Importance of nondiffusive transport for soil CO2 efflux in a temperate mountain grassland

Abstract Soil respiration and its biotic and abiotic drivers have been an important research topic in recent years. While the bulk of these efforts has focused on the emission of CO2 from soils, the production and subsequent transport of CO2 from soil to atmosphere received far less attention. However, to understand processes underlying emissions of CO2 from terrestrial ecosystems, both processes need to be fully evaluated. In this study, we tested to what extent the transport of CO2 in a grassland site in the Austrian Alps could be modeled based on the common assumption that diffusion is the main transport mechanism for trace gases in soils. Therefore, we compared the CO2 efflux calculated from the soil CO2 concentration gradient with the CO2 efflux from chamber measurements. We used four commonly used diffusion‐driven models for the flux‐gradient approach. Models generally underestimated the soil chamber effluxes and their amplitudes, indicating that processes other than diffusion were responsible for the transport of CO2. We further observed that transport rates correlated well with irradiation and, below a soil moisture content of 33%, with wind speed. This suggests that mechanisms such as bulk soil air transport, due to pressure pumping or thermal expansion of soil air due to local surface heating, considerably influence soil CO2 transport at this site. Our results suggest that nondiffusive transport may be an important mechanism influencing diel and day‐to‐day dynamics of soil CO2 emissions, leading to a significant mismatch (10–87% depending on the model used) between the two approaches at short time scales.


Introduction
Soil CO 2 efflux is the largest source of CO 2 from terrestrial ecosystems; annually, approximately 98 Pg CO 2 is emitted from soils [Bond-Lamberty and Thomson, 2010]. Although in recent years the number of studies on soil CO 2 fluxes has largely increased, and high-frequency measurements have provided new insights in short-term dynamics of CO 2 efflux [see, e.g., Vargas et al., 2011], the efflux of CO 2 from soil to atmosphere and its biotic and abiotic drivers remain an important topic of debate [e.g., Subke and Bahn, 2010]. A major reason for this ambiguity is related to the fact that in the short term, soil CO 2 efflux does not equal to soil CO 2 production (also termed soil respiration, the sum of microbial and root respiration). Our limited knowledge of the CO 2 transport through the soil restricts our understanding of the role of the various abiotic and biotic controls on soil respiration [Phillips et al., 2011;Subke and Bahn, 2010].
Most often, soil CO 2 efflux is measured using soil chambers, but since the early 2000s, solid-state CO 2 sensors that measure soil CO 2 concentrations at different soil depths are becoming more common. In contrast to soil chambers, solid-state CO 2 sensors allow continuous high-frequency measurements of the CO 2 gradient with minimal disturbance of the natural conditions, such as air pressure or wind velocity [Pingintha et al., 2010;Tang et al., 2003] and soil microclimate. For this reason, estimation of the soil CO 2 efflux from soil CO 2 concentrations, the so-called flux-gradient approach, is rapidly gaining popularity [e.g., Hirano et al., 2003;Jassal et al., 2005;Jassal et al., 2004;Pumpanen et al., 2008;Tang et al., 2003;Tang et al., 2005;Turcu et al., 2005;Vargas and Allen, 2008a;Vargas and Allen, 2008b]. This method uses Fick's law of diffusion (equation (1)) to compute soil CO 2 efflux and thus implies the assumption that diffusion is the only transport mechanism for CO 2 through the soil. Potential effects of, for example, air pressure differences (following advection or wind shear) are often neglected. Soil CO 2 efflux F is calculated via the flux-gradient method as Gas diffusion in soils differs from that in free air, because solid and liquid obstacles reduce the cross-sectional area and increase the mean path length for the diffusing molecules [Sallam et al., 1984;Werner et al., 2004]. Soil properties such as water content, texture, and bulk density therefore determine the rate of diffusion [Moldrup et al., 1999;Pumpanen et al., 2003;Vargas et al., 2010]. Reliable estimates for the diffusion coefficient are of critical importance when using Fick's law to estimate soil CO 2 efflux from soil CO 2 concentrations. Several commonly used models have been proposed to calculate the diffusion coefficient, all of them depending primarily on the air-filled pore space and thus varying inversely with soil water content [Jassal et al., 2005].
Generally, it is assumed that provided that a good estimate of the diffusion coefficient is available, the soil CO 2 concentration gradient directly translates to soil CO 2 efflux. However, there is limited evidence that nondiffusive transport, such as pressure pumping (summarized in Takle et al. [2004]) and advective transport due to heating of the soil surface [Ganot et al., 2014], may strongly influence soil CO 2 emissions at the time scale of seconds. Air pressure at the soil surface fluctuates whenever turbulent air moves over the surface and enhances the exchange of gases at shallow depths [Kimball and Lemon, 1971]. This bulk air gas transport is increased with increasing permeability of the soil, corresponding to a decreasing soil water content, and by thermal advection. As the soil water content decreases, the air-filled porosity increases, enhancing both diffusive and nondiffusive transports.
While the potential relevance of nondiffusive transport has been mostly addressed at a very short time scale, it is important to test if it plays a role at half-hourly time steps, which is the highest time resolution typically achieved in soil respiration studies. So far, few such studies have tested how well rates of chamber-measured soil CO 2 efflux and those estimated from the flux gradient approach compare across the season [Riveros-Iregui et al., 2008], when nondiffusive transport may intermittently decouple fluxes derived from these two approaches.
We aim to deduce the importance of nondiffusive transport for soil CO 2 effluxes by comparing two in situ measurement methods (chamber and soil concentration gradients). Given that the CO 2 efflux is derived from the concentration gradient using diffusion models, the discrepancy between CO 2 effluxes from both measurements can be an indication for nondiffusive gas transport.
We tested the hypotheses that the role of nondiffusive transport (i.e., the mismatch between the two approaches) increases with increasing radiation and wind speed and with decreasing soil moisture.

Site Description
The study was carried out in a mountain meadow at Kaserstattalm, Neustift, in the Austrian Central Alps [cf. Bahn et al., 2009]. Mean annual temperature and precipitation are 3.0°C and 1097 mm, respectively. The meadow is located at 1820 m above sea level and is fertilized with manure in spring, cut once in late July or early August, and lightly grazed in September. The dominating plant species include the grasses Anthoxanthum odoratum L. and Festuca rubra L. and the forbs Alchemilla vulgaris L., Leontodon hispidus L., and Trifolium repens L. The soil is a cambisol on siliceous bedrock with a topsoil pH of 5.5. The soil texture is 43% sand, 47% silt, and 11% clay; the bulk density is 860 kg m À3 . The meadow is characterized by a comparatively high productivity and high soil respiration rates, typical for non-water-limited central European mountain meadows Schmitt et al., 2010].

Measurements
Soil CO 2 concentration measurements were made during the growing season of 2009 using Vaisala CARBOCAP solid-state CO 2 sensors (model GMT 221, Vaisala, Helsinki, Finland) at depths of 10 and 5 cm and the Li-8150 system (Li-Cor, Lincoln, NE, USA) at 0 cm. At the same depths, soil temperature (averaging soil thermocouple probe TCAV; Campbell Scientific) and moisture (ML2x; Delta-T Devices, Cambridge, UK) were measured, and incident photosynthetically active radiation (PAR) (BF2H; Delta-T Devices) was measured above the canopy at 2 m height. Continuous recordings at 0.05 Hz were averaged and half-hourly values recorded using an automated station (CR10X; Campbell Scientific). Values of soil CO 2 concentration were corrected for temperature and pressure using the ideal gas law according to the manufacturer (Vaisala, Helsinki, Finland). Soil CO 2 efflux at the soil surface was measured using an automated soil respiration system (Li-8100 and Li-8150; Li-Cor, Lincoln, NE, USA) over  (1)) to calculate soil CO 2 efflux from the soil CO 2 concentration gradient requires good estimates of the diffusion coefficient D s (m 2 s À1 ), also named effective diffusivity. D s can be estimated as where D a (m 2 s À1 ) is the CO 2 diffusion coefficient in free air and ξ (m 3 m À3 ) is the so-called tortuosity factor, the product of the air-filled porosity ε a and the tortuosity τ [Jassal et al., 2005;Jury et al., 1991]. It accounts for the increase in path length and decrease in cross-sectional area in soils.
The variation of D a with temperature and pressure is given by with T as the temperature (K), P as the air pressure (Pa), and D a0 as a reference value at T 0 (293.15 K) and P 0 (1.013 × 10 5 Pa), given as 1.47 × 10 À5 m 2 s À1 [Jones, 1992].
The air-filled pore space ε a (m 3 m À3 ) is defined as the difference between total porosity ϕ and the volumetric water content θ (m 3 m À3 ) of the soil.
In equation (8), S is the percentage of mineral soil with particle size >2 μm (S = 0.8 for our study site), and β is a constant equal to 2.9. The total porosity at the site is 0.57 m 3 m À3 . Note that in all four models, the air-filled pore space and thus total porosity, is a key factor determining the calculated efflux. Measurements of porosity on soil cores are often subject to uncertainties, especially on heterogeneous soils, and 10% uncertainty in estimated porosity translates into 27-80% uncertainty in calculated efflux (depending on the model used). For this uncertainty, corresponding to a porosity range of 0.51 to 0.63 m 3 m À3 at our study site, the Millington and Quirk's [1961] model is the most sensitive (up to 80% uncertainty on the efflux), while the Penman's [1940] model is the least sensitive (27% uncertainty on the efflux).

Apparent Diffusivity, D app
The combination of chamber measurements and solid-state sensors allows the calculation of the diffusion coefficient solely from measurements. To make a distinction with the effective diffusivities D s calculated from equations (5)-(8), we refer to the empirically obtained diffusivity coefficient as "apparent diffusivity, D app ." To calculate this, we used the difference between the CO 2 concentration measurements at 5 and 0 cm depth, which should capture the most productive zone of the grassland rhizosphere. When calculating D app from Fick's law (equation (1)), it is necessary to account for the temperature gradient in the soil that causes changes in the soil air density and thus in the absolute gas concentration [Kowalski and Argueso, 2011]. When this concentration Journal of Geophysical Research: Biogeosciences

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gradient is proportional to the gradient in air density, it will not result in diffusional transport and yield wrong fluxes. Therefore, we expressed CO 2 concentration as a molar fraction and accounted for the air density.
where F is the mass flux (kg m À2 s À1 ), ρ is the density of air (kg m À3 ), and C is the relative CO 2 concentration (dimensionless) at depth z (m) in the soil. D app can then be calculated by rearranging this equation: It is important to note that if the chamber soil CO 2 efflux results from transport mechanisms other than diffusion, these are also comprised by D app .

Measurements of Soil CO 2 Concentrations and Soil CO 2 Efflux
Chamber-based measurements of soil CO 2 efflux showed most variability at daily time scales, with an amplitude apparently in phase with variations in temperature, light (PAR), and wind speed (Figure 1). Soil CO 2 concentrations measured with solid-state sensors at 5 cm and 10 cm depths and measured with the Li-8150 system at 0 cm depth were much less variable both at seasonal and daily time scales. As the CO 2 gradient is a driver of the CO 2 efflux, we expected a clear relationship between the two types of measurements, but we found that the soil CO 2 concentration gradients from 5 to 0 cm and from 10 to 5 cm depths were uncoupled from the efflux measured with the chambers. Slopes of the correlations between the concentration measurements at 10 cm and at 5 cm depth with the fluxes were not significantly different from zero (p = 0.92 and p = 0.33, respectively).

Calculation of Soil CO 2 Efflux With Flux-Gradient Approach
Using Fick's law (equation (1)), we calculated the soil CO 2 efflux from the measured soil CO 2 concentrations at 5 and 0 cm depths and the modeled diffusivity. We will refer to this calculated flux as the solid-state CO 2 efflux as distinct from the chamber CO 2 efflux. Note that we did not use the concentrations at 10 cm depth in   Figure 2). Importantly, none of the four models was able to reproduce the large daily variation in soil CO 2 efflux that was observed with the chamber-based measurements ( Figure 2).
The diurnal course of the solid-state fluxes clearly followed that of the CO 2 concentrations, soil temperature, and soil moisture content, while the course of the chamber fluxes followed that of wind speed and PAR. As a result, the daily peaks of solid-state fluxes lagged the chamber fluxes with approximately 4 h.

Effective and Apparent Diffusivities, D s and D app
By inverting Fick's law and combining the chamber-based CO 2 efflux measurements and the solid-state CO 2 concentration measurements, we calculated D app and compared this with the four commonly used models to calculate D s . D s calculated from all four models strongly differed from   (Figure 3a). While D s linearly decreases with increasing soil moisture, D app revealed a different pattern (Figure 3a). Only for soil water contents above 33%, D app markedly decreased with increasing soil moisture. At soil water contents below 33%, D app was unrelated to soil moisture and substantially varied even at similar values of soil water content.
Because soil moisture is the primary determinant of gas diffusion in soils (see equations (4)-(8)), the high variation of D app at similar soil moisture, especially at soil moisture levels below 33%, suggests that processes other than diffusion influence the transport of CO 2 from soil to atmosphere. Therefore, we tested whether light (PAR), soil temperature, and wind speed affected D app . Figures 3b and 3c show that D app indeed responded positively to variations in light and wind speed. We found no correlation between the soil temperature and D app , and the temperature dependence of D s was very weak (data not shown). We further explore the correlations of D app with light and wind speed by fitting for each day the 48 half hourly values of D app versus PAR and wind speed. The correlation of D app and wind speed was consistently positive for days with relatively low soil water content (<33%; Figure 4a, asterisks). Correlations between D app and PAR were positive for almost all days (Figure 4b), indicating that D app and thus the rate of CO 2 transport increases with higher irradiation. Furthermore, the slopes of the 24 h fits of D app versus PAR were positively correlated with wind speed (Figure 4c), indicating that the coupling of D app and irradiation are amplified under windy conditions. To rule out any bias in either of our field measurement series, we subjected other data sets of combined solid-state and chamber measurements, from the previous year and with different placement, to this analysis and found similar results (data not shown).
We tested how much of the overall variation in D app could be attributed to variation in PAR, wind speed, and soil moisture, both for days above and below the threshold of 33% soil moisture content. The results of these multiple linear regressions are summarized in Table 1. For the entire data set, the combination of the three parameters explained 67% of the variation in D app . The combination of wind speed and PAR explained a larger part of the variation in D app under moderately wet conditions (47%) than under very wet conditions (40%).
Comparing half hourly values of soil CO 2 concentrations with soil CO 2 efflux measured once every half hour implies comparing different integration times. To avoid statistical bias related to a reduction in variability due to longer integration time, we tested how the soil CO 2 efflux depended on the integration time of the flux-gradient approach. To this end, we used the Penman's [1940] equation, because it yielded the best result in predicting the effective diffusivity in the soil (see Figure 2). Increasing the integration time of the solid-state  a Regressions were carried out on the whole data set, on the subset of data where SWC was below the threshold of 33% and on the subset of data where SWC was above this threshold.

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andchamber measurements resulted in slightly improving accordance between D app and D s (Figure 5), but even increasing the integration time to one month yielded poor agreement between D app and D s .

Discussion
Soil CO 2 concentrations and effluxes were studied at a mountain meadow in the Stubai Valley (Austrian Alps) during the period of peak biomass production in 2009. Diurnal variations in concentrations were small, while they were much larger for the chamber measurements, exceeding even the seasonal variability. Furthermore, when pooling all data pairs, both types of measurements seemed largely uncoupled, which is surprising given that the concentration difference of CO 2 between soil and atmosphere is assumed to be the main driver of the soil CO 2 efflux. Part of this uncoupling might be attributable to a time lag between photosynthesis and CO 2 efflux, as reported by Vargas et al. [2011], but since such lag was not observed in the times series of soil CO 2 concentration and efflux (Figure 1), we expect it to play a minor role here. The importance of a storage term was evaluated by looking at the instantaneous changes in soil CO 2 concentrations, but as these turned out to be very small, a storage flux is unlikely to explain the uncoupling of concentration and flux measurements here. Flechard et al. [2007] pointed out that storage occurs only when diffusive transport prevails.
To evaluate the importance of nondiffusive transport mechanisms in determining the soil CO 2 efflux at this site, we compared solid-state CO 2 fluxes, calculated with the flux-gradient approach, to the chamber CO 2 fluxes. The use of Fick's law in the flux-gradient approach requires estimates of soil diffusivity that are in turn determined by the tortuosity factor. Different models exist for calculation of this tortuosity factor, all of them strongly depending on the air-filled pore space and thus on the soil water content [Werner et al., 2004]. Among the models tested here, the Penman [1940] and Marshall's [1959] models performed better with respect to the overall magnitude of the flux, the Penman's model also being the least sensitive to uncertainties in porosity estimates. The Penman's model yielded the highest soil CO 2 effluxes, which in contrast to what has been frequently reported [Pingintha et al., 2010;Sallam et al., 1984;Werner et al., 2004], did not exceed chamber fluxes but predicted fluxes within the same range. The other three models resulted in fluxes (much) lower than those from chamber measurements. This was especially the case for the Moldrup et al. [1999] and Millington and Quirk's [1961] model, although these have often been reported as yielding the best results [Pingintha et al., 2010;Sallam et al., 1984;Werner et al., 2004]. In our study, the most important outcome was that none of these diffusivity models was able to predict the short-term (i.e., diel and day to day) variation of the soil CO 2 efflux in an acceptable way (Figure 2).
Further analyses pointed out that this disagreement is related to the fact that the tortuosity models, based on diffusive transport, depend almost completely on the soil water content. The role of the moisture content on diffusive transport is twofold. First, by decreasing the air-filled pore space, as diffusion of CO 2 through water is much slower than diffusion through air. Second, there can be a hysteric effect of the water content on the effective diffusivity, D s being higher at a similar water content during wetting than during drying [Goffin et al., 2014;Rouf et al., 2012]. It is important to note here that the short-term response of soil respiration to changes in soil moisture is also not monotonic; CO 2 production increases from low to intermediate soil moisture, reaches a plateau at optimum moisture, and decreases again at high soil moisture [Vicca et al., 2014]. At our site, however, the rate of CO 2 transport from soil to atmosphere depended not only on soil moisture but also on irradiation (PAR) and wind speed. The correlation coefficients of the fits of apparent diffusivity, D app , versus wind speed were consistently positive on days that were not very wet, i.e., when soil water content was below 33% (Figure 4a). D app was also positively related to PAR (Figure 4b), indicating a positive light effect on CO 2 transport from soil to atmosphere. Last, the slopes of the linear regressions showed that the coupling of D app and PAR became stronger as wind speed increased (Figure 4c). Note that higher values of PAR and wind speed were recorded in periods when soil moisture content was below 33%, therefore leading also to higher values of D app in these periods. The response of D app to these drivers, on the other hand, did not differ for periods with soil moisture content above and below 33% (intercepts of the correlations differed but not the slopes). The effect of wind speed on D app was similar during day and nighttime.
The large diel variations we observed in D app and its tight coupling to PAR should not be mistaken for a soil respiration-driven effect on diffusive CO 2 transport. Soil respiration is known to be strongly influenced by temperature and thus exhibits a pronounced diel pattern. This diel pattern can be further amplified by the linkage between belowground carbon allocation and photosynthetic activity. The increase in photoassimilates allocated below ground was often shown to stimulate autotrophic and heterotrophic respiration [Bahn et al., 2009;Hogberg et al., 2001;Janssens et al., 2001;Kuzyakov, 2006;Kuzyakov and Gavrichkova, 2010].
The diurnal pattern in soil respiration was clearly seen in the chamber-based soil CO 2 efflux measurements, but surprisingly much less in the soil CO 2 concentration measurements. This suggests that an increased transport rate, exceeding diffusion, during the day must have prevented soil CO 2 concentrations to rise, while soil respiration did increase. Diffusion primarily depends on soil moisture and on the concentration gradient, both of which varied only little during the day. Enhanced transport of CO 2 through the soil via other processes should thus explain the discrepancy between the large diel amplitude of soil CO 2 efflux and the relatively steady soil CO 2 concentrations.
Several mechanisms causing the bulk flow of CO 2 -enriched soil air have been described in literature (see Kuang et al. [2013] for an extensive review) and can occur in all soils when pores are connected and not blocked by water [Cuezva et al., 2011]. An increasing number of authors have demonstrated a positive correlation between pressure pumping and soil CO 2 efflux [Arneth et al., 1998;Baldocchi and Meyers, 1991;Lewicki et al., 2010;Subke et al., 2003]. Takle et al. [2004] found that these pressure fluctuations penetrated into a dry soil up to 50 cm with little attenuation, and Bowling and Massman [2011] found a temporarily transport enhancement through a forest snowpack up to 40% higher than diffusion. Pressure pumping is controlled by the degree of permeability of the medium and the direction and magnitude of the pressure gradient [Massman et al., 1995;Takle et al., 2003]. Pressure gradients can be caused by barometric waves, passage of synoptic weather systems, short-period atmospheric turbulence, and wind blowing across irregular topography [Elberling et al., 1998;Massman et al., 1997;Takle et al., 2004].
Bulk air transport (in this context called ventilation) was described in permeable, dry, and fractured media, such as karst systems, and was found to be coupled to pressure gradients as well as wind [Rey et al., 2012;Sanchez-Canete et al., 2013;Serrano-Ortiz et al., 2010].
The bulk exchange of gases is enhanced when drying of the soil increases the air-filled porosity and by high wind speeds [Hirsch et al., 2004;Kimball and Lemon, 1971;Maier and Schack-Kirchner, 2014;Sanchez-Canete et al., 2013;Subke et al., 2003]. The positive correlation that we found between D app and wind under relatively dry conditions could therefore be attributable to pressure changes caused by wind shear at the soil surface.
Advective bulk air transport can also be triggered by the local heating of the soil surface [Ganot et al., 2014]. This heating would not be recorded by the soil temperature sensors, which were installed at 5 and 10 cm depths, but inevitably coincides with measurements of irradiation. A second light-coupled process that may amplify bulk soil air transport is the breaking of the soil boundary layer following thermal expansion and uplifting of the air at the soil-atmosphere interface.
Several things could improve the ability to accurately estimate CO 2 efflux from vertical concentration gradients. First, D s , and thus porosity and tortuosity, should be independently estimated using intact soil cores [DeSutter et al., 2008;Jassal et al., 2005] or in situ field methods based on inert tracers such as radon Journal of Geophysical Research: Biogeosciences 10.1002/2014JG002788 [Risket al., 2008], although even these methods cannot fully capture the spatial and temporal dynamics of the soil gas diffusivity . Next, part of the discrepancy that we observed between solid-state and chamber CO 2 efflux might be reconciled when both types of measurements are carried out with the exact same measuring frequency and interval, as the variability of solid-state concentrations with longer integration time will typically be lower otherwise. This was also brought up by Riveros-Iregui et al. [2008], stating that solid-state sensors might not capture rapid changes in soil properties and respiration, e.g., due to rainfall events. Several authors state that the efflux rates calculated from concentration gradients might be unsuited for deriving short-term fluxes, but that they could be useful for flux estimates over longer time periods [e.g., Vargas et al., 2010] when the importance of nondiffusive transport decreases. However, even after integration over 1 month, we found that apparent diffusivity was higher than effective diffusivity ( Figure 5), thus still resulting in an underestimation of soil respiration rates by the flux-gradient approach. Substantial uncertainty may furthermore arise from the assumption of a linear CO 2 concentration gradient in the soil , although Monson et al. [2006] found it a minor source of error compared to the estimations of D s . The exact measurement height of the 0 cm concentration holds a negligible error, given that the magnitude and diel variability of soil CO 2 above the surface are small due to the atmospheric buffer and affects the gradient only very little [Riveros-Iregui et al., 2008, and own analysis].
Several previous studies did find good agreements between solid-state CO 2 efflux and chamber CO 2 efflux [Jassal et al., 2005;Liang et al., 2004;Pumpanen et al., 2008;Tang et al., 2005]. These studies were conducted in dense forests, where in contrast to grasslands, both light and wind have difficulty penetrating into layers close to the soil surface. This is probably why their effect on soil gas transport was insignificant. Under such diffusion-dominated conditions, the flux-gradient approach can be successfully applied to predict the soil CO 2 efflux.

Conclusions and Recommendations
Over the last decade, research in this field has focused on the measurement of fluxes at the soil surface using a variety of chambers and micrometeorological methods. Recently, the flux-gradient approach proved to be a very cost-efficient way to calculate the soil CO 2 efflux that minimizes soil surface perturbations and provides insights into subsurface CO 2 dynamics. This method uses estimates for effective diffusivity, derived from different models primarily based on the air-filled pore space. Testing four commonly used models, we found substantial deviation between observed and modeled diffusivities, leading to poor predictions of the soil CO 2 efflux when using the flux-gradient approach at shorter time scales.
Gaseous diffusion is often considered as the only mechanism for CO 2 to move from the soil to the atmosphere, while in reality, several gas transport mechanisms can be distinguished in unsaturated porous media like soils, e.g., advective mass transport and pressure pumping. We found strong evidence for such nondiffusive CO 2 transport at our site, given that the rate of transport was coupled to irradiation, with an even stronger coupling under increasing wind speed. Wind speed also had a direct positive effect on the efflux rate when the soil moisture content is comparatively low (<33%), resulting in higher air-filled porosity.
Considering the importance of alternative transport processes is a prerequisite when using solid-state CO 2 concentration measurements to estimate soil CO 2 efflux at any given site. Deviation between apparent (data-based) and effective (model-based) diffusivities may be a first indication of nondiffusive gas transport. Apparent diffusivity can be evaluated by calculation from combined chamber and solid-state sensor measurements (as demonstrated here) or by direct in situ soil gas diffusivity measurements (e.g., with natural or injected 222 Radon as done by Risk et al. [2008]).
Given that nondiffusive transport is especially important at very short time scales and its influence decreases with increasing time scale, we recommend that future studies further explore the importance of the time scale considered (high-frequency versus low-frequency data) and the effects of uncertainties in porosity on this. Combined high-frequency measurements of soil CO 2 concentrations and its potential physical drivers, including air pressure and friction velocity, under a wider range of soil moisture conditions, are needed to obtain a more detailed picture of the mechanisms and time scales relevant for nondiffusive transport of CO 2 on soils.