# Atmospheric turbulence triggers pronounced diel pattern in karst carbonate geochemistry

M. Roland, P. Serrano-Ortiz, A. S. Kowalski, Y. Godderis, E. P.

Sanchez-Canete, Philippe Ciais, F. Domingo, S. Cuezva, S. Sanchez-Moral,
Bernard Longdoz, et al.

► To cite this version:

M. Roland, P. Serrano-Ortiz, A. S. Kowalski, Y. Godderis, E. P. Sanchez-Canete, et al. Atmospheric turbulence triggers pronounced diel pattern in karst carbonate geochemistry. Biogeosciences, 2013, 10 (7), pp.5009-5017. 10.5194/bg-10-5009-2013. hal-01268211

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# Atmospheric turbulence triggers pronounced diel pattern in karst carbonate geochemistry

M. Roland<fnref n="1" />, P. Serrano-Ortiz<fnref n="2" />,<fnref n="3" />, A. S. Kowalski<fnref n="3" />,<fnref n="4" />, Y. Goddéris<fnref n="5" />, E. P. Sánchez-Cañete<fnref n="2" />,<fnref n="3" />, P. Ciais<fnref n="6" />, F. Domingo<fnref n="2" />, S. Cuezva<fnref n="7" />, S. Sanchez-Moral<fnref n="8" />, B. Longdoz<fnref n="9" />, D. Yakir<fnref n="10" />, R. Van Grieken<fnref n="11" />, J. Schott<fnref n="5" />, C. Cardell<fnref n="12" />, and I. A. Janssens<fnref n="1" />

*Correspondence to:* M. Roland (marilyn.roland@ua.ac.be)

Received: 27 November 2012 – Published in Biogeosciences Discuss.: 28 January 2013

Revised: 21 May 2013 – Accepted: 6 June 2013 – Published: 24 July 2013

**Abstract.** CO₂ exchange between terrestrial ecosystems and the atmosphere is key to understanding the feedbacks between climate change and the land surface. In regions with carbonaceous parent material, CO₂ exchange patterns occur that cannot be explained by biological processes, such as disproportionate outgassing during the daytime or nighttime CO₂ uptake during periods when all vegetation is senescent. Neither of these phenomena can be attributed to carbonate weathering reactions, since their CO₂ exchange rates are too small. Soil ventilation induced by high atmospheric turbulence is found to explain typical CO₂ exchange between carbonaceous systems and the atmosphere. However, by strongly altering subsurface CO₂ concentrations, ventilation

can be expected to influence carbonate weathering rates. By imposing ventilation-driven CO₂ outgassing in a carbonate weathering model, we show here that carbonate geochemistry is accelerated and does play a surprisingly large role in the observed CO₂ exchange pattern of a semi-arid ecosystem. We found that by rapidly depleting soil CO₂ during the daytime, ventilation disturbs soil carbonate equilibria and therefore strongly magnifies daytime carbonate precipitation and associated CO₂ production. At night, ventilation ceases and the depleted CO₂ concentrations increase steadily. Dissolution of carbonate is now enhanced, which consumes CO₂ and largely compensates for the enhanced daytime carbonate precipitation. This is why only a relatively

<footnote n="1">¹Department of Biology, University of Antwerp, Universiteitsplein 1, 2610 Wilrijk, Belgium</footnote>

<footnote n="2">²Estación Experimental de Zonas Áridas, Consejo Superior de Investigaciones Científicas (CSIC), Carretera de Sacramento s/n, 04120 Almería, Spain</footnote>

<footnote n="3">³Grupo de Física de la Atmósfera, Centro Andaluz de Medio Ambiente (CEAMA), Avenida del Mediterráneo s/n, 18006 Granada, Spain</footnote>

<footnote n="4">⁴Departamento de Física Aplicada, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada, Spain</footnote>

<footnote n="5">⁵Geosciences Environnement Toulouse (GET), Observatoire Midi-Pyrénées, CNRS, Avenue Edouard Belin 14, 31400 Toulouse, France</footnote>

<footnote n="6">⁶Laboratoire des Sciences du Climat et de l'Environnement (LSCE), CEA CNRS UVSQ, Orme des Merisiers s/n, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="7">⁷Departamento de Ciencias de la Tierra y del Medio Ambiente, Universidad de Alicante, Campus de Sant Vicent del Raspeig, 03080 Alicante, Spain</footnote>

<footnote n="8">⁸Departamento de Geología, Museo Nacional Ciencias Naturales (MNCN-CSIC), José Gutiérrez Abascal 2, 28006 Madrid, Spain</footnote>

<footnote n="9">⁹Ecologie et Ecophysiologie Forestières (EEF), UMR1137, INRA, 54280 Champenoux et Université de Lorraine, 54500 Vandoeuvre Les Nancy, France</footnote>

<footnote n="10">¹⁰Environmental Sciences and Energy Research, Weizmann Institute of Science, 76100 Rehovot, Israel</footnote>

<footnote n="11">¹¹Department of Chemistry, University of Antwerp, Universiteitsplein 1, 2610 Wilrijk, Belgium</footnote>

<footnote n="12">¹²Departamento Mineralogía y Petrología, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada, Spain</footnote>
small effect on global carbonate weathering rates is to be expected. On the short term, however, ventilation has a drastic effect on synoptic carbonate weathering rates, resulting in a pronounced diel pattern that exacerbates the non-biological behavior of soil-atmosphere CO₂ exchanges in dry regions with carbonate soils.

# 1 Introduction

The net carbon balance of ecosystems has become a key focus in the study of the global carbon cycle. The assessment of net ecosystem CO₂ fluxes on different scales of time and space is enabled through eddy covariance measurements that are being performed on “flux towers” around the globe (Baldocchi et al., 2001). Usually these net CO₂ exchanges with the atmosphere are interpreted as the sum of the photosynthetic and respiratory components, while little is known about the role of geological carbon cycling in the soil-atmosphere CO₂ exchange. Recent studies in regions with carbonate bedrock, however, have reported ecosystem CO₂ flux patterns that are not easily explained only by photosynthesis and respiration (Schlesinger et al., 2009; Serrano-Ortiz et al., 2010; Stone 2008; Wohlfahrt et al., 2008; Xie et al., 2009). Daytime CO₂ emissions several orders of magnitude larger than what could be expected from biological principles (Emmerich 2003; Kowalski et al., 2008; Mielnick et al., 2005), and nighttime CO₂ uptake during periods when plants are dormant (Hastings et al., 2005; Kowalski et al., 2008) imply that other processes are playing a role in this exchange. Weathering of carbonates (including both dissolution and precipitation) was suspected to contribute to the observed fluxes (Emmerich 2003; Kowalski et al., 2008; Mielnick et al., 2005; Schlesinger et al., 2009; Serrano-Ortiz et al., 2010; Stone, 2008). Given that carbonate systems cover more than 10% of the world’s land surface (Durr et al., 2005), the hypothesized important contribution of carbonate weathering to the CO₂ flux measurements needs to be tested.

Under steady state conditions, CO₂ is connected to soil carbonates via the following summarized carbonate weathering reaction (Berner et al., 1983; Kaufmann and Dreybrodt, 2007):

$$CACO_{3}(s) + CO_{2}(aq) + H_{2}O(aq) \rightleftharpoons Ca^{2+}(aq) + 2HCO_{3}^{-}(aq) \quad (1)$$

In the absence of external drivers, this system approaches equilibrium closely within minutes (Dreybrodt et al., 1996). In the real world, fluctuations in CO₂ production, soil water content and atmospheric conditions maintain carbonate reactions permanently in disequilibrium. The reactions are also affected by changes in soil pH induced by atmospheric deposition and drainage (downward leaching of Ca²⁺ and DIC; dissolved inorganic carbon) (Suchet and Probst, 1995). The most important driver is probably the soil moisture content as it determines how much DIC and Ca²⁺ can be in solution. In dryer regions or periods, daytime evaporative water

losses induce oversaturation of DIC and thus precipitation of calcium carbonate and associated production of CO₂. In dry conditions, these daytime water losses are often compensated during the night, at least partly, by water vapor condensation or adsorption (Kosmas et al., 2001; Verhoef et al., 2006), causing undersaturation of DIC that leads to the reverse reactions: dissolution of carbonates and CO₂ uptake. If this dissolution exceeds CO₂ production within the soil, then nighttime CO₂ uptake from the atmosphere could occur, as occasionally reported in literature (Hastings et al., 2005; Kowalski et al., 2008). The diel pattern of CO₂ uptake and release due to carbonate geochemical reactions is thus opposite in sign compared to the biological pattern. Note that ambiguity exists among the terms “source” and “sink” when considering the CO₂ exchange between carbonate rocks and the atmosphere on one hand, and carbon sequestration in carbonate rocks on the other hand (Eshel et al., 2007). Here we consider carbonate dissolution a sink as it holds CO₂ uptake by the ecosystem and carbonate precipitation a source as it causes CO₂ emission to the atmosphere. In terms of the soil carbon pool, however, carbonate precipitation is considered a sink as it implies carbon sequestration and carbonate dissolution is considered a source as it implies a loss from the soil carbon pool.

Whereas CO₂ transport along the soil profile is determined primarily by diffusion, CO₂ movement in permeable, dry and fractured sub-soil and its release at the soil surface are strongly influenced by non-diffusional mechanisms, such as pressure gradients, gusts and turbulence (Rey et al., 2012), which from now on we call ventilation. The term refers to different processes causing mass transfer of soil and cave air to the atmosphere and vice versa, such as pressure pumping, deep penetration of eddies or the Venturi effect. Ventilation occurs in all porous media, such as non-saturated soils and karst systems, when pores are connected (open porosity) and not blocked by water (Cuezva et al., 2011). Takle et al. (2004) found that pressure fluctuations causing mass transfer through the soil penetrated into a dry soil up to 50 cm with little attenuation. The airflow induced by 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). Turbulent wind can instigate ventilation when large eddies penetrate deep into the soil and result in mixing of soil and atmospheric air. This is further enhanced when the surface is heated and the air at the soil surface becomes buoyant and unstable, enabling better mixing. It is important to distinguish between ventilation, which is the physical air mass transfer process, and the CO₂ outgassing as a consequence of ventilation, which depends on the concentration of CO₂ present in the soil.

By pumping in CO₂-poor air, and pumping out CO₂-rich air, ventilation drastically reduces the belowground CO₂ concentrations in soil pores and caves (Cuezva et al., 2011; Kowalski et al., 2008). These rapid changes in underground
CO₂ concentrations induce a strong carbonate disequilibrium and can thus be expected to interact with carbonate weathering rates. In this paper we use a modeling approach to determine to what degree the occurrence of ventilation affects carbonate geochemistry.

# 2 Materials and methods

## 2.1 Study area

Data were taken from a study area in the southeast of Spain (province of Almería), El Llano de los Juanes, where ventilation has been reported (Serrano-Ortiz et al., 2010; Sanchez-Cañete et al., 2011). It is located in the Sierra de Gádor, a mountain range which reaches 2246 m above sea level (Li et al., 2007, 2008). The Sierra consists of an up to 1000 m thick series of Triassic carbonate rocks (limestone and dolomite) that are highly permeable and fractured.

The study site El Llano de los Juanes, with an elevation of about 1660 m above sea level is a relatively flat shrubland area corresponding to a well-developed karstic plateau (Serrano-Ortiz et al., 2007). The carbonate rocks here are mainly dark limestone, with 98% calcite (X-ray diffraction analysis) (Were et al., 2010). The site is characterized by a semiarid montane Mediterranean climate, with a mean annual temperature of 12 °C and mean annual precipitation of ca. 475 mm, falling mostly during autumn and winter, and by a very dry season in summer (Serrano-Ortiz et al., 2007; Kowalski et al., 2008). Thickness of the soil overlaying the bedrock ranges from 0 to 0.5 m. The vegetation, so-called “Macchia” or “Matorral”, at this study site is sparse and only around 0.5 m in height, but nonetheless bio-diverse. More information on the study area can be found in the Supplement (A1.2 Site description and geological context)

## 2.2 Model description

Chemical weathering of carbonates was simulated using an updated version of the WITCH box-model (Goddéris et al., 2010; Goddéris et al., 2006; Roelandt et al., 2010). WITCH simulates the time evolution of the chemical composition of belowground waters and air, as well as their vertical fluxes. For each water reservoir, corresponding to a given soil and weathering profile layer, the mass balance is solved for every time step. The outputs of these budget equations – i.e., carbon content, dissolved calcium, and total alkalinity in each modeled layer – are injected at each time step into the specification module that calculates the complete carbonate specification accounting for the environmental conditions (such as the fluctuating temperature and water volumetric content). A detailed description of the WITCH model can be found in the Supplement (A1.1 Model description.)

The gas transport mechanism in the standard version of WITCH is diffusion, but here we also needed to prescribe a CO₂ efflux as a result of ventilative outgassing. As several

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Measured CO₂ efflux from an ecosystem on carbonate (dry season). Example of a period in which atmospheric turbulence induces CO₂ outgassing events during the daytime in a dry Spanish “Matorral” vegetation growing on karst. The inset shows that outgassing increases exponentially with $u_*$, a measure for atmospheric turbulence. Because of the drought during this time of year, plants are in a dormant stage and the observed daytime CO₂ effluxes have to be attributed to ventilation. In 2009, ventilation was observed here daily from the end of 24 June until the beginning of 7 September. The figure shows the clearest case of ventilation, peak daytime effluxes averaged around 2 µmol m⁻² s⁻¹ (ranging between 0.5–6.4 µmol m⁻² s⁻¹) in 2009.</figcaption></figure>

authors showed a strong correlation between the amount of atmospheric turbulence and ventilation measured at this site, we set up an equation using the friction velocity $u_*$ (see Fig. 1 inset, and also Kowalski et al., 2008; Sanchez-Cañete et al., 2011; Serrano-Ortiz et al., 2010).

$u_*$ (m s⁻¹) is related to surface shear stress, responsible for generating turbulence, and therefore a proxy for atmospheric turbulence. Other parameters included in this equation are the soil water content, which determines the degree of coupling between the underground system and the atmosphere, and the belowground CO₂ concentrations. The CO₂ efflux (µmol m⁻² s⁻¹) due to ventilation ($F_{Vent}$) was therefore prescribed as

$$F_{Vent} = k \cdot u_* \cdot \Delta[\text{CO}_2] \cdot I_r \cdot u_{*\theta}, \quad (2)$$

where $\Delta[\text{CO}_2]$ is the difference in CO₂ concentration between the layer where ventilation occurs and the atmosphere. Ventilation ceases if soil CO₂ concentrations are depleted. $I_r$ is the solar radiation deduced from measurements of PPFD (photosynthetic photon flux density). It accounts for surface heating, which induces mass transport through convective flows. k is a constant accounting for the site specific texture of the belowground system. The more fractionated it is and the more caves occur in it, the higher the value of k. Ventilation is promoted in highly fractionated karst systems such as our study area. $u_*$ (m s⁻¹) is a threshold depending on the ratio between the amplitude of atmospheric turbulence and the amount of water in the soil ($u_*/VWC$), and on the maximum water content for enabling ventilation (VWC$_{Vmax}$). In these simulations we allowed ventilation only when $u_{*\theta} > 2$ (VWC expressed in m³ m⁻³ and $u_*$ in m s⁻¹) and VWC$_{Vmax} \le 0.1$. Estimations for k and $u_{*\theta}$ are site specific. By adjusting the parameters in this
equation to meet the observed fluxes, we achieved a realistic estimate for the amount of CO₂ that is extracted from the soil by ventilation.

At this point we emphasize that the ventilation equation cannot be fully validated and site-specific parameters should be evaluated before applying them to other study areas. Besides the techniques for such validation not being in reach, it was not found to be of critical importance for the purpose of this study, which was to test to what degree ventilation affects geochemical fluxes, rather than quantifying ventilative outgassing itself. The latter requires detailed insight in the three-dimensional structure of the karst system to estimate macropore interconnectivity and the presence of caves and cracks that serve as preferential CO₂ outflows.

We designed the model simulations to accord with the conditions of the Mediterranean study area (see Supplement A1.2 Site description and geological context). The weathering profile was prescribed as a ten-layer structure with a total thickness of 100 m, the two upper layers having soil properties (porosity 0.59 m³ m⁻³ – measured on site – and thickness 15 cm each) and the others layers having bedrock properties (porosity of 0.03 m³ m⁻³ – measured on site – and thickness resp. 4 m, 4 m, 4 m, 10 m, 10 m, 10 m, 10 m and 47.7 m with increasing depth). Half hourly meteorological data (see Sect. 2.3) were used to force the model, these include the soil water content (which defines the volumetric size of each reservoir and the fraction of the total reactive mineral surface that is available for weathering), rainfall, soil temperature and inputs of CO₂ from biological production. The latter was estimated by means of a Q₁₀ function (Q₁₀ was 2.2 and basal rate respiration was 0.5 µmol m⁻² s⁻¹), combined with an adjustment factor for drought. We used nighttime CO₂ fluxes from eddy covariance measurements during biologically active periods when geochemical fluxes were negligible. This production was prescribed only in the two upper layers (soil) and was assumed to be zero during the drought period, during which all plants are senescent and CO₂ efflux was typically zero in the absence of high turbulence. The measured daytime effluxes in this season could therefore not be attributed to respiration, making this the appropriate period to study ventilation. In order to reproduce the observed CO₂ concentrations in both the upper and deeper layers, we encountered the need to also include very little (0.1 µmol m⁻² s⁻¹) but continuous CO₂ production in one of the deeper layers in the model. Possible sources of this deep CO₂ production in the karst system are treated in the discussion below.

## 2.3 Measurements

In 2009, the fluxes of CO₂ and H₂O were estimated from 10 Hz eddy covariance measurements at 2.5 m height. The extent of fetch, i.e., the distance upwind over the homogeneous surface, is several hundreds of meters from the tower in every direction. An open-path infrared gas an-

alyzer (Li-Cor 7500, Lincoln, NE, USA) measured densities of CO₂ and H₂O; it was calibrated monthly using an N₂ standard for zero and a 500.1 µmol(CO₂) mol⁻¹ gas standard as a span. Wind speed and sonic temperature were measured by a three-axis sonic anemometer (CSAT-3, Campbell Scientific, Logan, UT, USA).

A thermohygrometer (HMP 35C, CSI, USA) at 1.5 m above the surface was used to measure air temperature and humidity. Soil water content (SWC) was measured by three water content reflectometers (CS615, CSI) at 4 cm depth. Soil temperature was determined as the mean of two pairs of thermocouples (TCAV, CSI) at 2 cm and 6 cm. Rainfall was measured by a tipping bucket (0.2 mm) rain gauge (model 785 M, Davis Instruments Corp., Hayward, CA, USA). Fluxes of incident and reflected photons in photosynthetic wavelengths, measured by two quantum sensors (Li-190, Li-Cor, Lincoln, NE, USA) at 1.5 m over a representative ground surface were used to determine Fp (photosynthetically active photon flux density).

The measurement system centers on a datalogger (CR3000, CSI) that calculated and stored means, variances and co-variances of 10 Hz data every 30 min. Eddy fluxes calculated from density fluctuations (Webb et al., 1980) and coordinate rotations (McMillen, 1988) were carried out in post-processing. Measurements of nighttime CO₂ fluxes with friction velocity lower than 0.2 m s⁻¹ were eliminated from the analysis to avoid possible underestimation due to low turbulence (Serrano-Ortiz et al., 2009); for further details see Serrano-Ortiz et al. (2009).

Deep CO₂ molar fraction was measured in a borehole (7 m depth and 0.1 m diameter) through the bedrock outcropping using a GMP-343 (Vaisala, Inc., Finland). These measurements were made every 30 s and stored as 5 min averages in a datalogger (CR23X, CSI).

## 3 Results

In order to test whether carbonate weathering processes alone (i.e., in the absence of ventilation) could be responsible for the atypical CO₂ fluxes measured over carbonate soils, we applied the geochemical model WITCH (Goddéris et al., 2006) and tested it at one of the sites where non-biological CO₂ flux behavior has been observed during specific periods, as shown in Fig. 1.

The diurnal pattern of calcium carbonate precipitation (positive, CO₂ production) and dissolution (negative, CO₂ consumption) is shown in Fig. 2 for three different scenarios using the WITCH model. The dotted line shows a typical day in the wet season (winter), when geochemical fluxes are close to zero and thus of marginal importance compared to biological fluxes. The dashed line shows a typical day in the dry season, showing that geochemical fluxes are now slightly larger than in the wet season, due to a larger relative difference in soil water content (SWC) between night and day. In
<figure><img src="image_5.png" /></figure>

**Fig. 2.** Diel patterns of carbonate weathering. Figure 2 shows the diurnal pattern of calcium carbonate precipitation (positive, CO₂ production) and dissolution (negative, CO₂ consumption) for three different scenario's using the WITCH model. The dotted line shows a typical day in the wet season (winter), when geochemical fluxes are close to zero and thus of marginal importance compared to biological fluxes. The dashed line shows a typical day in the dry season when ventilation was not included in the model. Geochemical fluxes are now slightly larger than in the wet season, due to a larger relative difference in soil water content (SWC) between night and day. The solid line shows the same day in the dry season, but here ventilation was included in the model. Calcium carbonate precipitation and dissolution are now strongly enhanced by ventilation.

these simulations, however, soil CO₂ outgassing was driven only by gas diffusion, while in reality pressure pumping and subsequent ventilation can be much more important determinants of soil gas exchange as well as soil CO₂ concentrations (Takle et al., 2004). By altering soil CO₂ concentrations, ventilation could be expected to affect carbonate weathering rates. To quantify this effect, we used the extended WITCH model, where ventilation was added as an alternative gas transport mechanism next to diffusion. The model with ventilation (Fig. 2, solid line), revealed much higher daytime carbonate precipitation rates as compared to the simulations without ventilation. Calcium carbonate reactions are strongly enhanced by ventilative outgassing and the peak of CaCO₃ precipitation with ventilation is 8 times higher than without ventilation for the same day in the dry season.

The modeled ventilation efflux calculated using Eq. (2) is shown for two different dry periods in Fig. 3. The model was able to capture days when ventilation occurred and predicted peaks with a magnitude comparable to the observations. The main discrepancies were the modeled ventilation occurring a few hours earlier and lasting a shorter time than the observed ventilation. However, model performance was found to be sufficient for the purpose of this study, which is the evaluation of the impact of ventilation on carbonate weathering. We evaluated the role of ventilation in modifying the chemical weathering rates at annual timescale and found that our model simulated, for the site under study, a reduction in net CO₂ uptake by carbonate dissolution of 16% (4 g C m⁻² yr⁻¹). This is thus of small importance relative to

the roles of biological CO₂ production and climate. The associated denudation rates calculated (according to Plan, 2005) for this study site were 83 mm kyr⁻¹ for simulations without ventilation and 68 mm kyr⁻¹ for simulations with ventilation. Thus, the 16% reduction in annual carbonate dissolution induced by ventilation amounts to 15 mm less chemical removal of carbonate rock over a millennium.

## 4 Discussion

Model outcomes suggest that carbonate weathering rates are highly dynamical, changing in sign and magnitude on hourly, daily and seasonal timescales. During wetter periods or periods with lower turbulence when ventilation does not occur (Serrano-Ortiz et al., 2010), the contribution of the geochemical flux to the total CO₂ efflux is marginal (Fig. 2, dotted line) and the CO₂ fluxes associated with Eq. (1) are generally too small to explain the large CO₂ fluxes presented in Fig. 1. On the other hand, when ventilation was included in the model, the peak geochemical fluxes during turbulent daytime periods in the dry season (Fig. 2, solid line) are much larger and even within the same order of magnitude as the observed atypical fluxes at this site (ranging between 0.5–6.4 µmol m⁻² s⁻¹ in the considered year). Carbonate geochemistry, when incited by atmospheric turbulence, can thus be an important contribution to synoptic CO₂ fluxes.

One of the main factors controlling ventilation is the amount of water in the soil, as this determines the degree of connectivity in the soil–atmosphere system. The drier the soil, the larger the potential for ventilation to remove CO₂ from the soil. Analysis of the flux observations in Sierra de Gácor, showed that ventilation occurs primarily during dry periods (here when soil water content < 11%, but this strongly depends on the site-specific soil properties), and then only when the surface is heated. Under these conditions, ventilation-driven CO₂ emissions are well correlated with evapotranspiration and the friction velocity $u_*$ (Kowalski et al., 2008, and see also inset Fig. 1; Sanchez-Cañete et al., 2011; Serrano-Ortiz et al., 2010). At higher $u_*$ (a proxy for atmospheric turbulence), the combination of a smaller surface boundary layer resistance and increased pressure pumping (Takle et al., 2004) enhances the export of CO₂ from the subterranean air to the atmosphere. Note that higher values of atmospheric turbulence tend to be associated with higher temperatures, leading to an increased CO₂ efflux at higher temperatures. This should, however, not be mistaken for the temperature dependency of respiration, given that attributing the atypical observations to biological respiration would come down to $Q_{10}$ values (the factor by which the soil respiration rate increases with a 10° rise in temperature) exceeding 100, which is biologically impossible (Davidson and Janssens, 2006). During the nighttime, on the other hand, the re-humidification of the soil that is observed during dry
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Comparison of measured and modeled CO₂ efflux. Comparison of the time series of the ventilative CO₂ efflux as measured (black line) and modeled (dotted line). Two different periods are displayed, each of years with a very distinct dry season.</figcaption></figure>

summers (due to condensation and hydraulic uplifting of water from deeper layers) (Kosmas et al., 2001; Verhoef et al., 2006), the lack of surface heating, and the lower level of air turbulence, limit the nocturnal ventilation and allow soil CO₂ concentrations to rise again.

Figure 4 gives an overview of the daily cycle. During the day, ventilation lowers the gaseous subterranean CO₂ concentrations, which stimulates carbonate precipitation and thus geochemical CO₂ production (Eq. 1). This geochemical CO₂ is in turn transported to the atmosphere by ventilation. The stronger the ventilation, the larger the reduction in soil pCO₂, and the more carbonate is precipitated. Carbonate continues to precipitate as long as soil pCO₂ continues to decline (Fig. 4, left).

Large daytime ventilation events bring surface soil pCO₂, at the end of the day, close to atmospheric values and this very small soil-atmosphere CO₂ gradient then leads to reduced diffusive CO₂ outgassing during the night. Also, nocturnal rewetting of the upper soil layers (due to condensation/adsorption processes (Agam and Berliner, 2006) and hydraulic redistribution (Scott et al., 2008)) reduces the open porosity and thus limits diffusion of CO₂ towards the atmosphere. This reduced diffusion, together with the lack of ventilation at night, allows soil CO₂ concentrations to slowly rise again throughout the night, as a result of biological production or upward migration of CO₂ from deeper soil layers. This slow but steady increase in soil CO₂ concentration continuously pushes carbonate weathering reactions towards dissolution and thus CO₂ consumption (Fig. 4, right). During periods of very low biological CO₂ production, this can even result in net CO₂ uptake by the soil at night as is occasionally observed (Fig. 1). A day with high ventilation will thus tend to be followed by a night with a large relative increase in soil pCO₂ and subsequent enhanced carbonate dissolution (see Fig. 2, solid line). In other words, the more ventilation, the more pronounced the diel weathering pattern, but

the effect on net daily carbonate weathering is small because of compensatory reactions during the night. Similarly, days with larger ventilation and net carbonate precipitation will be compensated by subsequent days with weak ventilation and net carbonate dissolution, constraining the net weathering rates at longer timescales. This mechanism was confirmed by our model simulations.

Note that outgassing of CO₂ through turbulence-induced pressure pumping also occurs on non-carbonate ecosystems, but in that case acts only on the gas transport from the uppermost soil layer and not on the production of CO₂ (Subke et al., 2003). In carbonate ecosystems, removal of CO₂ via turbulence-driven mass transport does affect its production by stimulating carbonate precipitation.

Uncertainty exists concerning the processes responsible for the replenishment of subterranean CO₂ levels at night, crucial for allowing ventilation to occur again the next day. As stated before, at the end of a well-ventilated day, the pCO₂ in the uppermost soil layers is not much higher than atmospheric values. This very low surface soil pCO₂ enhances upward CO₂ diffusion from pores and cavities in the bedrock deeper below. However, this would deplete the CO₂ reserves in these deeper layers, which is not observed in the field. Also, the observed CO₂ concentrations in both the upper and deeper layers could only be simulated well with our model by including a very small (0.1 µmol m⁻² s⁻¹) but continuous production of CO₂ in the deeper layers. Possible sources of this upward CO₂ migration from deep below, include microbial decomposition of dissolved organic carbon (DOC), calcite precipitation in deeper layers, or geotectonic activity. Very high CO₂ concentrations in cavities deep in the bedrock have indeed been measured at this site (> 15 000 ppm at -7 m; Sanchez-Cañete et al., 2011) and other karst sites in the surrounding area, and many field studies support our assumption of an additional deep CO₂ source originating at or immediately above the water table (Benavente et al., 2010;
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Overview of the diurnal cycle of carbonate geochemistry with ventilation. Figure 4 shows a conceptual framework that may explain why and how diurnal cycle of carbonate dissolution and precipitation can be exacerbated by ventilation.</figcaption></figure>

(a) During the day, gaseous subterranean CO₂ concentrations are kept low by ventilation, which stimulates carbonate precipitation and concurrent geochemical CO₂ production. This CO₂ is then again removed by ventilation, thus sustaining prolonged CO₂ emission events even in the absence of respiratory CO₂ production. The stronger the ventilation, the more carbonate precipitates.

(b) At night, ventilation ceases and diffusion of CO₂ from the soil to the atmosphere is reduced by: first, nocturnal rewetting of the upper soil layer that reduces open porosity and, second, the small CO₂ concentration difference between soil and atmosphere resulting from a day with ventilation. CO₂ from deeper layers migrates upwards to the depleted upper layers, where it stimulates carbonate dissolution and thus CO₂ consumption.

Linan et al., 2008; Walvoord et al., 2005; Wood et al., 1993). Both biotic and abiotic processes have been demonstrated as sources of CO₂ in studies conducted in the proximity of the considered study site: (a) geotectonic mantle-derived CO₂ migrating upward from deeper parts of the crust through regional faults and seismic activity (Ceron et al., 1998), (b) microbial decomposition of dissolved and solid organic carbon near the groundwater table (typically hundreds of meters deep) (Benavente et al., 2010) and (c) CO₂ from local calcite precipitation near the groundwater table (Benavente et al., 2010). The exact origin of the CO₂ production that we prescribed at this study site remains uncertain.

At most sites and during most of the year, biological fluxes are much larger than geochemical CO₂ production or consumption, and therefore mask their contribution to the ecosystem CO₂ exchange with the atmosphere. However, our results show that in some regions carbonate weathering rates are not negligible relative to biological fluxes during dry (low biological activity and system prone to ventilation) and windy periods. Under such conditions, biology-based standardized schemes to partition the measured net CO₂ exchange into its components – as are used by the FLUXNET (Baldocchi et al., 2001) community – are not applicable and gas exchange measurements fail to reveal any information on the biological activity at these sites (Were et al., 2010). Quantification of the short-term and annual contribution of carbonate weathering rates to the measured ecosystem-atmosphere

CO₂ exchange can now be achieved by coupling the modified WITCH model to existing soil vegetation atmosphere transfer (SVAT) models. Given that carbonate systems cover more than 10% of the world's land surface (Durr et al., 2005) and most of these occur in relatively dry regions, a potential contribution of carbonate weathering to the short-term CO₂ flux measurements should not a priori be discarded. The 15 mm kyr⁻¹ reduction in denudation rates due to ventilation is small relative to erosion, but may not be trivial on longer timescales.

**Supplementary material related to this article is available online at: http://www.biogeosciences.net/10/5009/2013/bg-10-5009-2013-supplement.pdf.**

*Acknowledgements.* M. Roland was granted by the Institute for Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). I. A. Janssens and R. Van Grieken acknowledge the Research Foundation – Flanders (FWO). P. Serrano-Ortiz is funded by a postdoctoral fellowship from the Spanish Ministry of Science and Innovation. S. Cuezva was funded by a postdoctoral fellowship from the Spanish Ministry of Science and Innovation, research programme Juan de la Cierva.

Edited by: F. X. Meixner
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