The C sequestration rate is a parameter used in C sink evaluations; however, various calculation methods are used and significant uncertainties remained. The reverse approach and forward modeling are two popular C sink estimation methods used in karst areas. Estimations using the reverse approach are suitable for small watersheds where rock types are clearly known, and hydrochemical relationships between river and rock weathering products are conducted on the basis (Hartmann, 2009). Forward modeling derives from the Temperate Stream Model, which is based on relationships between rock types, rock-weathering rates, and runoff effects (Meybeck, 1987; Suchet and Probst, 1993; Suchet and Probst, 1995; Velbel and Price, 2007). According to numerous studies, the following equation expresses an existing global empirical model on C uptake rates:

where F₁ represents C sequestration in a karst area; q_s and q_u represent the monthly mean flux of surface water and underground water, respectively; a is the empirical parameter dependent on the rock type; and a is 0.0294 g C mm^-1, estimated by Bluth (Bluth and Kump, 1994), and 0.0383 g C mm^-1, estimated by Suchet (Suchet and Probst, 1993). By applying this empirical equation to the Houzhai River basin in southwest China, Yan et al. (2011) estimated the value of C sequestration at 22.3 g C m^-2 yr^-1 and 29.0 g C m^-2 yr^-1, respectively (Yan et al., 2011). This result is inconsistent with other estimated values, primarily because both parameters lack data support in China.

Popular methods used in China are the solute load method, the carbonate-rock-tablet test, the diffusion boundary layer (DBL) theory, model simulations, and the inverse modeling method as well as other methods that derive from the above methods (Liu and Zhao, 2000; Liu et al., 2010; Liu, 2011b; Yan et al., 2011). The solute load method is suitable for C sink estimations of closed and complete drainage basins on a macro scale. This method, however, demands a large amount of hydrochemical data and strict conditions. Nevertheless, mixed C forms can still be released from the Earth’s interior as well as from exogenous acid effects (Lerman et al., 2007; Gaillardet and Galy, 2008; Hurwitz et al., 2010; Zhang and Li, 2012). Bicarbonate concentrations in surface runoff, groundwater, and water discharge are essential parameters used in estimating C sequestration rates. Moreover, new monitoring technologies, such as eddy covariance, remote sensing, stable isotope tracers, and GIS-based spatial analysis, are combined in global C cycling observation systems (Cao et al., 2004; Yu et al., 2011). The current challenge remains to combine observational data with multiple models for estimating or forecasting.

Chemical weathering reactions of limestone and dolomite differ as follows:

CaCO₃ + CO₂ + H₂O Ca²⁺ + 2HCO^- ₃ (2)

CaMg(CO₃)₂ + 2CO₂ + 2H₂O Ca²⁺ +Mg²⁺ +4HCO^- ₃ (3)

The two chemical equations above show that 1 or 2 mols of CO₂ would be needed when 1 mol of CaCO₃ or CaMg(CO₃)₂ dissolved. Although the CO₂ required for rock weathering does not directly derive from the atmosphere (deriving partly from soil), rock weathering C uptake processes could still be considered an atmospheric CO₂ sink because the CO₂ released from the soil to the atmosphere will decrease in conjunction with C uptake rock weathering processes.

The following equation describes the solute load method:

where F₂ is the C sequestration rate; c is the HCO^- ₃concentration in karst runoff; q is water discharge; M_c and are the relative molecular mass of C and HCO^- ₃, respectively. Yan (2011) calculated the C sequestration rate in the Houzhai River basin within the southwestern karst zone in China using this formula. The result, which derived from surface and subsurface water data from 1986 to 2007, was 20.7 g C m^-2 yr^-1, being much higher than the 8.6 g C m^-2 yr^-1 estimated by Jiang (Jiang and Yuan, 1999; Liu and Zhao, 2000; Yan et al., 2011).

The carbonate-rock-tablet test is suitable for karst areas where no carbonatite overlies soil. This mature method has been widely used for its simple operation and short duration period. At the same time, however, it has limitations, such as representativeness and scale conversions, and this is on account of the vast heterogeneity of karst soil and the diversity in runoff erosion (Liu, 2011b; Zeng et al., 2014). All these issues could cause great differences in final estimations. One hydrologic year is generally required to test weight decreases in the tablet, which is the key information required to calculate C sequestration.

where F is the C sequestration rate (g C m^-2 yr^-1); is the absolute quality of carbonatite corrosion (g); R is the relative content percentage of CaCO₃ in the tablet; S is the superficial area of the tablet (cm²); T is burial time (d). Using this method, Zhang et al. determined the sequestration rate in an order of magnitude from farmland>woodland> cultivated land>fallow land>bush fallow land (Zhang et al., 2006).

The global C sink is 0.8242 Pg C yr^-1, of which the net C sink is 0.7052 Pg C yr^-1, which was estimated by Liu et al., who took accounted of carbonatite weathering and aquatic organism (Liu et al., 2010). Using the multiple estimation method, the terrestrial ecosystem C sequestration rate was from 0.19 to 0.26 Pg C yr^-1, which converts to 0.26 Pg C yr^-1 using the inverse modeling method (Piao et al., 2009). According to mean bicarbonate ion concentrations and runoff modulus, the C sink in the karst area of China is 10.09 Tg C yr^-1, estimated using the solute load method (Jiang et al., 2011). However, there exists some deviation in this estimation that must be recalculated (Zhang, 2012; Jiang et al., 2013). Jiang et al. (2013) divided China karst area into four regions, which were the southern karst region, the northern karst region, the Tibetan Plateau karst region, and the buried karst region, and their occupied areas were 5.648×10⁵ km², 3.258×10⁵ km², 5.560×10⁵ km², and 2.001×10⁶ km², respectively (Figure 3 and Table 1). We reevaluated C sink in the karst zone in China by remedying the data of the northern karst and buried karst regions, and we used a correction coefficient (a=0.65) to eliminate interference from sulfuric acid and nitric acid caused by carbonatite dissolution. As Tables 1 and 2 show, the total C sink in the karst zone of China is 4.74 Tg C yr^-1, which is roughly approximate with the estimation reported by Jiang (2013).

There are great differences in the mechanisms, operations, and purposes of terrestrial ecosystem models now. Given that few models have been specifically developed for karst areas, such models face significant challenges and uncertainty. Even the Community Land Model (CLM), one of the most highly developed terrestrial system models, established by the National Center for Atmospheric Research (NCAR) of the United States of America, performed poorly in Tibetan Plateau, China (Luo et al., 2013). Various types of models have been applied in China, such as the Atmosphere-Vegetation Interaction Model (AVIM2); the Carbon Exchange in the Vegetation-Soil-Atmosphere model (CEVSA); the Geoscience Knowledge Integration Protocol (GeoPro) based on C, nitrogen (N), and water coupling system; the Global Erosion Model for CO₂ fluxes model (GEM-CO₂) based on different weathering coefficients of rocks; the Global Production Efficiency Model (GLO-PEM), Carnegie-Ames- Stanford Approach (CASA), and GEOLUE models based on the efficiency of photosynthesis and autotrophic respiration; and the Terrestrial Ecosystem Model (TEM) based on eco-models (Suchet and Probst, 1993; Suchet and Probst, 1995; Qiu et al., 2004). Net primary productivity (NPP) of the Tibetan Plateau is 302.44 Tg C yr^-1, which was estimated using TEM (Zhou et al., 2004). The 50-year mean Net Ecosystem Productivity (NEP) of Guizhou Province, China, dominated by karst landforms under a semitropical climate, is 23.9 g C m^-2 yr^-1, which was estimated using AVIM2 (Ma et al., 2013). Moreover, this result was roughly one-fifth of the non-karst area in the Qilian Mountains, Qinghai Province, China, which was also estimated using AVIM2. Additionally, GEM-CO₂ has been used to estimate rock weathering C sink in a karst region in China (Liu et al., 2015). Rock weathering C sink flux is 14.1 Tg C yr^-1 in China, which was estimated using GEM-CO₂, and contributions of carbonatite and silicate rocks were 52.65% and 47.35%, respectively (Qiu et al., 2004). However, there is much work to be done to increase model applicability in karst areas. The combination and mutual authentication of ecosystem C cycle models, regional scale inversion models, and remote sensing observation systems will provide strong support and greater accuracy in C sink estimations in karst areas. Discovering how to optimize terrestrial ecosystem models for application in karst ecosystems by adding correction coefficients or redefining model parameters would be a significant step forward.

Bicarbonate ions can be generated from reactions of nitric acid with carbonatite, and sulfuric acid with carbonatite as well (the exception of carbon acid). As a result, bicarbonate ion concentrations are rather high in karst water. As shown in Eqs. (6) and (7), neither atmospheric CO₂ nor soil participated in such reactions. Both the chemical mass balance model and stable isotope analysis confirmed that these processes had a nonnegligible effect on C sink estimations.

(Ca_(1-x)Mg_x)CO₃+HNO₃ (1-x)Ca²⁺+xMg²⁺+NO^- ₃+ HCO^- ₃ (6)

2(Ca_(1-x)Mg_x)CO₃+H₂SO₄ 2(1-x)Ca²⁺+2xMg²⁺+SO₄^2-+2 HCO^- ₃ (7)

Yan (2011) found that Ca²⁺, Mg²⁺, HCO^- ₃, and accounted for 96% of the total dissolved solids, and the proportion of negative ions from was second only to HCO^- ₃. Moreover, concentrations in water have a direct relationship with its contribution to

rock weathering (Yan et al., 2011). Liu (2008) estimated that CO₂ released from sulfuric acid-driven carbonatite weathering in southwestern China was 4.4 Tg yr^-1; therefore, it was calculated that 28 Tg yr^-1 was the CO₂ flux released from karst areas in China, which accounted for 33% of rock weathering C sink (Liu, 2008). On a smaller scale, results from an agriculture dominant karst catchment within the Qingmuguan subterranean watershed area in Chongqing City, China, showed that DIC produced by sulfuric and nitric acids accounted for 33.8% of the total DIC in subterranean water, which took up almost the same percentage (Zhang et al., 2012). Additionally, other carbonatite areas showed a slightly smaller influence from sulfuric and nitric acids. In the Yalong River, that drains into the eastern Tibetan Plateau, China, approximately 13% of DIC originated from sulfuric and nitric acid-driven carbonate weathering (Li et al., 2014). In another small drainage basin of the Qinhe River in northern China, CO₂ released from sulfuric acid-driven carbonate weathering was 0.63×10⁵ mol km^-2 yr^-1, which accounted for 44% of CO₂ released by carbonate weathering (Zhang et al., 2015). Thus, applying a 0.35 calibration factor is scientifically-based and appropriate for use in the above reevaluation.

Furthermore, water from non-karst catchments will also directly result in deviations in uncertainty during C sink evaluations. However, given that the dilution effect is difficult to quantify, this has seldom been considered before. Moreover, spatial scale conversions are one of the most difficult and recurrent problems which cause immeasurable uncertainty in C sink estimations.

Many studies have also proposed that carbonate weathering may not lead to a stable C sink, but silicate weathering can absorb atmospheric CO₂ as a net C sink on a geological timescale (Gaillardet et al., 1999; Larson, 2011; Curl, 2012; Groves et al., 2012). Because the chemical equations (Eqs. (2) and (3)) are reversible, an equal quantity of CO₂ will be released when subterranean karst water returns to the surface. Thus, silicate weathering is considered the only way for C sequestration to occur in these studies.

2CO₂ +3H₂O +CaSiO₃ = Ca²⁺ +2HCO^- ₃ +H₄SiO₄ (8)

Like Eq. (8) shows, CO₂ sequestrated by silicate weathering could be transported into oceans and then settle as carbonate, which results in stable, long-term C sequestration storage in the duration of millions of years (Berner et al., 1983). CO₂ consumption rates of global silicate weathering are from 9.86 to 14.01×10¹² mol yr^-1, which was deduced through the chemistry of large rivers (Gaillardet et al., 1999; Moon et al., 2014).

At the same time, other studies have shown that HCO^- ₃ will not deliver all CO₂ back to the atmosphere. Biological cycling could increase both rates and the stability of rock weathering C sequestration. Moreover, biological behavior can participate in carbonate weathering processes both directly and indirectly. Carbonatite dissolution can be raised one order of magnitude by means of carbonic anhydrase. Additionally, 88% of C uptake from photosynthetic processes of aquatic plants derives from water; and particulate organic carbon (POC) uptake by aquatic organisms is also an important means of C sequestration (Liu, 2001; Lian et al., 2011; de Montety et al., 2011). Liu (2010) estimated that the terrestrial aquatic ecosystem contributes 0.2334 Pg C yr^-1 or 33.1% of the net sink of carbonate dissolution, the global water cycle, and photosynthetic uptake by aquatic organisms (Liu et al., 2010). Therefore, C emission from rock weathering can be sequestrated by multiple means.

With the exception of rock weathering C sink, many other processes could also result in CO₂ fixation in the karst critical zone. Unlike non-karst areas, both soil-plant organic processes and biological pump processes, under a precondition of high DIC concentrations in karst water, could result in significant differences.

In conjunction with global climate change, the C sink from carbonatite weathering is predicted to increase by 21% to 0.18 Pg C yr^-1 (Liu et al., 2010). However, not only feedback mechanisms of global ecosystems but also anthropogenic activities can provide means for C sink management. In the past 50 years, for example, a large bicarbonate flux increased in the Mississippi River, the United States of America, mainly due to land-use changes and management (Raymond et al., 2008). At the same time, it has also been demonstrated that groundwater is a CO₂ sink because limestone weathering has caused a 20% increase in groundwater CO₂ concentrations (Macpherson et al., 2008).

The favorable succession order of karst vegetation is bare rock with sparse grass > grassland > scrub-grassland > scrub > liana-scrubland > broad deciduous forests > climax community. However, the path of succession could be more complex in consideration of different conditions of soil, climate, species reproduction strategies, internal community environments, and anthropogenic interference. Saltational evolution could occur under artificial restoration, and reverse succession could occur under anthropogenic disturbances. Previous studies have shown that ecological restoration and land-use pattern conversions could enhance the capacity of C sinks in karst areas. Dissolution rates of different land utilization types showed significant differences, and subterranean C sinks of primary forests were three times greater than that of secondary forests and nine times greater than that of scrubland. After conversion from cultivated land and scrubland to secondary forests, C sinks can increase by 5.71-7.02 g C m^-2 yr^-1 after conversion from cultivated land and scrubland to secondary forests, and will increase by 24.86-26.17 g C m^-2 yr^-1 if those lands could develop into primary forests (Zhang, 2011).

Therefore, based on the discussion above, land-use strategy optimization and ecosystem restoration are efficient ways to increase C sink in the karst critical zone. To increase karst C sink under an integrate framework, it is indispensable that researchers get a comprehensive understanding of the rock-soil-biology-atmosphere continuum. In China, a series of policies, such as afforestation, which converts farmland back to forests, and ecomigration have been applied for karst critical zone restoration. However, NPP is considered only a short-term solution for C sequestration in terrestrial ecosystems, and there are limitations in increasing C sink in a fragile karst system due to the equilibrium of the carbon-nitrogen- water coupling relationship (Tao et al., 2001; Tao et al., 2003; Gao et al., 2014). To date, an increase in biomass remains an efficient C sink strategy under vegetation degradation in the karst critical zone. However, this will cause a significant and undefined issue, that is, the determination of the actual C sink threshold.

Another way to increase C sink capacities is reducing soil loss. However, due to its thin and spare soil layer, C sequestration in karst soil is smaller than in non-karst soil. At the same time, reducing soil loss can foster forward vegetation succession, which may promote a virtuous cycle (Figure 4).

The critical zone (CZ) is a holistic framework for integrated studies of water in conjunction with soil, rocks, air, and biotic resources in near-surface terrestrial environments (Lin, 2010). Karst CZ focuses on the rock-soil-biology-atmosphere continuum, which is characterized by three-dimensional and dualistic structures. The soil ecosystem is the core of the karst CZ, which interacts with the surface crust (vegetation, bedrock, and groundwater) through rock weathering and runoff erosion.

Karst areas have developed conduit systems include natural rock fractures, cenotes, and funnels at macroscopic scale, and soil pore and vascular bundle at microcosmic scale. Matter and energy transport through karst conduit systems are mainly in the form of solute transport. In terms of soil-atmosphere interfacial processes, interaction and feedback mechanisms between photosynthesis and transpiration are mainly dominated by stomatal behavior, which is sensitive to available soil water content. In terms of the soil-root system interface, how rhizospheric microorganisms obtain C depends on root exudates and degradable organic matter in surface soil.

Furthermore, NPP is the core assessment index of ecosystem service functions and vegetation activity. Ecosystem C cycle is a representation of the close correlation between biology and abiotic systems. Gao et al. (2013) reported that the carbon-nitrogen-water coupling cycle relationship dominates the C thresholds and balances of soil ecosystems. According to the C mass balance model, this relationship may cause excessive C uptake by karst ecosystem during rock weathering process, and surplus C loss will occur via soil erosion or other ecological processes.