Details of the Konza site are in the Supplement and references therein. Here we provide brief information relevant to this work. Konza is a mesic native grassland where experimentally manipulated, long-term burning regimes have led to woody encroachment in up to 70 % of the catchment area in some catchments. The mean annual temperature and precipitation are 13 ∘C and ∼ 835 mm, respectively (Tsypin and Macpherson, 2012). The bedrock contains repeating Permian couplets of limestone (1–2 m thick) and mudstone (2–4 m) (Macpherson et al., 2008). The limestone is primarily calcite with traces of dolomite, while the mudstone is dominated by illite, chlorite, and mixed layers of chlorite–illite and chlorite–vermiculite, varying in abundance from major to trace amounts. With an average thickness of 1–2 m in the lowlands, soils mostly have carbonate less than 25 % (Macpherson et al., 2008). Data suggest that the Konza landscape is undergoing a hydrogeochemical transition that coincides with and may be driven by woody encroachment. Parallel to these changes is a detectable decline in streamflow and an increase in weathering rates (Macpherson and Sullivan, 2019b) and groundwater pCO2. The concentration–discharge relationships have exhibited chemodynamic patterns (i.e., solute concentrations are sensitive to changes in discharge) for geogenic species (e.g., Mg and Na) in woody-encroached sites compared to grass sites. Sullivan et al. (2019a) hypothesized that concentration–discharge relationships may be affected by woody species with deeper roots, which altered flow paths and mineral–water interactions (Fig. 1). We focus on the upland watershed N04d in Konza (Fig. S1) that has experienced a 4-year burning interval since 1990 and has seen considerable woody encroachment and changes in hydrologic fluxes (Sullivan et al., 2019a).

Daily total meteoric precipitation and evapotranspiration were from the Konza data website (http://lter.konza.ksu.edu/data, last access: 22 November 2020). Wet chemistry deposition data were from the National Atmospheric Deposition Program (NADP, http://nadp.slh.wisc.edu/, last access: 22 November 2020). Data used in this work include monthly data of soil gases (at depths of 16, 84, and 152 cm from land surface), soil water (17 and 152 cm from land surface), and groundwater (366 cm from land surface) in 2009 and 2010 (Tsypin and Macpherson, 2012) (Fig. 2a). The sampling points were about 30 m away from the stream. More information on field and laboratory methods was included in the Supplement.

A 1-D reactive transport model was developed using the code CrunchTope (Steefel et al., 2015). The code solves mass conservation equations integrating advective and diffusive/dispersive transport and geochemical reactions. It has been extensively used in understanding mineral dissolution, chemical weathering, and biogeochemical reactions (e.g., Lawrence et al., 2014; Wen et al., 2016; Deng et al., 2017). In this study, the base case had a porosity of 0.48 and a depth of 366.0 cm at a resolution 1.0 cm. Soil temperature was assumed to decrease linearly from 17 ∘C at the land surface to 8 ∘C at 366.0 cm, within typical ranges of field measurements (Tsypin and Macpherson, 2012). Detailed setup of domain, soil mineralogy, initial condition, and precipitation chemistry are in the Supplement.

Numerical experiments were set up for grasslands and woodlands. The base case from Konza was used to represent grasslands: data from the Calhoun site (the Calhoun Critical Zone Observatory in South Carolina, USA) were used as representative for woody sites (Billings et al., 2018). Grasslands are typically characterized by a high proportion of horizontal macropores induced by dense, lateral-spread of roots mostly at depths less than 0.8 m (Jackson et al., 1996; Frank et al., 2010). These characteristics promote lateral flow (QL) at the shallow subsurface (Fig. 1a). At Konza, over 90 % of grass roots were at the top 0.5 m, leading to high hydrologic conductivity in top soils (Nippert et al., 2012). In the woodland, a greater proportion of deep roots enhances vertical macropore development (Canadell et al., 1996; Nardini et al., 2016), reduces permeability contrasts at different depths (Vergani and Graf, 2016), and is thought to facilitate more vertical water flow to the depth (QG). At the Calhoun site, over 50 % of roots are in the top 0.5 m in woodlands, with the rest penetrating deeper (Jackson et al., 1996; Eberbach, 2003; Billings et al., 2018).

The experiments aimed to compare the general, averaged behaviors rather than event-scale dynamics so the annual-average soil CO2 data and corresponding prescribed CO2(aq) concentrations were used (Table 2). The experiments focused on calcite weathering (Reactions 0–4) and excluded silicate weathering reactions (Reactions 5–7). The mineral-dissolution parameters from the base case were used for all experiments. We compared the relative significance of the hydrological (i.e., lateral versus vertical flow partitioning) vs. respiratory (i.e., CO2 generation) influences of deepening roots. Though other potential differences might be induced by deepening roots (e.g., water uptake, water table, and transpiration) (Li, 2019) and influence weathering, we assumed they remain constant across the grassland and woodland simulations to examine the relative influences of flow path vs. CO2 generation on carbonate weathering.

Each scenario in Table 3 includes a grassland and woodland case, with their respective profiles of calcite distribution and soil pCO2 kept the same (columns 3 and 4 in Table 3). The only difference in different scenarios is the flow partitioning (column 5). Soil pCO2 in the grassland (red line in column 4) was set to reflect the annual average of the Konza site. Soil pCO2 (blue line) in the woodland was set to reflect the annual average from the forest-dominant Calhoun site (Billings et al., 2018). In all scenarios, we assumed that grasslands and woodlands had the same total CO2(g∗) producing CO2 gas and CO2(aq) but differed in depth distributions. The CO2(g∗) depth distribution was constrained by CO2(g) field data (Table 2). The distribution of CO2(g∗) in grasslands is slightly steeper than that in the woodland, with higher density of roots and more abundant CO2(g∗) in the upper soils. Below the rooting depth, CO2(g∗) was assumed to be smaller (by 10 times) to represent the potential soil CO2 sources from microbial activities (Billings et al., 2018).

Scenario 1 considered flow partitioning (Table 3). With the large permeability contrast of soil and bedrock (over 4 orders of magnitude) in Konza (Macpherson, 1996), the GrassPF case (with QL=95 % × QT and QG=5 %  × QT) represents an end-member case for the grassland. The woodland (WoodPF) case was set to have 60 % lateral flow and 40 % vertical flow into the deeper subsurface. This groundwater percentage is at the high end of flow partitioning and serves as an end-member case for woodlands (Vergani and Graf, 2016). Scenarios 2 and 3 had no flow partitioning. Scenario 2 had two cases with 100 % vertical flow via the bottom outlet (VF; WoodVF and GrassVF); Scenario 3 had two cases with 100 % horizontal flow (HF; WoodHF and GrassHF) via the shallow outlet at 50 cm. These cases represent the end-member flow cases with 100 % lateral flow or 100 % vertical flow. In addition, because the two cases have the same flow scheme, they enable the differentiation of effects of soil CO2 distribution versus hydrology differences. All scenarios were run under infiltration rates from 3.7 × 10-2 to 3.7 m/a (10-4–10-2 m/d), the observed daily variation range at Konza. This was to explore the role of flow regimes and identify conditions where the most and least significant differences occur.

Each case was run until steady state, when concentrations at the domain outlet became constant (within ± 5 %) over time. The time to reach steady state varied from 0.1 to 30 a, depending on infiltration rates. The lateral flux (soil water, ML=QL × CL) and vertical fluxes (groundwater, MG=QG × CG) were calculated at 50 and 366 cm, in addition to total fluxes (weathering rates, MT). These fluxes multiplied with unit cross-section area (m2) convert into rates in units of moles per year (mol/a).

To compare the propagation of weathering fronts over longer timescales, we carried out two 300-year simulations for Scenario 1 with flow partitioning under the base-case infiltration rate of 0.37 m/a (i.e., GrassPF and WoodPF in Table 3). During this long-term simulation, we updated calcite volume, porosity, and permeability. The calcite volume changes were updated in each time step based on corresponding mass changes, which were used to update porosity. Permeability changes were updated based on changes in local porosity following the Kozeny–Carman equation: κiκi,0=∅i∅i,03×1-∅i,01-∅i2 (Kozeny, 1927; Costa, 2006), where κi and ∅i are permeability and porosity in grid i at time t, and κi,0 and ∅i,0 are the initial permeability and porosity, respectively.

To quantify the overall weathering rates and CO2–carbonate contact in each scenario, we used the framework from a previously developed upscaled rate law for dissolution of spatially heterogeneously distributed minerals (Wen and Li, 2018). The rate law says that three characteristic times are important. The equilibrium time τeq represents the characteristic timescale of mineral dissolution to reach equilibrium in a well-mixed system. The residence time τa, i.e., the timescale of advection, quantifies the overall water contact time with the whole domain. It was calculated by the product of domain length (L) and porosity divided by the overall infiltration rate (QT): τa=LϕQT. The reactive transport time τad,r quantifies the water contact time with calcite as influenced by both advection and diffusion/dispersion. The upscaled rate law is as follows: 1Rcalcite=kcalciteAT1-exp⁡-τeqτa×1-exp⁡-Lτaτad,rα. Here k is the intrinsic rate constant measured for a mineral in a well-mixed reactor, AT is the total surface area, L is domain length, α is geostatistical characteristics of spatial heterogeneity, and τaτad,r is the reactive time ratio quantifying the relative magnitude of the water contact time with the whole domain versus the contact time with the reacting mineral. This rate law consists of two parts: the effective dissolution rates in homogeneous media represented by kAT1-exp⁡-τeqτa and the heterogeneity factor 1-exp⁡-Lτaτad,rα that quantifies effects of preferential flow paths arising from heterogeneous distribution of minerals. When τaτad,r>1, the water contact time with calcite zone is small, meaning the water is replenished quickly compared to the whole domain, leading to higher CO2–carbonate interactions. In contrast, a small τaτad,r ratio (<1) reflects that water is replenished slowly in the reactive calcite zones, leading to less CO2–carbonate contact. These different timescales were calculated for Scenario 1–3 based on the flow characteristics and dissolution thermodynamics and kinetics, as detailed in the Supplement. Values of τeq, τa, and τad,r for all experiments are listed in Table S2. Note that numerical experiments in Scenario 1–3 focused on the short-term scale, with negligible changes in the solid phase.

The calibrated model reproduced the temporal dynamics with a Nash–Sutcliffe efficiency (NSE) value > 0.6 and was considered satisfactory (Fig. 2). Note that the y axis is inverted to display upper soils at the top and deep soils at the bottom to be consistent with their subsurface position shown in Fig. 2a. The measured CO2(g) varied between 0.24 % and 7.30 % (Fig. 2b right axis), 1 to 2 orders of magnitude higher than the atmospheric level of 0.04 %. The estimated CO2(aq) (Fig. 2b left axis) generally increased with depth except in July and August when horizon B was at peak concentration. The timing of the peaks and valleys varied in different horizons. The CO2(aq) reached maxima in summer in soil horizons A and B and decreased to less than 0.5 mM in winter and spring. The groundwater CO2(aq) exhibited a delayed peak in September and October and dampened seasonal variation compared to the soil horizons. The temporal trends of alkalinity, DIC, and Ca in groundwater mirrored those of soil CO2 at their corresponding depths, indicating the predominate control of soil CO2 on carbonate weathering. The groundwater concentrations of these species were also higher than soil concentrations. The simulated groundwater DIC (approximately summation of CO2(aq) and alkalinity) was > 6 times higher than that in upper soil (∼ 1.0 mM). The dissolved mineral volume was negligible for the simulation period (<0.5 % v/v). Sensitivity analysis revealed that changes in flow velocities influenced concentrations in horizon A where anorthite is the dominating dissolving mineral (0–1.8 m); their effects are negligible in horizon B and groundwater where fast-dissolving calcite rapidly approaches equilibrium.

Several measurements/parameters were important in reproducing data. These include soil CO2, which determined the CO2(aq) level and its spatial variation, and equilibrium constant (Keq) of calcite dissolution. Imposition of monthly variations and depth distributions of soil CO2 were essential to capture the variation of alkalinity and Ca data at different horizons. The imposition of calcite Keq was also critical for reproducing Ca concentrations. Impurities were suggested to affect Keq of natural calcite by a factor of ∼ 2.0 (Macpherson and Sullivan, 2019a). Calcite Keq in upper soils had to be reduced by a factor of 3.8 in the model to reproduce concentrations in horizon A. The alkalinity and Ca concentrations were not sensitive to kinetic parameters nor precipitation, because carbonate dissolution rapidly approaches equilibrium.

Scenario 1 for hydro-biogeochemical effects with flow partitioning (WoodPF and GrassPF). Figures 3A1–E1 show depth profiles of calcite and soil CO2 production rates and steady-state concentrations of reaction products. The soil CO2 production rate was highest in the upper soil at around 10-6.5 mol/s and decreased to ∼ 10-9.5 mol/s at 366 cm (Fig. 3B1), consistent with the decline with soil depth observed in natural systems. The CO2(g) level (released from CO2(g∗)) increased with depth due to lower efflux into the atmosphere in deeper zone and downward fluxes of CO2–charge water from the upper soil (Fig. 3C1). Concentrations of reaction products (Ca, DIC) were lower in the top 40 cm, reflecting the lower carbonate-mineral background level, and higher at depths over 60 cm. The transition occurred between 35 and 60 cm in the vicinity of the calcite–no-calcite interface at 55 cm, where concentrations of Ca and DIC increased abruptly until reaching equilibrium. This thin transition was driven by fast calcite dissolution and rapid approach to equilibrium, resulting in a short equilibrium distance. The equilibrated DIC and Ca concentrations below 60 cm followed the similar increasing trend of CO2(g) with depth in the deep zone (Fig. 3C1–E1).

Figure 3F1 shows that Ca concentrations in soil water (light color) were lower than groundwater (dark color) and varied with infiltration rates. The difference between soil water and groundwater Ca concentrations was relatively small at low infiltration rates because both reached equilibrium but diverged at high infiltration rates. Higher infiltration rates diluted soil water but not as much for groundwater. As expected, concentrations in the stream water, a mixture of soil water and groundwater (solid line), were in between these values but closely resembled soil water in the grassland. In both cases, stream concentration decreased as infiltration increased, indicating a dilution concentration–discharge relationship.

Scenario 2–3 for biogeochemical effects (without flow partitioning). Scenarios 2 and 3 were end-member cases that bracketed the range of rooting effects. Calcite and soil CO2 were distributed the same way as their corresponding flow partitioning (PF) cases (Table 3). The WoodVF and GrassVF cases had 100 % flow going downward via the deeper calcite zone maximizing the CO2–water–calcite contact. In the WoodHF and GrassHF cases (Table 3), all water exited at 50 cm, bypassing the deeper calcite-abundant zone and minimizing the CO2–water–calcite contact. Figure 3A2–F2 and 3A3–F3 show the VF (WoodVF and GrassVF) and HF (WoodHF and GrassHF) cases, respectively. Similar to the flow partitioning cases, the concentrations of reaction products were low in the shallow zone and increased over 10 times within a short distance ∼ 5 cm at the depth of ∼ 50 cm. The woodland cases increased slightly more than the grassland cases because of the slightly steeper soil CO2 distribution (Fig. 3C2 and 3C3). Figure 3F2 indicates that the effluent Ca concentrations were slightly higher in WoodVF due to the high soil CO2 level at the bottom outlet. The GrassHF and WoodHF case almost had the same effluent Ca concentrations at the upper soil (Fig. 3F3).

Concentration–discharge relationship and weathering rates in all cases. The VF cases had the highest effluent concentrations and weathering rates, whereas the HF cases had lowest concentrations and weathering rates, and the GrassPF and WoodPF cases fell in between (Fig. 4a, b). This is because the VF cases maximized the CO2–calcite contact with 100 % flow through the calcite zone, whereas the HF cases had minimum CO2–calcite contact with most water bypassing the calcite zone (column 3–4 in Table 3). The GrassPF and WoodPF cases allowed different extent of contact prescribed by the amount of flow via the calcite zone. A case run without soil respiration (i.e., no CO2(g∗), not shown) indicated that Ca and DIC concentrations were more than an order of magnitude lower than cases with soil respiration. In addition, the PF and HF cases generally showed dilution patterns with concentration decreasing with infiltration rates, as compared to the VF cases where a chemostatic pattern emerged with almost no changes as infiltration rates vary. This is because in the VF cases the concentrations mostly reached equilibrium concentration. In the PF and HF cases, a large proportion of water flows through soils with negligible calcite where the water moves away from equilibrium as infiltration rates increase.

Although weathering rates generally increased with infiltration rates, the woodland increased more (4.6 × 10-2 to 2.4 mol/a in WoodPF). The Ca fluxes in the VF cases (100 % vertical flow) were higher than flow partitioning cases because they enabled maximum CO2-charged water content with unweathered calcite at depth. Within each pair with the same flow pattern, the difference was mainly due to the distribution of soil CO2. The difference in weathering fluxes was 1 %–12 % and 1 %–5 % between HF cases and VF cases, respectively, much smaller than differences between the PF cases. Comparing the HF and VF cases, differences in weathering fluxes were 73 % at 3.7 × 10-2 m/a and 721 % at 3.7 m/a, which is about 1–2 orders of magnitude higher than differences induced by soil CO2 distribution. Between the GrassPF and WoodPF cases, the differences were in the range of 17 %–207 % at the flow range of 3.7 × 10-2–3.7 m/a. The DIC fluxes showed similar trends.

Development of reaction fronts at the century scale. To explore the longer-term effects, we ran the PF cases at 0.37 m/a for 300 years. More water flowing vertically through abundant calcite zones in WoodPF resulted in faster weathering and a deeper reaction front at a depth of ∼ 210 cm compared to ∼ 95 cm in GrassPF (Fig. 5a). The depletion of calcite led to an increase in porosity (Fig. 5b), which was over 1 order of magnitude higher at the domain scale of the woodland than that in the grassland (Fig. 5c). Permeability evolution had a similar trend to porosity (not shown here). This indicates that if deeper roots promoted more water into deeper soils, they would push reaction fronts deeper and control the position where chemically unweathered bedrock was transformed into weathered bedrock. At timescales longer than century scale, calcite may become depleted, which ultimately reduces weathering rates (White and Brantley, 2003) and lead to similar weathering fronts in grasslands and woodlands.

Natural systems are characterized by preferential flow paths such that flow distribution is not uniform in space. Weathering in such systems with preferential flow in zones of differing reactivities has been shown to hinge on the contact time between water and the reacting minerals instead of all minerals that are present (Wen and Li, 2018) (Eq. 1). Here we contextualize the weathering rates in different scenarios (symbols) with predictions from an upscaled rate law developed by Wen and Li (2018) that incorporates the effects of heterogeneities in flow paths (Fig. 6). The time ratio τaτad,r compares the domain water contact time (or residence time) with the contact time with dissolving calcite. Note that τa is total domain pore volume VT/total water flow QT, and τad,r is total reactive pore volume Vr/total water fluxes passing through reactive zone Qr. Also note that water passing through the reactive zone stays in the subsurface longer, such that it is older water in general. The ratio τaτad,r is therefore akin to the fraction of older water compared to the total water fraction. The older water fraction Fow is the counterpart of the young water fraction Fyw discussed in the literature (Kirchner, 2016, 2019). In GrassVF and WoodVF (open circles) where all CO2-charged water flew through the deeper calcite zones, CO2–calcite interactions reached maximum such that values of τaτad,r approached 1.0, meaning all water interacted with calcite. Under this condition, weathering rates were the highest among all cases. In contrast, in WoodHF and GrassHF (open diamonds) where all CO2-charged water bypassed the deeper calcite zone, τaτad,r can be 1–3 orders of magnitude lower, and weathering rates were at their minima. The τaτad,r value in the water partitioning cases (GrassPF and WoodPF, filled circles) fell in between. At the same τa, the WoodPF case with deepening roots promoted CO2–water–calcite contact (i.e., larger τaτad,r) and dissolved calcite at higher rates.

The magnitude of the rate difference also depends on the overall flow rates (or domain contact time τa). At fast flow with small τa (large symbols and thick lines in Fig. 6), flow partitioning has a larger influence. At τa of 0.47 years, the weathering rates in the VF cases were more than an order of magnitude higher than those in the PF cases. The weathering rate in the woodland was over 7 times that of the grassland. In contrast, at τa of 47 years, the rate differences between grass and woody cases were less than 25 %, largely because the dissolution has reached equilibrium. In the VF and HF cases where flow conditions were the same, the soil CO2 distribution in grassland and woodland differed only slightly, leading to similar values of τaτad,r and weathering rates and indicating minimal impacts of soil CO2 distribution. These rates from numerical experiments closely follow the prediction from the upscaled reaction rate law (gray lines, Eq. 1). The rate law predicted that weathering rates increased from HF cases with small τaτad,r values to VF cases where τaτad,r approached 1. It also showed that weathering rates reached their maxima when all water flows through the reactive zone, i.e., when the fraction of older, reactive water is essentially 1.0.

The base-case data and simulation showed that calcite dissolution reaches equilibrium rapidly and is thermodynamically controlled (Sect. 4.1), which is generally well known and echoes observations from literature (Tsypin and Macpherson, 2012; Gaillardet et al., 2019). The extent of dissolution, or solubility indicated in Ca and DIC concentrations, is determined by soil CO2 levels that in turn hinge on ecosystem functioning and climate. In hot, dry summer, soil respiration rates reach maxima in upper soil horizons and pCO2 peaks (Fig. 2). In wet and cold winter, soil pCO2 plummets, leading to much lower Ca and DIC concentrations. Based on Reactions (0–4) (Table 1) and temperature dependence of equilibrium constants, the following equations can be derived (detailed derivation in the Supplement) for Ca and DIC concentrations in carbonate-dominated landscapes: 2CCa=[Kt,25×ef(T)×pCO2]133CDIC=2[Kt,25×ef(T)×pCO2]13+K1,25×ef(T)×pCO2wheref(T)=-ΔH1∘4R1T-1298.15 Here CCa and CDIC are concentrations of Ca and DIC (mol/L); pCO2 is in units of atm; Kt,25 is the total equilibrium constant Kt(=aCa2+aHCO3-2pCO2=K1K4) of the combined Reactions (1) and (4) at 25 ∘C; ΔHt∘ is the corresponding standard enthalpy (-35.83 kJ/mol); K1,25 and ΔH1∘ (-19.98 kJ/mol) are the equilibrium constant and standard enthalpy of Reaction (1) (in Table 1); R is the gas constant (= 8.314 × 10-3 kJ/K/mol). Equations (2) and (3) imply that DIC and Ca in upper soil water (0.2 m) are lower compared to groundwater (3.6 m) in the base case at Konza, due to lower dissolved CO2(aq) at higher temperature and higher diffusion rates in upper soil.

Equations (2) and (3) were tested with soil pCO2 and spring water chemistry data from eight carbonate-dominated catchments (Dandurand et al., 1982; Lopez-Chicano et al., 2001; Moral et al., 2008; Ozkul et al., 2010; Kanduc et al., 2012; Calmels et al., 2014; Abongwa and Atekwana, 2015; Huang et al., 2015) (also see the Supplement for details). As shown in Fig. 7, spring water (representing groundwater) DIC and Ca concentrations increase with pCO2. Equations (2)–(3) can describe these data and DIC and Ca levels from numerical simulations from this work (empty dots in Fig. 7). The lines of Eqs. (2)–(3) describe the relationship at 10 ∘C, the mean annual temperature, confirming the thermodynamics control of carbonate dissolution by soil CO2 levels. The equation lines closely predicted Ca and DIC under high-pCO2 and lower-pH conditions (<8.0), because these conditions ensure the validity of the assumption of negligible CO32- in the derivation of the equations. The presence of cations and anions other than Ca and DIC can complicate the solution and can bring significant variations of DIC and Ca concentrations under the same pCO2 conditions.

High temperature (T=17 ∘C) leads to lower DIC and Ca concentrations by about 10 % due to the lower calcite and CO2 solubility at higher T. Higher T also elevates pCO2 by enhancing soil respiration. Various equations have been developed in literature to predict soil pCO2 based on climate and ecosystem functioning indicators such as net primary production (NPP) (Cerling, 1984; Goddéris et al., 2010; Romero-Mujalli et al., 2019a). These equations can be used together with Eqs. (2–3) for the estimation of Ca and DIC concentrations in carbonate-derived waters. Gaillardet et al. (2019) showed that pCO2 can increase by 2 times with T increasing from 9 to 17 ∘C, which can elevate DIC and Ca concentrations over 50 %. Macpherson et al. (2008) observed a 20 % increase in groundwater pCO2 in Konza over a 15-year period and suggested that increased soil respiration under warmer climate may have elevated soil and groundwater pCO2. Zhi et al. (2020) showed that the stream concentrations of dissolved organic carbon, a product of soil respiration, tripled in warmer years as minimum average temperature approaches 0 ∘C in a high elevation mountain. Hasenmueller et al. (2015) demonstrated topographic controls on soil CO2. Soil CO2 and Ca and DIC concentrations are an integrated outcome of climate, soil respiration, subsurface structures, and hydrological conditions.

Evidence from field data. Data in Konza show that although soil pCO2 peaks in summer, these peaks do not occur right away in deeper groundwater until about 2 months later. Macpherson et al. (2008) and Tsypin and Macpherson (2012) contributed this lag time to the water travel time from the soil to the groundwater aquifer. The calculation of travel time based on depth difference in soil and groundwater sampling location (214 cm) and average velocity (0.37 m/a) indicates that it will take 7–8 months on average for water to reach deeper groundwater. The 2-month delay, much shorter than the estimated 7–8 months, suggests that CO2-charged water may arrive at deeper zones via preferential flow facilitated by roots or other types of macropores such as large conduits that are often observed in carbonate formations (Hartmann et al., 2014; Husic et al., 2019).

The numerical experiments suggest that the root-relevant hydrology can play an essential role in enhancing chemical weathering (Figs. 4 and 6). In general, the hydrological enhancement of weathering rates also alludes to the key connection between weathering and the transit (travel) time distribution (McGuire and McDonnell, 2006; Sprenger et al., 2019). In particular, water that routes through lateral paths is younger; water that penetrates deeper is older. Figure 6 says that weathering rates increase with increasing reactive water fraction, until reaching their maxima when all water is in contact with reactive minerals. This aligns with observations at Konza that woody-encroached watersheds exhibit higher Ca fluxes in streams and supports the hypothesis that deeper roots can enhance mineral–water interaction via deeper flow paths (Sullivan et al., 2019a). Deepening roots can also enhance connectivity between shallow and deeper zones, therefore reducing concentration contrasts between soil water and groundwater. This can lead to more chemostatic C–Q relationships as shown in WoodPF (b=-0.14 in C=aQb) compared to GrassPF (b=-0.33) (Fig. 4). These findings echo conclusions from Zhi et al. (2019) and Zhi and Li (2020) that chemistry differences in shallow versus deeper waters regulate C–Q patterns. The b values from the C–Q relationships coming out of the 1-D modeling (Fig. 4) suggest that if flow partitioning is the only difference between the grassland and woody watersheds, a C–Q relationship exhibiting dilution with negative b values is expected in the grassland. The Konza stream data in Sullivan et al. (2019a) however showed that C–Q slopes in grasslands (b=-0.003) and in woody-encroached lands (b=0.013) are both close to zero (Figs. 7 and 8 in Sullivan et al., 2019a). The root influence on the C–Q relationship therefore remains equivocal.

Limitations of the model. This discrepancy may suggest that catchment features that are not represented in the simple 1-D model can influence C–Q relationships. The model does not explicitly simulate how and to what degree root distribution at depth alters flow pathways. Instead we focus on the first-order principles of the hydrological ramification of roots. The numerical experiments took general observations of rooting characteristics in grasslands and woodlands and assumed that deepening roots in woodlands promote higher flow partitioning into the deep subsurface (Canadell et al., 1996; Nardini et al., 2016; Pawlik et al., 2016). In natural systems, however, other factors can also influence flow partitioning. For example, contrasts in flow-conducting properties (i.e., porosity and permeability) in shallow and deep zones, physical and chemical heterogeneity in carbonate distribution (Wen and Li, 2018; Salehikhoo and Li, 2015), connectivity between different areas of the catchment in dry and wet times (Wen et al., 2020), and water table and corresponding lateral flow depth associated with the rainfall frequency and intensity (Li et al., 2017; Harman and Cosans, 2019). All these factors may affect the water–calcite contact, leading to changes in weathering rates (Fig. 6). In addition to the alterations of hydrological flow paths, deepening roots may also affect the proportion of plant water uptake or soil water loss through transpiration (Pierret et al., 2016; Zhu et al., 2018), further modifying recharge into the deep subsurface layers. For example, studies show that woody species in semiarid places predominantly use deep subsurface water while grasses predominantly use soil water from the upper soil layer (Ward et al., 2013). Furthermore, shallower root distributions in grasslands may be more efficient in using water from small rainfall events than forests with their deeper root distributions (Mazzacavallo and Kulmatiski, 2015). Other studies have also documented significant competition for water uptake in upper soil layers among both woody and grass species (Scholes and Archer, 1997). It remains inconclusive how these water uptake characteristics are best represented in numerical experiments. These processes are therefore not included at this point.

In addition, distributions of microbes and organic acids associated with rooting structures vary with sites and seasons and root channels. Dry conditions may trigger calcite reprecipitation. Microbial activities surrounding living and dead roots can also lead to calcite precipitation and infilling of fractures and other macropores, as well as alter flow pathways (Lambers et al., 2009). Organic acids can decrease soil water pH, increase mineral solubilities through organic–metal complexations, and accelerate chemical weathering (Pittman and Lewan, 2012; Lawrence et al., 2014). Their impacts on carbonate weathering kinetics might be smaller (due to the fast kinetics) compared to their alteration of calcite solubility in natural systems. Such processes further complicate how to represent biogeochemical processes in models. Although we do not explicitly simulate these competing processes, the model was constrained by the field data in grasslands and woodland that have already integrated these effects in natural systems. Indeed, the weathering rates can be understood as the net weathering rates that are the net difference between dissolution and reprecipitation. This is reflected in lower carbonate weathering rates under low infiltration (low flow) conditions.

The need for root characterization. The data–model discrepancy highlights the limitation of a simple model but also points to the need for measurements. In fact, because carbonate weathering is transport limited and depends largely on water flow via carbonate-rich zones, colocated measurements of rooting characteristics, flow, and water chemistry at depth are essential. Root measurements however rarely go deeper than 30 cm (Richter and Billings, 2015). Existing work exploring root influence on weathering focused primarily on effects of soil CO2 and root exudates (Drever, 1994; Lawrence et al., 2014; Gaillardet et al., 2019). Although it is well known that roots play a paramount role in modulating macropores and subsurface flow (Fan et al., 2017), the interactions between root characteristics, flow partitioning, and chemical weathering have remained poorly understood. Rooting characteristics depend on climate, plant species, topography, soil properties, and geology (Canadell et al., 1996; Mazvimavi et al., 2004; Price, 2011; Nardini et al., 2016). Further studies are needed to characterize root distribution beyond 30 cm, how they vary with intrinsic plant species and external conditions, and how and to what extent they alter subsurface flow. The first step could link rooting characteristics, including density and depth, to soil properties and borrow insights from existing relationships between soil properties and subsurface structure. For example, images of roots and pore structures can be used to characterize the spatiotemporal heterogeneity of fluxes (Renard and Allard, 2013). Geostatistical indices such as permeability variance and correlation length can be used to quantify rooting structure and relate to flow partitioning and mineral weathering via numerical experiments (Wen and Li, 2017). The combination of numerical reactive transport experiments built on realistic rooting structure can help develop models for estimating the influence of rooting dynamics on water and carbon cycles at the catchment scale.

Mounting evidence has shown that the terrestrial system has become a stronger carbon sink in recent decades (Heimann and Reichstein, 2008), potentially accounting for the missing carbon sink as large as ∼ 1 Pg C/a in the global carbon budget (Houghton, 2007; Cole et al., 2007). Although still much debated, recent studies have proposed the downward transport of soil-respired CO2 and DIC into groundwater aquifers in deserts as a possible carbon sink in the global carbon cycle (Ma et al., 2014; Li et al., 2015). Considering the longer residence time of DIC in groundwater (102–104 years) than in the atmosphere (∼ 101–102 years; Archer and Brovkin, 2008), groundwater may act as a CO2 storage sink. This work indicated that deepening roots can potentially reroute DIC fluxes to deeper groundwater storage. In particular, vegetation in dry places like deserts often has deep roots (Gupta et al., 2020). In fact, plants are known for growing deeper roots to tap groundwater during droughts (Brunner et al., 2015). Deepening roots can enhance downward water drainage (i.e., high vertical connectivity) to the depth and potentially facilitate the transport of DIC fluxes into the deep subsurface. As the pace of climate change accelerates, summer droughts are expected to intensify, which can potentially channel more CO2 into the deeper subsurface via deepening roots.

With constraints from soil CO2 data, the simulated CO2 production rates in GrassPF and WoodPF are similarly at ∼ 0.6 mol C/m2/a under the infiltration rate of 0.37 m/a (Fig. S2). This is at the low end of the belowground net production (NPP) estimations at the Konza site (∼ 2.0–30.0 mol C/m2/a), assuming that belowground NPP accounts for 50 % of the total NPP (Lett et al., 2004; Knapp and Ojima, 2014). The simulations showed that in woodlands the DIC downward fluxes can be > 2.0 times higher than those in grasslands (Fig. 4). In other words, more soil-respired CO2 can transport to groundwater and become stored there for centuries to millennia before entering a stream. At the short timescale, this enhanced downward transport will reduce CO2 escape back into the atmosphere. This may explain the observations at Konza that woody encroachment increased NPP; however, soil CO2 flux was significantly reduced compared to the open grassland (Lett et al., 2004). Changing land cover (e.g., woody encroachment and boreal forest creep) however is not the only mechanism for a carbon sink (Stevens et al., 2017; Wang et al., 2020). Older aged forests also tend to have deepening roots and may act as the carbon sink (Luyssaert et al., 2008), although this is not the case in Konza.