In this study, chambers of traditional and the new design described in Lin et al. (2012) were inter-compared. The hemi-cylindrical TDFC made of quartz with an open bottom area of 0.06  m2 has been used extensively in our group and elsewhere (Feng et al., 2005; Fu et al., 2008, 2010, 2012; Li et al., 2010; Wang et al., 2005, 2007; Zhu et al., 2013a). The NDFC was fabricated of thin polycarbonate sections and enclosed a soil surface of 0.09 m2 (for details, see Lin et al., 2012). The NDFC internal flow condition was precisely controlled to relate to the applied flushing flow rate to the atmospheric boundary shear condition (therefore wind shear condition) and the calculated flux was re-scaled to boundary shear condition (Eq. 2 below). Both DFCs were operated at a relatively high flushing flow rate of 15 L min-1, corresponding to turn-over times (TOTs) of 0.32 min and 0.47 min for TDFC and NDFC, respectively. The flux from TDFC and NDFC were calculated following Eq. (1) and (2), respectively (Xiao et al., 1991; Lin et al., 2012): FHg0TDFC=Q(Co-Ci)A FHg0NDFC=Q(ΔC)Akmass(a)kmass(m)=Q(Co-Ci)A4.86+0.03(h/l)[hu∗/(6kz0)](DH/D)1+0.016{(h/l)[hu∗/(6kz0)](DH/D)}2/34.86+0.03(h/l)(Q/Ac)(DH/D)1+0.016[(h/l)(Q/Ac)(DH/D)]2/3, where FHg0TDFC is Hg0 flux measured from the TDFC method, FHg0NDFC is Hg0 flux from the NDFC method, Q is applied flow rate (0.9 m3 h-1), A is footprint (0.06 m2 for TDFC, 0.09 m2 for NDFC), Co and Ci are the DFC outlet and inlet air Hg0 concentration, and kmass(a) and kmass(m) are the overall mass transfer coefficient (m s-1) in the near-surface boundary layer and in the internal layer within NDFC, respectively. Ac is the NDFC flow cross-sectional area (0.009 m2), l is the distance measured from the starting point of the measurement zone (0.15 m), h is the height of NDFC (0.03 m), u∗ is the atmospheric boundary layer friction velocity, and z0 is surface roughness height (m). DH and D are the NDFC hydraulic radius (0.0545 m) and diffusivity of Hg0 (1.194 × 10-5 m2 s-1), respectively.

Descriptive statistics of the DFC Hg0 flux observations are presented in Table 1. In a comparison, NDFC-derived Hg0 fluxes spanned over a broader range and exhibited a higher mean. Figure 4a displays the time series of Hg0 fluxes gauged by the two DFC methods. Both series showed similar diurnal features with daytime evasion (maximum occurred at midday) and a shallow minimum of bi-directional exchange during nighttime. The pattern is consistent with observations made over background soils worldwide (Gustin et al., 2011 and the references therein).

The median ± MAD (median absolute deviation) of Hg0 flux was -0.9 ± 3.2 and -1.7 ± 4.3 ng m-2 h-1 for TDFC and NDFC, respectively. Probability plots of both DFC data sets showed positive kurtosis (3.0 and 4.1) and skewness (1.6 and 2.1) (Fig. 5) as a consequence of stronger emission and increased friction velocity at daytime. The substantial fraction of NDFC data points elevated in magnitude outlying the 1.5⋅IQR (interquartile range) bound is associated with periods of high wind speed (i.e., showing the dependence of friction velocity in Eq. 2). Moreover, as indicated in Fig. 5, the shortest half (50 %) of the chamber flux data is positioned more towards dry deposition for the novel compared to the traditional chamber technique. Nevertheless, the intrinsic divergence of the microenvironment inside enclosures in relation to that of near-surface air layer tends to promote efflux.

In the Nevada STORMS campaign, seven flow-through enclosures (DFCs) with different operational parameters and designs were located in an arid area with naturally Hg-enriched substrate. The observed DFC Hg0 fluxes showed similar diurnal profiles but diverged in magnitude by an order of magnitude (Gustin et al., 1999; Wallschläger et al., 1999; Gustin and Lindberg, 2000). The observed difference was partially attributed to the substrate heterogeneity with respect to Hg content. In this study, the surface soil Hg content within the methodological footprint range is at large homogeneous and therefore does not pose an interfering factor.

Eckley et al. (2010) examined experimentally a series of operational and instrumental factors that may influence DFC-derived flux. The DFC flushing flow rate was identified to have substantial positive influence. In the present study, the TOT of TDFC is 50 % smaller than that of the NDFC. Moreover, the footprint of the traditional type is about two-thirds of the NDFC footprint and therefore a higher flux is expected using the NDFC method (Eckley et al., 2010; Lin et al., 2012). Figure 6 shows a scatterplot of the fluxes measured by the NDFC and TDFC approach before and after turbulence correction. The data were significantly positive correlated (R=0.93, R=0.95 between TDFC and NDFC fluxes calculated with Eq. (2) and Eq. (1) respectively; p<0.01). Quantitatively, direct measured flux was consistent for the two chambers (slope 1.01). After accounting for the atmospheric boundary shear condition by Eq. (2), the well-developed turbulence (higher friction velocity, Fig. 2) during daytime caused the NDFC-inferred Hg0 flux to be approximately 2.5 times higher than the TDFC flux. Given that fluxes derived from a DFC of conventional type do not allow for re-scaling to represent natural surface shear stress conditions, TDFCs are prone to underestimate the soil Hg emission, particularly when operated at low air exchange rates. The ability to incorporate an atmospheric turbulence property such as friction velocity makes the NDFC method a more favorable approach for estimating Hg0 gas exchange over soils compared to the TDFC method.

Figure 4a and b show the time series of normalized vertical Hg0 concentration gradient (ng m-4) and Hg0 flux (ng m-2 h-1) derived from the turbulent diffusion methods (MBR and AGM). Hg0 concentration gradients were observed in the similar ranges of -0.49 to 0.33 and -0.48 to 0.25 ng m-4 in both campaigns (Table 1 and Fig. 4), though the more occasionally shifting conditions of weak and developed turbulence in IC#1 tend towards promoting a higher scale of diurnal gradient variability (IC#1 vs. IC#2 standard deviation: 0.09 vs. 0.06). Our gradient observations are in alignment with measurement over temperate grasslands (-0.40 to 0.27 ng m-4) (Fritsche et al., 2008b).

Basic statistics of the MM Hg0 flux observations is presented in Table 1. The variability in our observations is similar with those reported from previous studies using the MM flux measurement technique over uncontaminated croplands (corn, soybean and rice paddy fields) (Baya and Van Heyst, 2010; Cobos and Baker, 2002; Kim et al., 2003; Cobbett and Van Heyst, 2007). The MM fluxes exhibited strong temporal variability during daytime and much weaker variability under low-quality turbulence during nighttime. In a typical campaign day, the turbulent flux data sets included both periods of emission and dry deposition. The median of nighttime flux was much smaller than the daytime flux for all MM methods (Mann–Whitney U test, MBR and AGM p<0.001, p<0.10 for REA).

The distribution of the turbulent fluxes and Hg0 concentration gradient in Fig. 4 deviated significantly from a Gaussian distribution in the Hg0 concentration gradient and in the derived MBR and AGM fluxes (Shapiro–Wilk's test rejected the hypothesis of normality of the distributions, p<0.01). The statistical MM fluxes (median ± MAD) in IC#1 (Fig. 7a) were -0.5 ± 8.9 and 0.1 ± 3.2 ng m-2 h-1 for AGM and MBR measurement, and 2.8 ± 29.0, 1.4 ± 15.2, and 8.8 ± 45.3 ng m-2 h-1 for AGM, MBR and REA in IC#2 (Fig. 7b), respectively. All the distributions of MM turbulent flux were associated with a positive kurtosis (3.8–16.2) and a slightly positive skewness (0.8–1.5). The observed flux frequency distributions for AGM and MBR peaked more strongly than that of REA (Fig. 7), with the MBR method giving the most confined distribution. Broader flux distribution measured by the REA sampling method has been reported in the measurements of turbulent fluxes for other gases (Fowler et al., 1995; Beverland et al., 1996; Nemitz et al., 2001). Previous studies suggest that vegetation canopy in the growing stage acts as an Hg0 sink by net uptake of Hg0 into foliage and therefore contributes to dry depositional flux (Bash and Miller, 2009; Stamenkovic and Gustin, 2007). However, the three MM techniques in this study derived significant higher average Hg0 emission fluxes in IC #2 compared to IC#1, indicating that the vegetation sink strength was not sufficient to offset the efflux from underlying soil surface for croplands. Even though not measured, it is credible to assume that the soil Hg0 efflux was higher during the warmer IC#2 due to higher temperature (Table 1) (Baya and Van Heyst, 2010; Gustin, 2011).

The larger variability in REA- compared to the gradient-derived fluxes is associated with a combination of methodological, instrumental and site-specific constraints influencing primarily the resolution of ΔCREA (Eq. 3) as identified and discussed in Part II of this paper series (Zhu et al., 2015b). Nevertheless, a Friedman two-way analysis of variance by ranks (a non-parametric method) showed that the median fluxes by the three MM methods were not significantly different (χ2=1.29<χp=0.052=5.99). This indicated that AGM, MBR and REA methods produced comparable results with respect to the median location of Hg0 turbulent flux during the inter-comparison.

The MBR method relies on scalar similarity (similarity in the scalar time series throughout the scalar spectra, Kaimal et al., 1972) between Hg0 and temperature used as the proxy in this study. Since we have no means of explicitly characterizing Hg0 scalar spectra, it is important to address the distribution of sources and sinks within the footprint area (Foken, 2008). By choosing a large flat and uniform fetch with confined Hg content in the soil substrate, significant divergence from scalar similarity between Hg0 and temperature is less likely to occur. Nevertheless, non-stationary effects (e.g., advection of Hg polluted air-masses and related changes in concentration with time) bias the measured turbulent flux in relation to the actual air–surface exchange process (see Sect. 3.4). The MBR method becomes uncertain and may significantly overestimate flux when the numerator and denominator in the formula of eddy diffusivity approach small numbers, which typically occurs in periods at dawn, dusk and during nighttime (Eq. 6, see Converse et al., 2010). As shown in Fig. 8, the 20-min-averaged AGM- and MBR-derived fluxes were well correlated during both campaigns (slopes of 0.76 and 0.86). However, when the sensible heat flux becomes small (small temperature gradient) at |H|<20 wm-2, the correlation coefficient diminishes drastically with a fall-off in slope (FAGM/FMBR=0.35–0.36) implying that the MBR method can significant overestimate turbulent Hg0 fluxes. MBR flux data collected in the presence of small scalar gradients (often during dawn and dusk transition periods) are therefore of questionable quality and should be considered for omission.

AGM fluxes were on an average 26.1 % lower than MBR fluxes during IC #1, but 13.8 % higher during IC#2. The disparate results may largely stem from methodological issues (Fritsche et al., 2008b). In some previous studies using the AGM method to gauge various trace gas fluxes including Hg0 (Edwards et al., 2001; Edwards et al., 2005; Simpson et al., 1997), normalization of Eq. (5) was introduced to mitigate for systematical failure of obtaining energy budget closures (Twine et al., 2000) by a factor of 1.3–1.35. The AGM method involves momentum flux, and an atmospheric stability parameterization in the flux calculation. For the conditions of weak developed turbulence to a greater extent prevailing under nocturnal stable stratification, where u∗ is very low, the AGM and MBR methods are prone to large uncertainties and corresponding fluxes are suggested to be flagged by applying wind or friction velocity thresholds (namely u∗<0.07–0.1 ms-1) (Fritsche et al., 2008b; Foken, 2008). During IC#2, when the REA system was included, the agreement between REA and the gradient-based methods was worst for small fluxes, which is inherently connected with the lower precision of the former system. As to be discussed in Zhu et al. (2015b), the non-constant (i.e., concentration and time dependent) sampling channel bias, which is difficult to entirely account for, is relatively more aggravating for the REA approach. For other gases (e.g., NH3, CH4) that have been studied with this triad of MM techniques, higher variability in REA flux is generically observed (Nemitz et al., 2001; Fowler et al., 1995; Moncrieff et al., 1998). In addition, systematic flux differences between a suite of NH3-REA systems as well as collocated AGM system inter-compared have been reported (Hensen et al., 2009).

While the footprint (enclosed soil surface) of the chamber methods is fixed and very small (0.06 m2 for TDFC and 0.09 m2 for NDFC), MM methods derive fluxes from a footprint of comparatively large spatial extension upwind of the sampling tower. The MM footprint is not constant over time but a complex function of the sensor height, surface roughness length and canopy structure together with changing meteorological conditions. The predicted source area (using the models of Kljun et al., 2004 and Kormann and Meixner, 2001) tends for upper sampling level (z2=zREA) to be extensive for flux periods associated with weakly developed turbulence (Flag 2). In contrast, ∼ 70 % and ∼ 86 % of the data cleared for good turbulence quality, x^70% (along-wind distance providing 70 % cumulative contribution to turbulent flux) fall within the unbroken field (150 m) for IC#1 and IC#2 respectively. For the lower sampling height (z1), the footprint falls almost entirely within the primary fetch. Nevertheless, heterogeneous structures (roads, streams, tree stands and low buildings) existing outside the primary fetch (> 150 m) are of minor spatial extent, and within a radius of ∼ 2 km the sampling tower can be regarded to be surrounded by unbroken farmlands.

Figure 9 shows box and whisker plots of the diurnal variation of Hg0 flux obtained by the five examined methods. Consistent in both campaigns, the MM methods exhibited highly variable fluxes, especially during daytime, where the magnitude in a single 20 min turbulent flux can exceed the flux derived by the chamber methods by many times. DFCs fluxes followed a well-defined diurnal pattern with consistent daytime emission and slight nighttime deposition. The pattern is similar to those for solar irradiance and temperature and reflects that the air–soil Hg0 flux derived from the DFC technique is primarily governed by thermal and light-induced controls (e.g., Bahlmann et al., 2006). In contrast, flux from MM measurements is subject to the constant changes of atmospheric turbulence within the planetary boundary layer. To facilitate a comparison between the DFC and MM data set on a diurnal basis, a Savitzky–Golay filter was applied on hourly averaged turbulent Hg0 flux data to smooth out the short-term variability. In Fig. 10, where the diurnal courses of flux are given by smoothing spline fits, there is a 2 h lag in the time of the day when turbulent and chamber-derived flux peaked (IC#1). For the DFCs, the observed Hg0 flux peaked within the period P2 (Fig. 10, IC#1) in concert with soil temperature, which is consistent with diurnal cycles reported for chamber measurements in the literature (Fu et al., 2008, 2012; Gustin, 2011; Zhu et al., 2013a).

The smoothed mean diurnal cycle derived by the gradient-based methods over the same period exhibits peaking Hg0 fluxes shortly before midday (P1 in Fig. 10, IC#1) but also includes a subsequent shoulder in the flux profile in the early afternoon (within P2 in Fig. 10, IC#1). The pattern resembles to an extent that of latent heat flux (evapotranspiration) (Liu and Foken, 2001) and may be interpreted as an effect of photo-reduction of previously deposited HgII to Hg0 into soil in conjunction with the presence of a water film (frost and dewfall) and emerging incoming solar radiation and temperature-driven air–surface exchange of soil Hg0 pool (Fritsche et al., 2008b). Nevertheless, measurement of air–surface Hg0 fluxes under the marked varying Hg0 concentrations in air is challenging. Under such conditions, the measured turbulent fluxes are altered by non-stationary bias, and thus they do not represent actual fluxes to surface. The rates of change in Hg0 concentration (up to ∼ ± 1.1 ng m-3 h-1) at the storage height of nearly 3 m relevant to this study imply vertical Hg0 flux divergence in the range ± 3 ng m-2 h-1. At low turbulence, advection in addition may as well gain some importance. However, to fully quantify the advection term for Hg0 requires an array of instrumentation and such an investigation was not feasible in this study.

The mean diurnal cycles calculated for the three coevally examined MM methods (Fig. 10, IC#2) are based on a significantly smaller set of input data (∼ 30 % of IC#1) and therefore plausibly less robust to provide adequate representativeness after smoothing. Moreover, the campaign is a composite of periods where near-neutral conditions prevailed on daytime as well as adjacent nights and periods with weakly developed turbulence during nighttime respectively. Accordingly, the MM methods unanimously gauged maximum fluxes slightly after noon-time (P2, IC#2). However, there are features (P1 and P3) in the constructed cycles that are difficult to fully couple to environmental responses.

The overall correlation matrix between Hg0 flux, ambient Hg0 concentration and other measured parameters (hourly averages) are displayed in Table 2. The fluxes derived from the two types of chambers were highly positively correlated (R=0.95, p<0.01). Among the MM methods, MBR and AGM fluxes were well correlated, while REA fluxes were not significantly correlated with fluxes derived by other techniques (R<0.2, p>0.05). A significant correlation was observed between DFCs and gradient fluxes (R ∼ 0.5 for DFCs and AGM). Using the dry deposition velocity (Vd) calculation in Poissant et al. (2004), the median Hg0 deposition velocity (dry deposition events) inferred from different measurement methods were 0.01 cm s-1 (MBR, 47 %) < 0.03 cm s-1 (TDFC, 56 %) < 0.04 cm s-1 (NDFC, 59 %) < 0.06 cm s-1 (AGM, 56 %) and 0.09 cm s-1 (AGM, 34 %) < 0.13 cm s-1 (MBR, 36 %) < 0.20 cm s-1 (REA, 36 %) for IC#1 and IC#2, respectively. The observed Hg0 dry deposition velocities from the two campaigns are in good agreement with the Vd of previous measurements over background soil (DFC methods, generally < 0.05 cm s-1) and agricultural canopies (MM methods, 0.05–0.28 cm s-1) (Zhang et al., 2009, and references therein).

The cumulative flux derived by the examined methods is presented in Fig. 11a, b. During IC#1, the cumulative fluxes measured by MBR and AGM fell between the fluxes measured by the two DFC methods. A period of divergence in the magnitude between the derived turbulent exchange parameters (eddy diffusivity of heat and υtr) resulted in intersected courses of MBR and AGM cumulative flux (17 November). MBR flux then stayed beyond the AGM flux on a cumulative basis for the rest of the campaign. The cumulative flux gauged by the TDFC method was the lowest (approximately 1/3 of MBR flux). Over the duration of IC#1, the net Hg0 flux estimated by MBR and NDFC methods was in good agreement (2.90 vs. 3.02 µg m2) while the AGM method derived a ∼ 25 % lower Hg0 net evasion. This indicates that the flux correction with synchronized surface shear properties in NDFC partially bridges frequently observed disparities in magnitude between the MM- and conventional chamber-derived fluxes (e.g., Gustin et al., 1999). Figure 12a shows the scatterplot of hourly flux specifically for MBR versus NDFC/TDFC – the correlation between individual hourly data points is weak. While in Fig. 12b, the deviation between MBR cumulative fluxes and NDFC/TDFC cumulative fluxes during the sampling campaign suggests that NDFC measurement shows a great advantage in bridging the flux gap between DFCs and MBR measurement. The significant scattering in Fig. 12a stems substantially from the inherent high variability in MBR flux prevalent during daytime. The difference between chamber and MBR flux depends to a certain degree on the diurnal variation of the atmospheric conditions. During daytime, the chamber produces a delay in the daytime flux evolution and fluxes become sustained in the late afternoon due to an artificial reduction in surface cooling within the chamber (Fig. 10).

During IC#2, the gradient-based MM techniques were evaluated together with the REA technique. The temporal features of the convoluted MBR and AGM cumulative fluxes are by and large concordant albeit the latter technique gauged ∼ 20 % higher Hg0 net flux (1.78 vs. 1.43 µg m-2). The relative magnitude of MBR and AGM flux showed an inverse order during the two campaigns, possibly caused by methodological limitations given by the diverging micrometeorological conditions (Zhu et al., 2015b). For an extended period, the cumulative flux of REA given in Fig. 11b evolved in a similar way to those of the gradient-based methods (18–21 April). However, considerably different fluxes, occasionally in reverse directions, occurred after 21 April. In particular, during 16–17 April (Fig. 11b), a large net emission event was observed by all three techniques but at different magnitude.