1 Introduction

Carbon dioxide (CO2), as of the greenhouse gases, is closely monitored in the context of global climate change (Florides and Christodoulides 2009; Ghommem et al. 2012; Lee et al. 2013; Hoppe et al. 2016; Szulejko et al. 2017; Liu and Chen 2017; Ishikura et al. 2018; Al-Ghussain 2019; Binet et al. 2020; Bhattacharyya et al. 2021; Mitevski et al. 2022). One of the most important natural components of the global carbon cycle is soil respiration (Zhao et al. 2017; Jian et al. 2018, 2021). CO2 is produced by biogenic processes such as root respiration or soil microorganism activity (see, e.g., Kuzyakov 2006; Kuzyakov and Gavrichkova 2010). Some of this CO2 escapes into the external atmosphere by CO2 efflux, while a part of the CO2 migrates to the subsoil by advective flux (Lang et al. 2017; Faimon et al. 2020), diffusive flux (Breecker et al. 2012; Garcia-Anton et al. 2014), and flux associated with dissolved CO2 in percolating water (see, e.g., Baldini et al. 2008; Milanolo and Gabrovšek 2015). In karst areas, this CO2 can accumulate in caves that therefore represent a kind of a CO2 reservoir.

Recently, it was suggested that the exchange of CO2 between caves and the atmosphere could contribute significantly to the global carbon cycle (Serrano-Ortiz et al. 2010; Krajnc et al. 2017; Garcia-Anton et al. 2017). This idea is based on the well-known annual cycle of CO2 in caves: dynamic caves accumulate CO2 during spring and summer and release in into the external atmosphere by cave ventilation during fall and winter. The amount of CO2 exchanged between caves and the atmosphere annually has been quantified only sporadically (Pla et al. 2016), and, thus, the extent / significance of this process is rather unknown. Therefore, the purpose of this work was (1) to estimate the annual exchange of CO2 in a chosen well known cave system: the Sloup-Šošůvka Caves in the Moravian Karst, (2) to extrapolate this result to all caves in the Moravian Karst, and (3) to estimate the importance of the process by comparing it with the total respiration of soils of the Moravian Karst. An additional goal was to analyze effects of external factors on CO2 flux into the cave during the accumulation regime.

1.1 Theoretical background

In addition to less common kinetic causes (effect of wind or water flow / fall; see, e.g., Mourzenko et al. 2014 or Bourret et al. 2019), cave airflow is mainly driven by differences in air pressures of the external atmosphere and cave air. These differences are generally caused by differences in air densities controlled mainly by temperature (Cigna 1968; de Freitas et al. 1982; Faimon and Lang 2013; Faimon et al. 2012, 2020). In addition to temperature, air density is influenced by contents of various gases such as water vapor, CO2, Rn, etc. Effects of these contents are usually factored in by using the so-called virtual temperature, i.e., the temperature corrected to be proportional to the actual air density (Kowalczk and Froelich 2010; Kowalski and Sánchez-Cañete 2010; Sánchez-Cañete et al. 2013). Differences in air densities induce buoyancy-driven cave ventilation, sometimes called the ‘chimney effect’ (see, e.g., Covington and Perne 2015). This ventilation is typical for dynamically ventilated caves, i.e., caves with two and more entrances at different altitudes (Bögli 1978). The airflow in a cave can be expressed simply as a function of the difference between virtual temperatures, Δ\(\textrm{T}^{\textrm{virt}}=\textrm T_{\textrm{ext}}^{\textrm{virt}}-\textrm T_{\textrm{cave}}^{\textrm{virt}}\). The direction of airflow through the cave is given by the sign of the difference: If ΔTvirt < 0, the air flows from the lower entrance to the upper one (the cave is in the upward airflow ventilation mode, UAF mode). If ΔTvirt > 0, the air flows from the upper entrance to the lower one (the cave is in the downward airflow ventilation mode, DAF mode); see Faimon et al. (2012) for details. Theoretical and experimental analysis of buoyancy-induced ventilation can be found in Tanny et al. (2008) or Chow and Gao (2011). Fluctuations in barometric pressure are an additional factor that influences the cave airflow (see barometric pumping; Stauffer et al. 2019). All main factors acting in the system karst soil - cave are summarized in the conceptual model in Fig. 1.

Fig. 1
figure 1

Two-box model of the soil–cave system: Boxes represent CO2 reservoirs in the soil (above) and the cave (below). The arrows represent CO2 fluxes and fluid flow (exchanged air and percolating water)

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1.2 Site of study

The Sloup-Šošůvka Caves (S-ŠC) are located in the northern part of the Moravian Karst (Czech Republic) (Fig. 2). The main entrance to the cave is localized at 16.73903 E, 49.41046 N. Moravian Karst is a middle Devonian to Mississippian carbonate unit comprising two formations: Macocha Fm., mostly reef to lagoonal limestones, and Líšeň Fm., mostly calciturbidites. These limestones are deposited on Cadomian crystalline rocks of the Brno massif (mainly granodiorites to tonalities) and a few meters of ‘Devonian basal clastics’. Macocha Fm., which forms the bulk of the up to 1000 m thick carbonate stack, was deposited in four cycles (Hladil 1986). The uppermost cycle together with the Líšeň Fm. are in the northern part of the Moravian Karst cut off by the basal detachment of the overlying Variscan flysch nappe stack, which is located ca. 70 m above S-ŠC. As a consequence of this proximity to the main thrust zone, the limestones of S-ŠC are heavily strained. The cave corridors follow the main NE-SW striking foliation (ca. 120/25).

Fig. 2
figure 2

Geological map of the northern part of the Moravian Karst (left) and map of the Sloup-Šošůvka Caves (right). Legend of the map is in the left bottom part of the map; dark gray polygons indicate urban areas (names of which are nearby). Numbers in the cave map indicate measuring stations: 1 - entrance (behind the door into the cave); 2 - crossings in front of the Nicová Cave; 3 – Eliška Cave, 4 - dug-through site (lattice on the ground), 5 - Cut Stone, 6 - railing above the Stupňovitá Abyss, 7 - bridge over the Stupňovitá Abyss; 8 - railings at the Kolmá Abyss; 9 - Nagel Abyss - lower bridge; 10 - Trámová Corridor; 11 - adit mouth behind the Kůlna Cave; 12 - adit to the Black Abyss (behind the door above); 13 - adit to the Black Abyss (in front of the lower door); 14 - adit to the Black Abyss (behind the lower door); 15 - Black Abbys; 16 - Břoušek Fairytale Hall; 17 - behind the Břoušek Fairytale Hall; 18 – Rieger Hall; 19 - At three big ones; 20 - Kaple (Chapel); 21 - at Hlinitá Corridor. Dashed olive line on the cave map indicates the formal border between the Sloup Caves and Šošůvka Caves

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The S-ŠC are the northern-most part of the western branch of the Amatérská cave system, the longest cave system in the Czech Republic. It is a two-story cave system that was eroded by the Sloup Brook, which sinks near the entrance. The entrance part of the Sloup Cave and the Kůlna Cave has been known since time immemorial. The northern-most part of the cave system is called the Eliška Cave (No. 3 in Fig. 2) and was discovered in 1879. The Šošůvka Cave part with the Břoušek Fairytale Hall (No. 17 in Fig. 2) and the Rieger Hall (No. 18 in Fig. 2) was discovered between 1889 and 1914. The total length of all known corridors is 4200 m. The cave system has been open to the public since 1881. The visitor route is 1760 m.

2 Methods

2.1 Monitoring schedule

Point measurements of microclimatic variables were carried out throughout the S-ŠC visitor route at 21 sites (Fig. 2) during individual visits from 2003 to 2021: in July 2003, August 2004, and August 2020 at DAF mode and in February 2004, April 2004, and January 2020 at UAF mode. Continuous monitoring with a step of 2 h was carried out in the Rieger Hall with the highest seasonal variations during three time periods between 2020 and 2021.

2.2 Monitoring equipment

CO2 measurements were performed by ALMEMO 2290-4 V5 or 2590-4AS data loggers with 2-beam infrared sensors FVA600CO2H (measuring range from 0 to 10,000 ppmv, accuracy ± 100 ppmv + 3% of the measured value) or FYAD00CO2B10 with automatic atmospheric pressure compensation (measuring range from 0 to 10,000 ppmv and accuracy ± 100 ppmv + 5% of the measured value), respectively.

All data in the Rieger Hall were logged using ALMEMO 2590-4AS datalogger with external Ahlborn sensors: CO2 sensor FYAD00CO2B10 (see above), integrated temperature (NTC, type N) / relative humidity (capacity) sensor FH A646-E1 (measuring range − 20 to + 60 °C and 0 to 100%, accuracy ± 0.1 °C and ± 2% of the measured value), and barometric pressure sensor FDA612-SA (measuring range 700 to 1050 mb, accuracy ± 0.5% of the measured value).

2.3 External data

Selected external data such as barometric pressure (recalculated to sea level), Pext, external temperature, Text, temperature near the surface of the ground, Tground, soil temperatures, Tsoil 1 and Tsoil 2, precipitations, Pr, global radiation, GR, and soil moisture, SM, with the monitoring step of 15 min were taken from the Macocha weather station (16.73022 E, 49.37215 N, 489 m a.s.l.). It is located 4 km SSW of S-SC (468 m a.s.l.). See the data in Fig. 5.

2.4 Data analysis

All data were processed in MS EXCEL. The time series of CO2 data from the Rieger Hall (S-ŠC, MK) were subjected to correlation analysis in order to find whether / how external factors control CO2 levels in the cave. Data were segmented using the concept of curve entropy (Denis and Crémoux 2002; Denis et al. 2005; Fernandez-Cortes et al. 2011), see Appendix for details. Resulting segments were then detrended (e.g., Hirsch et al. 1982; Hirsch and Slack 1984) by differentiation and correlated with selected external variables. A cross-correlation method was applied to find any lag in the dependent variables. All calculations were performed with Statistica 14 (TIBCO Statistica 2022).

2.5 Cave volume estimation

The volume of S-ŠC was estimated via a simplified box model, where individual cave parts (corridors, halls, etc.; see Fig. 3) were approximated by simplified boxes. Volumes of these boxes were calculated by multiplying the footprint area of the cave corridor segment by its mean height estimated in the field (based on multiple laser measurements). Concentrations of CO2 in a given period were assigned to the volumes of respective boxes and the weight of CO2 in them was calculated. Based on the nearly uniform concentration of CO2 in longer cave passages, one measured value was used for several adjacent boxes. The sum of all partial weights of CO2 gave the total weight of CO2 in the cave. Finally, the difference between the weight of CO2 during the summer and winter periods gave the resulting mass of CO2 exchanged per year.

Fig. 3
figure 3

Block model of the Sloup-Šošůvka Caves composed of 91 rectangular segments. Segment numbers are consistent with Table 2

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3 Results

3.1 Distribution of CO2 in the Sloup-Šošůvka Caves

The purpose of these measurements was to survey the distribution of CO2 throughout S-ŠC during key seasons: summer and winter (Fig. 4). The results of these measurements were structured according to the ventilation mode (Fig. 4a, b). The differences between the individual values of CO2 concentrations measured at individual ventilation modes are presented in Fig. 4c. Data from all campaigns showed a similar pattern with lower values (up to 1500 ppmv) at sites #1 to #12 and #21, and maximums up to 9160 ppmv at site #18 except for the campaign from August 2004 with local peak (up to 5800 ppm) at sites #12 to #14 (Fig. 4a). Compared to the DAF mode, lower CO2 concentration values were recorded at all monitoring sites during the UAF mode: up to 950 ppmv at sites #1 to #12 and #21; up to 1900 ppm at site #18 (Fig. 6b). Calculation of the difference in CO2 between DAF and UAF modes was based on the time series from August and January 2020 (Fig. 4c). Based on low values of the UAF mode, the pattern of the resulting CO2 curve was similar to the pattern of DAF mode. While the differences in CO2 concentrations at sites #1 to #12 and #21 reached up to 1000 ppmv, a much higher value of 7350 ppmv was observed at site #18 (Fig. 4c).

Fig. 4
figure 4

Distribution of CO2 concentrations in the Sloup-Šošůvka Caves. Distribution during DAF mode (a), UAF mode (b), and differences in CO2 concentrations between DAF and UAF modes (c). Data acquired during individual measurements from July 2003 to August 2020. Numbers of sites on the x axis are consistent with site numbers in Fig. 2

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3.2 Annual evolution of CO2 concentrations in the cave

3.2.1 Cave accumulation mode

Detail evolution of microclimatic variables during the Cave Accumulation Mode (CAM) was monitored at DAF ventilation mode in the Rieger Hall from 26 March to 19 August 2021. These data were supplemented with external data from the weather station. The CO2 concentration increased from initial 1608 ppmv to the final 9700 ppmv concentration with a slope of approximately 1.3 ppmv hour−1 during the period from 3 March 2021 to 6 April 2021 and of 3.2 ppmv hour−1 during the period from 6 April 2021 to 8 August 2021 (Fig. 5a). After 8 August 2021, CO2 concentrations almost stagnated without any uniform trend. Differences of virtual temperatures, Δ\(\textrm{T}^{\textrm{virt}}=\textrm T_{\textrm{ext}}^{\textrm{virt}}-\textrm T_{\textrm{cave}}^{\textrm{virt}}\), for the entire monitoring period are presented in Fig. 5a to indicate ventilation modes in the cave. Absolute barometric pressure (Pcave) in the cave atmosphere ranged between 941.5 and 973.5 mb (Fig. 5b), the air temperature ranged between 9.0 and 10.0 °C, and the relative humidity was approximately 100%.

Fig. 5
figure 5

Spring/summer increase in CO2 concentration in the Rieger Hall (Sloup-Šošůvka Caves, Moravian Karst; time period from 26 March to 19 August 2021). Evolution of CO2 concentration (CO2) and difference in virtual temperatures (ΔTvirt ) (a); barometric pressure (P) (b); external temperature (Text ) (c); ground temperature (Tground ) (d); global radiation (GR) (e), soil moisture (SM), soil temperature (Tsoil 1, 2), precipitation (Pr) (f). Additional curves in the data series are the polynomial trend lines of 4th to 6th order (smooth curves in Fig.  5a, b, c, d, e) and the central moving averages of 95th order (the curves varying somewhat less than the data curve, Fig.  5c, d, e, f). The values of external variables came from the Macocha Weather Station. The relative humidity throughout the measurement periods was roughly 100% (it is not presented)

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External variables were chosen from variety of data from the Macocha weather station, based on their potential to control the CO2 concentration in soil/epikarst and in the cave system. External temperature (Text) varied in the range from − 6.2 °C to 33.3 °C, oscillating in a diurnal cycle with an amplitude of 4–15 °C (26 March to 6 May 2021) and 20–22 °C (after 6 May 2021) (Fig. 5c). The maximum increase trend in Text was 0.21 to 0.26 deg day−1 (20 April to 15 May 2021). Later (up to 30 June 2021), the increase trend varied between 0.09 and 0.18 deg day−1. After 4 July 2021, the trend in Text was roughly constant (from − 0.04 to 0.05 deg day−1), except for a transient decline (20 July to 6 August 2021) and an increase (after 14 August 2021). The ground temperature, Tground, showed a trend similar to that of Text; however, the peak values reached 40 °C (Fig. 5d). Global radiation, GR, oscillating in a diurnal cycle approached peak values of 1000 W m−2 (Fig. 5e). Soil temperatures (Tsoil) also followed a trend similar to that in Text and Tground. They varied between 1.6 and 21.3 °C showing diurnal oscillations with higher amplitude in shallower layers (soil 1) compared to deeper layers (soil 2) (Fig. 5f). The mean precipitation was 1.8 mm day−1 with a cumulative value of 267.9 mm, reaching peak values of 8.6 mm. Soil moisture varied between 17.7 and 36.0% following precipitation trends (Fig. 5f).

3.2.2 Cave decumulation mode

Changes of microclimatic variables during the Cave Decumulation Mode (CDM) was monitored in detail in the Rieger Hall between 25 September and 10 October 2020 and was supplemented with selected external data (Fig. 6). During the period from 25 September to 30 September, CO2 concentrations systematically decreased from 8885 to 6466 ppmv with a slope of -375 ppmv day−1 (Fig. 6a), while Text ≤ Tcave (Fig. 6c) and ΔTvirt ≤ 0 (Fig. 6a), except for a few peak values. During the period from 30 September to 2 October, CO2 concentration decreased from 6880 to 6540 ppmv with a lower slope (−152 ppmv day−1) (Fig. 6a). ΔTvirt oscillates between 10 °C and 0 °C, respectively, during this period (Fig. 6a and c). A transient increase in CO2 concentration was observed from 6540 to 7380 ppmv with a slope of 253 ppmv day−1 in the period between 2 October and 5 October (Fig. 6a). During this period, Text exceeded Tcave (Fig. 6c) and ΔTvirt > > 0 (Fig. 6a). During the subsequent period (5 October to 6 October), CO2 concentration decreased from 7380 to 7035 ppmv with a slope of −527 ppmv day−1, after the transition of ΔTvirt from positive to negative values in the diurnal cycle. Finally, from 6 October to 10 October, CO2 concentrations systematically decreased from 7433 to 6348 ppmv with a slighter slope of −116 ppmv day−1 whereas ΔTvirt and Text oscillated in a diurnal cycle around zero (Fig. 6a) and around Tcave (Fig. 6c), respectively. Barometric pressure (934.9 to 964.3 mb) (Fig. 6b) and precipitation (2.5 mm maximally, 52.4 mm in summary) (Fig. 6d) do not appear to have any effect on CO2 concentrations.

Fig. 6
figure 6

Part of the fall/winter decrease in CO2 concentration in the Rieger Hall (Sloup-Šošůvka Caves, Moravian Karst; time period from 25 September to 10 October 2021). Evolution of the cave CO2 concentrations, CO2, and the difference between virtual external and virtual cave temperatures, ΔTvirt (a), barometric pressure, Pcave (b), cave, external and soil temperatures (c), and precipitation, Pr (d)

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3.2.3 Anthropogenic impact

Anthropogenic impact was tested in the Rieger Hall during the period from 27 to 31 August 2021 (Fig. 7), during which 55 groups of tourists (maximum of 57 visitors in one group, 703 persons in total) visited the hall. CO2 concentration varied between 10,727 and 10,896 ppmv showing two local maxima (Fig. 7a). Absolute barometric pressure varied between 949.0 and 960.7 mb inversely to the CO2 concentrations (Fig. 7a). Relative humidity was 100% during the entire monitoring period (Fig. 7b). The cave temperature fluctuated in a narrow range between 10.0 and 10.2 °C with several tiny peaks (Fig. 7b) that do correspond with the entry of visitors (compare Fig. 6b and c). In contrast, no clear effect of visitors on CO2 concentration was distinguished (compare Fig. 7a and c).

Fig. 7
figure 7

Effect of cave visitors. Monitored in the Rieger Hall (Sloup-Šošůvka Caves) during time period from 27 to 31 August 2020. Evolution of cave CO2 concentrations and barometric pressure, P (a), cave temperature, Tcave, and relative humidity, RH (b), and cave visitor number, N (c)

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3.2.4 Correlation analyses

The purpose of this correlation analysis was to determine whether / how external factors control CO2 levels in the cave during accumulation mode. The time series of CO2 concentrations were divided into five segments, A, B, C, D, and E, each with constant entropy (i.e. statistically homogeneous) (Fig. 8). CO2 concentrations in individual segments were assumed to depend on a specific set of external variables. Each segment was subjected to a correlation analysis to determine relationships between cave CO2 concentration and appropriate external variables, such as relative barometric pressure recalculated to sea level, P0, external temperature, Text, ground level temperature, Tground, soil temperatures, Tsoil 1 and Tsoil 2, precipitation, Pr, global radiation, GR, and soil moisture, SM. Results of the correlation analysis are summarized in Table 1. Segment A does not show statistically significant correlations, except for a weak positive CO2/SM correlation. Segment B exhibits a weak negative correlation for CO2/P0(ext) and a weak positive correlation for CO2/Tground. Segment C indicates moderate negative correlations for P0(ext) and strong positive correlations for Text, Tground, Tsoils 1, 2 and global radiation. Segment D shows moderate negative correlations for CO2/P0(ext) and positive correlations for soil moisture. Furthermore, it shows strong positive correlations for CO2/Text, CO2/Tground, CO2/Tsoil 1, and CO2/global radiation. Segment E reveals stronger negative correlations for CO2/P0(ext) and CO2/SM. Furthermore, it shows strong positive correlations for CO2/Tground, CO2/Tsoil 1, and CO2/GR. Note that some correlations are associated with a delay in CO2 after the driving variable.

Table 1 Correlations of CO2 concentrations in the cave air (Rieger Hall, Sloup-Šošůvka Caves, Moravian Karst) with external variables (Weather Station, Macocha) during cave accumulation mode (dominating DAF ventilation mode)
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Fig. 8
figure 8

Segmentation of CO2 time series (Accumulation Mode) based on the entropy of the curves. L(t) is the fluctuating tortuous path of a curve in a plane. A, B, C, D, and E are individual data sequences with constant entropy H(t), see Appendix for details

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4 Discussion

4.1 CO2 exchange between the S-Š caves and the atmosphere

Masses of CO2 exchanged annually in individual parts of S-ŠC (see the box model in Fig. 3) were summed, giving a total mass of exchanged CO2 of approximately 348 kg (see the calculation in Table 2). Related to the S-ŠC volume of 131,580 m3, it yields the normalized value of 2.68 × 10−3 kg CO2 m−3. This value can easily be compared with CO2 exchanged by other caves worldwide, for example, with the 57 kg of exchangeable CO2 in the Rull Cave (Spain, Alicante province), see, Pla et al. (2016). Based on this cave’s volume of 9915 m3, the normalized value is 5.75 × 10−3 kg CO2 m−3, which is twice as large as in S-ŠC. The reason may be higher soil CO2 production at the external temperature between 10.4 and 30.1 °C, together with different local conditions (soils, vegetation, etc.).

Table 2 Calculation of the total CO2 mass exchanged in the Sloup-Šošůvka Caves
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The ratio of the S-ŠC area (17,950 m2) and the total area of all the caves in the Moravian Karst (352,079 m2) is 0.051 (Table 2), that is, S-ŠC represents 5.1% of all MK caves. By extrapolating the exchanged 348 kg of CO2 by S-ŠC to the entire Moravian Karst, we estimate the total exchangeable CO2 to be 6823 kg. All caves in MK represents approximately 0.6% of the entire MK area (see the calculations based on the 1:50,000 geological map in Table 3). The mass of 6823 kg of CO2 released from MK caves recalculated in the MK limestone area (57,830,480 m2) yields a mean annual exchange flux of CO2 of 118 kg km−2 year−1.

Table 3 Selected Moravian Karst objects and their areas (based on GIS calculations)
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4.2 External influences

Positive correlations of cave CO2 with temperatures and soil moisture reflect well-known relationships between these variables in soils (Davidson et al. 1998; Chang et al. 2014; Faimon and Lang 2018) and consecutive migration of soil CO2 into cave by water flow and diffusive / advective fluxes (see, e.g., Milanolo and Gabrovšek 2009; Lang et al. 2017; Faimon et al. 2020; Kukuljan et al. 2021). The positive correlation of global radiation with CO2 is associated with the temperature effect. Furthermore, global radiation undoubtedly increases the share of autotrophic CO2 (Tang et al. 2005; Bahn et al. 2009; Kuzyakov 2006; Kuzyakov and Gavrichkova 2010; Han et al. 2014). The lack of a correlation of CO2 with precipitation is somewhat surprising. A strong influence of evapotranspiration on water infiltration may be the reason (see, e.g., Turc 1961; Abtew and Melesse 2013; Faimon et al. 2016). Then, soil moisture appears to be a better driving variable for CO2 (see segment D). The negative correlation CO2/P0(ext) indicates that positive fluctuations in barometric pressure increase cave ventilation that decreases CO2 concentrations in the cave (see, e.g., Baldini et al. 2006; Mourzenko et al. 2014; Bourret et al. 2019).

4.3 Global effect

Estimating the contribution of CO2 fluxes from cave to the global carbon cycle is very difficult due to many factors such as latitude, altitude, local climate, land cover, slope of the terrain, cave orientation worldwide. On a local scale, however, we can compare the S-ŠC flux with soil respiration, representing generally the second-largest terrestrial carbon flux of the carbon cycle (e.g., Bond-Lamberty and Thomson 2010; Chen et al. 2013; Hashimoto et al. 2015). Typical CO2 efflux from MK soils varied temporally and spatially between 1 and 6 µmol m−2 s−1 (Faimon and Lang, unpublished data). The mean value of 3.5 µmol m−2 s−1 is in very good agreement with published values, e.g., Eler et al. (2013) for the Podgorski Karst (sub-Mediterranean region of Slovenia). Extrapolation of this value to the MK area of 57,830,480 m2 gives the total mean soil respiration of 2.809 × 108 kg CO2 yr−1. Therefore, the cave flux of 6.823 × 103 kg CO2 yr−1 does not appear to be very significant, representing only 0.024‰ of the soil respiration. These results are representative of the temperate zone conditions. However, since the flux of CO2 into and out of a cave is closely related to CO2 production in soils, the ratio of the flux of CO2 associated with soil respiration to the flux of CO2 associated with seasonal cave ventilation should remain conservative. Thus, similar ratios may be expected in other climate zones (for example, in dry and continental zones). However, in the tropical zone, the ratio could be somewhat lower: although increased soil CO2 production will lead to higher soil respiration and higher cave CO2 concentrations, the winter CO2 flux from the cave to the exterior will be lower due to a lower range of annual external temperatures (see James et al. 2015) and therefore due to a lower temperature gradient controlling cave ventilation (see, e.g., de Freitas et al. 1982; Faimon et al. 2012; Faimon and Lang 2013).

In our opinion, the study of contribution of cave CO2 to the external atmosphere cannot be done in other way than by a string of individual case studies – only a comparison of results of these studies will allow us to draw a definitive conclusion. For now, we have to state that the assumptions about significance of seasonal cave-atmosphere exchange for the global carbon cycle were not confirmed. However, the CO2 flux associated with cave air exchange could be important in a rather different aspect: it could contribute to seasonal fluctuations of CO2 concentrations in the atmosphere with a summer minimum and a winter maximum (see, e.g., Lv et al. 2020).

5 Conclusions

The study of CO2 exchange between the Sloup-Šošůvka Caves and external atmosphere can be used to draw following conclusions:

  • Two modes of CO2 variations were distinguished: (1) the Cave Accumulation Mode (CAM) operating during the spring/summer seasons and (2) the Cave Decumulation Mode (CDM) acting during the fall / winter seasons.

  • Maximum levels of CO2, approaching 10,000 ppmv, were recorded in the Rieger Hall during CAM.

  • Minimum CO2 levels in the cave approached 400–500 ppmv during CDM.

  • Anthropogenic contribution (respiration of cave visitors) to the total cave CO2 appears to be of little importance.

  • The flux of CO2 out of the cave during CDM is controlled by differences in virtual temperatures switching the downward airflow ventilation mode to upward airflow ventilation mode.

  • The total flux of CO2 associated with the air exchange between the Sloup-Šošůvka Caves and the external atmosphere was about 350 kg yr−1.

  • Extrapolating this value to the total area of all the Moravian Karst caves yielded the total flux of about 6820 kg CO2 yr−1.

  • This flux represents only 0.024‰ of the total soil respiration of the Moravian Karst area (about 2.81 × 108 kg CO2 yr−1).

  • Globally, the CO2 released from caves in fall / winter could contribute to seasonal fluctuations in the CO2 concentration in the external atmosphere.

  • Correlation analysis indicates that the CO2 flux into the cave during the accumulation mode could be controlled by various external variables such as barometric pressure (negative correlation) and external/ground temperatures, soil temperature, global radiation, or soil moisture (all positive correlations).