Cave ventilation is influenced by variations in the CO2-dependent virtual temperature

Headnote

Abstract: Dynamics and drivers of ventilation in caves are of growing interest for different fields of science. Accumulated CO2 in caves can be exchanged with the atmosphere, modifying the internal CO2 content, affecting stalagmite growth rates, deteriorating rupestrian paintings, or creating new minerals. Current estimates of cave ventilation neglect the role of high CO2 concentrations in determining air density - approximated via the virtual temperature (T^sub v^) -, affecting buoyancy and therefore the release or storage of CO2. Here we try to improve knowledge and understanding of cave ventilation through the use of T^sub v^ in CO2-rich air to explain buoyancy for different values of temperature (T) and CO2 content. Also, we show differences between T and T^sub v^ for 14 different experimental sites in the vadose zone, demonstrating the importance of using the correct definition of T^sub v^ to determine air buoyancy in caves. The calculation of T^sub v^ (including CO2 effects) is currently available via internet using an Excel template, requiring the input of CO2 (%), air temperature (°C) and relative humidity (%).

Keywords: buoyancy; carbon dioxide; caves; soil ventilation; ventilation; virtual temperature

Received 26 June 2012; Revised 4 September 2012; Accepted 11 September 2012

Citation: Sánchez-Cañete E.P., Serrano-Ortiz P., Domingo F. and Kowalski A.S. 2013. Cave ventilation is influenced by variations in the CO2-dependent virtual temperature. International Journal of Speleology, 42 (1), 1-8. Tampa, FL (USA) ISSN 0392-6672 http://dx.doi.org/10.5038/1827-806X.42.1.1

(ProQuest: ... denotes formulae omitted.)

INTRODUCTION

There is currently growing interest in characterizing storage and ventilation of CO2 in caves, both from external (atmospheric) and internal (speleological) perspectives. Measurements of rising atmospheric CO2 by Keeling (1960) since the mid-20th century reveal that anthropogenic activities are causing CO2 accumulation in the atmosphere and forcing global warming. Soils are a large pool of terrestrial carbon (C), estimated to contain 2344 Pg C in solid form in the top 3 m (Jobbagy & Jackson, 2000) - three times the aboveground biomass C reservoir and double that of the atmosphere (Schlesinger, 1997) - and also have an enormous capacity to store gaseous CO2 in subsurface cracks, pores and cavities. The vadose zone is enriched in CO2 and some caves often exceed 5% (volumetric CO2 fraction of 50,000 ppm; Ek & Gewelt, 1985; Howarth & Stone, 1990; Denis et al., 2005; Batiot-Guilhe et al., 2007; Benavente et al., 2010) representing important air compositional differences with respect to the external atmosphere, currently near 395 ppm. Accumulated CO2 in caves can be exchanged with the atmosphere (Weisbrod et al., 2009; Serrano-Ortiz et al., 2010; Sanchez-Cañete et al., 2011), modifying the internal CO2 content and affecting stalagmite growth rates (Banner et al., 2007; Baldini et al., 2008), deteriorating rupestrian paintings (Fernández et al., 1986) and creating new minerals (Badino et al., 2011). However due to the complexity and peculiarity of caves, as well as the variety of meteorological conditions that determine the degree and timing of ventilation (Fairchild & Baker, 2012), such exchanges are not well understood and their contributions to regional atmospheric CO2 budgets remain unknown.

Estimation of cave ventilation can be realized by a number of means, the most common of which has traditionally neglected the role of high CO2 concentrations and requires refinement. The drivers implicated in the cave ventilation can be classif ied as either dynamic or static (Cigna, 1968). Dynamic drivers are defined by moving fluids such as water or wind (Nachshon et al., 2012), while static drivers include variations of pressure, temperature or air composition (water vapor, CO2, CH4, etc.). Ventilation rates can be measured directly using anemometers, estimated indirectly through variations in Radon content (Hakl et al., 1997; Faimon et al., 2006), or other tracer gases (de Freitas et al., 1982) or variations in air density. Most commonly, air density variations are approximated to evaluate buoyancy according to temperature differences between the internal (Tint ) and exterior atmosphere (Text ), neglecting air composition (Fernàndez-Cortes et al., 2006; Baldini et al., 2008; Liñan et al., 2008; Milanolo & Gabrovsek, 2009; Faimon et al., 2012). Faimon et al. (2012) modelled the airflows into a cave, and found that the temperature explained more than 99% of variations in air density; therefore, temperature could be used as an alternative airflow predictor. However, de Freitas et al. (1982) concluded that reversal of airflow occurs when the densities in the cave and the exterior are equal, rather than when thermal conditions of the cave and external air are the same. For this reason, they suggest that the gradient in virtual temperature (Tv ) between the cave and outside air would be the appropriate indicator. In this sense, Kowalczk & Froelich (2010), improved the determination of internal /external air densities by including the influence of water vapor, using the traditional definition of the virtual temperature. Nevertheless, in cases where CO2 molar fractions of internal air exceed atmospheric values by an order of magnitude or more, it is necessary to take into account the heaviness of CO2 when calculating the virtual temperature (Kowalski & Sanchez-Cañete, 2010).

Whereas high CO2 values registered in cave air have been attributed most often to the seepage of CO2- enriched water from the root zone, the possibility of sinking flows of dense, CO2-rich air should also be considered. Biological CO2 is produced near the surface by respiration of plant roots and microorganisms (Kuzyakov, 2006); in most caves, isotopic studies confirm a clear biological origin of cave CO2 (Bourges et al., 2001, 2012). Soil CO2 generally increases with depth, from near-atmospheric concentrations at a few centimeters to an order of magnitude more a few meters down (Amundson & Davidson, 1990, Atkinson, 1977). High concentrations of CO2 at depth have been explained in terms of shallow CO2 dissolution, downward transport by seepage, and subsequent precipitation from water in deeper layers (Spötl et al., 2005), whereas surface layers are depleted in CO2 by exchange with the atmosphere. At depth and for caves in particular, another input of CO2 could be due to the injection of dense, CO2-rich air, f lowing down through fissures due to differences in buoyancy, whose characterization is poorly known and requires information regarding Tv. This virtual temperature has been little applied to soils and caves, but could explain why CO2 accumulates at depth yielding concentrations much higher than those in the atmosphere.

Here we show the error produced in determining the virtual temperature when not taking into account CO2 effects, and demonstrate its repercussions for the determination of air buoyancy in caves. We try to improve knowledge and understanding of cave ventilation through the use of virtual temperature in CO2-rich air. Accurate determinations of virtual temperature allow numerical evaluation of buoyancy, and thus can determine exactly when ventilation is possible, and therefore when a cave can release or store CO2. Also we represent Tv -explaining the relative buoyancy relevant for cave ventilation- for different values of T and CO2 content. Then, we show differences between T and Tv , -calculated both with and without accounting for CO2 content- for 14 different experimental sites in the vadose zone, demonstrating the importance of using the correct def inition of Tv to determine air buoyancy in caves.

DERIVATIONS AND DEFINITIONS

For purposes of characterizing air buoyancy, meteorologists define the virtual temperature (Tv ) as the temperature that dry air must have to equal the density of moist air at the same pressure. The virtual temperature for the atmosphere is approximated as (see appendix A):

Tv = T(1 + 0.61r) (1)

where T and Tv are the absolute temperature (K) and virtual temperature (K) respectively and r is the mixing ratio (dimensionless), defined as the ratio of the mass of water vapor to that of dry air.

Thus variations in the virtual temperature serve as a proxy for those in air density (Stull, 1988), which can be obtained through the equation of state for moist air:

p = ρRdTv (2)

where p, ρ and Rd are the pressure (Pa=J m-3), air density (kg m-3) and particular gas constant for dry air (286.97 J kg-1 K-1) respectively. Equation (2) makes clear that, for a given altitude level (pressure), air density is related directly to Tv , which serves therefore as a surrogate variable for determining buoyancy.

Equation (2) is only valid for the free atmosphere, while for caves or soils it should not be used due to high concentrations of CO2 in the air. This equation, normally used for assessing the buoyancy of an air mass by changes in its density, is valid in the atmosphere because the molar mass of dry air (md ) is very constant, 0.02897 kg.mol-1, since air composition is very constant once water vapor has been excluded. However the air composition in soils or caves differs from that of the atmosphere due to higher amounts of CO2.

The correct equations to calculate the virtual temperature including CO2 effects were developed by Kowalski & Sanchez-Cañete (2010). Frequently caves exhibit values exceeding 0.4% in volumetric fraction of CO2, ten times the atmospheric concentration (Howarth & Stone, 1990; Denis et al., 2005; Batiot-Guilhe et al., 2007; Benavente et al., 2010). This CO2 increment with respect to atmospheric concentrations provokes changes in the composition of dry air and its molar mass (md ) so that the definition of the virtual temperature in eq. (1) is inappropriate. An approximation to calculate the virtual temperature (Tv ) including CO2 effects is via the following equation (see appendix):

Tv = T + (1 + 0.6079rv - 0.3419rc) (3)

where rv and rc are the water vapour and carbon dioxide mixing ratios respectively (dimensionless).

Therefore for determining air density in caves or soils including CO2 effects, the virtual temperature can be used in the ideal gas law with the particular gas constant (Rnoa, 287.0 J K-1 kg-1) for the mixture of nitrogen (N2), oxygen (O2), and argon (Ar).

p = ρ . Rn0a . Tv (4)

This parameter can be computed exactly using an Excel template found at http://fisicaaplicada.ugr. es/pages/tv/!/download, where it is only necessary to enter values of CO2 (%), air temperature (°C) and relative humidity (%).

RESULTS AND DISCUSSION

The difference between internal (cave) and external (atmosphere) virtual temperatures can be used to determine the potential for buoyancy flows. The virtual temperature is a variable used traditionally by meteorologists to determine air buoyancy. Knowing the internal and external virtual temperatures allows determination of air densities (using equation 4) and therefore calculation of the possibility of buoyancy f lows. The following results are organized into two sections. First, general differences between T and Tv , including CO2 effects and comparing the interior and exterior environments, are presented to highlight the importance of using the appropriate variable (Tv ) to characterize air density. Then, differences are shown for the conditions of specif ic caves selected from the literature.

Quantifying Tv -T for caves in general

Differences between air temperature (T) and virtual temperature (Tv ) (eq. 3) at different volumetric fractions of CO2 are shown in Fig. 1, assuming 100% relative humidity (RH) as is typical for internal conditions. To give an example, a cave with 3% CO2, and 10°C would have a Tv 3°C lower than T (see dashed lines). Positive values (orange color) indicate that the virtual temperature is higher than the temperature due to the dominant influence of water vapor on compositionally determined air density (for low CO2 concentrations). This is greater for higher temperatures since warm air can store more water vapor than cold air, decreasing the molar mass below that of dry air (28.96 g mol-1) due to the increased importance of water vapor (18 g mol-1), thus reducing the density.

Figure 2 shows that whenever the internal and external atmospheres have the same temperature and relative humidity, higher values of CO2 inside the cave explain stagnation of the cave environment. For example, a cave with 3% CO2 and exterior and interior temperature of 10°C would have a virtual temperature 4.3°C colder than that of the external air; consequently the internal air is denser than the exterior and therefore stagnant.

Whereas differences between external and internal virtual temperatures are necessary for the correct interpretation of cave ventilation, the difference between external and internal temperatures is commonly used (Spötl et al., 2005; Fernàndez-Cortes et al., 2006, 2009; Baldini et al., 2008; Liñan et al., 2008; Milanolo & Gabrovsek, 2009; Faimon et al., 2012). Thus, with similar values of Text and Tint, the differences between virtual temperatures can be more than 10°C (Fig. 2).

Fixing the internal CO2 content (e.g., at 3% to continue with the example presented above), we can analyze differences between external and internal virtual temperatures (Fig. 3) at different temperatures. Negative values indicate that the interior air is denser than the exterior and therefore stagnant. For example, a cave with 3% CO2, 100% RH and 10°C presents neutral buoyancy when the external temperature is approximately 6°C. Consistent with the results of Fig. 2, when both cave and external atmosphere are at 10°C, Tv is lower than T by 4.3°C. Higher values of the external temperature imply stagnant air inside the cave.

Quantifying T v -T for specific caves

To determine when buoyancy flows are possible, scientists must compare the differences between external and internal virtual temperatures. Thus, if virtual temperatures are equal (independent of the amount of water vapor or CO2) both air masses will be in equilibrium. On the other hand, if air mass A has a virtual temperature higher than air mass B, then air mass A will have the lower density. In this way, comparing the virtual temperatures of air masses specifies their relative densities (from eq. 4) and thus the tendency to float or sink.

Maximum CO2 values and mean temperatures of 14 caves and boreholes of the world are shown in Table 1. These published data were taken as examples to calculate the differences between the virtual temperature and temperature. Although such differences also depend on the temperature, caves in excess of 1% CO2 generally present negative differences between Tv and T, while lower values of CO2 present positive differences (Fig. 4). However, for example, the subtropical Hollow Ridge cave (D) presents more positive values of Tv-T than does the temperate Císarská cave (C), despite similar volumetric fractions of CO2 (0.42 and 0.4%, respectively). Such differences are due to differences in water vapor content, according to temperature (19.6 versus 9.6° C in Hollow Ridge and Císarská cave, respectively).

Virtual temperature differences between the exterior and interior are compared to distinguish between periods of stagnant versus buoyant cave air for each experimental site, using their maximum values of CO2 and the mean T (Fig. 5). Differences between the virtual temperatures (Tv_ext-Tv_int) increase with increasing CO2 molar fraction and therefore higher CO2 implies greater differences between internal and external densities, with the internal air denser than the external air and therefore causing stagnation (in the case of a cave lying below its entrance). For example, the Natural Bridge Caverns (I) with 4% CO2 presents a difference of 6 °C between the (mean annual) external and internal virtual temperatures. Therefore, the internal air is denser than that of the external atmosphere (on average), inducing its stagnation and explaining the storage of CO2. In the Nerja cave borehole (M), with 6% and 0.0395% CO2 for the internal and external atmosphere, respectively, the virtual temperature in the borehole is 8.9°C lower than the outside (Fig. 5). This difference in Tv implies that the internal air is denser, inhibiting convective ventilation. Therefore, researchers who use differences between exterior/ interior air temperatures to determine ventilation, may find differences between virtual temperatures close to 9 °C, when the exterior/interior air temperature is the same in both, and therefore over- or under-estimate the ventilation periods.

Differences between virtual temperatures in two air masses indicate density differences between both, and thus the potential for ventilation due to buoyancy. However, two possible issues must be considered that hamper or facilitate ventilation of the cave. The first includes atmospheric conditions such as the wind (Kowalczk & Froelich, 2010) and pressure changes (Denis et al., 2005; Baldini et al., 2006) inside and outside of the cave. The relevancy of buoyancy-induced cave ventilation is greatest on days with atmospheric stability, where there are little pressure changes and low winds. During these days static processes (Cigna, 1968) are dominant. The second issue is the number of entrances to the cave and their different altitudes and orientations (up or down). In caves with a single entrance the air will flow inward along the floor or roof, and return outward along the roof or floor, according to the sign of the density difference. However if the cave has many entrances at different levels, it may be necessary to monitor more than one entrance (Cigna, 1968). Due to the strong spatial variability of the temperature, simply knowing Tv at a single point inside (and outside) the cave may not necessarily be sufficient for determining the potential for ventilation.

CONCLUSIONS

We used the information of several caves together with gas law to demonstrate that the difference between external and internal virtual temperatures including CO2 effects determines the buoyancy and should be used for the correct interpretation of cave ventilation. Often scientists estimate ventilation neglecting CO2 effects, but this can cause errors close to 9 °C in the difference between external and internal virtual temperatures when the air temperature is the same in both. Thus, the common use of the difference between external and internal temperatures could over- or under-estimate the existence of ventilation processes, depending on CO2 content and relative humidity.

ACKNOWLEDGEMENTS

This research was funded by the Andalusian regional government project GEOCARBO (P08- RNM-3721) and GLOCHARID, including European Union ERDF funds, with support from Spanish Ministry of Science and Innovation projects Carbored- II (CGL2010-22193-C04-02), SOILPROF (CGL2011- 15276-E) and CARBORAD (CGL2011-27493), as well as the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 244122. The authors thank three anonymous reviewers for constructive comments that helped to substantially improve the manuscript.

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Appendix

(ProQuest: Appendix omitted.)