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

## Abstract

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.

## Introduction

Soil carbon dioxide (CO2) efflux is the second largest contributor to terrestrial CO2 exchanges, similar in scale to uptake by terrestrial photosynthesis1,2. Soil CO2 efflux (Fsoil) is defined as the rate of CO2 exchange between soil and atmosphere, and it is the result of soil CO2 production (Rsoil) and its transport to the atmosphere. Rates of Rsoil are the result of heterotrophic respiration during the decomposition of organic matter by microbes and autotrophic respiration by roots3. Both Fsoil and Rsoil act together in response to the interactions between biotic and abiotic factors4,5,6. Generally, Fsoil increases with the productivity of an ecosystem7, driven by increases in temperature and precipitation1,8. With ample water, temperature is the dominant driver of Fsoil, however, in arid and semiarid ecosystems, patterns of Fsoil are often driven by precipitation pulses9,10,11,12,13 and variation in soil moisture.

Fsoil can be measured using manual or automatic chambers14,15 that capture CO2 emitted from the soil surface to the atmosphere or estimated by the gradient method through measures of the soil CO2 molar fraction at multiple depths16,17. Commonly, Fsoil is considered equal to Rsoil, and the two terms are used interchangeably within the literature and in land surface models. However, a considerable fraction of the Rsoil can fail to actually emerge from the soil surface (Fsoil) due to a host of different processes, such as aqueous phase partitioning18, calcite dissolution reactions19, gravitational percolation due to a higher density20, or CO2 dissolution in xylem water21. Therefore, simple estimations of Fsoil are likely lower than actual rates of Rsoil. Misrepresenting Fsoil as Rsoil 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 CO2 loss pathways is illustrated when considering that soil can store an order of magnitude greater CO2 as dissolved inorganic carbon (DIC, inclusive of dissolved CO2, carbonic acid, bicarbonate, and carbonate) in the aqueous-filled relative to gas-filled pore space22. As a result, large CO2 losses can be produced by DIC leaching in all ecosystems around the world, with increased CO2 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 sink23. For this reason, distributed measures of O2, which has an aqueous solubility 29.7 times lower than CO2 at 15 °C and does not form additional chemical species by dissolution in water, provides a useful constraint on determining soil CO2 production that might otherwise be missing from Rsoil.

The ratio of soil CO2 efflux to O2 influx, known as the apparent respiratory quotient (ARQ), allows one to estimate the CO2 losses from Rsoil22. A diagram, with the main variables involved in exchange and loss of CO2, is shown in Fig. 1. Here we present the first study using continuous ARQ estimates to evaluate annual CO2 losses of carbon from Rsoil (Rsoil_ARQ, where Rsoil_ARQ = Rsoil + Rloss). Our goals were (i) to quantify the values, patterns, and seasonality of ARQ at different soil depths within a semi-arid coniferous forest and then (ii) to estimate the amount of soil CO2 removed through biological and non-biological processes (Rsoil_ARQ) (iii) in order to illustrate the disparity between Fsoil using traditional assumptions that Rsoil = Fsoil and an estimate of Fsoil that takes into account CO2 losses (Rloss) and actual rates of Rsoil, as determined using the ARQ. Having better estimates of Rsoil is key to understanding the true influence of aboveground production on Rsoil, CO2-induced mineral weathering, and other biologically-driven processes within the critical zone.

## 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 CO2 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 CO2 driven by precipitation events, with larger amplitude responses during warmer months. Mean O2 volumetric fraction decreased with increasing depth from 20.27%, to 19.27% and 18.04% at 10, 30 and 60 cm, respectively. The mean O2 volumetric fraction was significantly different at the three depths, and this difference was sustained through the entire year (F2,336 = 213.9; P < 0.05). Minimum O2 values occurred in the deepest depths during the snowmelt period, and O2 variations were anti-correlated with CO2 at 10 cm (R2 0.94, p > 0.05) and 30 cm (R2 0.89, p > 0.05) throughout the year. However, at 60 cm a poor correlation (R2 0.11, p > 0.05) was found due to the decoupling during the snowmelt. When the snowmelt period (from January 8 to February 20) was excluded from regression analysis, the correlation between O2 and CO2 increased notably in deeper layers, with R2 values of 0.95, 0.92 and 0.46 at 10, 30 and 60 cm, respectively. Large O2 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 O2 consumption, but with near saturation conditions limiting diffusion of O2 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. Fsoil was at its maximum during summer and minimum during winter, with an annual mean of 1.64 µmol m2 s−1. Means, standard deviations, minima, maxima, and correlation coefficients for variables shown in Fig. 2 are included in Supplementary Information (Tables 1S and 2S). Monthly descriptive statistics for edaphic variables and ARQ are also included there (Fig. 1S).

We also examined, in one soil pedon at 30 min averages, the dynamic behaviour of CO2 and O2 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 CO2 induced by rain events were counteracted by rapid decreases in O2, 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 CO2, O2, 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 O2 fluctuations at 10 cm.

The annual cumulative Fsoil, including consideration of the CO2 loss (Rsoil_ARQ, 2012 ± 223 gC m−2) was 3.2 times higher than traditional estimates of Fsoil derived using the gradient method (622 ± 86 gC m−2, using eq. 1). This suggests that ca. 1400 gC m−2 were removed from Rsoil (Fig. 4) prior to efflux from the soil surface. These ca. 1400 gC m−2 represent the soil CO2 efflux not emitted to the atmosphere (Rloss) in the vicinity of production. If Rsoil was fully emitted to the atmosphere locally, by upward gaseous diffusion processes, with zero Rloss, then Rsoil would accurately reflect Fsoil. However, this was not the case. The smallest differences between Fsoil using the traditional assumption of equalling Rsoil verses using Rsoil_ARQ were in March, April, September and October, but even then, our recalculated Fsoil was still 2.7–3.0 times higher (Fig. 4). Maximum differences were produced in January and December, when our recalculated Fsoil was 5.3–5.6 times higher. Our two estimates of Fsoil (with and without accounting for Rsoil_ARQ) followed similar monthly patterns despite the differences found in ARQ. The degree of agreement between Fsoil, estimated using the gradient method (Fig. 2g), and periodic chamber measurements of Fsoil 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 CO2 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 O2 consumed per mole of CO2 produced during respiration of organic matter, which average ca. 1.124 equivalent to ARQ = 0.9), highlight the important role of subsurface biological and non-biological processes in removing CO2 from Rsoil. These processes are discussed further below.

If all Rsoil were emitted directly to the atmosphere by gaseous diffusion processes (that is, if Fsoil = Rsoil), as is commonly assumed, Fsoil would be on average approximately three times higher (due to ratio between ARQ theoretical/ARQ measured, 0.9/0.3). Therefore, assuming that all O2 consumption is associated with respiration, in this semiarid forest only 1/3 of Rsoil 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 Fsoil22, which reported a mean ARQ of 0.26 and, therefore, an Rsoil that is 3.8 times higher than Fsoil estimated in their experimental site (Yatir forest). In that study, researchers collected CO2 and O2 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 CO2 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 CO2-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 matter24, but if we had used for example the 0.74 value measured for a grassland soil25, the calculated annual Fsoil would be 1023 g C m−2, which would be only 1.6 times higher Fsoil (assuming that all Rsoil is emitted by diffusion processes). This highlights the fact that the contribution of Rsoil_ARQ to Fsoil 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 CO2 (or O2) 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 Rsoil and diffusion of O2 and CO2 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 122,26,27,28,29, but similar to or exceeding those of other soils ranging from 0.21 to 0.4022,30,31,32,33. 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 protein34. 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 lipids35, suggesting that low RQ substrates cannot alone explain our results; there must also be CO2 or O2 consuming processes contributing to these very low values.

Significant soil CO2 losses can also be driven by DIC drainage and chemical reactions in the soil. The solubility of CO2 in water is described by Henry’s law, which states that the number of moles of dissolved CO2 plus carbonic acid per liter of water (collectively referred to as [H2CO3*]) are directly proportional to the CO2 partial pressure and inversely proportional to temperature. In this study, based on aqueous geochemical calculations36, the potential CO2 removed as DIC during the whole year would be 15.35 gC m−2. This would represent roughly 2.5% of the cumulative Fsoil (622 gC m−2) and a 1.1% in the C removed from the cumulative Rloss (1390 gC m−2). These low values of downward DIC transport to groundwater are consistent with the low values of flux estimated globally37. 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 CO2 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 CO2-enriched water percolates to depth and is then transported laterally to groundwater discharge locations, where it may subsequently degas to the atmosphere directly23,38,39. 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 CO2 that are, on average, 5.4 ± 3.1 times higher than atmospheric40. Furthermore, stream discharge of highest [H2CO3*] waters is followed a couple of weeks later by a pulse of dissolved silicon derived from rock weathering40. With respect to chemical reactions, only those that consume CO2 or O2 lead a decrease in RQ. Potential CO2 consuming reactions include those wherein CO2 is a reactant in mineral dissolution, such as the dissolution of primary and secondary silicates41, (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 CO2 is consumed in its weathering to form kaolinite, also observed in our profiles (Table 1). The CO2-driven weathering of plagioclase to kaolinite consumes two moles of CO2 per mole of plagioclase. Numerous prior laboratory and field studies have measured rates of 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 m2 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 CO2 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 CO2 removed in our study.

O2 consuming reactions include the oxidation of Fe(II), NH4+, NO2, mineral sulfides, H2S and SO244. The rates of pyrite (FeS2) oxidation in regolith are controlled by the delivery of O2 to the weathering zone, which consumes 3.75 moles of O2 per mole of pyrite oxidized, and hence this can be a significant sink for O2 in soil systems45. 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 O2 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 Ca2+, Mg2+, K+, Na+, as found in the region46, could have contributed to lowering RQ values due to chemical reactions. Calcite dissolution plays an important role in producing and consuming CO2 in carbonate-containing soils19, with one mole of CO2 consumed per mole of calcite dissolved. The relative contribution of this reaction to subsurface CO2 consumption is unclear because CaCO3 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 CO2 and O2 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 CO2 produced per mole of O2 consumed depends, in part, on the microbial carbon-use efficiency (i.e., the ratio of growth to carbon uptake) of the heterotrophic community47. 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 CO2 produced per mole of O2 consumed for a given substrate. The minimum ARQ was obtained at 60 cm during the snowmelt period (Fig. 2f) induced by the minimum O2 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 CO2 produced per mole of O2 consumed. Furthermore, chemolithoautotrophic and photoautotrophic organisms can assimilate CO2 without O2 production using different metabolic pathways. Photoautotrophic and chemoautotrophic organisms that fix CO2 and transform it into microbial biomass have been found to be highly abundant in forests48, with a global rate for microbial synthesis of organic C of 4.9 to 37.5 gC m−2 year−1 in different soils49. Methanogenic bacteria that metabolize CO2 to decompose organic matter to CH4 under anaerobic conditions50 have been observed even in well aerated soils such as those found in deserts51. Therefore, the low ARQ and RQ values found in our soils could indicate one or several processes whereby (i) CO2 is being removed laterally as dissolved H2CO3*, (ii) CO2 and O2 are consumed in geochemical reactions, or (iii) a biological O2 consumption occurs without emission of CO2 and vice versa.

Subsurface CO2 consumption has been studied both in soil-atmosphere CO2 exchanges and in CO2 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 CO2 coming from deeper layers at night could be stimulating carbonate dissolution and, thus, consuming CO2. Hamerlynck, et al.,53 found a negative Fsoil at night in a Chihuahuan desert shrubland, both using an automatic soil chamber and using the gradient method with CO2 sensors buried in the shallowest layer, similarly attributing the CO2 consumption to carbonate dissolution. Additionally, temperature influences on the solubility of CO2 (Henry’s Law) were suggested in explaining negative Fsoil in Antarctic dry valley ecosystems54,55, and soil electrical conductivity and pH were correlated with CO2 uptake in alkaline desert soils56. All of these studies found negative Fsoil, highlighting that CO2 consumptive processes in the soil were higher than CO2 production processes. This is not unexpected in such ecosystems, where Rsoil is very low due to low biological activity and therefore even small changes in Rsoil can change the sign of the soil-atmosphere CO2 gradient. In our ecosystem, Fsoil was always positive, but the complementary O2 measurements provided a novel insight, confirming that even in ecosystems with high biological production, non-biological processes are masked by high Rsoil and therefore, are difficult to detect from Fsoil measurements alone.

In conclusion, this study highlights the important and dynamic, but often overlooked, roles played by subsurface transport and weathering processes that differentiate Rsoil from surface measures or estimates of Fsoil. 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 Rsoil studies from an inappropriately conceived system in which all CO2 is produced by biology, to a dynamic system where the soil CO2 is produced and removed by the interaction of combinatorial biological processes, hydrologic transport, and associated geochemical reactions. Because the fraction of Rsoil contributing to Fsoil depends on the ARQ chosen, we recommend that future Fsoil studies use a combination of soil CO2 and O2 sensors to determine ARQ values. Such an approach can yield important information to quantify the CO2 removed by biological and non-biological processes. ARQ and RQ values are key in estimating CO2 sinks deduced from changes in atmospheric O2 concentration57 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 (Reco). This may be problematic because that Reco consists of an aboveground component attributed to plant respiration and a belowground component, Fsoil that we now know may incompletely quantify soil respiration. In our ecosystem, if soil CO2 losses were calculated from Fsoil 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.

## Material and Methods

### Site description

The field site is a mixed conifer forest located at 2573 m a.s.l. on Mt. Bigelow north of Tucson, Arizona, in the Santa Catalina Mountains-Jemez River Basin Critical Zone Observatory58. The climate is semi-arid, with a mean annual temperature of 9.4 °C and mean annual precipitation of 750 mm, falling mostly during the summer monsoon. Snow falls during winter, usually persisting from December to March. Ponderosa pine (Pinus ponderosa) and Douglas fir (Pseudotsuga menziesii) dominate the site with a mean canopy height of 10 m. The soil has a sandy loam texture of 32.3% sand, 41.4% silt and 26.4% clay with a pH of 5.4 and a depth to bedrock of ca. 1 m. Additional information about mineral composition and other soil proprieties can be found in Table 1.

### 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), O2 molar fraction (SO-110, Apogee, USA; Manufacturer reports a sensitivity of 26 µV per 0.01% and repeatability < 0.1% of reading), and CO2 molar fraction at 10, 30 and 60 cm depth. A drift correction was applied to the O2 sensors assuming a constant linear signal decrease as the manufacturer reported (1 mV per year). The measurement range of the CO2 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 CO2 and O2 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, CO2 and O2 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 Fsoil

Estimates of Fsoil were obtained using the gradient method through the equation59:

$${F}_{soil}=-\,\rho {k}_{s}\frac{\partial c}{\partial x}$$
(1)

where Fsoil (µmol CO2 m−2 s−1), ρ is the air density (mol air m−3), $$\partial c$$ is the CO2 molar fraction gradient (µmol CO2 mol air−1) calculated using the difference between atmospheric CO2 molar fraction (400 ppm) and the CO2 value at 10 cm depth, $$\partial x$$ is the vertical gradient (m) and ks is the in situ CO2 transfer coefficient (m2 s−1) obtained by rearranging Eq. 1:

$${k}_{s}=-\,\frac{{F}_{chamber}\,\partial x}{\rho \,\partial c}$$
(2)

where Fchamber was measured by a portable soil CO2 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, ks was modelled using a power function (ks/ Da = a θa b) of the soil air porosity (θa = soil porosity-soil water content), where Da is the diffusion coefficient of CO2 in free air (m2 s−1) and a and b are coefficients obtained by least squares regression.

### Procedure to estimate ARQ

The ratio of soil CO2 efflux to soil O2 influx, designated as apparent respiratory quotient (ARQ), was estimated following Angert et al.22:

$$ARQ=\frac{{F}_{C{O}_{2}}}{{F}_{{O}_{2}}}=\frac{-\rho {D}_{{S}_{CO2}}\,\frac{\partial c}{\partial z}}{-\rho {D}_{{S}_{O2}}\frac{\partial o}{\partial z}}$$
(3)

simplifying,

$$ARQ=\frac{-{D}_{{S}_{CO2}}\,}{-{D}_{{S}_{O2}}}\frac{\partial c}{\partial o}=-\,0.76\frac{\partial c}{\partial o}$$
(4)

where the constant “0.76” is derived from the ratio of CO2/O2 diffusion coefficients in air, $$\partial \,$$c is the CO2 molar fraction gradient calculated using the discrete difference between the atmosphere and the CO2 value at each depth and $$\partial \,$$o is the O2 molar fraction gradient calculated using the difference between atmosphere and the O2 value at each depth. Consumption of either soil CO2 or soil O2 will decrease the ARQ; consumption of soil CO2 decreases the difference in the numerator ($$\partial c$$) and hence decreases ARQ, whereas consumption of soil O2 increases the difference represented in the denominator ($$\partial o$$), 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 CO2 produced per mole of O2 consumed during Rsoil, or the oxidative ratio (OR), defined as moles of O2 consumed per mole CO2 produced (i.e., 1/RQ). Therefore, if we assume that only Rsoil 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 Severinghaus28). In soils, RQ values have been reported to vary from 0.83–0.95 for different biomes inside Biosphere 228, 0.82–1.04 for Boreal, Temperate Subtropical and Mediterranean ecosystems29, 0.90 in a cool temperate deciduous forest27, and a mean value of 1 in the Amazonian tropical forest26. Therefore, based on previous research, an ARQ value of ca. 0.9 ± 0.1 is consistent with Rsoil and diffusion processes alone. However, ARQ values below this would indicate removal of CO2 or O2 by non-respiratory processes22. Therefore, assuming both abiotic O2 removal and autotrophic microorganisms in the soil are negligible, to estimate the Fsoil taking into account the CO2 loss from the soil, one can multiply Rsoil (or Fsoil, assuming that all Rsoil is emitted to the atmosphere by gaseous diffusion processes, and therefore, Fsoil = Rsoil) by 0.9 ± 0.1 /ARQ, as was done in the current study and previously by Angert et al.22.

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## Acknowledgements

This project and data were supported by NSF awards 1417101 and 1331408, as well as by the European Commission project DIESEL (FP7-PEOPLE-2013-IOF, 625988) and the Spanish Ministry of Economy and Competitiveness (IJCI-2016-30822). All data used in this study are freely available (http://criticalzone.org/catalina-jemez/data/datasets/). The authors wish to thank Rebecca Larkin Minor and Nate Abramson for their careful operation and maintenance of the field measurement devices. The program “Unidades de Excelencia Científica del Plan Propio de Investigación de la Universidad de Granada” funded the cost of this publication.

## Author information

G.A.B-G. and J.C. conceived and designed the research. E.P.S.-C. analysed the data, prepared tables and figures and wrote the draft manuscript. E.P.S.-C., G.A.B-G. and J.C. wrote the paper.

### Competing Interests

The authors declare no competing interests.

Correspondence to Enrique P. Sánchez-Cañete.