Fs,O3syn. Filling this one variable would significantly reduce the fraction of missing data in our analysis. Monin–Obukhov similarity theory predicts that friction velocity will be proportional to wind speed in the surface layer, for a given roughness length and stability regime (Foken, 2017). On this basis, we regress the available friction velocity measurements against wind speed and net radiation (a proxy for stability) separately for each site and month (a proxy for vegetation roughness). This gap filling was possible at 91 sites that report net radiation measurements.

The predicted friction velocities from the regression model are correlated with available observations (R2 > 0.5) and have minimal mean bias (±10 %) at 85 out of 91 eligible sites (Fig. S3 in the Supplement), with most sites (63 out of 91) showing strong correlations (R2 > 0.7). At the remaining six sites with lower regression model performance (R2 < 0.5) we do not use u∗ gap filling. The u∗ gap filling increases the number of Fs,O3syn estimates by 1 %–20 %. Time periods with u∗ gaps have no significant bias in meteorological conditions (e.g., mean wind speed, radiation, energy fluxes) compared to periods with u∗ measurements. As a result, the differences in monthly mean Fs,O3syn with and without gap filling are small (10 % rms). So, although the u∗ gap filling is a potential source of uncertainty, the Fs,O3syn estimates are robust. The following analysis will use the gap-filled data, but our results do not change in any meaningful way if we use the unfilled data.

We quantify the errors in FO3syn, Fs,O3syn, and all other calculated variables from the measurement uncertainties using standard techniques for propagation of errors through all equations (see Supplement S2). This method provides the uncertainty, quantified as the standard deviation, of each variable in each half-hour interval. The error analysis reveals that Fs,O3syn and other derived quantities have uncertainties that change from hour to hour by 2 orders of magnitude (Fig. S2). In addition, many extreme values of Fs,O3syn, gs, and other variables have very large uncertainties. We retain these outliers in our analysis and use the error analysis to appropriately reduce their influence on averages and other statistics, as described below, without discarding data.

The FLUXNET2015 dataset contains error estimates for sensible and latent heat measurements. We use these reported values in the error analysis. Where uncertainties in these fluxes are missing, we fill the gaps using a linear regression of available flux errors against flux values for that site. For friction velocity, the uncertainty is the prediction error in the linear model used for gap filling (Sect. 2.3). Based on expert judgment, the standard deviation of O3 mole fraction is set to 20 %, pressure to 0.5 hPa, temperature to 0.5 K, relative humidity to 5 %, and canopy height to the lesser of 15 % or 2 m. For remotely sensed leaf-area index, the uncertainty is 1.1 m2 m-2 for all vegetation types (Claverie et al., 2013, 2016). Snow depth uncertainty in MERRA2 is 0.08 m (Reichle et al., 2017). The Zhang et al. (2003) gns parameterization has five vegetation-specific parameters and all are assigned 50 % standard deviation. Zero error is assumed for the flux tower height. Based on these inputs, the median relative uncertainty in Fs,O3syn is 44 %, but it rises to several hundred percent for some half-hour intervals. The error analysis shows that most of the uncertainty in Fs,O3syn derives from uncertainty in the latent heat flux measurement.

Daily and monthly averages of Fs,O3syn and other quantities are constructed in stages. We first calculate a mean diurnal cycle for the day or month by pooling measurements during each hour in a maximum likelihood estimate, a weighted average that accounts for the uncertainty in each measurement. The maximum likelihood estimate is appropriate when combining values from the same distribution, which is expected to apply for measurements within a particular hour, but not across hours of the day. We then average across hours with an unweighted mean to calculate the daily or monthly value. For the daily averages, there are one to two observations within each hour. For the monthly averages, there are typically 30 to 60 in each hour of the day. We calculate seasonal averages with an unweighted mean of monthly values. Uncertainties are propagated through each stage of these averages, as detailed in Supplement S2. We compared averages with and without uncertainty weighting. The uncertainty-weighted averages tend to be smaller and less variable than unweighted averages because the error propagation identifies when outliers and large values have greater uncertainty. For example, the monthly values of gc derived from observations at Harvard Forest are 0.57±0.11 cm s-1 with uncertainty weighting and 0.68±0.17 cm s-1 without. Our discussion focuses on uncertainty-weighted daily averages of daytime data.

Analyses are performed in Python 3.5 with NumPy, Pandas, PySolar, and Statsmodels (Reda and Andreas, 2005; Van Der Walt et al., 2006; McKinney, 2010; Seabold et al., 2010). We quantify linear relationships between variables using the coefficient of determination (R2), a parametric slope estimator (standard major axis or SMA, Warton et al., 2006) and a non-parametric slope estimator (Thiel–Sen slope, Sen, 1968), which is more robust against outliers.

The SynFlux dataset produced in this work is available at https://doi.org/10.5281/zenodo.1402054 (last access: 30 August 2018). The dataset includes synthetic stomatal and total O3 fluxes, O3 concentrations, O3 deposition velocity, canopy conductance, stomatal conductance, and all of their propagated uncertainties. Monthly mean values are provided with and without u∗ gap filling, for 103 sites totaling 926 site years.

Figure 4 compares daily daytime averages of synthetic Fs,O3syn to Fs,O3 observation-derived Fs,O3obs. Fs,O3syn and Fs,O3obs are calculated from the same observation-derived stomatal conductance (gs) and aerodynamic resistances (ra and rb), but differ in the O3 mole fraction and non-stomatal conductance (gns) that they use (see Sects. 2.1 and 2.2). At all three sites, Fs,O3syn is strongly correlated with measured values (R2=0.83–0.93). The mean and median biases are -16 % to -21 % and at least 95 % of Fs,O3syn values agree with measurements within a factor of 2. The majority of Fs,O3syn values lie near the 1:1 line with Fs,O3obs and the slopes (0.71 to 0.85) reflect this. The half-hourly or hourly measured and synthetic fluxes still have some outliers (Fig. S2), but the error analysis reveals that many of the outlying points have large uncertainties. For 98 % of points, the differences between Fs,O3syn and Fs,O3obs are less than the 95 % confidence interval derived from the error analysis (two-sided t-test). Thus, the errors in Fs,O3syn are consistent with the propagated uncertainty in the observations. The half-hourly Fs,O3syn values perform similarly well against observations (Fig. S4), but our analysis focuses on averages. The performance of daily Fs,O3syn is partially due to resolving the seasonal cycle. If we subtract the mean seasonal cycle from both synthetic and observation-derived daily Fs,O3, the residual correlation is R2=0.5–0.7 (vs. 0.9 with the seasonal cycle included). This represents the skill of SynFlux at reproducing within-month and interannual variability. Overall, these results suggest that synthetic Fs,O3syn is a reliable estimate of stomatal O3 uptake into plants that can be used at flux tower sites without O3 measurements.

The measurements also enable us to evaluate synthetic total deposition, FO3syn, and synthetic O3 deposition velocity, vdsyn, although these are less relevant to ecosystem impacts than stomatal uptake, Fs,O3syn. For daily averages, Fig. S5 shows that FO3syn bias (-13 % to +65 %), slope (0.3–1.4), and R2 (0.05–0.43) are all worse than for Fs,O3syn. The daily vdsyn performance is similar (Fig. S6, bias: -26 % to +41 %, slope: 0.3–1.1, R2: 0.16–0.37). Monthly averages of vdsyn and FO3syn both improve the correlation with observations (R2 ∼ 0.12–0.54). The reasons for the better performance of Fs,O3syn compared to FO3syn can be derived from Eq. (3). The canopy resistance for O3 is normally much greater than the quasi-laminar layer and aerodynamic resistances, meaning rc≫raandrc≫rb, often by a factor of 3–10. Therefore, the O3 deposition velocity is approximately vd≈rc-1=gc. Under these conditions, Eq. (1) simplifies to FO3≈nχ(gs+gns) and Eq. (3) simplifies to Fs,O3≈nχgs. While gs is calculated from measured H2O fluxes, gns comes from a parameterization, which inevitably introduces error into gns and FO3syn. However, Fs,O3syn has little sensitivity to gns regardless of whether stomatal or non-stomatal conductance is larger. We confirm this insensitivity in tests where the parameterized gns value is doubled at 10 sites. The hourly Fs,O3syn values change only 3 %–8 %. Since Fs,O3syn has little sensitivity to gns or its errors, it can be calculated more accurately than FO3syn, as seen when comparing Figs. 4 and S4. Despite its larger errors, the means of FO3syn and vdsyn are within 50 % of the observed value at two sites and within a factor of 2 at all, which may be useful for some applications, given the scarcity of prior FO3 measurements and observation-derived estimates of vd.

Figure 5 shows the seasonal cycles of observation-derived O3 deposition velocity and its important components at the three study sites with O3 flux measurements. For low or moderately reactive gases like O3, canopy resistance is typically greater than aerodynamic or quasi-laminar layer resistance, so it controls the overall deposition velocity. At these three sites, deposition velocity is lowest in winter (0.1–0.2 cm s-1) and highest in summer (0.5–0.6 cm s-1). Stomatal conductance peaks during warm and wet months, which explains most of this seasonal variation, except at Blodgett Forest as discussed below. Traditionally, stomatal conductance was thought to exceed non-stomatal conductance during the growing season at most vegetated sites (Wesely, 1989; Zhang et al., 2003), although this has been challenged more recently (Altimir et al., 2006; Stella et al., 2011a; Wolfe et al., 2011; Plake et al., 2015). At both Harvard and Hyytiälä forests, the mean stomatal conductance (0.2–0.6 cm s-1) is 1.5–6 times larger than non-stomatal conductance (0.08–0.2 cm s-1) during the growing season, so about 60 %–90 % of O3 deposition occurs through stomatal uptake. At Blodgett, non-stomatal conductance slightly exceeds stomatal conductance in summer (0.4 vs. 0.3 cm s-1). The fast non-stomatal deposition is explained by O3 reacting with biogenic terpenoid emissions below the flux measurement height (Kurpius and Goldstein, 2003; Fares et al., 2010). As documented in past work, these biogenic emissions depend strongly on temperature and light and have a large seasonal cycle with maxima in summer and minima in winter, so stomatal uptake is generally < 50 % of O3 deposition at Blodgett in the summer but > 70 % in winter (Kurpuis and Goldstein, 2003; Fares et al., 2010; Wolfe et al. 2011).

A recent analysis of O3 flux measurements at Harvard Forest suggests that non-stomatal deposition averages 40 % of daytime O3 deposition during summer months, with a range of 20 %–60 % across years (Clifton et al., 2017). Our analysis of the same site does not support such a large role for non-stomatal deposition at this site in summer. For each year, we calculate summer daytime means of gs and gc by averaging the June–September values, and then calculate the non-stomatal fraction of deposition (1-gs/gc). Averaged across years 1993–2000, we find that 8 % of daytime O3 deposition is non-stomatal during the summer, with a range of -33 % to 34 % across years. Negative fractions mean that stomatal conductance is large enough to explain all O3 deposition. A large negative non-stomatal fraction (-33 %) occurs in only one year (1996) and no other year is less than -11 %, which is within uncertainty of 0 % (2σ) according to the error propagation. Despite the small or zero non-stomatal fraction found here, our results continue to support the large year-to-year variability of this fraction reported by Clifton et al. (2017). The re-calibrated latent heat flux measurements are the main reason that our results differ from prior work and Supplement S3 provides further details. At Hyytiälä Forest, our results are consistent with prior work that found that the non-stomatal deposition is 26 % to 44 % of daytime O3 deposition during the growing season (Rannik et al., 2012). Nevertheless, non-stomatal deposition equals or exceeds stomatal uptake where there are large terpene emissions (e.g., Blodgett) and at some other temperate sites that probably lack large biogenic emissions (Fowler et al., 2001; Cieslik, 2004; Lamaud et al., 2009; Stella et al., 2011b; El-Madany et al., 2017). We also examined interannual variation in O3 deposition velocity. We find that the mean summer daytime vd is 0.40–0.68 cm s-1 at Harvard Forest, 0.42–0.65 cm s-1 at Blodgett Forest, and 0.43–0.51 cm s-1 at Hyytiälä. This range for Harvard Forest is somewhat smaller than other recent work (0.5–1.2 cm s-1; Clifton et al., 2017) because of the uncertainty-weighted averages used here (Sect. 2.4).

The data here also provide an opportunity to evaluate the parameterization of gns non-stomatal conductance (Zhang et al., 2003). The parameterized gns has a similar mean to observation-derived values in summer at Harvard Forest (0.16 vs. 0.12 cm s-1) and Hyytiälä (0.15 vs. 0.25 cm s-1). At Blodgett Forest, the parameterized gns is about half of observation-derived gns in summer, but this is not surprising since the parameterization does not account for O3 reactions with biogenic volatile organic compounds (BVOCs), which are known to be important at this site (Fares et al., 2010). In winter, however, the parameterized gns values at Blodgett Forest are similar to observations (0.10 vs. 0.08 cm s-1). The parameterization is therefore able to roughly predict mean non-stomatal conductance in the absence of major BVOC emissions. Nevertheless, the parameterization reproduces almost none of the daily variability of gns at any site (R2 < 0.1, Fig. S7). This corroborates the recent field assessment that non-stomatal conductance is a weak point of most current dry deposition algorithms (Wu et al., 2018). We attempted, unsuccessfully, to use BVOC emissions from the MEGAN biogenic emission model (Guenther et al., 2012) to improve the gns parameterization, but the correlations between compounds that react fastest with O3 (monoterpenes and sesquiterpenes) and the observation-derived daily mean gns were poor (R2≤0.15). On that basis, FO3syn may also underestimate total O3 deposition at other sites with high monoterpene and sesquiterpene emissions, such as warm-weather pine forests, but Fs,O3syn should retain its quality everywhere.

Across the 43 sites in the US shown in Fig. 3, mean Fs,O3syn during the growing season ranges from 0.5 to 11.0 nmol O3 m-2 s-1 with an average of 4.4 nmol O3 m-2 s-1. The highest Fs,O3syn generally occurs in the Midwest (5–9 nmol O3 m-2 s-1 in Wisconsin, Michigan, Nebraska, and Ohio) due to its moderate O3 concentrations (Fig. S6) and moisture levels, which promotes stomatal conductance (Fig. 1). The western US has higher average O3 concentrations, but generally lower moisture and stomatal conductance, especially the southwestern US, so Fs,O3syn (0–4 nmol O3 m-2 s-1) is mostly lower than the Midwest. Land cover, land management, and plant types can drive large differences in Fs,O3syn between nearby sites, even when O3 concentrations and meteorology are similar. For example, three Nebraska sites are all crop fields and O3 concentrations are nearly identical, but two irrigated fields have higher stomatal conductance and higher Fs,O3syn than the nearby rainfed field (6.2 vs. 4.8 nmol O3 m-2 s-1). Two sites in central California have high gs and Fs,O3syn compared to surrounding sites due to irrigation and naturally wet soil in the California Delta. A combination of topography and climate is also an important factor in California: forest sites in the Sierra Nevada have lower gs and Fs,O3syn than the lowland crops and wetland grasses. In Oregon, an evergreen needleleaf site regrowing after a fire has higher gs and Fs,O3syn than two older forest stands nearby. The differences between nine Wisconsin forest sites, however, are mostly due to different years of data at each site combined with interannual variability in Fs,O3syn; fluxes at these sites are similar in overlapping years.

Variability across the 60 sites in Europe is controlled by similar factors. Stomatal uptake ranges from 1.4 to 9.6 nmol O3 m-2 s-1, with an average of 4.7 nmol O3 m-2 s-1 (Fig. 3). The Mediterranean region has high O3 concentrations (Fig. S8) but generally low stomatal conductance due to the dry climate (Fig. 1). Within this region, vegetation type explains broad patterns. Shrub sites in Spain, France, and Sardinia have very low gs (∼0.15 cm s-1), so Fs,O3syn is low (1–3 nmol O3 m-2 s-1), while most of the sites in mainland Italy are broadleaf and evergreen forests that have slightly greater gs (∼0.2–0.4 cm s-1) and Fs,O3syn (3–6 nmol O3 m-2 s-1), despite similar climate and O3. In central and northern Europe, temperate climate promotes higher stomatal conductance, while O3 concentrations remain modest throughout the growing season. The largest Fs,O3syn is 9.8 nmol O3 m-2 s-1 at a deciduous broadleaf forest in Switzerland, while nearby evergreen forests, cereal crops, and grasslands all have lower fluxes (6–8 nmol O3 m-2 s-1). While Finland has a generally low Fs,O3syn of 2–5 nmol O3 m-2 s-1, the high end of this range is similar to rural sites in Germany, illustrating that O3 can impact remote ecosystems with high stomatal conductance, even where O3 concentrations are low.

Table 2 quantifies SynFlux, O3 deposition velocity, and conductance for each plant functional type. Wetlands, crops, and forests have the highest average Fs,O3syn, which is about 2 times higher than woody savanna or shrublands, the vegetation types with the lowest Fs,O3syn. At wetland sites, gs andFs,O3syn could be overestimated due to evaporation of surface water (Sect. 2.1), but any error is likely modest because our estimates of stomatal conductance at these sites (0.48±0.16 cm s-1; Table 2) are reasonable for wetland vegetation (up to 1 cm s-1; Drake et al., 2013). The vegetation types rank in the same order for stomatal conductance, again showing stomata as the main control on O3 uptake into vegetation. Stomatal uptake exceeds non-stomatal uptake for all plant functional types except woody savanna and shrubland. O3 deposition velocities reported in Table 2 fall within the ranges of past literature, as reviewed by Silva and Heald (2017). However, while Silva and Heald found that the mean deposition velocity was greater over deciduous forests than coniferous forests, crops, or grass, we do not. Rather, we find that variability between sites within each of these categories is large, having a standard deviation of about 30 % of the multi-site mean.

Since O3 injures plants mainly by internal oxidative damage after entering the leaves through stomata, the most physiological predictor of plant injuries is the cumulative uptake of O3 (CUO, Reich, 1987; Fuhrer, 2000; Karlsson et al., 2004; Cieslik, 2004; Matyssek et al., 2007). CUO is defined as the cumulative stomatal O3 flux exceeding a threshold flux Y that can be detoxified by the plant, integrated over a period of time: CUOY=∑iH(Fs,O3,i-Y)(Fs,O3,i-Y)Δti.

Here, H(x) is the Heaviside step function and Δti is the time elapsed during measurement of Fs,O3,i. The sum is carried out over time i in the growing season, which we define based on GPP (Sect. 2.1). The detoxification threshold varies across vegetation types, even among related species (Karlsson et al., 2004; Büker et al., 2015), and thresholds for specific FLUXNET sites are generally unknown. As a compromise, we calculate CUO, with Y=0, and also CUO3, with Y=3 nmol O3 m-2 s-1, which has been suggested as a reasonable generic threshold (Mills et al., 2011). CUO is always greater than CUO3, but the sites with high CUO tend to also have high CUO3, so their spatial patterns are similar (Fig. S8).

While CUO is a physiological dose, concentration-based metrics remain common for assessing ozone impacts because they are easier to measure. Concentration-based metrics quantify O3 in ambient air irrespective of whether that O3 enters leaves. These metrics follow the general form M=∑iwχiχi-χcΔti, where w(χ) is a weighting function applied to the O3 mole fraction χ, and χc is a constant. Like CUO, the sum is usually over time i during the growing season. Three of the most common concentration-based O3 metrics are the mean O3 concentration, the accumulated concentration over a threshold of 40 ppb (AOT40; UNECE, 2004), and the sigmoidal-weighted index (W126; Lefohn and Runeckles, 1987). For mean, wχ=∑Δti-1 and χc=0. For AOT40, w(χ)=H(χ-χc) and χc= 40 ppb. For W126, wχ=1+4403exp⁡-126ppb-1χ-1 and χc=0. Both AOT40 and W126 use only daytime (08:00–20:00) measurements and W126 also takes the maximum value over all 3-month periods during the growing season. The weighting functions for AOT40 and W126 give little or no weight to O3 concentrations below 40 ppb. In addition, W126 gives increasing weight to concentrations up to about 110 ppb and full weight for higher concentrations based on the understanding that exposure to high O3 concentrations is more injurious than moderate or low concentrations. Other concentration-based metrics (e.g., SUM60) use other thresholds or weighting functions, but many are strongly correlated with AOT40 or W126 or otherwise qualitatively similar (Paoletti et al., 2007).

The spatial patterns of AOT40 and W126 closely resemble that of mean O3 concentration in the US and Europe despite their different weighting functions (Fig. S9). AOT40 and W126 are well correlated with each other across sites (R2=0.87) and with mean O3 mole fraction (R2=0.76 and R2=0.52 for mean O3 vs. AOT40 and W126, respectively) despite their different weighting functions. As a result, all of these concentration-based metrics have similar spatial patterns in the US and Europe. The CUO and CUO3 spatial patterns, however, are similar to Fs,O3syn and distinct from the concentration-based metrics. This illustrates that locations with high AOT40 or W126, like the southwestern US or Mediterranean Europe, can have low CUO.

Even though concentration-based metrics do not measure the physiological O3 dose to plants, they can be useful if the metric is proportional to the flux-based dose and injuries. Indeed, many controlled experiments and observational studies have documented correlations between both AOT40 and W126 and either uptake or plant injuries (e.g., Fuhrer et al., 1997; Cieslik, 2004; Musselman et al., 2006; Matyssek et al., 2010). However, many of these studies were carried out at a single site or under conditions where stomatal conductance was relatively steady while O3 concentrations varied, for example by maintaining well-watered soil. When stomatal conductance varies widely, such as between arid and humid climates or seasons, concentration-based metrics may not correlate with stomatal O3 flux (Mills et al., 2011).

Figure 6 shows that all of the concentration-based metrics are poorly correlated with CUO across the sites (AOT40: R2=0.05, W126: R2=0.03, mean O3: R2=0.04). Humidity helps explain some of the scatter in Fig. 6. The sites with high concentration-based metrics and low CUO have high vapor pressure deficit (VPD) and low stomatal conductance, and are mostly in the western US and Mediterranean Europe. Restricting the analysis to humid sites (VPD < 1.5 kPa) does not improve the correlation (R2≈0.05) and at the arid sites (VPD > 1.6 kPa) the concentration-based metrics are modestly anti-correlated with CUO (AOT40: R2=0.19, W126: R2=0.05, mean O3: R2=0.37). This result reinforces that concentration-based metrics can misrepresent CUO and plant injuries (Mills et al., 2011).

From the CUO values in Table 2, we can estimate the range of O3 impacts on biomass production at the FLUXNET sites. Although species vary in their sensitivity to O3 (Lombardozzi et al., 2013), several studies suggest that the biomass production of broadleaf and needleleaf trees decreases by 0.2 % to 1 % per mmol O3 m-2 of CUO (Karlsson et al., 2004; Wittig et al., 2007; Hoshika et al., 2015). Combining the mean CUO for each plant functional type (Table 2) with these sensitivities, our work implies that O3 reduces the biomass production at these FLUXNET sites by 6 %–29 % for deciduous broadleaf forests and 4 %–20 % for needleleaf forests. The range represents the spread of reported dose–response sensitivities within each plant type, meaning the least and most O3-sensitive species. Several broadleaf crops are more sensitive to O3, with biomass reductions of 1.3 %–1.6 % per mmol O3 m-2 of CUO3 (Mills et al., 2011). That sensitivity implies a 20 %–24 % drop in biomass production at FLUXNET crop sites. Some studies have quantified O3 dose–response relationships with other thresholds Y=1.6 to 6 nmol O3 m-2 s-1 (e.g., Karlsson et al., 2007; Pleijel et al., 2004, 2014), but the sensitivities have a similar magnitude. Fares et al. (2013) also demonstrated 12 %–19 % reduction in gross primary production due to O3 at some of the same crop and forest FLUXNET sites. Using prognostic models of O3 concentrations and stomatal uptake, several past studies have also suggested that O3 reduces biomass production and CO2 sequestration by 4 %–20 % in the US and Europe (Sitch et al., 2007; Wittig et al., 2007; Mills et al., 2011; Yue et al., 2014, 2016; Lombardozzi et al., 2015). Our results support this range of impacts, although some FLUXNET sites and species likely experience greater O3 injury, but here the CUO is highly constrained from observations and therefore avoids the additional uncertainties of atmosphere–biosphere models.