A considerable fraction of soil-respired CO2 is not emitted directly to the atmosphere

Soil CO2 efflux (Fsoil) is commonly considered equal to soil CO2 production (Rsoil), and both terms are used interchangeably. However, a non-negligible fraction of Rsoil can be consumed in the subsurface due to a host of disparate, yet simultaneous processes. The ratio between CO2 efflux/O2 influx, known as the apparent respiratory quotient (ARQ), enables new insights into CO2 losses from Rsoil not previously captured by Fsoil. We present the first study using continuous ARQ estimates to evaluate annual CO2 losses of carbon produced from Rsoil. We found that up to 1/3 of Rsoil was emitted directly to the atmosphere, whereas 2/3 of Rsoil was removed by subsurface processes. These subsurface losses are attributable to dissolution in water, biological activities and chemical reactions. Having better estimates of Rsoil is key to understanding the true influence of ecosystem production on Rsoil, as well as the role of soil CO2 production in other connected processes within the critical zone.

Soil carbon dioxide (CO 2 ) efflux is the second largest contributor to terrestrial CO 2 exchanges, similar in scale to uptake by terrestrial photosynthesis 1,2 . Soil CO 2 efflux (F soil ) is defined as the rate of CO 2 exchange between soil and atmosphere, and it is the result of soil CO 2 production (R soil ) and its transport to the atmosphere. Rates of R soil are the result of heterotrophic respiration during the decomposition of organic matter by microbes and autotrophic respiration by roots 3 . Both F soil and R soil act together in response to the interactions between biotic and abiotic factors [4][5][6] . Generally, F soil increases with the productivity of an ecosystem 7 , driven by increases in temperature and precipitation 1,8 . With ample water, temperature is the dominant driver of F soil , however, in arid and semiarid ecosystems, patterns of F soil are often driven by precipitation pulses [9][10][11][12][13] and variation in soil moisture.
F soil can be measured using manual or automatic chambers 14,15 that capture CO 2 emitted from the soil surface to the atmosphere or estimated by the gradient method through measures of the soil CO 2 molar fraction at multiple depths 16,17 . Commonly, F soil is considered equal to R soil , and the two terms are used interchangeably within the literature and in land surface models. However, a considerable fraction of the R soil can fail to actually emerge from the soil surface (F soil ) due to a host of different processes, such as aqueous phase partitioning 18 , calcite dissolution reactions 19 , gravitational percolation due to a higher density 20 , or CO 2 dissolution in xylem water 21 . Therefore, simple estimations of F soil are likely lower than actual rates of R soil . Misrepresenting F soil as R soil can have significant consequences for interpretation of both biotic and abiotic processes because it not only underestimates the contributions of aboveground function to belowground processes, but it also yields a misguided understanding of the rates and drivers of subsurface biogeochemistry and the potential for carbon exports from the system through hydrological transport.
The importance of these alternative CO 2 loss pathways is illustrated when considering that soil can store an order of magnitude greater CO 2 as dissolved inorganic carbon (DIC, inclusive of dissolved CO 2 , carbonic acid, bicarbonate, and carbonate) in the aqueous-filled relative to gas-filled pore space 22 . As a result, large CO 2 losses can be produced by DIC leaching in all ecosystems around the world, with increased CO 2 losses in ecosystems with higher precipitation and higher soil solution pH. In semiarid regions, this DIC leaching may explain a portion of the missing terrestrial carbon sink 23 . For this reason, distributed measures of O 2 , which has an aqueous solubility 29.7 times lower than CO 2 at 15 °C and does not form additional chemical species by dissolution in water, provides a useful constraint on determining soil CO 2 production that might otherwise be missing from R soil .

Results
The annual time series of climatic and edaphic variables are shown in Fig. 2. During 2015, mean air temperature was 9.4 °C, ranging from −10 to 22 °C with synoptic scale fluctuations driven by atmospheric pressure variations associated with passing of frontal systems (Fig. 2a). Mean soil temperature across all depths was ca. 9.3 °C, with variability decreasing in amplitude with depth (Fig. 2b). Volumetric soil water content (VWC) averaged 20% across all depths with variation over time driven by rainfall events, falling mainly during the monsoon period (typically July-October; Fig. 2c). In 2015, however, the precipitation period extended until mid-November due to an El Niño southern oscillation event. The high VWC measured in January-February was due to snowmelt. When precipitation intensity was greater than 3 mm in 30 min, the delay between precipitation and a VWC response was less than 30 min.
Dynamics of the variables considered to control soil gas concentrations and their exchange with the atmosphere are shown in Fig. 2d-g. Mean CO 2 volumetric fraction increased with depth, with average values of 0.25, 0.57 and 0.64% at 10, 30 and 60 cm, respectively. We found a clear annual pattern analogous to the temperature pattern, with maxima in summer and minima in winter. Superimposed on this seasonal trend is pulsed increases in the volumetric fraction of CO 2 driven by precipitation events, with larger amplitude responses during warmer months. Mean O 2 volumetric fraction decreased with increasing depth from 20.27%, to 19.27% and 18.04% at 10, 30 and 60 cm, respectively. The mean O 2 volumetric fraction was significantly different at the three depths, and this difference was sustained through the entire year (F 2,336 = 213.9; P < 0.05). Minimum O 2 values occurred in the deepest depths during the snowmelt period, and O 2 variations were anti-correlated with CO 2 at 10 cm (R 2 0.94, p > 0.05) and 30 cm (R 2 0.89, p > 0.05) throughout the year. However, at 60 cm a poor correlation (R 2 0.11, p > 0.05) was found due to the decoupling during the snowmelt. When the snowmelt period (from January 8 Figure 1. Measurements of apparent respiratory quotient (ARQ), i.e., the ratio of soil CO 2 efflux/O 2 influx, have the potential to provide improved quantification of soil respiration, and partitioning of soil respiratory CO 2 into vertical (upward) gaseous and lateral or downward dissolved fluxes. Here, R soil is the soil CO 2 production measured, either using the traditional efflux method (R soil_trad ) or on the basis of ARQ (R soil_ARQ ). F soil , which is the soil CO 2 (upward) efflux estimated by the CO 2 gradient method, is typically equated to soil respiration (R soil_trad ). However, direct continuous measurements of ARQ, as conducted in the current work, reveal that a significant fraction of CO 2 produced by soil respiration is transported or consumed in the subsurface, and not locally emitted to the atmosphere. Hence, a substantial amount of respired CO 2 -unaccounted for by quantifying F soil alone, and denoted here as R loss -can be estimated on the basis of concurrent measures of O 2 influx to soil. The ARQ method reveals a significant component of soil respiration (R loss ) that is not emitted locally to the atmosphere. R loss is the CO 2 produced, but unaccounted for, in traditional measures of CO 2 surface efflux. This R loss is consumed by subsurface processes attributable to dissolution in water, vertical and lateral transport along hydrologic flow paths, chemical reactions (including, e.g., silicate and carbonate mineral weathering), and potential degassing upon groundwater discharge (e.g., to streams). Non-negligible values of R loss indicate that (i) flux based measurements alone significantly underestimate local soil respiration and (ii) an important fraction of soil respiratory CO 2 production is consumed in subsurface reactions. R soil_ARQ is the total soil CO 2 production, and the sum of R soil and R loss .
Scientific REPORtS | (2018) 8:13518 | DOI:10.1038/s41598-018-29803-x to February 20) was excluded from regression analysis, the correlation between O 2 and CO 2 increased notably in deeper layers, with R 2 values of 0.95, 0.92 and 0.46 at 10, 30 and 60 cm, respectively. Large O 2 fluctuations at 60 cm during the snowmelt period could be due to the snowmelt during daytime producing a wetting front that percolates to lower permeability soil horizons (higher clay content) at depth, stimulation of soil respiration and hence O 2 consumption, but with near saturation conditions limiting diffusion of O 2 into the soil from above. ARQ showed similar mean values at all depths (ca. 0.3), reaching minimum values at 60 cm during snowmelt (January-February) and maximum values at 10 cm in April. F soil was at its maximum during summer and minimum during winter, with an annual mean of 1.64 µmol m 2 s −1 . Means, standard deviations, minima, maxima, and correlation coefficients for variables shown in Fig. 2 (Tables 1S and  2S). Monthly descriptive statistics for edaphic variables and ARQ are also included there (Fig. 1S).

are included in Supplementary Information
We also examined, in one soil pedon at 30 min averages, the dynamic behaviour of CO 2 and O 2 through several rain pulse events to capture their combined effects on ARQ (Fig. 3). ARQ slightly increased at 10 cm and 30 cm in response to rain pulses, but remained stable at 60 cm. Interestingly, the rapid increases in CO 2 induced by rain events were counteracted by rapid decreases in O 2 , causing only small variations in the ARQ range (c.a. 0.2-0.3). The time to return to values similar to those prior to the precipitation event for CO 2 , O 2 , ARQ and VWC was not delayed with depth. At 10 cm depth, diurnal ARQ fluctuations showed a higher amplitude than at deeper depths, driven by higher amplitude in the O 2 fluctuations at 10 cm.
The annual cumulative F soil , including consideration of the CO 2 loss (R soil_ARQ , 2012 ± 223 gC m −2 ) was 3.2 times higher than traditional estimates of F soil derived using the gradient method (622 ± 86 gC m −2 , using eq. 1). This suggests that ca. 1400 gC m −2 were removed from R soil (Fig. 4) prior to efflux from the soil surface. These ca. 1400 gC m −2 represent the soil CO 2 efflux not emitted to the atmosphere (R loss ) in the vicinity of production. If R soil was fully emitted to the atmosphere locally, by upward gaseous diffusion processes, with zero R loss , then R soil would accurately reflect F soil . However, this was not the case. The smallest differences between F soil using the traditional assumption of equalling R soil verses using R soil_ARQ were in March, April, September and October, but even then, our recalculated F soil was still 2.7-3.0 times higher (Fig. 4). Maximum differences were produced in January   and December, when our recalculated F soil was 5.3-5.6 times higher. Our two estimates of F soil (with and without accounting for R soil_ARQ ) followed similar monthly patterns despite the differences found in ARQ. The degree of agreement between F soil , estimated using the gradient method (Fig. 2g), and periodic chamber measurements of F soil can be found as Supplementary Information (Fig. 2S).

Discussion
Given the significant role of soil carbon dynamics in determining other bio-hydro-geochemical processes in the critical zone, there is a need to better understand the dynamic nature of CO 2 production and loss from an ecosystem. The low ARQ values we found here (ARQ ≈ 0.3, Fig. 2 and Table 1S) in comparison to oxidative ratios expected for natural organic matter (i.e., moles of O 2 consumed per mole of CO 2 produced during respiration of organic matter, which average ca. 1.1 24 equivalent to ARQ = 0.9), highlight the important role of subsurface biological and non-biological processes in removing CO 2 from R soil . These processes are discussed further below.
If all R soil were emitted directly to the atmosphere by gaseous diffusion processes (that is, if F soil = R soil ), as is commonly assumed, F soil would be on average approximately three times higher (due to ratio between ARQ theoretical/ARQ measured, 0.9/0.3). Therefore, assuming that all O 2 consumption is associated with respiration, in this semiarid forest only 1/3 of R soil is emitted directly to the atmosphere and 2/3 are removed by subsurface processes. These results are actually quite similar to those found in the only other paper that has calculated in situ ARQ for estimates of F soil 22 , which reported a mean ARQ of 0.26 and, therefore, an R soil that is 3.8 times higher than F soil estimated in their experimental site (Yatir forest). In that study, researchers collected CO 2 and O 2 samples in a pine forest overlying chalk and limestone bedrock with a mean annual precipitation of 280 mm. Despite their site receiving only 1/3 of the precipitation of our site, and therefore less potential for CO 2 reaction with soil water, a similar ARQ was obtained. This could be attributed to a different composition (and hence oxidative ratio) of the soil organic matter undergoing decomposition, and the effect of CO 2 -consuming calcium carbonate dissolution reactions in their soils. Here, we used ARQ = 0.9 as a representative respiratory quotient (RQ) value since it is the mean value corresponding to biomolecular components of natural organic matter 24 , but if we had used for example the 0.74 value measured for a grassland soil 25 , the calculated annual F soil would be 1023 g C m −2 , which would be only 1.6 times higher F soil (assuming that all R soil is emitted by diffusion processes). This highlights the fact that the contribution of R soil_ARQ to F soil will depend on the oxidative ratio of the organic matter undergoing degradation, which could potentially change seasonally or with location. Nonetheless, our results are in accordance with Angert et al. 22 and underscore the important contribution of subsurface processes in removing CO 2 (or O 2 ) from the soil gas phase prior to its efflux from the soil surface, and the need for a better understanding of the mechanisms involved in those losses.
Prior measurements of RQ have been mostly limited to laboratory experiments using air samples from natural soils or incubated soils, and we do not know of any other studies with in-situ and continuous estimates of RQ as a function of soil depth. In our case, assuming that only R soil and diffusion of O 2 and CO 2 give rise to ARQ, ARQ will be equal to RQ and the oxidative ratio (OR) of organic matter undergoing degradation. In this study, the annual mean RQ (calculated as ARQ/0.76) across all depths was 0.38, which was lower than RQ values for some soils ranging from 0.82 to 1 22,26-29 , but similar to or exceeding those of other soils ranging from 0.21 to 0.40 22,[30][31][32][33] . Incubation studies have found a decrease in RQ values with time, often attributed to a depletion of labile organic matter (organic acids and carbohydrates). In such conditions, the microbiota shift to metabolizing less energetically favourable compounds with lower RQ values, such as lipids, lignin and protein 34 . Therefore, the low RQ values found here might suggest that the carbon in the organic matter undergoing degradation was of relatively low oxidation state. However, RQ values were far lower than the common values of 0.88 for lignin and 0.73 for lipids 35 , suggesting that low RQ substrates cannot alone explain our results; there must also be CO 2 or O 2 consuming processes contributing to these very low values.
Significant soil CO 2 losses can also be driven by DIC drainage and chemical reactions in the soil. The solubility of CO 2 in water is described by Henry's law, which states that the number of moles of dissolved CO 2 plus carbonic acid per liter of water (collectively referred to as [H 2 CO 3 *]) are directly proportional to the CO 2 partial pressure and inversely proportional to temperature. In this study, based on aqueous geochemical calculations 36 , the potential CO 2 removed as DIC during the whole year would be 15.35 gC m −2 . This would represent roughly 2.5% of the cumulative F soil (622 gC m −2 ) and a 1.1% in the C removed from the cumulative R loss (1390 gC m −2 ). These low values of downward DIC transport to groundwater are consistent with the low values of flux estimated globally 37 . Since they only had individual measurements taken at specific time points, Angert et al. 22 posited that measurements and considerations of ARQ might become less important on annual and longer timescales when the effects of CO 2 storage and release might be cancelled out. However, using continuous sensing of gas phase composition, we find the opposite. Based on our estimates, when accumulated over an annual time scale, the amount of loss was significant. This may be due, in part, to the complex topography at our mountain site, where the CO 2 -enriched water percolates to depth and is then transported laterally to groundwater discharge locations, where it may subsequently degas to the atmosphere directly 23,38,39 . Indeed, we have observed that the ephemeral stream draining the mountain study site, which runs during snowmelt or intense rainfall events, is in equilibrium with partial pressures of CO 2 that are, on average, 5.4 ± 3.1 times higher than atmospheric 40 . Furthermore, stream discharge of highest [H 2 CO 3 *] waters is followed a couple of weeks later by a pulse of dissolved silicon derived from rock weathering 40 . With respect to chemical reactions, only those that consume CO 2 or O 2 lead a decrease in RQ. Potential CO 2 consuming reactions include those wherein CO 2 is a reactant in mineral dissolution, such as the dissolution of primary and secondary silicates 41 , (oxyhydr)oxides or calcite.
Given that plagioclase is a kinetically labile primary silicate mineral present in the soil profiles of our study site, it is reasonable to expect that some portion of the respired CO 2 is consumed in its weathering to form kaolinite, also observed in our profiles ( Table 1). The CO 2 -driven weathering of plagioclase to kaolinite consumes two moles of CO 2 per mole of plagioclase. Numerous prior laboratory and field studies have measured rates of Scientific REPORtS | (2018) 8:13518 | DOI:10.1038/s41598-018-29803-x plagioclase dissolution at pH values similar to those of the pore waters at our site (ca. pH 5.4). Laboratory-derived weathering rates of plagioclase are typically two to three orders of magnitude higher than those derived from field data (White & Buss, 2014). Hence, whereas steady state laboratory rates are approximately 1.5 × 10 −12 moles m −2 s −1 , field-measured rates are closer 1 × 10 −14 moles m −2 s −1 or lower (normalization in this case is to plagioclase surface area) 42 . Given the mass fraction of plagioclase in the study soils, a soil bulk density of 1.5 g cm −3 , and assuming a specific surface area for the plagioclase as 5.6 m 2 g −1 (estimated as 3/(particle density x particle radius)) 43 , we calculate that the steady state rates of plagioclase dissolution could account for consumption of ca. 3.0 to 230 gC m −2 y −1 . Importantly, plagioclase is only one of the primary silicates present in our soils; other labile silicates, such as K-feldspar and mica, will consume comparable quantities of CO 2 during dissolution and both are present at higher mass concentrations. Nonetheless, it seems clear that silicate dissolution alone is unlikely to explain all of the CO 2 removed in our study. O 2 consuming reactions include the oxidation of Fe(II), NH 4 + , NO 2 − , mineral sulfides, H 2 S and SO 2 44 . The rates of pyrite (FeS 2 ) oxidation in regolith are controlled by the delivery of O 2 to the weathering zone, which consumes 3.75 moles of O 2 per mole of pyrite oxidized, and hence this can be a significant sink for O 2 in soil systems 45 . In our site, this potential contribution may be limited (though not negligible) because of low pyrite content in the schist-derived mineral assemblage. However, biotite (mica) content in our micaceous schist derived soil is significant, representing up to 14% of the bulk soil mineral mass (Table 1), and it can contain up to three moles of Fe(II) per mole of formula, with 0.25 moles of O 2 being consumed per mole of Fe(II) oxidized to Fe(III) during biotite weathering. Although nitrification processes were already considered in the RQ values previously shown, the deposition of calcareous atmospheric dust along with high inputs of Ca 2+ , Mg 2+ , K + , Na + , as found in the region 46 , could have contributed to lowering RQ values due to chemical reactions. Calcite dissolution plays an important role in producing and consuming CO 2 in carbonate-containing soils 19 , with one mole of CO 2 consumed per mole of calcite dissolved. The relative contribution of this reaction to subsurface CO 2 consumption is unclear because CaCO 3 does not accumulate to levels quantifiable by X-ray diffraction and soil pH (5.4) is moderately acidic. Nonetheless, the mineralogical and geochemical composition of the soil (Table 1) indicate that all of the previously mentioned reactions could consume CO 2 and O 2 to varying degrees, contributing the low ARQ value we measured here.
Microbial composition likely also impacts the ARQ observed in a given soil. The moles of CO 2 produced per mole of O 2 consumed depends, in part, on the microbial carbon-use efficiency (i.e., the ratio of growth to carbon uptake) of the heterotrophic community 47 . Hence, microbial community composition and environmental conditions (e.g. temperature, tends to decline carbon-use efficiency with increasing temperature) will likewise influence the moles of CO 2 produced per mole of O 2 consumed for a given substrate. The minimum ARQ was obtained at 60 cm during the snowmelt period (Fig. 2f) induced by the minimum O 2 values. However, the maximum ARQ occurred in April. We speculate that this may be the result of the accumulation, over winter, of labile and energetically favourable organic compounds (organic acids and carbohydrates) that are oxidized by a heterotrophic microbial community activated by increasing spring temperatures. Oxidation of such compounds, containing carbon in a higher oxidation state, results in a higher ratio of moles of CO 2 produced per mole of O 2 consumed. Furthermore, chemolithoautotrophic and photoautotrophic organisms can assimilate CO 2 without O 2 production using different metabolic pathways. Photoautotrophic and chemoautotrophic organisms that fix CO 2 and transform it into microbial biomass have been found to be highly abundant in forests 48 , with a global rate for microbial synthesis of organic C of 4.9 to 37.5 gC m −2 year −1 in different soils 49 . Methanogenic bacteria that metabolize CO 2 to decompose organic matter to CH 4 under anaerobic conditions 50 have been observed even in well aerated soils such as those found in deserts 51 . Therefore, the low ARQ and RQ values found in our soils could indicate one or several processes whereby (i) CO 2 is being removed laterally as dissolved H 2 CO 3 *, (ii) CO 2 and O 2 are consumed in geochemical reactions, or (iii) a biological O 2 consumption occurs without emission of CO 2 and vice versa.
Subsurface CO 2 consumption has been studied both in soil-atmosphere CO 2 exchanges and in CO 2 exchanges at the ecosystem level. Roland et al. 52 used a chemical carbonate weathering model to explain non-biological fluxes detected at ecosystem scale in a karst, finding that the CO 2 coming from deeper layers at night could be stimulating carbonate dissolution and, thus, consuming CO 2 . Hamerlynck, et al., 53 found a negative F soil at night in a Chihuahuan desert shrubland, both using an automatic soil chamber and using the gradient method with CO 2 sensors buried in the shallowest layer, similarly attributing the CO 2 consumption to carbonate dissolution. Additionally, temperature influences on the solubility of CO 2 (Henry's Law) were suggested in explaining negative F soil in Antarctic dry valley ecosystems 54,55 , and soil electrical conductivity and pH were correlated with CO 2 uptake in alkaline desert soils 56 . All of these studies found negative F soil , highlighting that CO 2 consumptive processes in the soil were higher than CO 2 production processes. This is not unexpected in such ecosystems,

Depth (cm) Quartz
Plag-Feldspar K-Feldspar Iron Oxides where R soil is very low due to low biological activity and therefore even small changes in R soil can change the sign of the soil-atmosphere CO 2 gradient. In our ecosystem, F soil was always positive, but the complementary O 2 measurements provided a novel insight, confirming that even in ecosystems with high biological production, non-biological processes are masked by high R soil and therefore, are difficult to detect from F soil measurements alone.
In conclusion, this study highlights the important and dynamic, but often overlooked, roles played by subsurface transport and weathering processes that differentiate R soil from surface measures or estimates of F soil . As Angert et al. 22 noted, variations in the ARQ in acidic and neutral soils (as we have here) are likely tied to substrates and processes not well understood at present, and such processes warrant further research. Therefore, we must change our point of view regarding R soil studies from an inappropriately conceived system in which all CO 2 is produced by biology, to a dynamic system where the soil CO 2 is produced and removed by the interaction of combinatorial biological processes, hydrologic transport, and associated geochemical reactions. Because the fraction of R soil contributing to F soil depends on the ARQ chosen, we recommend that future F soil studies use a combination of soil CO 2 and O 2 sensors to determine ARQ values. Such an approach can yield important information to quantify the CO 2 removed by biological and non-biological processes. ARQ and RQ values are key in estimating CO 2 sinks deduced from changes in atmospheric O 2 concentration 57 and are highly influential in evaluating ecosystem productivity. Currently, ecosystem productivity is estimated using values of net ecosystem exchange, as the sum of gross primary production (GPP) and ecosystem respiration (R eco ). This may be problematic because that R eco consists of an aboveground component attributed to plant respiration and a belowground component, F soil that we now know may incompletely quantify soil respiration. In our ecosystem, if soil CO 2 losses were calculated from F soil alone, GPP estimates would be erroneously low, and if this is consistent across other ecosystems, it could have enormous implications on carbon exchange studies from ecosystem to global scale.  Table 1.

Material and Methods
Experimental design. Field measurements were conducted during the complete calendar year of 2015.
Three instrumented pedons were equipped to measure each of the following, using co-located sensors: temperature and humidity (5 TM, Decagon, USA), O 2 molar fraction (SO-110, Apogee, USA; Manufacturer reports a sensitivity of 26 µV per 0.01% and repeatability < 0.1% of reading), and CO 2 molar fraction at 10, 30 and 60 cm depth. A drift correction was applied to the O 2 sensors assuming a constant linear signal decrease as the manufacturer reported (1 mV per year). The measurement range of the CO 2 sensors was up to 10,000 ppm at 10 cm and 20,000 ppm at 30 and 60 cm (GMM222 and GMM221, Vaisala, Finland; accuracy 1.5%, repeatability 2% of reading). Both CO 2 and O 2 values were corrected for variations in temperature, humidity, and pressure per instructions from the manufacturer. Atmospheric pressure, air temperature, and precipitation were obtained from a meteorological tower. Data-loggers (CR1000, Campbell scientific, USA) collected measurements every 30 s and stored 30 min averages. The instrumented pedons are separated from each other by distances of ca. 10 meters, and they are located, respectively, on a south facing slope, a north facing slope, and in a convergent valley position within a zero order basin. One-way ANOVA for mean values of soil temperature, soil water content, CO 2 and O 2 between 3 pedons at 3 depths, showed significant differences among all the means at each depth for each variable. Here, we aggregated the three pedons and analysed the average values and their standard error to show the uncertainty in the spatial variability.
Procedure to estimate F soil . Estimates of F soil were obtained using the gradient method through the equation 59 : where F soil (µmol CO 2 m −2 s −1 ), ρ is the air density (mol air m −3 ), ∂c is the CO 2 molar fraction gradient (µmol CO 2 mol air −1 ) calculated using the difference between atmospheric CO 2 molar fraction (400 ppm) and the CO 2 value at 10 cm depth, ∂x is the vertical gradient (m) and k s is the in situ CO 2 transfer coefficient (m 2 s −1 ) obtained by rearranging Eq. 1: where F chamber was measured by a portable soil CO 2 efflux chamber (Li-8100, Li-Cor, USA) from 18 collars around the instrumented pedons, follow a transect from the south face to the north face going through the valley, every two weeks during the months without snow cover (n=20). Later, k s was modelled using a power function (k s / D a = a θ a b ) of the soil air porosity (θ a = soil porosity-soil water content), where D a is the diffusion coefficient of CO 2 in free air (m 2 s −1 ) and a and b are coefficients obtained by least squares regression. Procedure to estimate ARQ. The ratio of soil CO 2 efflux to soil O 2 influx, designated as apparent respiratory quotient (ARQ), was estimated following Angert et al. 22 : where the constant "0.76" is derived from the ratio of CO 2 /O 2 diffusion coefficients in air, ∂ c is the CO 2 molar fraction gradient calculated using the discrete difference between the atmosphere and the CO 2 value at each depth and ∂ o is the O 2 molar fraction gradient calculated using the difference between atmosphere and the O 2 value at each depth. Consumption of either soil CO 2 or soil O 2 will decrease the ARQ; consumption of soil CO 2 decreases the difference in the numerator (∂c) and hence decreases ARQ, whereas consumption of soil O 2 increases the difference represented in the denominator (∂o), and hence also decreases ARQ. ARQ values have previously only been reported by Angert et al. 22 , who found that ARQ ranged from 0.14-1.23 across six different experimental sites. Most previous studies have focused either on the respiratory quotient (RQ), defined as the moles of CO 2 produced per mole of O 2 consumed during R soil , or the oxidative ratio (OR), defined as moles of O 2 consumed per mole CO 2 produced (i.e., 1/RQ). Therefore, if we assume that only R soil drives ARQ, it will be equal to RQ or 1/OR.
The natural biochemical variation in RQ is large depending on the kind of compound undergoing oxidation, ranging from (mean values reported for each biomolecular type) 1.47 for organic acids, 1.00 for carbohydrates, 0.95 for soluble phenolics, 0.88 for proteins and lignins, and 0.73 for lipids (OR values in Randerson et al., 35 ). From stoichiometric considerations, mean RQ values were calculated as 0.95 for different types of wood and 0.89 for humic acid and humin (OR values in Severinghaus 28 ). In soils, RQ values have been reported to vary from 0.83-0.95 for different biomes inside Biosphere 2 28 , 0.82-1.04 for Boreal, Temperate Subtropical and Mediterranean ecosystems 29 , 0.90 in a cool temperate deciduous forest 27 , and a mean value of 1 in the Amazonian tropical forest 26 . Therefore, based on previous research, an ARQ value of ca. 0.9 ± 0.1 is consistent with R soil and diffusion processes alone. However, ARQ values below this would indicate removal of CO 2 or O 2 by non-respiratory processes 22 . Therefore, assuming both abiotic O 2 removal and autotrophic microorganisms in the soil are negligible, to estimate the F soil taking into account the CO 2 loss from the soil, one can multiply R soil (or F soil , assuming that all R soil is emitted to the atmosphere by gaseous diffusion processes, and therefore, F soil = R soil ) by 0.9 ± 0.1 /ARQ, as was done in the current study and previously by Angert et al. 22 .